加速度计和陀螺仪联合校准

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Autonomous vehicle technology is rapidly advancing (see “Summary”). A key enabling factor is the advancing capabilities and declining cost of computing and sensing systems that enable sensor fusion for awareness of the vehicle’s state and surroundings (see “Nontechnical Article Summary”). For control purposes, the vehicle’s state must be estimated accurately, reliably, at a sufficiently high sample rate, and with a sufficiently high bandwidth. For systems with a high bandwidth, these requirements are often achieved by an aided inertial navigation system (INS) (see “Aided Inertial Navigation System History”) <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> , <xref ref-type="bibr" rid="ref2" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[2]</xref> , <xref ref-type="bibr" rid="ref3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[3]</xref> , <xref ref-type="bibr" rid="ref4" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[4]</xref> , <xref ref-type="bibr" rid="ref5" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[5]</xref> , <xref ref-type="bibr" rid="ref6" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[6]</xref> . An INS integrates data from an inertial measurement unit (IMU) through a kinematic model at the high sampling rate of the IMU to compute the state estimate. An aided INS corrects this state estimate using data from aiding sensors [for example, vision, lidar, radar, and global navigation satellite systems (GNSS)]. State estimation by sensor fusion may be accomplished using a variety of methods: Kalman filter (KF) <xref ref-type="bibr" rid="ref7" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[7]</xref> , <xref ref-type="bibr" rid="ref8" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[8]</xref> , <xref ref-type="bibr" rid="ref9" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[9]</xref> , <xref ref-type="bibr" rid="ref10" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[10]</xref> , <xref ref-type="bibr" rid="ref11" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[11]</xref> , extended KF (EKF) <xref ref-type="bibr" rid="ref12" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[12]</xref> , <xref ref-type="bibr" rid="ref13" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[13]</xref> , <xref ref-type="bibr" rid="ref14" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[14]</xref> , <xref ref-type="bibr" rid="ref15" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[15]</xref> , unscented KF (UKF) <xref ref-type="bibr" rid="ref16" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[16]</xref> , <xref ref-type="bibr" rid="ref17" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[17]</xref> , <xref ref-type="bibr" rid="ref18" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[18]</xref> , particle filter (PF) <xref ref-type="bibr" rid="ref19" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[19]</xref> , <xref ref-type="bibr" rid="ref20" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[20]</xref> , <xref ref-type="bibr" rid="ref21" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[21]</xref> , and maximum a posteriori (MAP) optimization <xref ref-type="bibr" rid="ref22" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[22]</xref> , <xref ref-type="bibr" rid="ref23" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[23]</xref> , <xref ref-type="bibr" rid="ref24" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[24]</xref> , <xref ref-type="bibr" rid="ref25" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[25]</xref> , <xref ref-type="bibr" rid="ref26" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[26]</xref> , <xref ref-type="bibr" rid="ref27" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[27]</xref> .

Inertial measurement units (IMUs) are fundamental for attitude control of drones. With the advancements in micro-electro-mechanical systems (MEMS) fabrication processes, size, power consumption, and price of these sensors have reduced significantly and attracted many new applications. However, this came at the expense of sensors requiring frequent recalibration, as they are highly contaminated with systematic errors. This paper presents a novel method to jointly calibrate the accelerometer, gyroscope, and magnetometer triad in a MEMS IMU without additional equipment. Opportunistic zero change in velocity and position updates, and inclination updates were used in conjunction with relative orientation updates from magnetometers in a robust batch least-squares adjustment. Solutions from the proposed self-calibration were compared to existing calibration methods. Empirical results suggest that the new method is robust against magnetic distortions and can achieve performance similar to a specialized calibration that uses a more accurate (and expensive) IMU as reference. The jointly estimated accelerometer and gyroscope calibration parameters can deliver a more accurate dead-reckoning solution than the popular multi-position calibration method (i.e., 54% improvement in orientation accuracy) by recovering the gyroscope scale error and other systematic errors. In addition, it can improve parameter observability as well as reduce calibration time by incorporating dynamic data with static orientations. The proposed calibration was also applied on-site pre-mission by simply waving the sensor by hand and was able to improve the orientation tracking accuracy by 73%.

Modeling and estimation of gyroscope and accelerometer errors is generally a very challenging task, especially for low-cost inertial MEMS sensors whose systematic errors have complex spectral structures. Consequently, identifying correct error-state parameters in a INS/GNSS Kalman filter/smoother becomes difficult when several processes are superimposed. In such situations, the classical identification approach via Allan Variance (AV) analyses fails due to the difficulty of separating the error-processes in the spectral domain. For this purpose we propose applying a recently developed estimation method, called the Generalized Method of Wavelet Moments (GMWM), that is excepted from such inconveniences. This method uses indirect inference on the parameters using the wavelet variances associated to the observed process. In this article, the GMWM estimator is applied in the context of modeling the behavior of low-cost inertial sensors. Its capability to estimate the parameters of models such as mixtures of GM processes for which no other estimation method succeeds is first demonstrated through simulation studies. The GMWM estimator is also applied on signals issued from a MEMS-based inertial measurement unit, using sums of GM processes as stochastic models. Finally, the benefits of using such models is highlighted by analyzing the quality of the determined trajectory provided by the INS/GNSS Kalman filter, in which artificial GNSS gaps were introduced. During these epochs, inertial navigation operates in coasting mode while GNSS-supported trajectory acts as a reference. As the overall performance of inertial navigation is strongly dependent on the errors corrupting its observations, the benefits of using the more appropriate error models (with respect to simpler ones estimated using classical AV graphical identification technique) are demonstrated by a significant improvement in the trajectory accuracy.

Motion sensors as inertial measurement units (IMU) are widely used in robotics, for instance in the navigation and mapping tasks. Nowadays, many low cost micro electro mechanical systems (MEMS) based IMU are available off the shelf, while smartphones and similar devices are almost always equipped with low-cost embedded IMU sensors. Nevertheless, low cost IMUs are affected by systematic error given by imprecise scaling factors and axes misalignments that decrease accuracy in the position and attitudes estimation. In this paper, we propose a robust and easy to implement method to calibrate an IMU without any external equipment. The procedure is based on a multi-position scheme, providing scale and misalignments factors for both the accelerometers and gyroscopes triads, while estimating the sensor biases. Our method only requires the sensor to be moved by hand and placed in a set of different, static positions (attitudes). We describe a robust and quick calibration protocol that exploits an effective parameterless static filter to reliably detect the static intervals in the sensor measurements, where we assume local stability of the gravity's magnitude and stable temperature. We first calibrate the accelerometers triad taking measurement samples in the static intervals. We then exploit these results to calibrate the gyroscopes, employing a robust numerical integration technique. The performances of the proposed calibration technique has been successfully evaluated via extensive simulations and real experiments with a commercial IMU provided with a calibration certificate as reference data.

Navigation involves the integration of methodologies and systems for estimating the time varying position and attitude of moving objects. Inertial Navigation Systems (INS) and the Global Positioning System (GPS) are among the most widely used navigation systems. The use of cost effective MEMS based inertial sensors has made GPS/INS integrated navigation systems more affordable. However MEMS sensors suffer from various errors that have to be calibrated and compensated to get acceptable navigation results. Moreover the performance characteristics of these sensors are highly dependent on the environmental conditions such as temperature variations. Hence there is a need for the development of accurate, reliable and efficient thermal models to reduce the effect of these errors that can potentially degrade the system performance. In this paper, the Allan variance method is used to characterize the noise in the MEMS sensors. A six-position calibration method is applied to estimate the deterministic sensor errors such as bias, scale factor, and non-orthogonality. An efficient thermal variation model is proposed and the effectiveness of the proposed calibration methods is investigated through a kinematic van test using integrated GPS and MEMS-based inertial measurement unit (IMU).

The Global Positioning System (GPS) is a worldwide navigation system that requires a clear line of sight to the orbiting satellites. For land vehicle navigation, a clear line of sight cannot be maintained all the time as the vehicle can travel through tunnels, under bridges, forest canopies or within urban canyons. In such situations, the augmentation of GPS with other systems is necessary for continuous navigation. Inertial sensors can determine the motion of a body with respect to an inertial frame of reference. Traditionally, inertial systems are bulky, expensive and controlled by government regulations. Micro-electro mechanical systems (MEMS) inertial sensors are compact, small, inexpensive and most importantly, not controlled by governmental agencies due to their large error characteristics. Consequently, these sensors are the perfect candidate for integrated civilian navigation applications with GPS. However, these sensors need to be calibrated to remove the major part of the deterministic sensor errors before they can be used to accurately and reliably bridge GPS signal gaps. A new multi-position calibration method was designed for MEMS of high to medium quality. The method does not require special aligned mounting and has been adapted to compensate for the primary sensor errors, including the important scale factor and non-orthogonality errors of the gyroscopes. A turntable was used to provide a strong rotation rate signal as reference for the estimation of these errors. Two different quality MEMS IMUs were tested in the study. The calibration results were first compared directly to those from traditional calibration methods, e.g. six-position and rate test. Then the calibrated parameters were applied in three datasets of GPS/INS field tests to evaluate their accuracy indirectly by comparing the position drifts during short-term GPS signal outages.

Calibration of inertial measurement units (IMU) is carried out to estimate the coefficients which transform the raw outputs of inertial sensors to meaningful quantities of interest. Based on the fact that the norms of the measured outputs of the accelerometer and gyroscope cluster are equal to the magnitudes of specific force and rotational velocity inputs, respectively, an improved multi-position calibration approach is proposed. Specifically, two open but important issues are addressed for the multi-position calibration: (1) calibration of inter-triad misalignment between the gyroscope and accelerometer triads and (2) the optimal calibration scheme design. A new approach to calibrate the inter-triad misalignment is devised using the rotational axis direction measurements separately derived from the gyroscope and accelerometer triads. By maximizing the sensitivity of the norm of the IMU measurement with respect to the calibration parameters, we propose an approximately optimal calibration scheme. Simulations and real tests show that the improved multi-position approach outperforms the traditional laboratory calibration method, meanwhile relaxing the requirement of precise orientation control.

