A Redundant Measurement-Based Maximum Correntropy Extended Kalman Filter for the Noise Covariance Estimation in INS/GNSS Integration

Wang, Dapeng; Zhang, Hai; Huang, Hongliang; Ge, Baoshuang

doi:10.3390/rs15092430

Cited by 3 publications

(1 citation statement)

References 51 publications

(81 reference statements)

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“…Recently, the research on filtering techniques under the maximum correntropy (MC) criterion has become an important orientation for the state estimation of stochastic systems in the presence of non-Gaussian noise [33][34][35][36]. Correntropy is a statistical metric to measure the similarity of two random variables in information theory; unlike the commonly used MMSE criterion, which uses second-order statistics, the MC criterion uses secondorder statistics and higher-order information, thus offering the probability of improving estimation accuracy for systems in the presence of non-Gaussian noise.…”

Section: Introductionmentioning

confidence: 99%

Filtering in Triplet Markov Chain Model in the Presence of Non-Gaussian Noise with Application to Target Tracking

Zhang,

Zeng

et al. 2023

Remote Sensing

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In hidden Markov chain (HMC) models, widely used for target tracking, the process noise and measurement noise are in general assumed to be independent and Gaussian for mathematical simplicity. However, the independence and Gaussian assumptions do not always hold in practice. For instance, in a typical radar tracking application, the measurement noise is correlated over time as the sampling frequency of a radar is generally much higher than the bandwidth of the measurement noise. In addition, target maneuvers and measurement outliers imply that the process noise and measurement noise are non-Gaussian. To solve this problem, we resort to triplet Markov chain (TMC) models to describe stochastic systems with correlated noise and derive a new filter under the maximum correntropy criterion to deal with non-Gaussian noise. By stacking the state vector, measurement vector, and auxiliary vector into a triplet state vector, the TMC model can capture the complete dynamics of stochastic systems, which may be subjected to potential parameter uncertainty, non-stationarity, or error sources. Correntropy is used to measure the similarity of two random variables; unlike the commonly used minimum mean square error criterion, which uses only second-order statistics, correntropy uses second-order and higher-order information, and is more suitable for systems in the presence of non-Gaussian noise, particularly some heavy-tailed noise disturbances. Furthermore, to reduce the influence of round-off errors, a square-root implementation of the new filter is provided using QR decomposition. Instead of the full covariance matrices, corresponding Cholesky factors are recursively calculated in the square-root filtering algorithm. This is more numerically stable for ill-conditioned problems compared to the conventional filter. Finally, the effectiveness of the proposed algorithms is illustrated via three numerical examples.

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Section: Introductionmentioning

confidence: 99%

Filtering in Triplet Markov Chain Model in the Presence of Non-Gaussian Noise with Application to Target Tracking

Zhang,

Zeng

et al. 2023

Remote Sensing

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An Adaptive Robust EKF Based on Mahalanobis Distance and Non-Holonomic Constraints for Enhancing Vehicle Positioning Accuracy

Zhang,

Yang

2024

IEEE Sensors J.

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Maximum Correntropy Extended Kalman Filtering with Nonlinear Regression Technique for GPS Navigation

Biswal,

Jwo

2024

Applied Sciences

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One technique that is widely used in various fields, including nonlinear target tracking, is the extended Kalman filter (EKF). The well-known minimum mean square error (MMSE) criterion, which performs magnificently under the assumption of Gaussian noise, is the optimization criterion that is frequently employed in EKF. Further, if the noises are loud (or heavy-tailed), its performance can drastically suffer. To overcome the problem, this paper suggests a new technique for maximum correntropy EKF with nonlinear regression (MCCEKF-NR) by using the maximum correntropy criterion (MCC) instead of the MMSE criterion to calculate the effectiveness and vitality. The preliminary estimates of the state and covariance matrix in MCKF are provided via the state mean vector and covariance matrix propagation equations, just like in the conventional Kalman filter. In addition, a newly designed fixed-point technique is used to update the posterior estimates of each filter in a regression model. To show the practicality of the proposed strategy, we propose an effective implementation for positioning enhancement in GPS navigation and radar measurement systems.

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A Redundant Measurement-Based Maximum Correntropy Extended Kalman Filter for the Noise Covariance Estimation in INS/GNSS Integration

Cited by 3 publications

References 51 publications

Filtering in Triplet Markov Chain Model in the Presence of Non-Gaussian Noise with Application to Target Tracking

Filtering in Triplet Markov Chain Model in the Presence of Non-Gaussian Noise with Application to Target Tracking

An Adaptive Robust EKF Based on Mahalanobis Distance and Non-Holonomic Constraints for Enhancing Vehicle Positioning Accuracy

Maximum Correntropy Extended Kalman Filtering with Nonlinear Regression Technique for GPS Navigation

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