Minimax robust nonstationary signal estimation based on a p-point uncertainty model

We propose a time-varying Wiener filter for nonstationary signal estimation that is robust in a minimax sense. This robust Wiener filter optimizes worst-case performance within novel “p-point” uncertainty classes of nonstationary random processes. Furthermore, it features constant performance within these uncertainty classes and requires less detailed prior knowledge than the ordinary time-varying Wiener filter. We also propose a time–frequency formulation that is intuitively appealing since signal subspaces are replaced by time–frequency regions, and an efficient on-line implementation using local cosine bases. Our theory is illustrated by numerical simulations and a real-data example.