Abstract: An approach for calibrating a low-cost IMU is studied, requiring no mechanical platform for the accelerometer calibration and only a simple rotating table for the gyro calibration. The proposed calibration methods utilize the fact that ideally the norm of the measured output of the accelerometer and gyro cluster are equal to the magnitude of applied force and rotational velocity, respectively. This fact, together with model of the sensors is used to construct a cost function, which is minimized with respect to the unknown model parameters using Newton’s method. The performance of the calibration algorithm is compared with the Cramér-Rao bound for the case when a mechanical platform is used to rotate the IMU into different precisely controlled orientations. Simulation results shows that the mean square error of the estimated sensor model parameters reaches the Cramér-Rao bound within 8 dB, and thus the proposed method may be acceptable for a wide range of low-cost applications. Keyword: Inertial measurement unit, MEMS sensors, Calibration. 1.

An inexpensive Attitude Heading Reference System (AHRS) for general aviation applications is developed by fusing low cost ($20-$1000) automotive grade inertial sensors with GPS. The inertial sensor suit consists of three orthogonally mounted solid state rate gyros. GPS is used for attitude determination in a triple antenna ultra short baseline configuration. A complementary filter is used to combine the information from the inertial sensors with the attitude information derived from GPS. The inertial sensors provide attitude information at a sufficiently high bandwidth to drive an inexpensive glass-cockpit type display for pilot-in-the-loop control. The low bandwidth GPS attitude is used to calibrate the rate gyro biases on-line. Data collected during laboratory testing is used to construct error models for the inertial sensors. Analysis based on these models shows that the system can coast through momentary GPS outages lasting 2 minutes with attitude errors less than 6 degrees. Actual performance observed during ground and flight tests with GPS off was found to be substantially better than that predicted by manufacturer supplied specification sheets. Based on this, it is concluded that off-line calibration combined with GPS based in-flight calibration can dramatically improve the performance of inexpensive automotive grade inertial sensors. Data collected from flight tests indicate that some of the automotive grade inertial sensors (180 deg/hr) can perform near the low end of tactical grade (10 deg/hr) sensors for short periods of time after being calibrated on-line by GPS.

The errors of low-cost inertial sensors, especially Micro-Electro Mechanical Systems (MEMS) ones, are highly dependent on environmental conditions such as the temperature. Thus, there is a need for the development of accurate and reliable thermal compensation models to reduce the impact of such thermal drift of the sensors. Since the conventional thermal calibration methods are typically time-consuming and costly, an efficient thermal calibration method to investigate the thermal drift of a full set of gyroscope and accelerometer errors (i.e., biases, scale factor errors and non-orthogonalities) over the entire temperature range in a few hours is proposed. The proposed method uses the idea of the Ramp method, which removes the time-consuming process of stabilizing the sensor temperature, and addresses its inherent problems with several improvements. We change the temperature linearly for a complete cycle and take a balanced strategy by making comprehensive use of the sensor measurements during both heating and cooling processes. Besides, an efficient 8-step rotate-and-static scheme is designed to further improve the calibration accuracy and efficiency. Real calibration tests showed that the proposed method is suitable for low-grade IMUs and for both lab and factory calibration due to its efficiency and sufficient accuracy.

Measurements from magnetometers and inertial sensors (accelerometers and gyroscopes) can be combined to give 3D orientation estimates. In order to obtain accurate orientation estimates it is imperative that the magnetometer and inertial sensor axes are aligned and that the magnetometer is properly calibrated for both sensor errors as well as presence of magnetic distortions. In this work we derive an easy-to-use calibration algorithm that can be used to calibrate a combination of a magnetometer and inertial sensors. The algorithm compensates for any static magnetic distortions created by the sensor plat- form, magnetometer sensor errors and determines the alignment between the magnetometer and the inertial sensor axes. The resulting calibration procedure does not require any additional hardware. We make use of probabilistic models and obtain the calibration algorithm as the solution to a maximum likelihood problem. The efficacy of the proposed algorithm is illustrated using experimental data collected from a sensor unit placed in a magnetically disturbed environment onboard a jet aircraft.

Abstract The proper calibration of a transducer has direct influence on its measurement accuracy. Procedures for calibrating MEMS-type IMUs generally require sophisticated and expensive equipment. An alternative procedure called multi-position calibration has shown to be efficient and only demands that the transducer be moved in different orientations. We investigate the influence of the repeatability of these orientations by comparing two different experimental procedures – robotic-motion and hand-motion of the IMU sensor. Statistical analysis of the results makes it clear that there are no significant differences for either variances or means of calibrated parameters between both experimental procedures

A calibration technique for a redundant inertial measurement unit (IMU) containing low-grade inertial sensors is proposed. In order to calibrate a redundant IMU that can detect and isolate faulty sensors, the fundamental coordinate frames in the IMU are defined and the IMU error is modeled based on the frames. Equations to estimate the error coefficients of the redundant IMU are formulated, and a test sequence using a 2-axis turntable is also presented. Finally, a redundant IMU with cone configuration is implemented using lowgrade inertial sensors, and the performance of the proposed technique is verified experimentally.

Inertial Measurement Units, the main component of a navigation system, are used in several systems today. IMU's main components, gyroscopes and accelerometers, can be produced at a lower cost and higher quantity. Together with the decrease in the production cost of sensors it is observed that the performances of these sensors are getting worse. In order to improve the performance of an IMU, the error compensation algorithms came into question and several algorithms have been designed. Inertial sensors contain two main types of errors which are deterministic errors like scale factor, bias, misalignment and stochastic errors such as bias instability and scale factor instability. Deterministic errors are the main part of error compensation algorithms. This study explains the methodology of how the deterministic errors are defined by 27 state static and 60 state dynamic rate table calibration test data and how those errors are used in the error compensation model. In addition, the stochastic error parameters, gyroscope and bias instability, are also modeled with Gauss Markov Model and instant sensor bias instability values are estimated by Kalman Filter algorithm. Therefore, accelerometer and gyroscope bias instability can be compensated in real time. In conclusion, this article explores how the IMU performance is improved by compensating the deterministic end stochastic errors. The simulation results are supported by real IMU test data.

An accurate inertial measurement unit (IMU) is a necessity when considering an inertial navigation system capable of giving reliable position and velocity estimates even for a short period of time. However, even a set of ideal gyroscopes and accelerometers does not imply an ideal IMU if its exact mechanical characteristics (i.e. alignment and position information of each sensor) are not known. In this paper, the standard multi-position calibration method for consumer-grade IMUs using a rate table is enhanced to exploit also the centripetal accelerations caused by the rotation of the table. Thus, the total number of measurements rises, making the method less sensitive to errors and allowing use of more accurate error models. As a result, the accuracy is significantly enhanced, while the required numerical methods are simple and efficient. The proposed method is tested with several IMUs and compared to existing calibration methods.

Visual and inertial sensors, in combination, are well-suited for many robot navigation and mapping tasks. However, correct data fusion, and hence overall system performance, depends on accurate calibration of the 6-DOF transform between the sensors (one or more camera(s) and an inertial measurement unit). Obtaining this calibration information is typically difficult and time-consuming. In this paper, we describe an algorithm, based on the unscented Kalman filter (UKF), for camera-IMU simultaneous localization, mapping and sensor relative pose self-calibration. We show that the sensor-to-sensor transform, the IMU gyroscope and accelerometer biases, the local gravity vector, and the metric scene structure can all be recovered from camera and IMU measurements alone. This is possible without any prior knowledge about the environment in which the robot is operating. We present results from experiments with a monocular camera and a low-cost solid-state IMU, which demonstrate accurate estimation of the calibration parameters and the local scene structure.

An inertial navigation system (INS) has been widely used in challenging GPS environments. With the rapid development of modern physics, an atomic gyroscope will come into use in the near future with a predicted accuracy of 5 × 10(-6)°/h or better. However, existing calibration methods and devices can not satisfy the accuracy requirements of future ultra-high accuracy inertial sensors. In this paper, an improved calibration model is established by introducing gyro g-sensitivity errors, accelerometer cross-coupling errors and lever arm errors. A systematic calibration method is proposed based on a 51-state Kalman filter and smoother. Simulation results show that the proposed calibration method can realize the estimation of all the parameters using a common dual-axis turntable. Laboratory and sailing tests prove that the position accuracy in a five-day inertial navigation can be improved about 8% by the proposed calibration method. The accuracy can be improved at least 20% when the position accuracy of the atomic gyro INS can reach a level of 0.1 nautical miles/5 d. Compared with the existing calibration methods, the proposed method, with more error sources and high order small error parameters calibrated for ultra-high accuracy inertial measurement units (IMUs) using common turntables, has a great application potential in future atomic gyro INSs.

Accelerometers (ACCs) and gyroscopes (gyros) are commonly known as inertial sensors and their orthogonal triads generally form an inertial measurement unit (IMU) used as a core means of a navigation system. Before the navigation system is to be used, it is necessary to perform its calibration. A typical process of the IMU calibration usually estimates scale-factors, orthogonality or misalignment errors, and offsets of both triads. These parameters compose the so-called sensor error model (SEM). The process of obtaining accurate information that describes the motion performed within the calibration generally requires a costly and specialized means [1], [2]. Therefore, much effort has been put into cost-effective calibration using an optical motion tracking system [3]–[6], or transferring the calibration into a state estimation problem [7]. In the ACC case, most of the current calibration methods utilize the fact that ACCs are affected by gravity when they are under static conditions. Therefore, we proceed with calibration performed under static conditions, which utilizes the knowledge of the gravity magnitude and ACC output measurements collected at predetermined orientations and performs ACC SEM estimation using nonlinear optimization [6], [8]–[10]. In the gyro case, calibration based on the Earth's rate might be inapplicable, for instance due to the fact that Earth's rate is under or around the resolution of the gyro, and thus other means to apply and measure angular rates need to be used. This situation commonly arises in the case of low-cost MEMS (Micro-Electro-Mechanical System) based gyros. Thus, expensive mechanical platforms are often inevitable [11]–[14].

This paper introduces the MAGnetometer-Inertial sensors Calibration and ALignment (MAG.I.C.AL.) methodology for unified calibration and joint axes alignment of three-axis magnetometer, three-axis accelerometer, and three-axis gyroscope. MAG.I.C.AL. compensates for all linear time-invariant distortions such as scale-factor, cross-coupling, and offset, including the soft-iron and hard-iron distortions of the magnetometer. It introduces a new, computationally efficient, least-squares-based iterative algorithm for the calibration of the magnetometer and the accelerometer. It aligns their axes and introduces a new way to calibrate the gyroscope based on their joint data. MAG.I.C.AL. is implemented in a 15-step sequence achieving fast convergence and high accuracy without using any external piece of equipment and without requiring external attitude references. Simulation and experimental results using low-cost sensors are presented to support the accuracy, efficiency, and the applications of the algorithm.

