Abstract
Non-Gaussian noise is common in industrial applications, and it is a severe challenge to existing state estimators. In this paper, a novel robust maximum correntropy finite impulse response (MCFIR) filter is proposed to deal with the state estimation problem in the linear state-space system corrupted by outliers. The filter operates as a finite memory form, and thus it obtains superior immunity to noise statistics and process uncertainties than existing Kalman-like robust filters. Gaussian correntropy is adopted to generate a new cost function, which improves the filter robustness to outlier interference. We derive an unbiased MCFIR filter that ignores noise statistics and propose an improvement bias-constrained MCFIR filter to achieve better estimate accuracy. To improve the filtering performance degradation caused by improper kernel size, an adaptive kernel size algorithm is further proposed, which adjusts the bandwidth within a specific range adaptively and achieves significant improvement in the MCFIR filter. An illustrative example based on moving target tracking is presented to evaluate the performance of the proposed filter, and simulation results confirmed that the MCFIR filter obtained superior immunity to outliers than the existing robust filters.
Highlights
The estimation problem has been one of the essential subjects from industrial applications to research areas, including signal processing, navigation, target tracking, etc
SIMULATION RESULTS we illustrate the performance of the proposed algorithms after applying them to a moving target tracking system
In addition to the classical KF, unbiased FIR (UFIR) filter of [29], several latest robust filters, Huber KF (HKF) [14] based on Huber m-estimator, a novel robust student-t Kalman filter (RSTKF) [9] derived for the heavy-tailed process, and maximum correntropy KF (MCKF) [17] based on maximum correntropy criterion, and optimal Kalman filter (OKF) with exact instantaneous noise covariance simulated as benchmarks for comparisons
Summary
The estimation problem has been one of the essential subjects from industrial applications to research areas, including signal processing, navigation, target tracking, etc. Correntropy based filters have introduced the concept of information entropy as a local similarity measure, which is robust to non-Gaussian noise. Different from the recursive ordinary least squares method derived for deterministic systems, the horizon length of the unbiased FIR filters cannot be infinitely increased due to process bias accumulation, which needs to be limited within an appropriate range to ensure reliable estimation of xk. Where Bk,s is the first vector row in Bk,s, the unbiased FIR filter ignores the noise vectors and assumes that xk ≈ Ak,sxs within the estimate window; the unbiased solution obtained by (17) can be regarded as a typical solution of a linear regression problem derived on the quadratic loss function xk = arg min ( Yk,s − Ck,sxk ). According to [29], appropriate deformations can be made to obtain a faster iterative Kalman-like unbiased MCFIR filter
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