# Robust Student's t based Stochastic Cubature Filter for Nonlinear Systems with Heavy-tailed Process and Measurement Noises

## TL;DR

This paper introduces a robust Student's t based stochastic cubature filter for nonlinear systems with heavy-tailed noises, improving estimation accuracy and computational efficiency over existing methods.

## Contribution

A novel stochastic Student's t spherical radial cubature rule is developed, enabling a robust filter that outperforms existing approaches in accuracy and efficiency.

## Key findings

- Achieves higher estimation accuracy than existing filters.
- Demonstrates robustness in heavy-tailed noise environments.
- Offers computational efficiency superior to particle filters.

## Abstract

In this paper, a new robust Student's t based stochastic cubature filter (RSTSCF) is proposed for nonlinear state-space model with heavy-tailed process and measurement noises. The heart of the RSTSCF is a stochastic Student's t spherical radial cubature rule (SSTSRCR), which is derived based on the third-degree unbiased spherical rule and the proposed third-degree unbiased radial rule. The existing stochastic integration rule is a special case of the proposed SSTSRCR when the degrees of freedom parameter tends to infinity. The proposed filter is applied to a manoeuvring bearings-only tracking example, where an agile target is tracked and the bearing is observed in clutter. Simulation results show that the proposed RSTSCF can achieve higher estimation accuracy than the existing Gaussian approximate filter, Gaussian sum filter, Huber-based nonlinear Kalman filter, maximum correntropy criterion based Kalman filter, and robust Student's t based nonlinear filters, and is computationally much more efficient than the existing particle filter.