Multisensor Suboptimal Fusion Student's $t$ Filter

Abstract

A multisensor fusion Student's <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$t$</tex-math></inline-formula> filter is proposed for time-series recursive estimation in the presence of heavy-tailed process and measurement noises. It extends the single-sensor Student's <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$t$</tex-math></inline-formula> Kalman filter to the multisensor setup based on the suboptimal arithmetic average (AA) fusion approach which is driven from information-theoretic density fusion optimization and able to deal with unknown correlation among sensors. To ensure computationally efficient, closed-form <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$t$</tex-math></inline-formula> density recursion, moment matching approximation has been used for averaging the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$t$</tex-math></inline-formula> densities aggregated from different sensors. Based on the same framework, we also extend the covariance intersection (CI) approach for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$t$</tex-math></inline-formula> density fusion. Simulation demonstrates the strength of the proposed multisensor AA fusion-based <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$t$</tex-math></inline-formula> filter in dealing with outliers as compared with the classic Gaussian estimator, and the advantage of the AA fusion in comparison with the CI approach and the augmented measurement fusion.

Topics & Concepts