Gyro-free Inertial Measurement Unit Research Articles

Gyro-Free Inertial Measurement Unit With Unfettered Accelerometer Array Distribution and for the Object With Position Change in Center of Gravity

Previous gyro-free inertial measurement units (GF-IMU) usually suffered from installation errors induced by mutual placements and mutual sensing directions of accelerometers, and underlying mechanism for eliminating the effect of position change in the center of gravity (PCGC) was not presented clearly. This paper reports a GF-IMU compensating for the effect of PCGC and installation errors by using two parallel mounted accelerometers as a group in designing accelerometer array configuration. The underlying kinematics is first developed and indicates that subtraction of accelerations within a group can remove the effect of PCGC. Nine acceleration subtractions from nine independent groups with irrelevant sensing directions and arbitrary installation distances can determine the square of angular velocity and angular acceleration directly, which does not induce installation errors. Then three configurations fitting different requirements are proposed based on three accelerometer placement rules. The motion quantities at the center of gravity (GC) can also be obtained if mutual installation distance among different groups is known. The validity and performance of schemes are finally verified by SimMechanics simulations. The rotational motion measurement scheme proposed in this paper does not need to know mutual placement information of accelerometers as well as the GC position, which greatly simplifies its installation, and make it possible to develop a convenient product for the rotational motion measurement with only accelerometers.

An $\omega$-Free Gyro-Free Accelerometer Pair Algorithm for 2D Trajectory Reconstruction

In general, a two-dimensional (2D) moving trajectory can be reconstructed using data collected from a 6-axis IMU (inertial measurement unit), which consists of a 3-axis gyroscope and a 3-axis accelerometer. Since the power consumption of a gyroscope is significantly larger than that of an accelerometer, to be energy-efficient, it is more preferable to use two gyro-free IMUs as alternatives. The existing gyro-free trajectory reconstruction approach is an angular velocity (i.e. $\omega$ ) -based method. The design of an $\omega$ -free gyro-free approach remains as a research gap, which motivates this research work. In this paper, an $\omega$ -free accelerometer pair (OFAP) method is proposed, which can yield a lower accumulated error, has a lower power consumption, is more scalable, and can deliver the same trajectory reconstruction performance as the existing approach.

Decoupled Scalar Approach for Aircraft Angular Motion Estimation Using a Gyro-Free Inertial Measurement Unit

Abstract In-flight aircraft angular motion estimation based on an all-accelerometers inertial measurement unit (IMU) is investigated in this study. The relative acceleration equation as the representative of a rigid-body kinematics is manipulated to present the state and measurement equations of the aircraft dynamics. A decoupled scalar form (DSF) of the system equations, as a free-singularity problem, is derived. Mathematical modeling and simulation of an aircraft dynamics, equipped with an all-accelerometers IMU, are employed to prepare measurement data. Taking into account the modeling of accelerometer error, the measurement data have been simulated as a real condition. Three extended Kalman filters (EKFs) are used in parallel to estimate aircraft angular motion. Performance of the estimation algorithm is assessed by Monte Carlo analysis. As a result, the presented decoupled scalar approach using a gyro-free IMU (GF-IMU) provides an uncorrelated estimate of the in-flight aircraft motion components.

Improvement of angular velocity and position estimation in gyro‐free inertial navigation based on vision aid equipment

In conventional navigation systems, inertial sensors consist of accelerometers and gyroscopes. These sensors suffer from in‐built errors, accumulated drift and high‐level noise sensitivity. The accurate gyroscopes are expensive and not suitable in cost‐effective applications. To minimise such disadvantages, one solution is the combination of inertial sensors with different aiding sensors. To lower the cost, utilisation of redundant accelerometer structure as gyro‐free inertial measurement unit (GFIMU) has been proposed. In this study, Gyro‐Free navigation errors using four tri‐axial accelerometers are illustrated. Compensation of errors in terms of angular velocity and position estimation is verified based on adding a simple gyroscope, inexpensive stereo cameras as well as creating an easy to use topological map. The topological map is easily created by means of scale‐invariant feature transform method. The estimation of angular velocity is corrected on the basis of fusing the measurements from GFIMU and a simple gyroscope using unscented Kalman filter. The correction of position is performed by comparing the estimated position from GFIMU and observation of stereo cameras together with topological map. The results of the research show that the collaboration of GFIMU, stereo cameras and simple gyroscope will improve the robustness and accuracy of navigation, significantly.

