Rank Kalman Filter-SLAM for Vehicle with Non-Gaussian Noise

2020 ◽  
Author(s):  
Tai-Shan Lou ◽  
Hong-Ye Ban ◽  
Su-Na Zhao ◽  
Zhen-Dong He ◽  
Ying Wang
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
Non Gaussian

Centered error entropy Kalman filter with application to satellite attitude determination

2021 ◽  
pp. 014233122110198
Author(s):  
Baojian Yang ◽  
Lu Cao ◽  
Dechao Ran ◽  
Bing Xiao
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
Attitude Determination ◽  
Complexity Analysis ◽  
Iteration Algorithm ◽  
Robust Algorithms ◽  
Convergence Conditions ◽  
Satellite Attitude ◽  
Heavy Tailed ◽  
Non Gaussian

Due to unavoidable factors, heavy-tailed noise appears in satellite attitude estimation. Traditional Kalman filter is prone to performance degradation and even filtering divergence when facing non-Gaussian noise. The existing robust algorithms have limited accuracy. To improve the attitude determination accuracy under non-Gaussian noise, we use the centered error entropy (CEE) criterion to derive a new filter named centered error entropy Kalman filter (CEEKF). CEEKF is formed by maximizing the CEE cost function. In the CEEKF algorithm, the prior state values are transmitted the same as the classical Kalman filter, and the posterior states are calculated by the fixed-point iteration method. The CEE EKF (CEE-EKF) algorithm is also derived to improve filtering accuracy in the case of the nonlinear system. We also give the convergence conditions of the iteration algorithm and the computational complexity analysis of CEEKF. The results of the two simulation examples validate the robustness of the algorithm we presented.

Maximum Correntropy Criterion Constrained Kalman Filter

2017 ◽  
Author(s):  
Seyed Fakoorian ◽  
Mahmoud Moosavi ◽  
Reza Izanloo ◽  
Vahid Azimi ◽  
Dan Simon
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
State Constraints ◽  
Statistical Information ◽  
Second Order ◽  
System Model ◽  
Error Covariance ◽  
Inequality State ◽  
Maximum Correntropy Criterion ◽  
Non Gaussian

Non-Gaussian noise may degrade the performance of the Kalman filter because the Kalman filter uses only second-order statistical information, so it is not optimal in non-Gaussian noise environments. Also, many systems include equality or inequality state constraints that are not directly included in the system model, and thus are not incorporated in the Kalman filter. To address these combined issues, we propose a robust Kalman-type filter in the presence of non-Gaussian noise that uses information from state constraints. The proposed filter, called the maximum correntropy criterion constrained Kalman filter (MCC-CKF), uses a correntropy metric to quantify not only second-order information but also higher-order moments of the non-Gaussian process and measurement noise, and also enforces constraints on the state estimates. We analytically prove that our newly derived MCC-CKF is an unbiased estimator and has a smaller error covariance than the standard Kalman filter under certain conditions. Simulation results show the superiority of the MCC-CKF compared with other estimators when the system measurement is disturbed by non-Gaussian noise and when the states are constrained.

scholarly journals Variational Bayesian-Based Improved Maximum Mixture Correntropy Kalman Filter for Non-Gaussian Noise

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 117
Author(s):  
Xuyou Li ◽  
Yanda Guo ◽  
Qingwen Meng
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
State Space Model ◽  
Performance Evaluations ◽  
Gaussian State ◽  
Variational Bayesian ◽  
Space Model ◽  
Bandwidth Parameter ◽  
Non Gaussian ◽  
Filtering Problem

The maximum correntropy Kalman filter (MCKF) is an effective algorithm that was proposed to solve the non-Gaussian filtering problem for linear systems. Compared with the original Kalman filter (KF), the MCKF is a sub-optimal filter with Gaussian correntropy objective function, which has been demonstrated to have excellent robustness to non-Gaussian noise. However, the performance of MCKF is affected by its kernel bandwidth parameter, and a constant kernel bandwidth may lead to severe accuracy degradation in non-stationary noises. In order to solve this problem, the mixture correntropy method is further explored in this work, and an improved maximum mixture correntropy KF (IMMCKF) is proposed. By derivation, the random variables that obey Beta-Bernoulli distribution are taken as intermediate parameters, and a new hierarchical Gaussian state-space model was established. Finally, the unknown mixing probability and state estimation vector at each moment are inferred via a variational Bayesian approach, which provides an effective solution to improve the applicability of MCKFs in non-stationary noises. Performance evaluations demonstrate that the proposed filter significantly improves the existing MCKFs in non-stationary noises.

scholarly journals Extended Particle-Aided Unscented Kalman Filter Based on Self-Driving Car Localization

2020 ◽  
Vol 10 (15) ◽  
pp. 5045 ◽  
Author(s):  
Ming Lin ◽  
Byeongwoo Kim
Keyword(s):  
Kalman Filter ◽  
Real World ◽  
Gaussian Noise ◽  
Unscented Kalman Filter ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Localization Problem ◽  
Simulation Results ◽  
Non Gaussian ◽  
Self Driving Cars

The location of the vehicle is a basic parameter for self-driving cars. The key problem of localization is the noise of the sensors. In previous research, we proposed a particle-aided unscented Kalman filter (PAUKF) to handle the localization problem in non-Gaussian noise environments. However, the previous basic PAUKF only considers the infrastructures in two dimensions (2D). This previous PAUKF 2D limitation rendered it inoperable in the real world, which is full of three-dimensional (3D) features. In this paper, we have extended the previous basic PAUKF’s particle weighting process based on the multivariable normal distribution for handling 3D features. The extended PAUKF also raises the feasibility of fusing multisource perception data into the PAUKF framework. The simulation results show that the extended PAUKF has better real-world applicability than the previous basic PAUKF.

