The problem of nonlinear filtering of random processes in bilinear systems with triangular matrices is discussed. ii method of constructing precise finite-dimensional eguations for the optimal rms estimation of the state vector is proposed, and examples are presented.

Optimal filtering for a wide class of discrete stochastic systems defined by nonlinear difference equations with unknown parameters is studied. Equations describing the conditional probability densities for the case in which the unknown parameter vector is continuous and discrete are derived. Recursive equations for the mean-square optimal filter are derived. Nonlinear systems with additive perturbations are studied in detail. For discrete nonlinear systems with unknown parameters, the optimal filter is shown to be described by the Lainiotis exact filtering equations. Using the Lainiotis separation theorem, new families of parallel recursive estimation algorithms are designed. The application of the results to pattern recognition, signal detection, and system identification is examined.

The problem of adaptive discrete nonlinear filtering is discussed. For the conditional densities, state estimates, and covariance matrices, there exist precise equations that are based on the Lainiotis separation theorem and define the state estimate and covariance matrix: of the system. II is proposed to solve them using the normal approximation of conditional densities, which leads to some efficient recurrent real-lime computational algorithms that were checked and compared using the standard problems of signal recognition and parameter identification.

We consider some topics of design of discrete-time conditionally optimal filters and identifiers and analysis of stochastic processes in linear and nonlinear discrete-time stochastic systems. The principles of development of intelligent software for filter design are discussed. The software package StS-Filter (Version 1) for IBM PC/AT and compatibles is briefly described. The software supports the information technologies of computer-aided research, computer-aided design, and computer-aided education .

We consider some issues of software development for the analysis of multidimensional stochastic systems (SS) described by stochastic differential and difference equations. A brief survey of basic approximate methods of SS analysis for commercial computing environments, and primarily for personal computers, is given. The MOMENT program package implementing these methods is described. Design principles of interactive application packages for SS analysis are discussed and a description of an interactive package for IBM PC/XT and AT is given.

A survey is given of problems of statistical analysis and on-line filtering of processes in nonlinear stochastic systems described by differential or difference or mixed differential-difference or integro-differentia equations and of efficient approximate methods for solving these problems. The related problems of designing the necessary software for the statistical analysis of such systems and for designing conditionally optimal filters for data processing in these systems are also considered.