Synthesis of reduced Kalman filter with the guaranteed estimation quality of dynamic system state

Abstract

Synthesis of a suboptimal reduced Kalman filter with the guaranteed estimation quality of a state of dynamic system subject to nonwhite noise disturbances is considered. A calculation model containing additional white noise disturbances is used for selection of parameters of such a filter. Intensity of the added disturbances is chosen in such a way that the calculation covariance matrix, which is found as the solution of the Riccati equation in the filter covariance channel, is larger than the real covariance matrix of the error estimate \( \hat X \)0(t) in the quadratic form inequality sense. In this case, it is possible to consider this matrix as a measure of accuracy of the performed estimation of a dynamic system state. An example of the filter synthesis for description of disturbances with stationary first-order Markov processes is given.