Abstract
New algorithms for solving the optimal filtering problem for continuous-timesystems with a random structure are proposed. This problem is to estimate the currentsystem state vector from observations. The mathematical model of the dynamic systemincludes nonlinear stochastic differential equations, the right side of which defines the systemstructure (regime mode). The right side of these stochastic differential equations may bechanged at random time moments. The structure switching process is the Markov or conditionalMarkov random process with a finite set of states (structure numbers). The state vectorof such system consists of two components: the real vector (continuous part) and the integerstructure number (discrete part). The switch condition for the structure number may bedifferent: the achievement of a given surface by the continuous part of the state vector orthe distribution of a random time period between structure switchings. Each ordered pairof structure numbers can correspond to its own switch law. Algorithms for the estimation of the current state vector for systems with a randomstructure are particle filters, they are based on the statistical modeling method (MonteCarlo method). This work continues the authors’ research in the field of statistical methodsand algorithms for the continuous-time stochastic systems analysis and filtering.
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