Kalman filtering with empirical noise models

TL;DR

This paper introduces a Kalman filter extension that models empirical measurement noise, improving accuracy over Gaussian assumptions and matching specialized algorithms in diverse real-world scenarios.

Contribution

The paper presents a novel algorithm for incorporating empirically measured noise models into Kalman filters, enhancing their robustness to non-Gaussian noise.

Findings

More accurate than Gaussian-based filters in experiments

Comparable to distribution-specific algorithms in accuracy

Effective with real measurement data from UWB and satellite sensors

Abstract

Most Kalman filter extensions assume Gaussian noise and when the noise is non-Gaussian, usually other types of filters are used. These filters, such as particle filter variants, are computationally more demanding than Kalman type filters. In this paper, we present an algorithm for building models and using them with a Kalman type filter when there is empirically measured data of the measurement errors. The paper evaluates the proposed algorithm in three examples. The first example uses simulated Student-t distributed measurement errors and the proposed algorithm is compared with algorithms designed specifically for Student-t distribution. Last two examples use real measured errors, one with real data from an Ultra Wideband (UWB) ranging system, and the other using low-Earth orbiting satellite magnetometer measurements. The results show that the proposed algorithm is more accurate than algorithms that use Gaussian assumptions and has similar accuracy to algorithms that are specifically designed for a certain probability distribution.