This paper presents a methodology for developing models for the post-calibration residual errors of inexpensive inertial sensors in the class normally referred to as “automotive” or “consumer” grade. These sensors are increasingly being used in real-time vehicle navigation and guidance systems. However, manufacturer supplied specification sheets for these sensors seldom provide enough detail to allow constructing the type of error models required for analyzing the performance or assessing the risk associated with navigation and guidance systems. A methodology for generating error models that are accurate and usable in navigation and guidance systems’ sensor fusion and risk analysis algorithms is developed and validated. Use of the error models is demonstrated by a simulation in which the performance of an automotive navigation and guidance system is analyzed.

An optimal calibration method for a micro-electro-mechanical inertial measurement unit (MIMU) is presented in this paper. The accuracy of the MIMU is highly dependent on calibration to remove the deterministic errors of systematic errors, which also contain random errors. The overlapping Allan variance is applied to characterize the types of random error terms in the measurements. The calibration model includes package misalignment error, sensor-to-sensor misalignment error and bias, and a scale factor is built. The new concept of a calibration method, which includes a calibration scheme and a calibration algorithm, is proposed. The calibration scheme is designed by D-optimal and the calibration algorithm is deduced by a Kalman filter. In addition, the thermal calibration is investigated, as the bias and scale factor varied with temperature. The simulations and real tests verify the effectiveness of the proposed calibration method and show that it is better than the traditional method.

In this paper, we propose a high-precision pose estimation algorithm for systems equipped with low-cost inertial sensors and rolling-shutter cameras. The key characteristic of the proposed method is that it performs online self-calibration of the camera and the IMU, using detailed models for both sensors and for their relative configuration. Specifically, the estimated parameters include the camera intrinsics (focal length, principal point, and lens distortion), the readout time of the rolling-shutter sensor, the IMU's biases, scale factors, axis misalignment, and g-sensitivity, the spatial configuration between the camera and IMU, as well as the time offset between the timestamps of the camera and IMU. An additional contribution of this work is a novel method for processing the measurements of the rolling-shutter camera, which employs an approximate representation of the estimation errors, instead of the state itself. We demonstrate, in both simulation tests and real-world experiments, that the proposed approach is able to accurately calibrate all the considered parameters in real time, and leads to significantly improved estimation precision compared to existing approaches.

The usage of inertial sensors has traditionally been confined primarily to the aviation and marine industry due to their associated cost and bulkiness. During the last decade, however, inertial sensors have undergone a rather dramatic reduction in both size and cost with the introduction of MEMS technology. As a result of this trend, inertial sensors have become commonplace for many applications and can even be found in many consumer products, for instance smart phones, cameras and game consoles. Due to the drift inherent in inertial technology, inertial sensors are typically used in combination with aiding sensors to stabilize andimprove the estimates. The need for aiding sensors becomes even more apparent due to the reduced accuracy of MEMS inertial sensors. This thesis discusses two problems related to using inertial sensors in combination with aiding sensors. The first is the problem of sensor fusion: how to combine the information obtained from the different sensors and obtain a good estimate of position and orientation. The second problem, a prerequisite for sensor fusion, is that of calibration: the sensors themselves have to be calibrated and provide measurement in known units. Furthermore, whenever multiple sensors are combined additional calibration issues arise, since the measurements are seldom acquired in the same physical location and expressed in a common coordinate frame. Sensor fusion and calibration are discussed for the combination of inertial sensors with cameras, UWB or GPS. Two setups for estimating position and orientation in real-time are presented in this thesis. The first uses inertial sensors in combination with a camera; the second combines inertial sensors with UWB. Tightly coupled sensor fusion algorithms and experiments with performance evaluation are provided. Furthermore, this thesis contains ideas on using an optimization based sensor fusion method for a multi-segment inertial tracking system used for human motion capture as well as a sensor fusion method for combining inertial sensors with a dual GPS receiver. The above sensor fusion applications give rise to a number of calibration problems. Novel and easy-to-use calibration algorithms have been developed and tested to determine the following parameters: the magnetic field distortion when an IMU containing magnetometers is mounted close to a ferro-magnetic object, the relative position and orientation of a rigidly connected camera and IMU, as well as the clock parameters and receiver positions of an indoor UWB positioning system.

The integration of observations issued from a satellite-based system (GNSS) with an inertial navigation system (INS) is usually performed through a Bayesian filter such as the extended Kalman filter (EKF). The task of designing the navigation EKF is strongly related to the inertial sensor error modeling problem. Accelerometers and gyroscopes may be corrupted by random errors of complex spectral structure. Consequently, identifying correct error-state parameters in the INS/GNSS EKF becomes difficult when several stochastic processes are superposed. In such situations, classical approaches like the Allan variance (AV) or power spectral density (PSD) analysis fail due to the difficulty of separating the error processes in the spectral domain. For this purpose, we propose applying a recently developed estimator based on the generalized method of wavelet moments (GMWM), which was proven to be consistent and asymptotically normally distributed. The GMWM estimator matches theoretical and sample-based wavelet variances (WVs), and can be computed using the method of indirect inference. This article mainly focuses on the implementation aspects related to the GMWM, and its integration within a general navigation filter calibration procedure. Regarding this, we apply the GMWM on error signals issued from MEMS-based inertial sensors by building and estimating composite stochastic processes for which classical methods cannot be used. In a first stage, we validate the resulting models using AV and PSD analyses and then, in a second stage, we study the impact of the resulting stochastic models design in terms of positioning accuracy using an emulated scenario with statically observed error signatures. We demonstrate that the GMWM-based calibration framework enables to estimate complex stochastic models in terms of the resulting navigation accuracy that are relevant for the observed structure of errors.

This paper presents a novel wearable device for gesture capturing based on inertial and magnetic measurement units that are made up of micromachined gyroscopes, accelerometers, and magnetometers. The low-cost inertial and magnetic measurement unit is compact and small enough to wear and there are altogether thirty-six units integrated in the device. The device is composed of two symmetric parts, and either the right part or the left one contains eighteen units covering all the segments of the arm, palm, and fingers. The offline calibration and online calibration are proposed to improve the accuracy of sensors. Multiple quaternion-based extended Kalman filters are designed to estimate the absolute orientations, and kinematic models of the arm-hand are considered to determine the relative orientations. Furthermore, position algorithm is deduced to compute the positions of corresponding joint. Finally, several experiments are implemented to verify the effectiveness of the proposed wearable device.

Calibration is an essential prerequisite for the combined application of light detection and ranging (LiDAR) and inertial measurement unit (IMU). However, current LiDAR-IMU calibration usually relies on particular artificial targets or facilities and the intensive labor greatly limits the calibration flexibility. For these reasons, this article presents a novel multifeature based on-site calibration method for LiDAR-IMU system without any artificial targets or specific facilities. This new on-site calibration combines the point/sphere, line/cylinder, and plane features from LiDAR scanned data to reduce the labor intensity. The main contribution is that a new method is developed for LiDAR extrinsic parameters on-site calibration and this method could incorporate two or more calibration models to generate more accurate calibration results. First of all, the calibration of LiDAR extrinsic parameters is performed through estimating the geometric features and solving the multifeature geometric constrained optimization problem. Then, the relationships between LiDAR and IMU intrinsic calibration parameters are determined by the coordinate transformation. Lastly, the full information maximum likelihood estimation (FIMLE) method is applied to solve the optimization of the IMU intrinsic parameters calibration. A series of experiments are conducted to evaluate the proposed method. The analysis results demonstrate that the proposed on-site calibration method can improve the performance of the LiDAR-IMU.

The calibration path of system-level calibration directly affects the incentive effect of the error term and thus the calibration accuracy. Currently, the planning of system-level calibration paths is predominantly designed based on personal experience, resulting in insufficient incentive for error terms, low calibration accuracy, and long calibration times. Therefore, this study proposes a system-level calibration optimal path planning method based on an improved Dijkstra’s algorithm. First, the system-level calibration optimal path planning problem was modeled as a multi-fork regular root tree model, and the adaptability of Dijkstra’s algorithm was improved. Second, a 30-dimensional Kalman filter model was designed for system-level calibration. Then, simulation experiments were conducted, and the results demonstrated that the calibration accuracy of the error term reached 90% within 330 s. Finally, a Micro-Electro-Mechanical system (MEMS) inertial sensor, model PA-IMU488B, was used for experimental verification, and the results were compared with the discrete calibration results. The results indicate that the bias and scale factor errors of the MEMS inertial sensor reached the target accuracy within 5 min. The optimal path planning method for system-level calibration proposed in this study is not dependent on a high-precision turntable, is applicable to sensors of different accuracies, and decreases calibration time while ensuring calibration accuracy.

Navigation grade inertial measurement units (IMUs) should be calibrated after Inertial Navigation Systems (INSs) are assembled and be re-calibrated after certain periods of time. The multi-position calibration methods with advantage of not requiring high-precision equipment are widely discussed. However, the existing multi-position calibration methods for IMU are based on the model of linear scale factors. To improve the precision of INS, the nonlinear scale factors should be calibrated accurately. This paper proposes an optimized multi-position calibration method with nonlinear scale factor for IMU, and the optimal calibration motion of IMU has been designed based on the analysis of sensitivity of the cost function to the calibration parameters. Besides, in order to improve the accuracy and robustness of the optimization, an estimation method on initial values is presented to solve the problem of setting initial values for iterative methods. Simulations and experiments show that the proposed method outperforms the calibration method without nonlinear scale factors. The navigation accuracy of INS can be improved by up to 17% in lab conditions and 12% in the moving vehicle experiment, respectively.

Ultralow-cost single-chip inertial measurement units (IMUs) combined into IMU arrays are opening up new possibilities for inertial sensing. However, to make these systems practical for researchers, a simple calibration procedure that aligns the sensitivity axes of the sensors in the array is needed. In this paper, we suggest a novel mechanical-rotation-rig-free calibration procedure based on blind system identification and a Platonic solid printable using a contemporary 3-D printer. The IMU array is placed inside the Platonic solid, and static measurements are taken with the solid subsequently placed on all sides. The recorded data are then used together with a maximum-likelihood-based approach to estimate the interIMU misalignment and the gain, bias, and sensitivity axis nonorthogonality of the accelerometers. The effectiveness of the method is demonstrated with calibration results from an in-house developed IMU array. MATLAB scripts for the parameter estimation and production files for the calibration device (solid) are provided.

