On noisy FIR filtering via total least squares estimation

Abstract

It is known that a problem of FIR filtering with noisy input and output data can be formulated as a total least squares (TLS) estimation problem. In this paper the sensitivity of the TLS algorithm with respect to the ratio between the variances of the input and output noises is studied. The sensitivity analysis shows that the assumption of the known noise variances ratio, which is vital to application of the TLS algorithm, can be relaxed to that of a rough range of this ratio. The practical workability of the TLS algorithm in noisy FIR filtering is thereby substantially increased. The theoretical findings are corroborated with computer simulation results.