Time Dependence in Kalman Filter Tuning

TL;DR

This paper introduces a novel approach to Kalman filter tuning that ensures a unique solution by tuning over multiple prediction intervals and employs Bayesian Optimization to handle noise and local minima.

Contribution

It proposes a method combining multi-interval tuning with Bayesian Optimization to improve Kalman filter noise parameter estimation.

Findings

Ensures unique tuning solutions through multi-interval approach.

Effectively handles noisy data with Bayesian Optimization.

Improves filter performance in practical noisy environments.

Abstract

In this paper, we propose an approach to address the problems with ambiguity in tuning the process and observation noises for a discrete-time linear Kalman filter. Conventional approaches to tuning (e.g. using normalized estimation error squared and covariance minimization) compute empirical measures of filter performance and the parameter are selected manually or selected using some kind of optimization algorithm to maximize these measures of performance. However, there are two challenges with this approach. First, in theory, many of these measures do not guarantee a unique solution due to observability issues. Second, in practice, empirically computed statistical quantities can be very noisy due to a finite number of samples. We propose a method to overcome these limitations. Our method has two main parts to it. The first is to ensure that the tuning problem has a single unique solution. We achieve this by simultaneously tuning the filter over multiple different prediction intervals. Although this yields a unique solution, practical issues (such as sampling noise) mean that it cannot be directly applied. Therefore, we use Bayesian Optimization. This technique handles noisy data and the local minima that it introduces.