Kullback-Leibler Divergence Approach to Partitioned Update Kalman Filter

TL;DR

This paper generalizes the partitioned update Kalman filter using a Kullback-Leibler divergence measure to better handle nonlinearity, leading to improved estimation accuracy across various Kalman filter extensions.

Contribution

It introduces a KL divergence-based nonlinearity measure to extend the partitioned update Kalman filter to any Kalman filter variant.

Findings

Improved estimation accuracy with the proposed method

Applicable to various Kalman filter extensions

Theoretically more sound nonlinearity measurement

Abstract

Kalman filtering is a widely used framework for Bayesian estimation. The partitioned update Kalman filter applies a Kalman filter update in parts so that the most linear parts of measurements are applied first. In this paper, we generalize partitioned update Kalman filter, which requires the use oft the second order extended Kalman filter, so that it can be used with any Kalman filter extension. To do so, we use a Kullback-Leibler divergence approach to measure the nonlinearity of the measurement, which is theoretically more sound than the nonlinearity measure used in the original partitioned update Kalman filter. Results show that the use of the proposed partitioned update filter improves the estimation accuracy.