An additional requirement for innovations testing in system identification

In [1], Boozer and McDaniel showed by means of a counterexample that whitening the measurement residual sequence output from the Kalman filter is not sufficient for identifying the transition matrix of a linear dynamic system. Recent work by the present authors, documented in [2], has shown that in many cases the identification can be accomplished by requiring further that the residual sequence have a zero mean. Imposing this requirement, the transition matrix of the Boozer and McDaniel example is identified.