Statistical filtering algorithms for systems with random structure

New algorithms for solving the optimal filtering problem for continuous-time systems with a random structure are proposed. This problem is to estimate the current system state vector from observations. The mathematical model of the dynamic system includes nonlinear stochastic differential equations, the right side of which defines the system structure (regime mode). The right side of these stochastic differential equations may be changed at random time moments. The structure switching process is the Markov or conditional Markov random process with a finite set of states (structure numbers). The state vector of such system consists of two components: the real vector (continuous part) and the integer structure number (discrete part). The switch condition for the structure number may be different: the achievement of a given surface by the continuous part of the state vector or the distribution of a random time period between structure switchings. Each ordered pair of structure numbers can correspond to its own switch law.
Algorithms for the estimation of the current state vector for systems with a random structure are particle filters, they are based on the statistical modeling method (Monte Carlo method). This work continues the authors' research in the field of statistical methods and algorithms for the continuous-time stochastic systems analysis and filtering.