A typical calibration scheme for a gimbaled inertial measurement unit (IMU) involves an estimation of error parameters of an IMU mounted on an inertial platform and the platform's misalignment angles. However, traditional calibration methods for the gimbaled IMU have some serious defects. The excitation for a gyro's scale factors and misalignment angles is only the Earth rate in multi-position calibration methods and dynamic errors (unneeded motion of gyro floaters) involved in a continuous calibration process. This paper presents a new continuous self-calibration scheme for the gimbaled IMU. By processing the multi-position and continuous rotation steps alternately, the dynamic errors are suppressed and the excitation is augmented. This is more effective than traditional methods. Additionally, the platform rotation trajectory is designed to provide adequate observability for all parameters through a new methodology. The Lie derivative is used to compute the observability, and the genetic algorithm is utilized to obtain the inertial platform's optimal rotation trajectory based on the measurement of observability for all parameters. Simulation results show that the error coefficients can be effectively calibrated within an hour by the proposed scheme, and it is of high significance for fast launching of missiles and rockets.

This work presents methods for the determination of a humanoid robot's joint velocities and accelerations directly from link-mounted Inertial Measurement Units (IMUs) each containing a three-axis gyroscope and a three-axis accelerometer. No information about the global pose of the floating base or its links is required and precise knowledge of the link IMU poses is not necessary due to presented calibration routines. Additionally, a filter is introduced to fuse gyroscope angular velocities with joint position measurements and compensate the computed joint velocities for time-varying gyroscope biases. The resulting joint velocities are subject to less noise and delay than filtered velocities computed from numerical differentiation of joint potentiometer signals, leading to superior performance in joint feedback control as demonstrated in experiments performed on a SARCOS hydraulic humanoid.

∗As an inertial sensors assembly, the inertial measurement unit (IMU) must be calibrated before being used. This paper proposes a new IMU multi-position calibration algorithm that takes the Earth’s rotation rate and gravity as inputs, and calculates calibration parameters based on the two facts that: 1) norm of the accelerometer measurement vector is equal to the magnitude of gravity; 2) the dot product of gyro measurement vector and accelerometer measurement vector is equal to minus dot product of the Earth’s rotation rate and gravity. Two theorems about the rank of the involved matrix are given to prove the feasibility of estimation. The algorithm features that no high-precise instruments such as a turntable are in principle necessary. Simulations show feasibility of the proposed calibration algorithm.

A maximum likelihood estimator is presented for self-calibrating both accelerometers and gyroscopes in an inertial sensor array, including scale factors, misalignments, biases, and sensor positions. By simultaneous estimation of the calibration parameters and the motion dynamics of the array, external equipment is not required for the method. A computational efficient iterative optimization method is proposed where the calibration problem is divided into smaller subproblems. Further, an identifiability analysis of the calibration problem is presented. The analysis shows that it is sufficient to know the magnitude of the local gravity vector and the average scale factor gain of the gyroscopes, and that the array is exposed to two types of motions for the calibration problem to be well defined. The proposed estimator is evaluated by real-world experiments and by Monte Carlo simulations. The results show that the parameters can be consistently estimated and that the calibration significantly improves the accuracy of the motion estimation. This enables on-the-fly calibration of small inertial sensors arrays by simply twisting them by hand.

In this paper, a novel calibration procedure for skew redundant inertial measurement units (SRIMUs) based on micro-electro mechanical systems (MEMS) is proposed. A general model of the SRIMU measurements is derived which contains the effects of bias, scale factor error and misalignments. For more accuracy, the effect of lever arms of the accelerometers to the center of the table are modeled and compensated in the calibration procedure. Two separate Kalman filters (KFs) are proposed to perform the estimation of error parameters for gyroscopes and accelerometers. The predictive error minimization (PEM) stochastic modeling method is used to simultaneously model the effect of bias instability and random walk noise on the calibration Kalman filters to diminish the biased estimations. The proposed procedure is simulated numerically and has expected experimental results. The calibration maneuvers are applied using a two-axis angle turntable in a way that the persistency of excitation (PE) condition for parameter estimation is met. For this purpose, a trapezoidal calibration profile is utilized to excite different deterministic error parameters of the accelerometers and a pulse profile is used for the gyroscopes. Furthermore, to evaluate the performance of the proposed KF calibration method, a conventional least squares (LS) calibration procedure is derived for the SRIMUs and the simulation and experimental results compare the functionality of the two proposed methods with each other.

In this article, an on-line calibration method for strap-down inertial navigation system (SINS)/Doppler velocity log (DVL) based integrated navigation system is proposed to jointly estimate the calibration parameters of SINS and DVL, where the DVL lever arm and gyroscope scale factor error are considered. The full-parameters, including the gyroscope scale factor error, gyroscope bias, accelerometer bias, DVL installation misalignment angle, and DVL lever arm, are modeled as calibration parameters. A new state–space model for on-line calibration of SINS/DVL integrated navigation system is established, which also introduces the measurements of the global navigation satellite system (GNSS) and celestial navigation system (CNS) to improve the observability of calibration parameters. To suppress the effects of nonlinear error introduced by large installation error between SINS and DVL, a full-parameters feedback correction scheme is proposed. In addition, a special trajectory for the proposed on-line calibration method is designed based on the observability analysis results and the actual motion conditions of the ship, which ensures those calibration parameters in the calibration model can be observed. Simulation results and semi-physical simulation results illustrate that the proposed on-line calibration method can achieve better calibration results than existing methods compared in this article, and the full-parameters can be jointly calibrated online, even in the case of large installation errors between SINS and DVL.

Based on a small, lightweight, low-cost high performance inertial Measurement Units(IMU), an effective calibration method is implemented to evaluate the performance of Micro-Electro-Mechanical Systems(MEMS) sensors suffering from various errors to get acceptable navigation results. A prototype development board based on FPGA, dual core processor's configuration for INS/GPS integrated navigation system is designed for experimental testing. The significant error sources of IMU such as bias, scale factor, and misalignment are estimated in virtue of static tests, rate tests, and thermal tests. Moreover, an effective intelligent calibration method combining with Kalman filter is proposed to estimate parameters and reduce the effect of IMU dynamic errors that can degrade the system performance. The efficiency of proposed approach is demonstrated by various experimental scenarios.

As sensor calibration plays an important role in visual-inertial sensor fusion, this article performs an in-depth investigation of online self-calibration for robust and accurate visual-inertial state estimation. To this end, we first conduct complete observability analysis for visual-inertial navigation systems (VINS) with full calibration of sensing parameters, including inertial measurement unit (IMU)/camera intrinsics and IMU-camera spatial-temporal extrinsic calibration, along with readout time of rolling shutter (RS) cameras (if used). We study different inertial model variants containing intrinsic parameters that encompass most commonly used models for low-cost inertial sensors. With these models, the observability analysis of linearized VINS with full sensor calibration is performed. Our analysis theoretically proves the intuition commonly assumed in the literature—that is, VINS with full sensor calibration has four unobservable directions, corresponding to the system's global yaw and position, while all sensor calibration parameters are observable given fully excited motions. Moreover, we, for the first time, identify degenerate motion primitives for IMU and camera intrinsic calibration, which, when combined, may produce complex degenerate motions. We compare the proposed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">online</i> self-calibration on commonly used IMUs against the state-of-art <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">offline</i> calibration toolbox Kalibr, showing that the proposed system achieves better consistency and repeatability. Based on our analysis and experimental evaluations, we also offer practical guidelines to effectively perform online IMU-camera self-calibration in practice.

Accurate intersensor spatiotemporal transformation is the fundamental prerequisite for multisensor fusion. However, traditional discrete-time calibration methods have natural shortcomings when dealing with distorted and asynchronous raw measurements collected by light detection and ranging (LiDAR) and rolling shutter cameras. To this end, we propose a two-step LiDAR/camera/inertial measurement unit (IMU) spatiotemporal calibration method using continuous-time batch optimization. This proposed method is target free and has no assumptions about the sensor configuration. Specifically, the LiDAR point-to-plane, gyroscope, and accelerometer factors are jointly optimized to obtain the optimal LiDAR-IMU extrinsic parameters, time offset, and poses of control points. Subsequently, combined with visual reprojection factor, the control points in the spline trajectory will be fixed to obtain the camera-IMU extrinsic parameters as well as its time offset. A series of experiments in both simulated and real-world environments were conducted to evaluate the effectiveness of the proposed calibration method. Moreover, the effects of different numbers of iterations, environments (indoor and outdoor), IMU sampling rates, and control point frequencies on the calibration performance are analyzed in detail.

In the field of surveying and mapping, inertial sensor deterministic errors are poorly understood, and error calibration and compensation are not carried out. Thus, in this study, the effects of three types of deterministic errors (i.e., bias, scale factor error, and installation error) in a conventional inertial measurement unit (IMU) error model on a navigation system are theoretically deduced and verified by simulation. Subsequently, navigation experiments are carried out to investigate the effects of the three deterministic errors on the navigation system. The experimental results show that the gyro bias has the strongest influence on the navigation and positioning accuracy of the system. Consequently, we designed a two-position continuous calibration scheme to calibrate the IMU. The calibration scheme can simultaneously calibrate the bias error of the gyroscope and the accelerometer. When calibrating the bias error of the 0.005°/h order of magnitude, the maximum relative error is 13.16%, and the rest of the calibration relative errors are less than 10%, which verifies the effectiveness of the calibration path designed in this paper. The system is compensated by using the IMU bias calibration results, and the navigation experiment results show that the position accuracy and heading accuracy are improved by 72.68% and 79.65%, respectively, through the calibration and compensation of IMU bias error. Therefore, the position and heading accuracy of the system will be greatly improved by calibrating and compensating the bias error through the two-position calibration path before the IMU is used.

