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Tham khảo tài liệu 'nonlinear dynamics part 15', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 15 A Detection-Estimation Method for Systems with Random Jumps with Application to Target Tracking and Fault Diagnosis Yury Grishin and Dariusz Janczak Bialystok Technical University Electrical Engineering Faculty Poland 1. Introduction Methods for detection and estimation of the structure or parameters of abrupt changes in dynamic systems play an important role for solving a number of problems encountered in practice. They have an important significance in different fields of telecommunications and control applications such as radar tracking of maneuvering targets fault diagnosis and identification FDI speech analysis signal processing in geophysics and biomedical systems. Most of these applications belong to the class of problems with nonlinear dynamics. Among them an important role is played by a wide class of systems with abrupt random jumps of parameters or structure. A dynamic system with jumps of this kind can be defined as a system in which the structure or parameters can change at any random time. Therefore in order to describe such a system it is convenient to introduce an unknown random vector i k that determines the current system structure and parameters. Then the system state and observation equations are dependent on this changing vector. The general case then is described as follows x k 1 F x k k w k 1 y k h x k 5 k v k 9 k eQ 2 where F and h are known nonlinear functions w k and v k are system and measurement noises respectively and Q is the space of possible values of the vector i9 k . The space Q can consist of finite or infinite sets of elements. The structure of the space Q and evolution of the vector i9 k in time determine the main approaches to solving the problem of detection-estimation in a dynamic system with jump structure. The classification of the statistical characteristics of the parameter vector ki is presented in Fig. 1. According to this classification after the jump the parameter vector i k can take on finite or infinite sets of .