scholarly journals Maximum Correntropy Criterion Kalman Filter for α-Jerk Tracking Model with Non-Gaussian Noise

Entropy ◽  
2017 ◽  
Vol 19 (12) ◽  
pp. 648 ◽  
Author(s):  
Bowen Hou ◽  
Zhangming He ◽  
Xuanying Zhou ◽  
Haiyin Zhou ◽  
Dong Li ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
Tracking Model ◽  
Maximum Correntropy Criterion ◽  
Non Gaussian

scholarly journals Underwater surveillance in non-Gaussian noisy environment

2020 ◽  
Vol 53 (1-2) ◽  
pp. 250-261
Author(s):  
B Omkar Lakshmi Jagan ◽  
S Koteswara Rao
Keyword(s):  
Kalman Filter ◽  
Lower Bound ◽  
Extended Kalman Filter ◽  
Gaussian Noise ◽  
Unscented Kalman Filter ◽  
Doppler Frequency ◽  
Gaussian Mixture ◽  
Noisy Environment ◽  
Sampled Measurements ◽  
Non Gaussian

The aim of this paper is to evaluate the performance of different filtering algorithms in the presence of non-Gaussian noise environment for tracking underwater targets, using Doppler frequency and bearing measurements. The tracking using Doppler frequency and bearing measurements is popularly known as Doppler-bearing tracking. Here the measurements, that is, bearings and Doppler frequency, are considered to be corrupted with two types of non-Gaussian noises namely shot noise and Gaussian mixture noise. The non-Gaussian noise sampled measurements are assumed to be obtained (a) randomly throughout the process and (b) repeatedly at some particular time samples. The efficiency of these filters with the increase in non-Gaussian noise samples is discussed in this paper. The performance of filters is compared with that of Cramer-Rao Lower Bound. Doppler-bearing extended Kalman filter and Doppler-bearing unscented Kalman filter are chosen for this work.

Three-Dimensional Submarine-to-Submarine Passive Target Tracking in the Presence of Non-Gaussian Noises

2021 ◽  
Vol 17 (3) ◽  
pp. 1-24
Author(s):  
Kavitha Lakshmi M. ◽  
Koteswara Rao S. ◽  
Subrahmanyam Kodukula
Keyword(s):  
Kalman Filter ◽  
Target Tracking ◽  
Gaussian Noise ◽  
Target Location ◽  
Unscented Kalman Filter ◽  
Three Dimensional ◽  
Noise Environment ◽  
Cubature Kalman Filter ◽  
Highly Nonlinear ◽  
Non Gaussian

In underwater surveillance, three-dimensional target tracking is a challenging task. The angles-only measurements (i.e., bearing and elevation) obtained by hull mounted sensors are considered to appraise the target motion parameter. Due to noise in measurements and nonlinearity of the system, it is very hard to find out the target location. For many applications, UKF is best estimator that remaining algorithms. Recently, cubature Kalman filter (CKF) is also popular. It is proposed to use UKF (unscented Kalman filter) and CKF (cubature Kalman filter) algorithms that minimize the noise in measurements. So far, researchers carried out this work (target tracking) in Gaussian noise environment, whereas in this paper same work is carried out for non-Gaussian noise environment. The performance evaluation of the filters using Monte-Carlo simulation and Cramer-Rao lower bound (CRLB) is accomplished and the results are analyzed. Result shows that UKF is well suitable for highly nonlinear systems than CKF.

scholarly journals Robust Derivative Unscented Kalman Filter Under Non-Gaussian Noise

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 33129-33136 ◽  
Author(s):  
Lijian Yin ◽  
Zhihong Deng ◽  
Baoyu Huo ◽  
Yuanqing Xia ◽  
Cheng Li
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
Unscented Kalman Filter ◽  
Non Gaussian

scholarly journals State of Charge Estimation of Lithium Battery Based on Improved Correntropy Extended Kalman Filter

Energies ◽  
2020 ◽  
Vol 13 (16) ◽  
pp. 4197
Author(s):  
Jiandong Duan ◽  
Peng Wang ◽  
Wentao Ma ◽  
Xinyu Qiu ◽  
Xuan Tian ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Gaussian Noise ◽  
Estimation Error ◽  
Weighted Least Squares ◽  
Equivalent Circuit Model ◽  
State Of Charge ◽  
Battery Management ◽  
Soc Estimation ◽  
Non Gaussian

State of charge (SOC) estimation plays a crucial role in battery management systems. Among all the existing SOC estimation approaches, the model-driven extended Kalman filter (EKF) has been widely utilized to estimate SOC due to its simple implementation and nonlinear property. However, the traditional EKF derived from the mean square error (MSE) loss is sensitive to non-Gaussian noise which especially exists in practice, thus the SOC estimation based on the traditional EKF may result in undesirable performance. Hence, a novel robust EKF method with correntropy loss is employed to perform SOC estimation to improve the accuracy under non-Gaussian environments firstly. Secondly, a novel robust EKF, called C-WLS-EKF, is developed by combining the advantages of correntropy and weighted least squares (WLS) to improve the digital stability of the correntropy EKF (C-EKF). In addition, the convergence of the proposed algorithm is verified by the Cramér–Rao low bound. Finally, a C-WLS-EKF method based on an equivalent circuit model is designed to perform SOC estimation. The experiment results clarify that the SOC estimation error in terms of the MSE via the proposed C-WLS-EKF method can efficiently be reduced from 1.361% to 0.512% under non-Gaussian noise conditions.

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