On noncausal weighted least squares identification of nonstationary stochastic systems

In this paper, we consider the problem of noncausal identification of nonstationary, linear stochastic systems, i.e., identification based on prerecorded input/output data. We show how several competing weighted (windowed) least squares parameter smoothers, differing in memory settings, can be combined together to yield a better and more reliable smoothing algorithm. The resulting parallel estimation scheme automatically adjusts its smoothing bandwidth to the unknown, and possibly time-varying, rate of nonstationarity of the identified system. We optimize the window shape for a certain class of parameter variations and we derive computationally attractive recursive smoothing algorithms for such an optimized case.