scholarly journals Variational Bayesian Iteration-Based Invariant Kalman Filter for Attitude Estimation on Matrix Lie Groups

Aerospace ◽  
2021 ◽  
Vol 8 (9) ◽  
pp. 246
Author(s):  
Jiaolong Wang ◽  
Zeyang Chen
Keyword(s):  
Kalman Filter ◽  
Lie Groups ◽  
Lie Group ◽  
A Priori ◽  
Attitude Estimation ◽  
Estimation Problem ◽  
Superior Performance ◽  
Process Noise ◽  
Variational Bayesian ◽  
Noise Statistics

Motivated by the rapid progress of aerospace and robotics engineering, the navigation and control systems on matrix Lie groups have been actively studied in recent years. For rigid targets, the attitude estimation problem is a benchmark one with its states defined as rotation matrices on Lie groups. Based on the invariance properties of symmetry groups, the invariant Kalman filter (IKF) has been developed by researchers for matrix Lie group systems; however, the limitation of the IKF is that its estimation performance is prone to be degraded if the given knowledge of the noise statistics is not accurate. For the symmetry Lie group attitude estimation problem, this paper proposes a new variational Bayesian iteration-based adaptive invariant Kalman filter (VBIKF). In the proposed VBIKF, the a priori error covariance is not propagated by the conventional steps but directly calibrated in an iterative manner based on the posterior sequences. The main advantage of the VBIKF is that the statistics parameter of the system process noise is no longer required and so the IKF’s hard dependency on accurate process noise statistics can be reduced significantly. The mathematical foundation for the new VBIKF is presented and its superior performance in adaptability and simplicity is further demonstrated by numerical simulations.

scholarly journals An Improved Invariant Kalman Filter for Lie Groups Attitude Dynamics with Heavy-Tailed Process Noise

Machines ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 182
Author(s):  
Jiaolong Wang ◽  
Chengxi Zhang ◽  
Jin Wu ◽  
Ming Liu
Keyword(s):  
Kalman Filter ◽  
Lie Groups ◽  
State Space Model ◽  
Attitude Estimation ◽  
Spacecraft Attitude ◽  
Attitude Dynamics ◽  
Process Noise ◽  
Space Model ◽  
Heavy Tailed ◽  
Scale Matrix

Attitude estimation is a basic task for most spacecraft missions in aerospace engineering and many Kalman type attitude estimators have been applied to the guidance and navigation of spacecraft systems. By building the attitude dynamics on matrix Lie groups, the invariant Kalman filter (IKF) was developed according to the invariance properties of symmetry groups. However, the Gaussian noise assumption of Kalman theory may be violated when a spacecraft maneuvers severely and the process noise might be heavy-tailed, which is prone to degrade IKF’s performance for attitude estimation. To address the attitude estimation problem with heavy-tailed process noise, this paper proposes a hierarchical Gaussian state-space model for invariant Kalman filtering: The probability density function of state prediction is defined based on student’s t distribution, while the conjugate prior distributions of the scale matrix and degrees of freedom (dofs) parameter are respectively formulated as the inverse Wishart and Gamma distribution. For the constructed hierarchical Gaussian attitude estimation state-space model, the Lie groups rotation matrix of spacecraft attitude is inferred together with the scale matrix and dof parameter using the variational Bayesian iteration. Numerical simulation results illustrate that the proposed approach can significantly improve the filtering robustness of invariant Kalman filter for Lie groups spacecraft attitude estimation problems with heavy-tailed process uncertainty.

scholarly journals Performance Analysis of Computational Intelligence Correction

2021 ◽  
Author(s):  
Nalini Arasavali ◽  
Sasibhushanarao Gottapu
Keyword(s):  
Kalman Filter ◽  
Performance Analysis ◽  
Computational Intelligence ◽  
A Priori ◽  
Covariance Matrices ◽  
System Model ◽  
Process Noise ◽  
Navigation Algorithm ◽  
Modified Kalman Filter ◽  
Measurement Noises

