Adaptive Kernel Kalman Filter

Mengwei Sun* (Lead Author), Michael E. Davies, Ian Proudler, James R. Hopgood (Group Leader)

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

Sequential Bayesian filters in non-linear dynamic systems require the recursive estimation of the predictive and posterior probability density functions (pdfs). This paper introduces a Bayesian filter called the adaptive kernel Kalman filter (AKKF). The AKKF approximates the arbitrary predictive and posterior pdfs of hidden states using the 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 dynamic system model. Specifically, particles are generated and updated in the data space. Moreover, the corresponding kernel weight means vector and covariance matrix associated with the particles’ kernel feature mappings 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 numbers of particles by comparing with the unscented Kalman filter (UKF), particle filter (PF), and Gaussian particle filter (GPF). For example, compared with the GPF, the AKKF provides around 50% logarithmic mean square error (LMSE) tracking performance improvement in the bearing-only tracking (BOT) system when using 50 particles.
Original languageEnglish
Pages (from-to)713-726
JournalIEEE Transactions on Signal Processing
Early online date8 Mar 2023
Publication statusE-pub ahead of print - 8 Mar 2023

Keywords / Materials (for Non-textual outputs)

  • Adaptive kernel Kalman filter
  • kernel Kalman rule
  • kernel mean embedding
  • non-linear dynamic systems
  • sequential Bayesian filters


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