Design and analysis of gyro-free inertial measurement units with different configurations

This study reports a gyro-free inertial measurement unit (IMU) using solely four triaxial accelerometers. Four different configurations which are feasible for the gyro-free IMU design are presented. The condition number of the configuration matrix is proposed as a fundamental criterion for configuration evaluation. Thus, an optimal design is identified from the four configurations. A scheme is proposed to identify and compensate for deterministic errors of accelerometer measurements. Then, the propagation of stochastic errors is analyzed. Results of error analysis further demonstrate the effectiveness of the proposed criterion. An unscented Kalman filter (UKF) is proposed for state estimation. Simulation results show that not only the system state is robustly estimated, but also effective error reductions on state estimation are provided. Furthermore, the proposed UKF significantly reduces the influence of the four different configurations on state estimation.

Gyro-Free INS Theory

A Gyro-Free Inertial Measurement Unit (GF-IMU) uses a configuration of accelerometers only to measure the linear and angular acceleration of a rigid body in 3-D space, wherefrom the mechanization equations are integrated to yield the navigation state. Whereas in the past attempts were made to design microelectromechanical systems (MEMS) based GF-IMUs, the renewed interest in GF-IMUs springs from the possibility offered by cold atom interferometry-based high-accuracy acceleration measurements. Thus, in this paper, the Gyro-Free Inertial Navigation System (GF-INS) theory is developed. The mechanization equations for a gyro-free inertial navigation system are obtained, and the GF-IMU navigation state's error equations are derived. The latter afford the prediction of the navigation accuracy of a GF-INS using covariance analysis, and also the development of a Kalman filter for optimally fusing the GF-INS measurements with the measurements provided by additional sensors, for example, a ring laser gyro or navigation quality conventional INS. Copyright © 2013 Institute of Navigation.

Angular Motion Estimation Using Dynamic Models in a Gyro-Free Inertial Measurement Unit

In this paper, we summarize the results of using dynamic models borrowed from tracking theory in describing the time evolution of the state vector to have an estimate of the angular motion in a gyro-free inertial measurement unit (GF-IMU). The GF-IMU is a special type inertial measurement unit (IMU) that uses only a set of accelerometers in inferring the angular motion. Using distributed accelerometers, we get an angular information vector (AIV) composed of angular acceleration and quadratic angular velocity terms. We use a Kalman filter approach to estimate the angular velocity vector since it is not expressed explicitly within the AIV. The bias parameters inherent in the accelerometers measurements' produce a biased AIV and hence the AIV bias parameters are estimated within an augmented state vector. Using dynamic models, the appended bias parameters of the AIV become observable and hence we can have unbiased angular motion estimate. Moreover, a good model is required to extract the maximum amount of information from the observation. Observability analysis is done to determine the conditions for having an observable state space model. For higher grades of accelerometers and under relatively higher sampling frequency, the error of accelerometer measurements is dominated by the noise error. Consequently, simulations are conducted on two models, one has bias parameters appended in the state space model and the other is a reduced model without bias parameters.

Constrained Angular Motion Estimation in a Gyro-Free IMU

In this paper, we present an extended Kalman filter (EKF)-based solution for the estimation of the angular motion using a gyro-free inertial measurement unit (GF-IMU) built of twelve separate mono-axial accelerometers. Using such a GF-IMU produces a vector, which we call the angular information vector (AIV) that consists of 3D angular acceleration terms and six quadratic terms of angular velocities. We consider the multiple distributed orthogonal triads of accelerometers that consist of three nonplanar distributed triads equally spaced from a central triad as a specific case to solve. During research for the possible filter schemes, we derived equality constraints. Hence we incorporate the constraints in the filter to improve the accuracy of the angular motion estimation, which in turn improves the attitude accuracy (direction cosine matrix (DCM) or quaternion vector).

