On smoothing opportunities in identification of time-varying systems — Beyond the posterior cramer-RAO bound

In certain applications of nonstationary system identification the model-based decisions can be postponed, i.e. executed with a delay. This allows one to incorporate in the identification process not only the currently available information, but also a number of “future” data points. The resulting estimation schemes, which involve smoothing, are noncausal. We show that a computationally attractive parameter smoothing algorithm can be obtained by means of compensating estimation delays which arise in the standard Kalman filter based tracker. Despite its simplicity, the proposed algorithm allows one to exceed the Cramér-Rao type lower tracking bound, which limits accuracy of causal estimators.