Discrete Kalman Filter Invariant to Perturbations

Abstract

Fault detection problems in dynamic objects and their localization are a very critical and rather challenging tasks for many practical applications. The Kalman-filter technology is used for these purposes most often. The correct operation indicator of the specified filter is the innovation process to be represented as a normal uncorrelated stochastic process with zero mean value and a priori calculated covariation matrix, except the specified conditions, are violated in case of unforeseen perturbations. The aim of the presented work is to develop a method allowing to restore the normal performance of the Kalman filter in the presence of uncertain disturbances. This aim is attained by applying a special one-to-one transformation of the output equation of the testing system, as a result of it, the disturbance component is modified by the extrapolation equation of the state vector dynamic system. This feature will be used in the sequel when modified Kalman filter is applied to the transformed system. The properties of the obtained filter concerning the stability of estimation errors, their convergence, and optimality are discussed. The efficiency of the method has been verified by the method of statistical modeling on a test example of a third-order dynamic system.