Vehicular positioning systems are necessary for the development of autonomous vehicles and advanced driver assistance systems (ADAS). In recent years, Inertial Measurement Units (IMU) based on micro-electromechanical systems (MEMS) have been included in proposals for multi-sensor positioning system architectures in order to take advantage of their cost and size. The measurement errors propagation to the positioning solution have limited its application for long-term positioning solution. However, it can play a key role in those applications where tri-axial attitude and accelerations can be indicators of curves, slopes, cants, etc. and it can be used as diagnostic of other sensors measurements. This work is focused on the use of IMUs for diagnostic applications and it compares medium-end (xSens MTi-100) and low-end (Bosch BMI160) grade MEMS-based IMUs in an experimental road test using a fusion of a high-end IMU (KVH GEO-FOG), GNSS and wheel speed sensor as reference. In addition, a research question about whether the calibration is the main reason between different grade IMUs has been formulated. Thus, a simple, manufacturable and cost-efficient calibration technique is applied to the low-end IMU in order to compare its performance improvement with the medium-end one. The raw measurements (angular rates and specific forces) and navigation states (tri-axial attitude and accelerations) are considered for diagnosis and they are statistically compared to evaluate the performance of each IMU. It is concluded that the calibration technique used makes the low-end IMU performance similar to that of the medium-end one. Consequently, this work contributes to optimizing the cost of land vehicular positioning systems when choosing the most appropriate sensor based on the accuracy and precision required for the application.

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A novel sensor fusion design framework is presented with the objective of improving the overall multisensor measurement system performance and achieving graceful degradation following individual sensor failures. The Unscented Information Filter (UIF) is used to provide a useful tool for combining information from multiple sources. A two-step off-line and on-line calibration procedure refines sensor error models and improves the measurement performance. A Fault Detection and Identification (FDI) scheme crosschecks sensor measurements and simultaneously monitors sensor biases. Low-quality or faulty sensor readings are then rejected from the final sensor fusion process. The attitude estimation problem is used as a case study for the multiple sensor fusion algorithm design, with information provided by a set of low-cost rate gyroscopes, accelerometers, magnetometers, and a single-frequency GPS receiver’s position and velocity solution. Flight data collected with an Unmanned Aerial Vehicle (UAV) research test bed verifies the sensor fusion, adaptation, and fault-tolerance capabilities of the designed sensor fusion algorithm.

Non-linear optimization on constraint graphs has recently been applied very successfully in a variety of SLAM backends. We combine this technique with a principled way of handling non-Euclidean spaces, 3D orientations in particular, based on manifolds to build a generic and very flexible framework, the Manifold Toolkit for Matlab (MTKM). We show that MTKM makes it particularly easy to solve non-trivial multi-sensor calibration problems while remaining generic enough to handle a very different class of problems, namely SLAM, as well: After an introductory example on single camera calibration we apply MTKM to calibration of stereo vision and IMU w.r.t. the kinematic chain of a service robot, RGB-D and accelerometer calibration of a Microsoft Kinect, stereo calibration on a Nao soccer robot, and several SLAM benchmark data sets illustrating MTKM's versatility. MTKM and all presented examples are available as open source from http://openslam.org/MTK.html.

This paper develops an improved hybrid calibration scheme for the strapdown inertial navigation system (SINS) that combines the advantages of an optimal rotational norm calibration method and an improved system-level calibration method. To accurately determine the scale factors and misalignment error of gyros triad, the optimal rotation norm calibration method is applied. Similarly, the improved system-level calibration method based on the 24-dimensional error state Kalman filter (ESKF) plays an important role in accelerometer calibration and gyro biases calibration. The clockwise and counterclockwise multi-cycles rotation scheme is designed to eliminate the effects of the Earth's rate and gyros biases, and then provide accurate rotational norm to completely determine the gyros triad scale factors and misalignment. In addition, the improved ESKF system-level calibration method is employed to estimate accelerometer parameters and gyros biases. Simulation test verify the validity of the proposed method, and the calibration experiences and the verification tests of the two high-precision optical gyros inertial measurement units (IMU) are carried out. For comparison, the traditional 30-dimensional system-level calibration is also performed. The attitude error of high maneuvering swing test indicate that the gyros calibration accuracy of hybrid calibration scheme is better than that of traditional system-level calibration scheme. Furthermore, the positioning error of pure inertial navigation solution in static and dynamic condition for two calibration methods indicate that the hybrid calibration scheme significantly improves the positioning accuracy, especially in the dynamic experiment, that is, the proposed scheme provides a more accurate calibration of the IMU.

A simulation model contributes to the development of both algorithms based on navigation sensors and their application in real nonlinear mechatronic systems. The Szabad(ka)-II hexapod walker robot is equipped with an inertial measurement unit (IMU), and this paper presents a novel calibration procedure of its simulation model. Various sinusoidal calibration movements were performed on both the model and the robot, and the raw IMU measurements were recorded simultaneously with motor electrical parameters and joint movement variables. The simulation model includes the model of IMU sensors, where the location, misalignments, and scaling parameters are also incorporated in the tuning procedure. Thus, this simulation environment enabled the calibration procedure to be performed based on the measurement data. The efficient optimization of both the unknown and estimated parameters of the robot model along with the IMU sensor model resulted in a simulation output that fits the measurement results satisfactorily. The nominal and remaining errors were analyzed both statistically and in the spectral domain. Due to the proposed method, the simulation error of the accelerometer and gyroscope measurements were decreased by 35%. The necessity of calibrating the sensor model was justified via the application of an extended Kalman filter (EKF) for the attitude estimation.

The demand for precise positioning grows up parallel to the advances in production of the geolocation instruments.Today, the Global Positioning System (GPS) is the most common positioning system in use because of its being very precise, convenient and cheap.However, when working in such areas that the external references (e.g.GPS satellites) are not available, a system that does not require information from any external source of information is required.Especially, these kinds of systems necessitate in detection of unexploded ordnances (UXO) buried in forestry areas, where precise position information is vital for removing them.The Inertial Navigation System (INS) operates in any environment and does not depended on any external source of information.It can operate alone or as an integrated system with GPS.However, the Inertial Measurement Unit (IMU) sensor outputs include some errors which can cause very large positioning errors.These errors can significantly be reduced by using calibration methods.The most accurate calibration methods are performed in laboratories and they require very precise instruments.However, the most significant IMU errors, biases and scale factor errors, change from turn on to turn on of the IMU and therefore they need to be estimated before every mission.The Multi-Position Calibration Method developed by Shin (2002) is a good example which is cost efficient and it can be applied in the field without use of any external calibration instrument.The method requires iii numerous IMU attitude measurements and use the gravity magnitude and Earth rotation rate as reference for calibration.The performance of the Multi-Position Calibration Method was tested by using a cart based geolocation system which includes 2 tactical grade IMUs, Honeywell HG1700 and HG1900.The calibration test was conducted in a parking lot of Ohio State University on 06 June 2010.The calibration estimations have shown that the navigation accuracy could be improved by up to 19.8% for the HG1700 and 17.8% for the HG1900.However, the results were not consistent among each other and in some cases decrease in the positioning accuracy was yielded.

Accurate attitude and heading reference system (AHRS) play an essential role in navigation applications and human body tracking systems. Using low-cost microelectromechanical system (MEMS) inertial sensors and having accurate orientation estimation, simultaneously, needs optimum orientation methods and algorithms. The error of attitude estimation may lead to imprecise navigation and motion capture results. This paper proposed a novel intermittent calibration technique for MEMS-based AHRS using error prediction and compensation filter. The method, inspired from the recognition of gyroscope's error and by a proportional integral (PI) controller, can be regulated to increase the accuracy of the prediction. The experimentation of this study for the AHRS algorithm, aided by the proposed prediction filter, was tested with real low-cost MEMS sensors consists of accelerometer, gyroscope, and magnetometer. Eventually, the error compensation was performed by post-processing the measurements of static and dynamic tests. The experimental results present about 35% accuracy improvement in attitude estimation and demonstrate the explicit performance of proposed method.

In this paper, the multi-position calibration method for low cost micro-electro mechanical systems inertial measurement unit (MEMS IMU) is significantly improved based on two principles. One is that the magnitude of the specific force should be equal to that of the gravity vector. Another is that the gravity vector should be equal to the computed gravity vector which is calculated with the gyroscope outputs. Thus, the error parameters of the MEMS IMU can be estimated without any equipment using the proposed method. Different from previous methods, this paper applied a Kalman filter to calibrate the gyroscopes. This makes the calibration method simple and convenient for the non-technical customers, as the calibration processes can be implemented only by hands. The validity of the method is verified by a real test with a set of low cost MEMS IMU, and the performance is compared with the traditional six-position and rate test methods. The results indicate that the proposed method is effective and efficient for it can be used to calibrate the low cost MEMS IMUs without any special equipment and significantly increase the measurement accuracy.

