The book deals with the problems of state estimation in discrete-time dynamic systems properties of which abruptly change at random time moments. Such systems are widely used in adaptive control of technological processes with rapid variations in operation mode when effects of failures are taken into account and in simulation of complex multiple-regime systems. The book covers various topics in this area such as optimal filtering, interpolation and extrapolation, detection of abrupt changes and problems of identification of models with variable parameters. The main achievement of the book is the development of a general unified approach to the investigation of estimation problems. This approach is based on the description of the processes considered by mixed Markov sequences. The methods obtained are illustrated by several practical examples with the help of digital computers.
From the summary: Chapter 1 contains mathematical models and the relations for a priori probabilistic characteristics of observation processes and disturbances with abruptly changing properties. Chapter 2 considers the optimal filtering problem in dynamic systems with abruptly changing properties for both linear and nonlinear cases. The relations that describe phase coordinates of a posteriori probability density propagation is also given. The following chapters relate to suboptimal filtering algorithms, interpolating and extrapolating probability densities, identification algorithms for mathematical model parameters varying in time and other estimation problems. The last chapter — chapter 7 contains examples of practical application.