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.

中文翻译：

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马尔可夫切换连续系统滤波问题中的最大截面法

针对具有随机结构和连续时间的系统，提出了最优滤波问题的新求解算法。这个问题在于根据测量结果估计系统的当前状态。系统的数学模型包括非线性随机微分方程，其右手边决定了动态系统的结构或操作模式。右手边可能会随机变化。假设系统的结构数是有限的，并且将结构改变为马尔可夫或条件马尔可夫的过程。这种系统的状态向量由两个分量组成，即具有实坐标的向量和整数结构数。