Abstract
The correlation-extremum systems theory is extended to stochastic systems with random structure or with switching parameters and the new suboptimal (due to the nonlinear system state and measurement equations) filtering and parameter identification algorithms and their linearized form are derived, which provide adaptive features and reliable operation for the proposed combined correlation-extremum dynamic systems with random structure under environment influences, and represent new solutions of the linearization problem for the case of great estimation errors. The obtained linearized solution allows the simplification of the filter a priori performance investigation at the signal processing system design stage.
Highlights
The known nonlinear filtering algorithms (e.g., the extended Kalman filter (EKF) and the most extended versions) developed for nonlinear systems are based on the assumption of linearization of the nonlinear functions in the state dynamics and measurements equations relative to estimation errors or about the current state estimate.These algorithms providing optimal or suboptimal estimates remain true when the estimation errors are small enough to satisfy a linearization
There is a significant class of the filtering and identification problems of interest, especially in tracking systems, such as the cases of great estimation errors, tracking interruption, abrupt increasing of the measurements noises, and jumping changes of the estimated process parameters (e.g., if a target exhibits considerably changing trajectory characteristics), and etc., when the performance of EKF becomes unstable
The proposed correlation-extremum filtering and identification algorithms including the differential equations for the a posteriori probabilities of states, the state estimates, and the variances are derived for stochastic dynamic systems with random structure for the adaptive estimation problem, when the system state and parameter models are described by Markov processes, and the measurements are the nonlinear STV signals of different physical nature fields against a background of the additive spatial-time-varying Gaussian white noise (STVGWN), whose intensity identification a) is first obtained 1) for STV signal processing 2) in systems with random structure, and b) reflects more adequately the true noise statistics existing in real external conditions
Summary
The known nonlinear filtering algorithms (e.g., the extended Kalman filter (EKF) and the most extended versions) developed for nonlinear systems (in particular, this relates to the case of radar or optics tracking of an airborne target when the vehicle dynamics is described by nonlinear differential equations) are based on the assumption of linearization of the nonlinear functions in the state dynamics and measurements equations relative to estimation errors or about the current state estimate. To overcome the mentioned contradiction between the normal conditional probability density existence in the case of grate estimation errors and the incorrectness of the traditional linearization theory application, the theory of stochastic systems with random structure or with switching parameters and Markov processes has been originally extended to the correlation-extremum systems and the new algorithms have been derived which are under consideration in this work. The purpose of the present scientific investigation is the solutions of the problem of correlation-extremum signal processing algorithms synthesis and analysis for stochastic dynamic systems with random structure or with switching parameters with noise statistics identification, and their linearization which can provide the filter adaptive capability and assure the system operation under varying natural or/and artificial environment influences in a number of their possible civil and military areas of application
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