Abstract
In this article, a statistical similarity measure is introduced to quantify the similarity between two random vectors. The measure is, then, employed to develop a novel outlier-robust Kalman filtering framework. The approximation errors and the stability of the proposed filter are analyzed and discussed. To implement the filter, a fixed-point iterative algorithm and a separate iterative algorithm are given, and their local convergent conditions are also provided, and their comparisons have been made. In addition, selection of the similarity function is considered, and four exemplary similarity functions are established, from which the relations between our new method and existing outlier-robust Kalman filters are revealed. Simulation examples are used to illustrate the effectiveness and potential of the new filtering scheme.
Highlights
T HE Kalman filter is best-known as an optimal recursive state estimator in the sense of minimum variance for a linear system with Gaussian noises
The estimation accuracy of the Kalman filter degrades dramatically for a linear system with non-Gaussian heavy-tailed noises which are often induced by state and measurement outliers from external interference or unreliable sensors [2]
Motivated by the fact that the outlier contaminated state and measurement noises often have non-Gaussian heavy-tailed distributions, many outlierrobust filters have been proposed by modelling the state and measurement noises as Student’s t distributed [14]–[23]. These robust filters can be divided into two categories: Student’s t filter and robust Student’s t based Kalman filter (RSTKF)
Summary
T HE Kalman filter is best-known as an optimal recursive state estimator in the sense of minimum variance for a linear system with Gaussian noises. The estimation accuracy of the Kalman filter degrades dramatically for a linear system with non-Gaussian heavy-tailed noises which are often induced by state and measurement outliers from external interference or unreliable sensors [2]. Motivated by the fact that the outlier contaminated state and measurement noises often have non-Gaussian heavy-tailed distributions, many outlierrobust filters have been proposed by modelling the state and measurement noises as Student’s t distributed [14]–[23] These robust filters can be divided into two categories: Student’s t filter and robust Student’s t based Kalman filter (RSTKF). Simulation results of a manoeuvring target tracking example illustrate that by selecting appropriate similarity functions, the proposed filters have improved estimation accuracy but higher computational complexities than the existing state-of-the-art filters.
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