Least squares optimal filtering with multirate observations

This paper addresses the problem of optimal filtering from a least squares perspective when multiple observation sequences are available with differing sampling rates. In such cases the processes are jointly cyclostationary and the resulting linear optimal filters are periodically time-varying. The data matrices for this problem have interesting structure and we develop the form of the resulting least squares multirate Wiener-Hopf equations. Filtering results are illustrated for atypical example and issues of computation and amount of training data needed are investigated.