Adaptive Kernel Kalman Filter

TL;DR

The paper proposes an adaptive kernel Kalman filter (AKKF) that uses kernel mean embeddings and particles in data space for improved non-linear Bayesian filtering, achieving better accuracy with fewer particles.

Contribution

It introduces AKKF, combining kernel mean embeddings with particle filtering in data space, enhancing non-linear Bayesian filtering performance.

Findings

AKKF outperforms UKF, PF, and GPF in simulations.

Achieves around 5% LMSE improvement over GPF in tracking.

Requires fewer particles for comparable or better accuracy.

Abstract

Sequential Bayesian filters in non-linear dynamic systems require the recursive estimation of the predictive and posterior distributions. This paper introduces a Bayesian filter called the adaptive kernel Kalman filter (AKKF). With this filter, the arbitrary predictive and posterior distributions of hidden states are approximated using the empirical kernel mean embeddings (KMEs) in reproducing kernel Hilbert spaces (RKHSs). In parallel with the KMEs, some particles, in the data space, are used to capture the properties of the dynamical system model. Specifically, particles are generated and updated in the data space, while the corresponding kernel weight mean vector and covariance matrix associated with the feature mappings of the particles are predicted and updated in the RKHSs based on the kernel Kalman rule (KKR). Simulation results are presented to confirm the improved performance of our approach with significantly reduced particle numbers, by comparing with the unscented Kalman filter (UKF), particle filter (PF) and Gaussian particle filter (GPF). For example, compared with the GPF, the proposed approach provides around 5% logarithmic mean square error (LMSE) tracking performance improvement in the bearing-only tracking (BOT) system when using 50 particles.