A new linear regression kalman filter with symmetric samples

Xiuqiong Chen, Jiayi Kang, Mina Teicher, Stephen S.T. Yau

Research output: Contribution to journalArticlepeer-review


Nonlinear filtering is of great significance in industries. In this work, we develop a new linear regression Kalman filter for discrete nonlinear filtering problems. Under the framework of linear regression Kalman filter, the key step is minimizing the Kullback–Leibler divergence between standard normal distribution and its Dirac mixture approximation formed by symmetric samples so that we can obtain a set of samples which can capture the information of reference density. The samples representing the conditional densities evolve in a deterministic way, and therefore we need less samples compared with particle filter, as there is less variance in our method. The numerical results show that the new algorithm is more efficient compared with the widely used extended Kalman filter, unscented Kalman filter and particle filter.

Original languageEnglish
Article number2139
Issue number11
StatePublished - Nov 2021

Bibliographical note

Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.


Funding: This research was funded by National Natural Science Foundation of China NSFC (grant no. 11961141005), Israel Science Foundation (joint ISF-NSFC grant) (grant no 20551), Tsinghua University start-up fund, and Tsinghua University Education Foundation fund (042202008).

FundersFunder number
National Natural Science Foundation of China11961141005
Israel Science Foundation
Tsinghua University
Sichuan University Education Foundation042202008


    • Dirac mixture approximation
    • Kalman filter
    • Kullback–Leibler divergence
    • Symmetric samples


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