Over the past decade and a half, the combination of low-cost, lightweight micro-electro-mechanical sensors (MEMS) technology and multisensor integration has enabled inertial sensors to be deployed over a much wider range of navigation applications [1]. Examples include pedestrian dead-reckoning using step detection technology [2, 3], aiding of GNSS signal tracking during jamming [4, 5], and simultaneous localisation and mapping (SLAM) using radio signals [6]. However, for best performance, a MEMS inertial measurement unit (IMU) must be calibrated in the laboratory prior to use, which increases the cost by more than $1000 per unit. In this paper, we examine and present a range of techniques which use an array of inexpensive MEMS sensors to improve the performance of a MEMS IMU without requiring a full calibration prior to use. As the cost of calibration of a high-performance MEMS IMU far outweighs the cost of the hardware, there is considerable scope to improve the performance by adding additional sensors, before the cost of the IMU reaches that of a laboratory calibrated equivalent. Combining MEMS IMUs in an array has been studied before. However, the most common approach was simply to take an average of the input of several identical sensors [7]. If the sensor errors were independent, this could be expected to improve performance by a factor of root-n where, n is the number of IMUs combined. In this paper more sophisticated techniques are investigated that use knowledge of the sensor characteristics to obtain better performance. Three different properties of MEMS sensors may potentially be exploited: 1) The common-mode errors of different sensors of the same design; 2) The different characteristics of in-plane and out-of-plane sensors; and 3) The complementary properties of MEMS sensors with different dynamic ranges. In [8], it is shown that different individual sensors of the same design exhibit similar bias variation with temperature and that improved accuracy may be obtained by differencing the outputs of two gyroscopes mounted with their sensitive axes in opposing directions. Here, this approach will be independently verified and the performance benefits assessed with a range of different MEMS accelerometers and gyros, including Bosch BMA180 accelerometers, Analogue Devices ADXL345 accelerometers, ST Microtronics L3G4200D gyroscopes. Preliminary indications are that there is considerable common bias variation with temperature for the in-plane sensors of L3G4200D gyroscopes, and some common mode behaviour for the low-cost accelerometers. The second idea presented is exploiting the differences between the in-plane and out-of-plane axis outputs of single-chip inertial sensor triads, to improve the performance of an array-based IMU. Early experiment s point to considerable differences between the two which could markedly affect navigation performance. Both accelerometer and gyro triads can exhibit smaller errors from the in-plane sensors than from the out-of-plane sensors. Therefore, experiments were conducted using mutually-perpendicular arrays of accelerometer and gyro triads to determine whether better performance could be obtained using only the in-plane sensors. The third idea is to combine the outputs of MEMS sensors with different dynamic ranges to exploit the lower noise exhibited by some lower-dynamic-range sensors compared to their higher-dynamic-range counterparts. The sensor outputs are thus weighted according to the platform dynamics. That is, predominantly using the high-precision sensor when dynamics are low and using the full-range sensor when the dynamics are high. Several versions of this weighted signal combination will be presented and compared. Early indications are that there can be a significant benefit in this approach for some sensor designs, but not others. Finally, this paper will also examine the efficacy of a once-only static calibration on purchase, performed by the user instead of the supplier, for improving navigation performance. It is essential for a user-performed calibration that the physical movements required of the sensor are very simple and easily understood and completed, even if the underlying method is complex. To this end data, recorded on different days from an array of MEMS sensors within a precisely manufactured rapid prototyped ‘calibration cube’, will be analysed. These measurements are taken at precisely orthogonal angles of the cubes six faces, and allow the scale factor errors, biases and axes alignments of the accelerometers to be determined. The computed calibration corrections over several days will be compared to enable the efficacy of the one-time calibration technique to be assessed. The development of a full calibration routine will be the subject of future research. In summary, this paper will present several new methods for utilising the output of an array of low-cost sensors to improve the performance of a MEMS IMU, and also expands on methods proposed in existing research. As uncalibrated MEMS IMUs are of low performance there is a great potential for new applications if the performance can be improved closer to the level of those which are factory calibrated. / References [1] Groves, P. D., Principles of GNSS, inertial, and multi-sensor integrated navigation systems, Second Edition, Artech House, 2013. [2] Gustafson, D., J. Dowdle, and K. Flueckiger, “A Deeply Integrated Adaptive GPS-Based Navigator with Extended Range Code Tracking,” Proc. IEEE PLANS 2000. [3] Groves, P. D., C. J. Mather and A. A. Macaulay, “Demonstration of Non-Coherent Deep INS/GPS Integration for Optimized Signal to Noise Performance,” Proc. ION GNSS 2007. [4] Ma, Y., W. Soehren, W. Hawkinson, and J. Syrstad, "An Enhanced Prototype Personal Inertial Navigation System," Proc. ION GNSS 2012. [5] Groves, P. D., et al., “Inertial Navigation Versus Pedestrian Dead Reckoning: Optimizing the Integration,” Proc. ION GNSS 2007. [6] Faragher, R. M., C. Sarno, and M. Newman, “Opportunistic Radio SLAM for Indoor Navigation using Smartphone Sensors,” Proc. IEEE/ION PLANS 2012. [7] Bancroft, J. B., and G. Lachapelle, “Data fusion algorithms for multiple inertial measurement units,” Sensors, Vol. 11, No. 7, 2011, pp. 6771-6798. [8] Yuksel, Y., N. El-Sheimy, N., and A. Noureldin, “Error modelling and characterization of environmental effects for low cost inertial MEMS units,” Proc. IEEE/ION PLANS 2010.

We address the problem of estimating the position of a rigid body moving indoors. Disturbances of the magnetic field observed in buildings are used to derive a reliable velocity estimate. The estimated velocity is expressed in the body reference frame, which imposes to simultaneously reconstruct the rotation of this frame with respect to an inertial frame of reference. For this, an inertial measurement unit (IMU) is used. To maximize the accuracy of the reconstructed motion, alignment and calibration of the inertial sensors have to be carefully treated, which minimizes projection errors. A first contribution of this paper is an alignment-calibration technique combining gyrometers and accelerometers to address the attitude estimation problem. A second contribution is an observer of the velocity, the convergence of which is proved. Finally, an experimental testbench is described and experimental results are provided.

A new calibration method for Inertial Measurement Unit (IMU) of strapdown inertial technology was presented. IMU has been composed of MEMS accelerometers, gyroscopes and a circuit of signal processing. Normally, a rate transfer test and multi-position tests are used for IMU calibration. The new calibration method is based on whole angle rotation or finite rotation. In fact it suggests to turn over IMU around three axes simultaneously. In order to solve the equation of calibration, it is necessary to provide an equality of a rank of basic matrix into degree of basic matrix. Normally MEMS gyroscopes have got g- and g <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -drifts. It is proposed a way of finding such drifts. The results of simulated IMU data presented to demonstrate the performance of the new calibration method.

In the field of high accuracy dual-axis rotational inertial navigation system (RINS), the calibration accuracy of the gyroscopes and accelerometers is of great importance. Although rotation modulation can suppress the navigation error caused by scale factor error and bias error in a static condition, it cannot suppress the scale factor errors thoroughly during the maneuvering process of the vehicle due to the two degrees of rotation freedom. The self-calibration method has been studied by many researchers. However, traditional calibration methods need several hours to converge, which is unable to meet the demand for quick response to positioning and orientation. To solve the above problems, we do the following work in this study: (1) we propose a 39-dimensional online calibration Kalman filtering (KF) model to estimate all calibration parameters; (2) Error relationship between calibration parameters error and navigation error are derived; (3) A backtracking filtering scheme is proposed to shorten the calibration process. Experimental results indicate that the proposed method can shorten the calibration process and improve the calibration accuracy simultaneously.

Nowadays, LiDAR-IMU systems have progressively prevailed in mobile robotic applications due to their excellent complementary characteristics. With the steady decline and shrinking in cost and size of these sensors, it has become feasible and even imperative to further leverage multiple sensor units for better accuracy and robustness. In such a fusion-based system, accurate spatiotemporal calibration is a fundamental prerequisite. However, existing calibration methods generally necessitate artificial targets or an overlapping field-of-view (FoV) between LiDARs. To this end, we propose an accurate and easy-to-use and spatiotemporal calibration approach tailored to multi-LiDAR multi-IMU systems based on continuous-time batch estimation, which supports both mechanical spinning LiDARs and small FoV solid-state LiDARs. Inspired by classical hand–eye calibration, a stepwise multistage nonlinear optimization problem is first built to recover the rotational extrinsic and poses of control points in the spline without using any artificial targets, special movements, or manual intervention. Meanwhile, a virtual IMU and LiDAR are constructed to bridge all IMUs and LiDARs based on the centralized principles in both temporal and spatial domains. Subsequently, the point-to-plane factors associated by different LiDARs, gyroscope, and accelerometer factors are jointly minimized to optimize all spatiotemporal parameters over multiple batches. Extensive simulation tests and real-world experiments were conducted to quantitatively evaluate the feasibility of the proposed method. Meanwhile, the proposed method is compared with the state-of-the-art methods and shows superior calibration performance.

To enhance the navigation precision of strapdown inertial navigation system, it is necessary to carry out a high accuracy calibration for the inertial measurement unit (IMU). In this paper, a novel network calibration method is proposed to satisfy the calibration for a number of IMUs, which is depending on multiple maneuvers of the test platform where IMUs are installed. With the specific maneuvers of the test platform, the uncalibrated parameters of gyros and accelerometers models can be excited. In order to obtain the optimal estimation of these parameters, the dual-loop filter algorithm based on Kalman filter is presented for the information fusion by tracking the velocity and position errors from the IMUs nearby. The simulation result shows that the parameters of gyros and accelerometers models can be well estimated in a short time. Comparing with the existing calibration methods, the proposed method has the following advantages: (1) it does not require special equipment such as a turntable to provide the angular rate and multi-position tests, (2) it is time efficient when compared with other time consuming methods, (3) it can calibrate a lot of IMUs simultaneously, but not one by one. Thus with the above advantages, the proposed calibration method will have a wide application prospect for the in-field calibration.

We demonstrate simultaneous extraction of the scale factor and cross axis sensitivity of a commercial 6-DOF Inertial Measurement Unit (IMU), which has three gyroscopes and three accelerometers, using a multi-axis, mm-scale piezoelectric dither stage. The stage is 25.4×25.4×0.5 mm, with a platform disk of diameter 7.5 mm, onto which the IMU chip is adhesively attached. The stage has small inertia allowing for high bandwidth on-the-fly calibration and tracking of scale factor drift using rotation dither rates and accelerations as high as 100 deg/sec and 90 m/s2, respectively. We measure the gyroscope cross-axis sensitivities of 2.4%, which is within the IMU specifications. Using the cross-axis sensitivity and the scale factors, we demonstrate a pathway to improving commercial IMUs, reaching performance needed for personal navigation.

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Sensor-to-segment calibration is a crucial step in inertial motion tracking. When two segments are connected by a hinge joint, for example in human knee and finger joints as well as in many robotic limbs, then the joint axis vector must be identified in the intrinsic sensor coordinate systems. There exist methods that identify these coordinates by solving an optimization problem that is based on kinematic joint constraints, which involve either the measured accelerations or the measured angular rates. In the current paper we demonstrate that using only one of these constraints leads to inaccurate estimates at either fast or slow motions. We propose a novel method based on a cost function that combines both constraints. The restrictive assumption of a homogeneous magnetic field is avoided by using only accelerometer and gyroscope readings. To combine the advantages of both sensor types, the residual weights are adjusted automatically based on the estimated signal variances and a nonlinear weighting of the acceleration norm difference. The method is evaluated using real data from nine different motions of an upper limb exoskeleton. Results show that, unlike previous approaches, the proposed method yields accurate joint axis estimation after only five seconds for all fast and slow motions.

