On Stability of a Class of Filters for Nonlinear Stochastic Systems

Toni Karvonen*, Silvere Bonnabel, Eric Moulines, Simo Särkkä

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

11 Citations (Scopus)
73 Downloads (Pure)


This article develops a comprehensive framework for stability analysis of a broad class of commonly used continuous- and discrete-time filters for stochastic dynamic systems with nonlinear state dynamics and linear measurements under certain strong assumptions. The class of filters encompasses the extended and unscented Kalman filters and most other Gaussian assumed density filters and their numerical integration approximations. The stability results are in the form of time-uniform mean square bounds and exponential concentration inequalities for the filtering error. In contrast to existing results, it is not always necessary for the model to be exponentially stable or fully observed. We review three classes of models that can be rigorously shown to satisfy the stringent assumptions of the stability theorems. Numerical experiments using synthetic data validate the derived error bounds.

Original languageEnglish
Pages (from-to)2023-2049
Number of pages27
JournalSIAM Journal on Control and Optimization
Issue number4
Publication statusPublished - 2020
MoE publication typeA1 Journal article-refereed


  • Nonlinear systems
  • Kalman filtering
  • Nonlinear stability analysis
  • Extended Kalman Filter
  • Performance evaluation
  • Exponential stability
  • Uniform propagation
  • Discrete
  • Convergence
  • Observer
  • Accuracy
  • Equation
  • Chaos


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