Quantification of Mismatch Error in Randomly Switching Linear State-Space Models

Parisa Karimi, Zhizhen Zhao, Mark D. Butala, Farzad Kamalabadi

Research output: Contribution to journalArticlepeer-review


Switching Kalman Filters (SKF) are well known for solving switching linear dynamic system (SLDS), i.e., piece-wise linear estimation problems. Practical SKFs are heuristic, approximate filters and require more computational resources than a single-mode Kalman filter (KF). On the other hand, applying a single-mode mismatched KF to an SLDS results in erroneous estimation. This letter quantifies the average error an SKF can eliminate compared to a mismatched, single-mode KF before collecting measurements. Derivations of the first and second moments of the estimators' errors are provided and compared. One can use these derivations to quantify the average performance of filters beforehand and decide which filter to run in operation to have the best performance in terms of estimation error and computation complexity. We further provide simulation results that verify our mathematical derivations.

Original languageEnglish (US)
Pages (from-to)2008-2012
Number of pages5
JournalIEEE Signal Processing Letters
StatePublished - 2021


  • Switching Kalman filter
  • detection
  • model mismatch
  • recursive estimation
  • switching linear dynamic systems

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering
  • Applied Mathematics


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