On “cheap smoothing” opportunities in identification of time-varying systems

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 into 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 not causal. Despite the possible performance improvements, the existing smoothing algorithms are seldom used in practice, mainly because of their high computational requirements. We show that the computationally attractive smoothing procedures can be obtained by means of compensating estimation delays that arise in the standard exponentially weighted least squares, least mean squares and Kalman filter-based parameter trackers.