What is optimal processing for nonstationary data?

For stationary data, an adaptive array processing algorithm can be optimized with ensemble averaging. Here we call such an algorithm "stationary-optimal". However, for nonstationary data, ensemble averages may not describe how real processors acquire the statistics, and the validity of ergodicity must be questioned in general. Acknowledging this, we ask, "what are the most relevant statistics"? and, "how can they be acquired"? Our example is a nonstationary scenario for a passive sonar array. We explore issues related to processing nonstationary data and compare the performance of previous algorithms (based on a data covariance matrix) to the multistage Wiener filter (based on direct subspace measurements of the interference).