In this work, we explore the importance of sensors' calibration in inertial navigation applications. We focus on the case of low-cost systems, typically using MEMS inertial sensors, where the extra calibration cost is a critical parameter. We highlight the importance of calibration by deriving a bound of the evolution of the attitude and velocity error as a function of the calibration parameters' error. Then, we use low-cost 3-axis accelerometer and 3-axis gyroscope along with a popular pedestrian inertial navigation algorithm to experimentally confirm that raw sensor's data can be highly inappropriate for navigation purposes. Finally, we use the MAG.I.C.AL. methodology for joint calibration and axes alignment of inertial and magnetic sensors to achieve high accuracy measurements resulting in a reliable inertial navigation system.

A μIMU which consists of microelectromechanical systems (MEMS) accelerometers, gyroscopes and magnetometers has been developed for real-time estimation of human hand motions. Along with appropriate transformation and filtering algorithms, the μ IMU was implemented as a Ubiquitous Digital Writing Instrument (UDWI), which could interface with PCs in real-time via Bluetooth wireless protocol, to record the handwriting on any flat surface. However, because of the MEMS sensors' intrinsic biases and random noise such as circuit thermal noise, an effective calibration system that provides good reference measurement parameters must be developed to compare the output of the μIMU sensors to human hand motions. In this paper, we present our development of a method to calibrate three-dimensional linear accelerations and angular velocities of human writing motions measured from MEMS sensors through optical tracking techniques. In our experiments, English alphabets were written by the UDWI on a horizontal plane. The sensor output from the writing motions were transmitted wirelessly to a PC and the data were stored in the PC. Simultaneously, we recorded the pen-tip motion during the writing of each alphabet with a high-speed camera, which allowed us to exact the acceleration, velocity, and position of the UDWI's tip through appropriate optical-tracking algorithms. Then, the information is compared with the motion information obtained from the MEMS sensors in the UDWI. The motion data obtained from the high-speed camera are much more accurate, and hence could be used as reference motion data to analyze the performance of the UDWI, and eventually allows improvement of the UDWI performance.

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Autonomous cars are the future of automotive industry. Autonomous or driverless cars must be able to rapidly and accurately sense and analyze their immediate environment to take appropriate maneuvering/navigation actions under various driving conditions. To undertake such challenging navigation task, autonomous vehicles make use of a multitude of sensor systems and networks including (i) Global Positioning System (GPS), (ii) Inertial Navigation System (INS), (iii) Inter-vehicle and cellular wireless networks, (iv) Video cameras, and (v) Light Detection And Ranging (LiDAR) system [1-3]. Sensor fusion algorithms are applied to fuse the data from the various devices, which ultimately enables the vehicle to take accurate navigation decisions. The INS system takes a dominant role in the vehicular sensor fusion algorithm in GPS-denied environments such as dense urban places, multi-level parking structures, and areas with thick tree-coverage. The INS unit incorporates dead-reckoning principle via mechanization equations to process the linear acceleration and angular velocity data. Here, Micro Electro Mechanical Systems (MEMS) based Inertial Measurement Unit (IMU) sensors are preferred due to their low cost and resistance to shock and vibration. However, MEMS inertial sensors are prone to various errors [4-6]. Thus, development of calibration and compensation techniques for errors reduction from sensors, both systematic and stochastic/random, are essential. In this paper, we describe for the first time a novel deep learning-based methodology to simultaneously remove many errors sources in the sensor signals, under laboratory environment. By correctly identifying the classification signal, we developed a Convolutional Neural Network (CNN) algorithm that inherently removes the sensor error sources. To test the efficiency of our algorithm, the results are compared with traditional approaches like Six-Position Static Test and Rate Test. Here, we achieved an accuracy of 80 % in correctly identifying the accelerometer and gyroscope signals.

Background: A new calibration method for Inertial Measurement Unit (IMU) of Strapdown Inertial Navigation Systems was presented. IMU consists of inertial sensors like accelerometers, gyroscopes and a circuit of signal processing. Normally, a rate transfer test and multi-position tests are used for IMU calibration. In fact, it suggests turning over IMU around three axes simultaneously. In order to solve the equation of calibration, it is necessary to provide an equality of a rank of basic matrix into degree of basic matrix. For convenient or mechanical gyroscopes with g – and g2 – drifts, it is proposed as a way of problem solving. Keywords: Inertial Measurement Unit, accelerometers, gyroscopes, calibration, output signals, matrix equation.

Reliable extrinsic calibration is critical to fuse camera and inertial measurement unit (IMU), which are usually used in stereo visual-inertial odometry (VIO), however, it is difficult to obtain extrinsic parameters in practice. This paper proposes a stereo VIO with the capability of calibrating the unknown extrinsic parameters online. The initial values of IMU-camera and camera-camera transformations are estimated during the initial process, which fully leverages commonly observed features between stereo cameras. The pose and velocity are estimated and the extrinsic parameters are jointly refined. Additionally, the accelerometer and gyroscope biases, and gravity direction are taken into account. The proposed VIO scheme have been demonstrated to be effective without prior knowledge of extrinsic parameters.

This paper proposes a novel vehicle state estimation (VSE) method that combines a physics-informed neural network (PINN) and an unscented Kalman filter on manifolds (UKF-M). This VSE aimed to achieve inertial measurement unit (IMU) calibration and provide comprehensive information on the vehicle's dynamic state. The proposed method leverages a PINN to eliminate IMU drift by constraining the loss function with ordinary differential equations (ODEs). Then, the UKF-M is used to estimate the 3D attitude, velocity, and position of the vehicle more accurately using a six-degrees-of-freedom vehicle model. Experimental results demonstrate that the proposed PINN method can learn from multiple sensors and reduce the impact of sensor biases by constraining the ODEs without affecting the sensor characteristics. Compared to the UKF-M algorithm alone, our VSE can better estimate vehicle states. The proposed method has the potential to automatically reduce the impact of sensor drift during vehicle operation, making it more suitable for real-world applications.

This paper introduces a simple and efficient calibration method for three-axis accelerometers and three-axis gyroscopes using three-axis motion rate table. Usually, the performance of low cost MEMS-based inertial sensors is affected by scale and bias errors significantly. The calibration of these errors is a bothersome problem, but the previous calibration methods cannot propose simple and efficient method to calibrate the errors of three-axis inertial sensors. This paper introduces a new simple and efficient method for the calibration of accelerometer and gyroscope. By using a three-axis motion rate table, this method can calibrate the accelerometer and gyroscope simultaneously and simply. Experimental results confirm the performance of the proposed method.

A novel data glove embedded low cost MEMS inertial and magnetic measurement units, is proposed for fingers motion capture. Each unit consists of a tri-axial gyroscope, a tri-axial accelerometer and a tri-axial magnetometer. The sensor board and processor board are compactly designed, which are small enough to fit the size of our fingers. The data glove is equipped with fifteen units to measure each joint angle of the fingers. Then the calibration approach is put up to improve the accuracy of measurements by both offline and online procedures, and a fast estimation method is used to determine the three orientations of fifteen units simultaneously. The proposed algorithm is easy to be implemented, and more precise and efficient measurements can be obtained as compared with existing methods. The fingers motion capture experiments are implemented to acquire the characteristics of the fingers and teleoperate the robotic hands, which prove the effectiveness of the data glove.

Two methods for kinematic sensing in a hand-held dynamometer using accelerometers and gyroscopes are presented. The first method integrates the angular velocity signal from the gyroscope, after calibration of gyroscope offset and joint angle from a static period immediately preceding each measurement. The second method estimates tangential and radial accelerations, enabling the estimation of the gravity components in the accelerometer signals under dynamic conditions, and thus angle reconstruction. The second method appeared to perform best in preliminary tests.

A new calibration method for Inertial Measurement Unit (IMU) of Strapdown Iner-tial Navigation Systems was presented. IMU has been composed of accelerometers, gyroscopes and a circuit of signal processing. Normally, a rate transfer test and multi-position tests are us-ing for IMU calibration. The new calibration method is based on whole angle rotation or finite rotation. In fact it’s suggested to turn over IMU around three axes simultaneously. In order to solve the equation of calibration, it is necessary to provide an equality of a rank of basic matrix into degree of basic matrix. The results of simulated IMU data presented to demonstrate the performance of the new calibration method.

This thesis provides a methodology of sensory system development for a hexapod robot, working toward the development of dynamic behaviors utilizing feedback controllers. We develop an approach to utilizing strain gauges together with a simple data driven phenomenological model that simultaneously delivers information of leg touchdown, leg configuration, and ground reaction force suitable for robots with compliant legs. The strain gauges are implemented and models are constructed on two versions of RHex robot compliant legs. Leg configuration is further evaluated under realistic robot operating conditions by means of a high speed visual ground truth system. We then introduce a continuous time 6 degree of freedom (DOF) body pose estimator for a walking hexapod robot. Our algorithm uses six leg configurations together with prior knowledge of the ground and robot kinematics to compute instantaneous estimates of the body pose. We implement this estimation procedure on RHex and evaluate the performance of this algorithm at widely varying body speeds and over dramatically different ground conditions by means of a 6 DOF vision-based ground truth measurement system (GTMS). We also compare the odometry performance to that of sensorless schemes---both legged as well as on a wheeled version of the robot---using GTMS measurements of traversed distance. Finally, we report on a hybrid 12-dimensional full body state estimator for a jogging hexapod robot on level terrain with regularly alternating ground contact and aerial phases of motion. We use a repeating sequence of dynamical models switched in and out of an Extended Kalman Filter to fuse measurements from a body pose sensor and inertial sensors. Our inertial measurement unit supplements the traditionally paired 3-axis gyroscope/accelerometer with a set of three additional 3-axis accelerometer suites, thereby providing additional angular acceleration measurement (inertia torque), avoiding the need for localization of the accelerometer at the center of mass on the robot's body, and simplifying installation and calibration. We implement this estimation procedure offline, using data extracted from numerous repeated runs of RHex and evaluate its performance with reference to GTMS, also comparing the relative performance of different fusion approaches implemented via different model sequences.

