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

15 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


  • 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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