Optimal Non-stationary Estimation of the Parameters of a Linear System with Gaussian Inputs †

Abstract

A linear system with gnusian inputs can be specified by its state transition equations. Assuming that the coefficients of the state transition matrix are initially unknown, a procedure, which gives a continuously up-dated estimate of these coefficients, is outlined. The procedure is extended to give an optimal estimate when the coefficients are random processes. Full knowledge of the state of the system as time proceeds is required. The puper shows how the result can be used to obtain an optimal estimate of the coefficients of the state transition and control matrices of a linear control system with gaussian inputs, provided that full knowledge of the value of the control signal is also available.