Robust Linear Estimation Of Moments For (almost) Cyclostationary Signals

The behavior of linear estimators of moments in a periodic or almost periodic non-stationary environment is analyzed. The performance of such estimators is evaluated in terms of their time-averaged variance and time-averaged squared bias. Optimal estimators that minimize a convex combination of bias and variance are derived. The superiority of such optimally-weighted averaging over the conventional (exponentially-windowed) moment estimation technique is demonstrated by means of a simple example. The same example also serves to illustrate the difficulties encountered when the construction of such optimal estimators relies on uncertain parametric information, as well as to demonstrate the feasibility of overcoming such difficulties by using appropriately designed (robust) optimal estimators.