A Detection-Estimation Method for Systems with Random Jumps with Application to Target Tracking and Fault Diagnosis

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 ( ) k θ 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:

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