Maximum cross section method in the filtering problem for continuous systems with Markovian switching

Tatyana A. Averina, Konstantin A. Rybakov

Research output: Contribution to journalArticlepeer-review


New solution algorithms of optimal filtering problem are proposed for systems with random structure and continuous time. This problem consists in estimating the current state of system based on the results of measurements. The mathematical model of the system includes nonlinear stochastic differential equations whose right-hand side determines the structure of the dynamic system or mode of operation. The right-hand side may vary at random time moments. The number of structures of the system is assumed to be finite and the process of changing the structure to be Markov or conditionally Markov. The state vector of such system consists of two components, namely, a vector with real coordinates and an integer structure number. The law of change of the structure number is determined by the distribution of the random time interval between switchings with a given intensity dependent on the state of system.

Original languageEnglish
Pages (from-to)127-137
Number of pages11
JournalRussian Journal of Numerical Analysis and Mathematical Modelling
Issue number3
Publication statusPublished - 1 Jun 2021


  • maximum cross section method
  • Monte Carlo method
  • particle filter
  • statistical modelling
  • Stochastic differential equation with Markovian switching
  • system with random structure




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