An uncoupling method for linear system identification

A method for identifying the transition, control, and noise covariance matrices of a linear discrete-time dynamic system is presented. It is shown that the identification problem can be uncoupled, in the sense that each of the above matrix types can be identified independently of errors that may exist in any of the other matrices. This uncoupling can provide computational efficiency since the matrices involved are of lower order and typically the number of computations increases as the square of the order. A Kalman filter, predicated on the best available knowledge of system parameters, is constructed. The transition and control matrices are identified by requiring that the mean of the measurement residual sequence be zero. Following this, identification of the noise covariance matrices can be accomplished by requiring that the residuals be time-wise uncorrelated. An adaptive stochastic approximation algorithm is used to iteratively adjust the system parameters so that the above requirements are satisfied. Results of applying the method to a numerical example are presented.