Abstract Kalman filter (KF) is a widely used navigation algorithm, especially for precise positioning applications. However, the exact filter parameters must be defined a priori to use standard Kalman filters for coping with low error values. But for the dynamic system model, the covariance of process noise is a priori entirely undefined, which results in difficulties and challenges in the implementation of the conventional Kalman filter. Kalman Filter with recursive covariance estimation applied to solve those complicated functional issues, which can also be used in many other applications involving Kalaman filtering technology, a modified Kalman filter called MKF-RCE. While this is a better approach, KF with SAR tuned covariance has been proposed to resolve the problem of estimation for the dynamic model. The data collected at (x: 706970.9093 m, y: 6035941.0226 m, z: 1930009.5821 m) used to illustrate the performance analysis of KF with recursive covariance and KF with computational intelligence correction by means of SAR (Search and Rescue) tuned covariance, when the covariance matrices of process and measurement noises are completely unknown in advance.

scholarly journals Adaptive Dual Extended Kalman Filter Based on Variational Bayesian Approximation for Joint Estimation of Lithium-Ion Battery State of Charge and Model Parameters

2019 ◽  
Vol 9 (9) ◽  
pp. 1726 ◽  
Author(s):  
Jing Hou ◽  
Yan Yang ◽  
He He ◽  
Tian Gao
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Lithium Ion ◽  
Measurement Noise ◽  
Estimation Accuracy ◽  
Variational Bayesian ◽  
Soc Estimation ◽  
Bayesian Approximation ◽  
Noise Statistics ◽  
Discharge Test

An accurate state of charge (SOC) estimation is vital for the safe operation and efficient management of lithium-ion batteries. At present, the extended Kalman filter (EKF) can accurately estimate the SOC under the condition of a precise battery model and deterministic noise statistics. However, in practical applications, the battery characteristics change with different operating conditions and the measurement noise statistics may vary with time, resulting in nonoptimal and even unreliable estimation of SOC by EKF. To improve the SOC estimation accuracy under uncertain measurement noise statistics, a variational Bayesian approximation-based adaptive dual extended Kalman filter (VB-ADEKF) is proposed in this paper. The variational Bayesian inference is integrated with the dual EKF (DEKF) to jointly estimate the lithium-ion battery parameters and SOC. Meanwhile, the measurement noise variances are simultaneously estimated in the SOC estimation process to compensate for the model uncertainties, so that the adaptability of the proposed algorithm to dynamic changes in battery characteristics is greatly improved. A constant current discharge test, a pulse current discharge test, and an urban dynamometer driving schedule (UDDS) test are performed to verify the effectiveness and superiority of the proposed algorithm by comparison with the DEKF algorithm. The experimental results show that the proposed VB-ADEKF algorithm outperforms the traditional DEKF algorithm in terms of SOC estimation accuracy, convergence rate, and robustness.

scholarly journals Three-Axis Attitude Estimation Of Satellite Through Only Two-Axis Magnetometer Observations Using LKF Algorithm

2015 ◽  
Vol 22 (4) ◽  
pp. 577-590 ◽  
Author(s):  
Mohamad Fakhari Mehrjardi ◽  
Hilmi Sanusi ◽  
Mohd. Alauddin Mohd. Ali
Keyword(s):  
Kalman Filter ◽  
Space Missions ◽  
Attitude Estimation ◽  
Estimation Problem ◽  
Sensor Data ◽  
Computationally Efficient ◽  
Satellite Attitude ◽  
Simulation Results

Abstract Estimation of satellite three-axis attitude using only one sensor data presents an interesting estimation problem. A flexible and mathematically effective filter for solving the satellite three-axis attitude estimation problem using two-axis magnetometer would be a challenging option for space missions which are suffering from other attitude sensors failure. Mostly, magnetometers are employed with other attitude sensors to resolve attitude estimation. However, by designing a computationally efficient discrete Kalman filter, full attitude estimation can profit by only two-axis magnetometer observations. The method suggested solves the problem of satellite attitude estimation using linear Kalman filter (LKF). Firstly, all models are generated and then the designed scenario is developed and evaluated with simulation results. The filter can achieve 10e-3 degree attitude accuracy or better on all three axes.

scholarly journals A SLAM Algorithm Based on Adaptive Cubature Kalman Filter

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Fei Yu ◽  
Qian Sun ◽  
Chongyang Lv ◽  
Yueyang Ben ◽  
Yanwei Fu
Keyword(s):  
Kalman Filter ◽  
A Priori ◽  
Statistical Parameters ◽  
Estimation Errors ◽  
Adaptive Estimator ◽  
Practical Applications ◽  
Localization And Mapping ◽  
Cubature Kalman Filter ◽  
Slam Algorithm ◽  
Noise Statistics

