Recursive total least squares algorithms for adaptive filtering

Abstract

An algorithm for efficiently computing the eigenvector associated with the minimum eigenvalue of a correlation matrix is designed. This algorithm can be used to compute the total least squares (TLS) solution to the linear regression problem which yields unbiased equation-error infinite impulse response (IIR) adaptive filters. The algorithm utilizes a two-channel fast Kalman filter and requires only inner products involving L*1 vectors where L is one greater than the total number of filter coefficients. The TLS solution also results in unbiased finite impulse response (FIR) adaptive filters when the filter input is distributed by additive noise, a condition which is usually ignored but may often occur in practice.< >