Optimal and Unbiased Filtering With Colored Process Noise Using State Differencing

Yuriy S. Shmaliy, Shunyi Zhao, Choon Ki Ahn

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


This letter develops the Kalman and unbiased finite impulse response filtering algorithms for linear discrete-time state-space models with Gauss-Markov colored process noise (CPN) employing state differencing. The approach avoids problems caused by matrix augmentation, but requires solving a nonsymmetric algebraic Riccati equation to specify the system matrix modified for CPN. Higher accuracy of the algorithms proposed is demonstrated by simulation. A comparative analysis of filtering estimates is provided based on navigation data of walking humans.

Original languageEnglish
Article number8638977
Pages (from-to)548-551
Number of pages4
JournalIEEE Signal Processing Letters
Issue number4
Publication statusPublished - 2019 Apr

Bibliographical note

Funding Information:
Manuscript received November 1, 2018; revised December 25, 2018; accepted February 6, 2019. Date of publication February 11, 2019; date of current version February 26, 2019. This work was supported by the 111 Project (B12018). The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Jun Liu. (Corresponding author: Yuriy S. Shmaliy.) Y. S. Shmaliy is with the Department of Electronics Engineering, Universidad de Guanajuato, Salamanca 36885, Mexico (e-mail:,shmaliy@ugto.mx).

Publisher Copyright:
© 2019 IEEE.


  • Kalman filter
  • State-space
  • colored process noise
  • state differencing
  • unbiased FIR filter

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering
  • Applied Mathematics


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