Two calibration procedures for a gyroscope-free inertial measurement system based on a double-pendulum apparatus

This paper presents a novel calibration algorithm to be used with a gyro-free inertial measurement unit (GF-IMU) based on the use of linear accelerometers (AC). The analytical approach can be implemented in two calibration procedures. The first procedure (P-I) is articulated in the conduction of a static trial, to compute the sensitivity and the direction of the sensing axis of each AC, followed by a dynamic trial, to determine the AC locations. By contrast, the latter procedure (P-II) consists in the calculation of the previously indicated calibration parameters by means of a dynamic trial only. The feasibility of the two calibration procedures has been investigated by testing two GF-IMUs, equipped with ten and six bi-axial linear ACs, with an ad hoc instrumented double-pendulum apparatus. P-I and P-II were compared to a calibration procedure used as a reference (P-REF), which incorporates the AC positions measured with an optoelectronic system. The experimental results we present in this paper demonstrate that (i) P-I is able to determine the calibration parameters of the AC array with a higher accuracy than P-II; (ii) consequently, the errors associated with translational (a0 − g) and rotational () acceleration components for the two GF-IMUs are significantly greater using P-II than P-I and (iii) the errors in (a0 − g) and obtained with P-I are comparable with the ones obtainable by using P-REF. Thus, the proposed novel algorithm used in P-I, in conjunction with the double-pendulum apparatus, can be globally considered a viable tool in GF-IMU calibration.

Design and analysis of an orientation estimation system using coplanar gyro-free inertial measurement unit and magnetic sensors

Conventionally, there are two ways to determine the orientation angles of an object. One uses 3-axis accelerometers and 3-axis magnetic sensors, while the other one uses additional 3-axis gyroscopes to achieve a higher sensing accuracy than the first one. This paper presents a novel orientation estimation system that uses seven single-axis linear accelerometers and 3-axis magnetic sensors. These seven linear accelerometers are deployed in a way to form a “coplanar” gyro-free inertial measurement unit (IMU). As such, they can perform the integrated measurements of gravity force and angular velocity for the subsequent sensor fusion algorithms. With the information of the angular velocity, this novel design achieves a comparable performance with the one that includes 3-axis gyroscopes. The analysis of the system observability indicates that the angular velocity measurements can improve the observability of the angle estimation under certain circumstances. This result suggests the possibility of using fewer sensors in an orientation estimation system. Simulation results indicate that the proposed design achieve a sensing accuracy of 0.11°, 0.09°, and 0.2°for the roll, pitch, and yaw angle; this leads to the improvement of 540%, 632%, and 754% over the one that does not include the measurement of the angular velocity.

Design and Analysis of a Fault-Tolerant Coplanar Gyro-Free Inertial Measurement Unit

This paper presents a novel design of a fault-tolerant, coplanar, and gyro-free inertial measurement unit (IMU) that consists of 13 single-axis linear accelerometers and can perform six degree-of-freedom (DOF) measurements for an object in motion. This design uses a combination of redundant accelerometers, an innovative real-time fault-identification technique, together with state-estimation techniques to facilitate robust six DOF measurements, even when some of its accelerometers produce faulty outputs. A design example indicates that the proposed fault-tolerant design and compensation algorithm can detect and correct the biased accelerometer outputs in real time. In this simulation example, the accelerometer measurement noise is assumed to be white and set at 0.1 m/s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . The minimum detectable dc-offset value is 0.1 m/s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , which is the same as the standard deviation of the accelerometer measurement noise. The compensated accelerometer outputs were used to construct an "observer-based" gyro-free IMU. The angular-velocity estimation accuracy is 4 X 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> rad/s, and the linear-acceleration accuracy is less than 0.24 m/s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . The IMU output accuracy is not affected by the proposed fault-compensation algorithm.

MEMS SoC: observer-based coplanar gyro-free inertial measurement unit

This paper presents a novel design of a coplanar gyro-free inertial measurement unit (IMU) that consists of seven to nine single-axis linear accelerometers, and it can be utilized to perform the six DOF measurements for an object in motion. Unlike other gyro-fee IMUs, this design uses redundant accelerometers and state estimation techniques to facilitate the in situ and mass fabrication for the employed accelerometers. The alignment error from positioning accelerometers onto a measurement unit and the fabrication cost of an IMU can greatly be reduced. The outputs of the proposed design are three linear accelerations and three angular velocities. As compared to other gyro-free IMUs, the proposed design uses less integral operation and thus improves its sensing resolution and drifting problem. The sensing resolution of a gyro-free IMU depends on the sensing resolution of the employed accelerometers as well as the size of the measurement unit. Simulation results indicate that the sensing resolution of the proposed design is 2° s−1 for the angular velocity and 10 μg for the linear acceleration when nine single-axis accelerometers, each with 10 μg sensing resolution, are deployed on a 4 inch diameter disc. Also, thanks to the iterative EKF algorithm, the angle estimation error is within 10−3 deg at 2 s.