Fast least squares FIR system identification

Abstract

If finite impulse response (FIR) system identification is performed by minimizing the squared error between the measured system output, a set of least-squares normal euqations to be solved for the FIR system coefficients is obtained. If the assumed FIR system is of duration M samples, the usual solution for the M least squares simultaneous equations requires a number of computational operations proportional to M3and storage of normal equation coefficients proportional to M2. The set of normal equations has an underlying structure, though, that can be exploited to yield a solution with computational operations proportional to M2and storage proportional to M. The outline of such an algorithm is presented here.