Abstract
In this paper, in order to improve the Student's t-matching accuracy, a novel Kullback-Leibler divergence (KLD) minimization-based matching method is firstly proposed by minimizing the upper bound of the KLD between the true Student's t-density and the approximate Student's t-density. To improve the Student's t-modelling accuracy, a novel KLD minimization-based adaptive method is then proposed to estimate the scale matrices of Student's t-distributions, in which the modified evidence lower bound is maximized. A novel KLD minimization-based adaptive Student's t-filter is derived via combining the proposed Student's t-matching technique and the adaptive method. A manoeuvring target tracking example is provided to demonstrate the effectiveness and potential of the proposed filter.
Highlights
T HE non-Gaussian filtering problem of a state-space model (SSM) with heavy-tailed noises has been attracting more and more attention
For a linear SSM with the moderately contaminated state and observation noises, the robust Student’s t-based KF (RSTKF) has better filtering accuracy than the s t-filter (STF) because the posterior filtering probability density function (PDF) can be better approximated by the Gaussian distribution as compared with the Student’s t-distribution [28]
We aim to improve the filtering accuracy of the existing STF by improving the Student’s tmatching accuracy and the Student’s t-modelling accuracy
Summary
T HE non-Gaussian filtering problem of a state-space model (SSM) with heavy-tailed noises has been attracting more and more attention. For a linear SSM with the moderately contaminated state and observation noises, the RSTKF has better filtering accuracy than the STF because the posterior filtering PDF can be better approximated by the Gaussian distribution as compared with the Student’s t-distribution [28]. For a linear SSM with strongly contaminated state and observation noises, the STF has better filtering accuracy than the RSTKF since the posterior filtering PDF may be approximated by the Student’s t-distribution better than the Gaussian distribution. Simulation examples illustrate that the proposed ASTF has improved filtering accuracy over the existing HKF, MCKF, STF and RSTKF for strongly heavy-tailed state and observation noises.
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