The problem of extracting the best estimate of a corrupted signal by using more than one source of information is of considerable engineering interest and has been examined by various authors in the past few years. The approach to the problem has generally taken two paths, the first being a direct derivation of optimum filters by using the criterion of minimum mean-squared error and the other, the derivation of the so-called distortionless type of filter which eliminates the signal distortion component of error completely. This approach simplifies the mathematics and the design problem but frequently at the expense of a greater over-all mean-squared error at the output.