Оцінювання стану динамічних систем у присутності несправностей каналу спостереження

Abstract

Methods for estimating the dynamic systems states have found wide application in various fields of applied research. The most well-known of these is the Kalman filter method. When using this method, the results of observations by the sensory subsystem serve as the information source for correcting the assessment and the innovation process serves as a correct operation indicator of the assessment algorithm. For nominal operation, the difference signal is a Gaussian uncorrelated random process with zero mean and a priori computational covariance matrix. In the event of sudden malfunctions or unforeseen structurally uncertain disturbances in the sensor subsystem, these conditions are violated. The aim of this work is to develop a method that allows the normal operation of the Kalman filter to be restored under the stated conditions. The set goal is achieved by applying a special one-to-one transformation of the system output equation under study, as a result of which the disturbance component is absorbed in the extrapolation equation of the dynamic system state vector. The assumptions used to solve the problem coincide with those usually accepted in classical linear filtering theory, while the disturbances are completely arbitrary, cannot be described probabilistically and have no upper limit. To ensure the correctness of the solution to the problem, assumptions are made regarding the boundedness of system matrices which allow avoiding indeterminate solutions. At the next stage, a modified Kalman filter is applied to the corrected system in a certain way. Considerable attention is paid to the analysis of the properties of the resulting filter related to the estimation errors stability. The functional performance of the proposed method was confirmed by statistical modeling on a test example of a third-order linear dynamic system. Unlike other known design methods, the proposed method is characterized by a relatively simple algorithm and implementation and verification of the conditions for the existence of a solution does not require overly complex procedures which makes it practical and convenient to use. Unlike other well-known design methods, the proposed method is characterized by a relatively simple algorithm and implementation but the conditions for the existence of the solution do not require overly complex procedures, all of which makes it practical and convenient to use.