Recursive Bayesian Filtering in Circular State Spaces

TL;DR

This paper develops a comprehensive Bayesian filtering framework for circular state spaces, introducing novel algorithms and formulas that improve estimation accuracy and computational efficiency for nonlinear circular systems.

Contribution

It presents a general recursive filtering approach using circular distributions, including new algorithms for prediction and density multiplication, handling non-additive noise and simplifying calculations.

Findings

The proposed methods outperform existing solutions in accuracy.

Efficient deterministic sampling enhances computational performance.

New formulas improve density multiplication in circular filtering.

Abstract

For recursive circular filtering based on circular statistics, we introduce a general framework for estimation of a circular state based on different circular distributions, specifically the wrapped normal distribution and the von Mises distribution. We propose an estimation method for circular systems with nonlinear system and measurement functions. This is achieved by relying on efficient deterministic sampling techniques. Furthermore, we show how the calculations can be simplified in a variety of important special cases, such as systems with additive noise as well as identity system or measurement functions. We introduce several novel key components, particularly a distribution-free prediction algorithm, a new and superior formula for the multiplication of wrapped normal densities, and the ability to deal with non-additive system noise. All proposed methods are thoroughly evaluated and compared to several state-of-the-art solutions.