We need to predict mathematical model of the system and a priori knowledge of the noise statistics when traditional simultaneous localization and mapping (SLAM) solutions are used. However, in many practical applications, prior statistics of the noise are unknown or time-varying, which will lead to large estimation errors or even cause divergence. In order to solve the above problem, an innovative cubature Kalman filter-based SLAM (CKF-SLAM) algorithm based on an adaptive cubature Kalman filter (ACKF) was established in this paper. The novel algorithm estimates the statistical parameters of the unknown system noise by introducing the Sage-Husa noise statistic estimator. Combining the advantages of the CKF-SLAM and the adaptive estimator, the new ACKF-SLAM algorithm can reduce the state estimated error significantly and improve the navigation accuracy of the SLAM system effectively. The performance of this new algorithm has been examined through numerical simulations in different scenarios. The results have shown that the position error can be effectively reduced with the new adaptive CKF-SLAM algorithm. Compared with other traditional SLAM methods, the accuracy of the nonlinear SLAM system is significantly improved. It verifies that the proposed ACKF-SLAM algorithm is valid and feasible.

Improving Navigational Accuracy for AUVs Based on an Adaptive Modified Square-Root Cubature Kalman Filter

2014 ◽  
Vol 945-949 ◽  
pp. 1430-1434
Author(s):  
Chen Sun ◽  
Jian Long Li
Keyword(s):  
Kalman Filter ◽  
Autonomous Underwater Vehicles ◽  
Linear Measurement ◽  
Square Root ◽  
Noise Variance ◽  
Process Noise ◽  
Cubature Kalman Filter ◽  
Measurement Function ◽  
Computational Errors ◽  
Noise Statistics

This paper addresses an adaptive modified square-root cubature Kalman filter for the navigation of autonomous underwater vehicles (AUVs). The standard square-root cubature Kalman filter (SCKF) implements the CKF using square-root filtering to reduce computational errors. It can be modified due to the nonlinear system with a linear measurement function. The modification leads to a decrease computational complexity. Sage-Husa noise statistics estimator is combined with the Modified SCKF to estimate the unknown and changing system process noise variance. The experimental results show that compared with the MSCKF and the EKF algorithm, the adaptive MSCKF show the best accuracy for a real system with unknown process noise variance.

Robust Square-Root Cubature FastSLAM with Genetic Operators

Robotica ◽  
2020 ◽  
pp. 1-21
Author(s):  
Ramazan Havangi
Keyword(s):  
Experimental Data ◽  
Kalman Filter ◽  
A Priori ◽  
A Priori Knowledge ◽  
Square Root ◽  
Genetic Operators ◽  
Proposal Distribution ◽  
Cubature Kalman Filter ◽  
Noise Statistics ◽  
Better Than

SUMMARY An improved FastSLAM based on the robust square-root cubature Kalman filter (RSRCKF) with partial genetic resampling is proposed in this paper. In the proposed method, RSRCKF is used to design the proposal distribution of FastSLAM and to estimate environment landmarks. The proposed method does not require a priori knowledge of the noise statistics. In addition, to increase diversity, it uses the genetic operators-based strategy to further improve the particle diversity. In fact, a partial genetic resampling operation is carried out to maintain the diversity of particles. The proposed method is compared with other methods via simulation and experimental data. It can be seen from the results that the proposed method provides significantly more accurate and robust estimation results compared with other methods even with fewer particles and unknown a priori. In addition, the consistency of the proposed method is better than that of other methods.

scholarly journals Some groups with T1 primitive ideal spaces

1985 ◽  
Vol 38 (1) ◽  
pp. 55-64 ◽  
Author(s):  
A. L. Carey ◽  
W. Moran
Keyword(s):  
Normal Subgroup ◽  
Lie Groups ◽  
Lie Group ◽  
Locally Compact Group ◽  
Primitive Ideal ◽  
Ideal Space ◽  
Solvable Lie Groups ◽  
Locally Compact ◽  
Simply Connected ◽  
Connected Lie Group

AbstractLet G be a second countable locally compact group possessing a normal subgroup N with G/N abelian. We prove that if G/N is discrete then G has T1 primitive ideal space if and only if the G-quasiorbits in Prim N are closed. This condition on G-quasiorbits arose in Pukanzky's work on connected and simply connected solvable Lie groups where it is equivalent to the condition of Auslander and Moore that G be type R on N (-nilradical). Using an abstract version of Pukanzky's arguments due to Green and Pedersen we establish that if G is a connected and simply connected Lie group then Prim G is T1 whenever G-quasiorbits in [G, G] are closed.

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