Why can Wiener-Hopf reach accurate solutions with poor statistical estimates?

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Weiss, Stephan and Proudler, Ian K.; (2025) Why can Wiener-Hopf reach accurate solutions with poor statistical estimates? In: 2025 IEEE Statistical Signal Processing Workshop (SSP). IEEE/SP Workshop on Statistical Signal Processing (SSP) . IEEE, GBR. (In Press)

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Abstract

The Wiener-Hopf solution is based on estimates of the covariance matrix and the cross-correlation vector, which will likely be poor for small sample sizes. Yet the solution can be very accurate. We explore why this is, and why it is disadvantageous to separately estimate the two statistics, or try to include explicit knowledge of the input process to the adaptive system. The results are based on a least squares interpretation of Wiener-Hopf and an exploration of the variances of estimates, which we underpin by simulations.

ORCID iDs

Weiss, Stephan ORCID logoORCID: https://orcid.org/0000-0002-3486-7206 and Proudler, Ian K.;
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