Multi-sensor Suboptimal Fusion Student's $t$ Filter

TL;DR

This paper introduces a multi-sensor Student's t filter for robust recursive estimation in heavy-tailed noise environments, extending single sensor filters with an efficient fusion method suitable for various Gaussian-based approaches.

Contribution

It develops a computationally efficient multi-sensor Student's t filter using an arithmetic average fusion approach, applicable to any Gaussian-oriented fusion method like covariance intersection.

Findings

Effective in handling outliers compared to Gaussian estimators

Advantages of AA fusion over CI and augmented measurement fusion

Demonstrated robustness in simulation scenarios

Abstract

A multi-sensor fusion Student's $t$ filter is proposed for time-series recursive estimation in the presence of heavy-tailed process and measurement noises. Driven from an information-theoretic optimization, the approach extends the single sensor Student's $t$ Kalman filter based on the suboptimal arithmetic average (AA) fusion approach. To ensure computationally efficient, closed-form $t$ density recursion, reasonable approximation has been used in both local-sensor filtering and inter-sensor fusion calculation. The overall framework accommodates any Gaussian-oriented fusion approach such as the covariance intersection (CI). Simulation demonstrates the effectiveness of the proposed multi-sensor AA fusion-based $t$ 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.