Adaptive Kernel Kalman Filter

This paper presents a novel model-based Bayesian filter called the adaptive kernel Kalman filter (AKKF). The proposed filter approximates the arbitrary probability distribution functions (PDFs) of hidden states as empirical kernel mean embeddings (KMEs) in reproducing kernel Hilbert spaces (RKHSs). Specifically, particles are generated and updated in the data space to capture the properties of the dynamical system model, while the corresponding kernel weight vector and matrix associated with the particles’ feature mappings are predicted and updated in the RKHS based on the kernel Kalman rule (KKR). We illustrate and confirm the advantages of our approach through simulation, offering detailed comparison with the unscented Kalman filter (UKF), particle filter (PF) and Gaussian particle filter (GPF) algorithms.