Stable recursive least squares filtering using an inverse QR decomposition

The performance of recursive-least-squares (RLS) algorithm based on an inverse QR decomposition is reported. