Using a lattice algorithm to estimate the Kalman gain vector in fast Newton-type adaptive filtering

We consider a recursive least squares (RLS) adaptive filtering problem where the input signal can be modelled as the output of a low order autoregressive (AR) process. We show how a good estimate of the Kalman gain vector can be obtained using a small least squares lattice (LSL) filter. This estimate can then be used in the normal way to determine the optimum filter coefficients. The resulting adaptive filtering algorithm is similar in concept to the fast Newton algorithm. The main difference is the use of the LSL instead of a low order covariance domain fast RLS algorithm. The potential advantage of this new algorithm is that, unlike a covariance domain algorithm, a LSL can be implemented in a numerically stable form