Robust Kalman Filter with Fading Factor Under State Transition Model Mismatch and Outliers Interference
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Robust Kalman Filter with Fading Factor Under State Transition Model Mismatch and Outliers Interference Peng Yun1 · Panlong Wu1 · Shan He1 · Xingxiu Li2 Received: 14 February 2020 / Revised: 18 October 2020 / Accepted: 22 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In practical applications, due to the complexity of the system, the process equation of the state space model is difficult to match the actual state transition model. In addition, the unreliability of the sensor will cause the measurement to be accompanied by outliers. In this paper, a novel robust Kalman filter with fading factor is proposed to improve the accuracy of state estimation for the linear system under state transition model mismatch and outliers interference. Firstly, in order to modify the state transition model, this filter introduces a fading factor which is modelled as the inverse gamma distribution to update the state prediction covariance. Then, aiming at the phenomenon that the measurement noise does not follow the Gaussian distribution and has non zero mean characteristics due to outliers interference, the measurement noise is modelled as the generalized hyperbolic skew Student’s t distribution. Finally, the state estimation is realized by using the variational Bayesian. The simulation results show that the estimation accuracy of the proposed filter is higher than that of the Kalman filter and the strong tracking filter. Keywords Robust Kalman filter · State transition model mismatch · Outliers interference · Inverse gamma distribution · Hyperbolic skew Student’s t distribution · Variational Bayesian
1 Introduction The problem of state estimation exists in many fields, such as target tracking and signal processing [7, 15, 23, 25]. For linear systems, Kalman filter (KF) [16] is a successful method to solve this problem. This filter needs to ensure that both measurement
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00034-02 0-01582-9) contains supplementary material, which is available to authorized users.
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Panlong Wu [email protected]
Extended author information available on the last page of the article
Circuits, Systems, and Signal Processing
noise and process noise are Gaussian white noise, and the corresponding process equation and measurement equation match these of actual system. However, in practical engineering such as the space object tracking [22], due to the unknown disturbance, the process equation has a deviation from the actual motion model, which leads to the problem of state transition model mismatch. Because of the external environment interference, the actual measurement noise is heavy - tailed non-Gaussian noise [2], and the unreliability of the sensor can lead to measurement noise that often does not have zero mean characteristics. If the KF is still used at this time, the state estimation accuracy is poor. The strong tracking filter (STF) [27, 28] and the input estimation (IE) [4] are good methods to solve the proble
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