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 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 MCC-CKF: A Distance Constrained Kalman Filter Method for Indoor TOA Localization Applications

Electronics ◽  
2019 ◽  
Vol 8 (5) ◽  
pp. 478 ◽  
Author(s):  
Cheng Xu ◽  
Mengmeng Ji ◽  
Yue Qi ◽  
Xinghang Zhou
Keyword(s):  
Kalman Filter ◽  
Negative Impact ◽  
Extreme Environment ◽  
State Constraint ◽  
Line Of Sight ◽  
Filter Method ◽  
Inequality State ◽  
Maximum Correntropy Criterion ◽  
Non Gaussian ◽  
Non Line Of Sight

Non-Gaussian noise may have a negative impact on the performance of the Kalman filter (KF), due to its adoption of only second-order statistical information. Thus, KF is not first priority in applications with non-Gaussian noises. The indoor positioning based on arrival of time (TOA) has large errors caused by multipath and non-line of sight (NLOS). This paper introduces the inequality state constraint to enhance the ranging performance. Based on these considerations, we propose a constrained Kalman filter based on the maximum correntropy criterion (MCC-CKF) to enhance the TOA performance in the extreme environment of multipath and non-line of sight. Pratical experimental results indicate that MCC-CKF outperforms other estimators, such as Kalman filter and Kalman filter based on maximum entropy.

Robust Kalman-Type Filter for Non-Gaussian Noise: Performance Analysis With Unknown Noise Covariances

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Seyed Fakoorian ◽  
Alireza Mohammadi ◽  
Vahid Azimi ◽  
Dan Simon
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
Optimality Criterion ◽  
Minimum Mean Square Error ◽  
Mean Square ◽  
Process Noise ◽  
Noise Covariance ◽  
Maximum Correntropy Criterion ◽  
Non Gaussian ◽  
Mean Square Errors

The Kalman filter (KF) is optimal with respect to minimum mean square error (MMSE) if the process noise and measurement noise are Gaussian. However, the KF is suboptimal in the presence of non-Gaussian noise. The maximum correntropy criterion Kalman filter (MCC-KF) is a Kalman-type filter that uses the correntropy measure as its optimality criterion instead of MMSE. In this paper, we modify the correntropy gain in the MCC-KF to obtain a new filter that we call the measurement-specific correntropy filter (MSCF). The MSCF uses a matrix gain rather than a scalar gain to provide better selectivity in the way that it handles the innovation vector. We analytically compare the performance of the KF with that of the MSCF when either the measurement or process noise covariance is unknown. For each of these situations, we analyze two mean square errors (MSEs): the filter-calculated MSE (FMSE) and the true MSE (TMSE). We show that the FMSE of the KF is less than that of the MSCF. However, the TMSE of the KF is greater than that of the MSCF under certain conditions. Illustrative examples are provided to verify the analytical results.

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.

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 Adaptive fading factor unscented Kalman filter with application to target tracking

2020 ◽  
Author(s):  
Peng Gu ◽  
Zhongliang Jing ◽  
Liangbin Wu
Keyword(s):  
Kalman Filter ◽  
Target Tracking ◽  
Unscented Kalman Filter ◽  
System Model ◽  
Mismatch Error ◽  
Tracking Accuracy ◽  
Model Mismatch ◽  
Error Covariance ◽  
Nonlinear Tracking ◽  
Fading Factor

AbstractOne purpose of target tracking is to estimate the states of targets, and unscented Kalman filter is one of the effective algorithms for estimating in the nonlinear tracking problem. Considering the characteristics of complex maneuverability, it is easy to reduce the tracking accuracy and cause divergence due to the mismatch between the system model and the practical target motion model. Adaptive fading factor is an effective counter to this problem, having been instrumental in solving accuracy and divergence problems. Fading factor can adaptively adjust covariance matrix online to compensate model mismatch error. Moreover, fading factor not only improves the filtering accuracy, but also automatically adjusts the error covariance in response to the different situation. The simulation results show that the adaptive fading factor unscented Kalman filter has more advantages in target tracking and it can be better applied to nonlinear target tracking.

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 A Second-Order Exact Ensemble Square Root Filter for Nonlinear Data Assimilation

2015 ◽  
Vol 143 (4) ◽  
pp. 1347-1367 ◽  
Author(s):  
Julian Tödter ◽  
Bodo Ahrens
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Second Order ◽  
Square Root ◽  
Computationally Efficient ◽  
Research Activities ◽  
Wide Range ◽  
Matrix Square Root ◽  
Non Gaussian ◽  
Ensemble Transform

Abstract The ensemble Kalman filter (EnKF) and its deterministic variants, mostly square root filters such as the ensemble transform Kalman filter (ETKF), represent a popular alternative to variational data assimilation schemes and are applied in a wide range of operational and research activities. Their forecast step employs an ensemble integration that fully respects the nonlinear nature of the analyzed system. In the analysis step, they implicitly assume the prior state and observation errors to be Gaussian. Consequently, in nonlinear systems, the analysis mean and covariance are biased, and these filters remain suboptimal. In contrast, the fully nonlinear, non-Gaussian particle filter (PF) only relies on Bayes’s theorem, which guarantees an exact asymptotic behavior, but because of the so-called curse of dimensionality it is exposed to weight collapse. Here, it is shown how to obtain a new analysis ensemble whose mean and covariance exactly match the Bayesian estimates. This is achieved by a deterministic matrix square root transformation of the forecast ensemble, and subsequently a suitable random rotation that significantly contributes to filter stability while preserving the required second-order statistics. The properties and performance of the proposed algorithm are further investigated via a set of experiments. They indicate that such a filter formulation can increase the analysis quality, even for relatively small ensemble sizes, compared to other ensemble filters in nonlinear, non-Gaussian scenarios. Localization enhances the potential applicability of this PF-inspired scheme in larger-dimensional systems. The proposed algorithm, which is fairly easy to implement and computationally efficient, is referred to as the nonlinear ensemble transform filter (NETF).

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