Spatial distributed MEMS accelerometers seem to be an economically attractive and alternate way to gyros by indirectly measuring the turn rates of vehicles. Considering the lever arms between the Inertial Measurement Unit (IMU) reference point and the accelerometers, the rotary acceleration in relation to the IMU reference rotary axis can be determined and integrated to turn rates. Recent publications on a so called Gyro-Free IMU (GF-IMU) describe different geometries for the distribution of the sensors in the GF-IMU and it is shown that an optimal configuration can be found [1]. This configuration offers the possibility of measuring angular acceleration independently of the actual turn rate in order to keep the transfer behavior stable. This concept has been used to construct and build a GFIMU based on MEMS accelerometers (Figure 1) within the research project UniTaS IV which is going on at the Institute of Flight Guidance (IFF) of the Technische Universitaet Braunschweig and funded by the German Federal Ministry of Economic and Technology. This paper deals with the specific constraints of calibrating the GF-IMU using turntables, the development of the integrated system and the evaluation of the overall system by means of flight trials. Therefore, the basic equations are introduced in combination with the underlying sensor correction model. In order to determine the parameters of the correction model a calibration procedure is developed and its results are discussed. Afterwards, the necessary navigation differential equations for a generalized GF-IMU are shortly introduced together with the principles of deriving a coupling filter model. This model is finally applied in a filter and verified using a simulation based on real flight tests as well as real GF-IMU data from dynamic tests with the institute’s own test vehicle.

Inertial measurement units (IMUs) have been widely used to provide accurate location and movement measurement solutions, along with the advances of modern manufacturing technologies. The scale factors of accelerometers and gyroscopes are linear when the range of the sensors are reasonably small, but the factor becomes nonlinear when the range gets much bigger. Based on this observation, this article presents a calibration method for low-cost IMU by effectively deriving the nonlinear scale factors of the sensors. Two motion patterns of the sensor on a rigid object are moved to collect data for calibration: One motion pattern is to upcast and rotate the rigid object, and another pattern is to place the rigid object on a stable base in different attitudes. The rotation motion produces centripetal and Coriolis force, which increases the measurement range of accelerometers. Four cost functions with different weight factors and two sets of data are utilized to optimize the IMU parameters. The weight factor comes from derived formula with input values which are the variance of the noise of the sampled data. The proposed approach was validated and evaluated on both synthetic and real-world data sets, and the experimental results demonstrated the superiority of the proposed approach in improving the accuracy of IMU for long-range use. In particular, the errors of acceleration and angular velocity led by our algorithm are significantly smaller than those resulted from the existing approaches using the same testing data sets, demonstrating a remarkable improvement of 64.12% and 47.90%, respectively.

A low cost, high precision hollow structure MEMS IMU has been developed to measure the roll angular rate of a high-spinning projectile. The hollow MEMS IMU is realized by designing the scheme of non-centroid configuration of multiple accelerometers. Two dual-axis accelerometers are respectively mounted on the pitch axis and the yaw axis away from the center of mass of the high-spinning projectile. Three single-axis gyros are mounted orthogonal to each other to measure the angular rates, respectively. The roll gyro is not only used to judge the spinning direction, but also to measure and compensate for the low rotation speed of the high-spinning projectile. In order to improve the measurement accuracy of the sensor, the sensor output error is modeled and calibrated by the least square method. By analyzing the influence of noise statistical characteristics on angular rate solution accuracy, an adaptive unscented Kalman filter (AUKF) algorithm is proposed, which has a higher estimation accuracy than UKF algorithm. The feasibility of the method is verified by numerical simulation. By using the MEMS IMU device to build a semi-physical simulation platform, the solution accuracy of the angular rate is analyzed by simulating different rotation speeds of the projectile. Finally, the flight test is carried out on the rocket projectile with the hollow MEMS IMU. The test results show that the hollow MEMS IMU is reasonable and feasible, and it can calculate the roll angular rate in real time. Therefore, the hollow MEMS IMU designed in this paper has certain engineering application value for high-spinning projectiles.

The calibration of micro inertial measurement units is important in ensuring the precision of navigation systems, which are equipped with microelectromechanical system sensors that suffer from various errors. However, traditional calibration methods cannot meet the demand for fast field calibration. This paper presents a fast field calibration method based on the Powell algorithm. As the key points of this calibration, the norm of the accelerometer measurement vector is equal to the gravity magnitude, and the norm of the gyro measurement vector is equal to the rotational velocity inputs. To resolve the error parameters by judging the convergence of the nonlinear equations, the Powell algorithm is applied by establishing a mathematical error model of the novel calibration. All parameters can then be obtained in this manner. A comparison of the proposed method with the traditional calibration method through navigation tests shows the classic performance of the proposed calibration method. The proposed calibration method also saves more time compared with the traditional calibration method.

Inertial Measurement Unit (IMU) calibration accuracy is easily affected by turntable errors, so the primary aim of this study is to reduce the dependence on the turntable's precision during the calibration process. Firstly, the indicated-output of the IMU considering turntable errors is constructed and with the introduction of turntable errors, the functional relationship between turntable errors and the indicated-output was derived. Then, based on a D-suboptimal design, a calibration method for simultaneously identifying the IMU error model parameters and the turntable errors was proposed. Simulation results showed that some turntable errors could thus be effectively calibrated and automatically compensated. Finally, the theoretical validity was verified through experiments. Compared with the traditional method, the method proposed in this paper can significantly reduce the influence of the turntable errors on the IMU calibration accuracy.

Errors compensation of micromachined-inertial-measurement-units (MIMU) is essential in practical applications. This paper presents a new compensation method using a neural-network-based identification for MIMU, which capably solves the universal problems of cross-coupling, misalignment, eccentricity, and other deterministic errors existing in a three-dimensional integrated system. Using a neural network to model a complex multivariate and nonlinear coupling system, the errors could be readily compensated through a comprehensive calibration. In this paper, we also present a thermal-gas MIMU based on thermal expansion, which measures three-axis angular rates and three-axis accelerations using only three thermal-gas inertial sensors, each of which capably measures one-axis angular rate and one-axis acceleration simultaneously in one chip. The developed MIMU (100 × 100 × 100 mm³) possesses the advantages of simple structure, high shock resistance, and large measuring ranges (three-axes angular rates of ±4000°/s and three-axes accelerations of ± 10 g) compared with conventional MIMU, due to using gas medium instead of mechanical proof mass as the key moving and sensing elements. However, the gas MIMU suffers from cross-coupling effects, which corrupt the system accuracy. The proposed compensation method is, therefore, applied to compensate the system errors of the MIMU. Experiments validate the effectiveness of the compensation, and the measurement errors of three-axis angular rates and three-axis accelerations are reduced to less than 1% and 3% of uncompensated errors in the rotation range of ±600°/s and the acceleration range of ± 1 g, respectively.

Inertial technology has been used in a wide range of applications such as guidance, navigation, and motion tracking. However, there are few undergraduate courses that focus on the inertial technology. Traditional inertial navigation systems (INS) and relevant testing facilities are expensive and complicated in operation, which makes it inconvenient and risky to perform teaching experiments with such systems. To solve this issue, this paper proposes the idea of using smartphones, which are ubiquitous and commonly contain off-the-shelf inertial sensors, as the experimental devices. A series of curriculum experiments are designed, including the Allan variance test, the calibration test, the initial leveling test and the drift feature test. These experiments are well-selected and can be implemented simply with the smartphones and without any other specialized tools. The curriculum syllabus was designed and tentatively carried out on 14 undergraduate students with a science and engineering background. Feedback from the students show that the curriculum can help them gain a comprehensive understanding of the inertial technology such as calibration and modeling of the sensor errors, determination of the device attitude and accumulation of the sensor errors in the navigation algorithm. The use of inertial sensors in smartphones provides the students the first-hand experiences and intuitive feelings about the function of inertial sensors. Moreover, it can motivate students to utilize ubiquitous low-cost sensors in their future research.

Accurate assessment of upper-limb movement alterations is a key component of post-stroke follow-up. Motion capture (MoCap) is the gold standard for assessment even in clinical conditions, but it requires a laboratory setting with a relatively complex implementation. Alternatively, inertial measurement units (IMUs) are the subject of growing interest, but their accuracy remains to be challenged. This study aims to assess the minimal detectable change (MDC) between spatiotemporal and quality variables obtained from these IMUs and MoCap, based on a specific protocol of IMU calibration and measurement and on data processing using the dead reckoning method. We also studied the influence of each data processing step on the level of between-system MDC. Fifteen post-stroke hemiparetic subjects performed reach or grasp tasks. The MDC for the movement time, index of curvature, smoothness (studied through the number of submovements), and trunk contribution was equal to 10.83%, 3.62%, 39.62%, and 25.11%, respectively. All calibration and data processing steps played a significant role in increasing the agreement. The between-system MDC values were found to be lower or comparable to the between-session MDC values obtained with MoCap, meaning that our results provide strong evidence that using IMUs with the proposed calibration and processing steps can successfully and accurately assess upper-limb movement alterations after stroke in clinical routine care conditions.

Navigation is the science and art that answers the questions of knowing where you are at the current moment and where you will be in the next moment. Modern navigation systems are based mainly on satellite and inertial sensors. Inertial sensor systems are becoming very popular in navigation systems because they are self contained sensors. The goal of this research is to develop novel approaches for improving the performance of inertial sensor systems and their integration algorithms with external sensors such as global positioning system (GPS) and magnetometers. The standalone inertial navigation system (INS) is dependent on the inertial measurement unit (IMU). An IMU is traditionally composed of three orthogonal gyroscopes and three orthogonal accelerometers.\nIn the inertial sensors side, we focus on the use of distributed accelerometers for inferring the angular motion from the angular information contained in their measurements. There exists a variety of reasons for conducting this research. In short, high quality gyros have high cost, high power consumption, large weight and large volume. On the other hand, accelerometers are less costly, easier to manufacture, have less power consumption and less weight than gyros. We developed different fusion approaches for benefiting from the angular information vector (AIV) resulting from the distributed accelerometers to form a gyro-free IMU (GF-IMU) or to aid the GF-IMU by conventional gyros. By improving the performance we mean reducing noise and bias level in the estimated inertial quantity.\nIn the integrated navigation side, we present different approaches to implement the GPS/INS integration filters and the attitude and heading reference system (AHRS) algorithms. We use direction cosine matrix (DCM) based algorithms which implies estimating the elements of the DCM directly within the filter. The basis for this method is the ground alignment method for attitude and heading determination. The attitude update of the DCM is performed using angle rotation vector. The filter is able to detect the gyro bias vector and follow its variation and hence it fits low-cost sensors as well as high grade sensor. We validated the efficiency of the algorithms using proper simulations and real-time implementations.\n