Efficient least squares FIR system identification

If finite impulse response (FIR) system identification is performed by minimizing the squared error between the measured system output and an estimate from an FIR system output, a set of least squares normal equations 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, however, that can be exploited to yield a solution with computational operations proportional to M²and storage proportional to M. Such an efficient algorithmic solution is presented here.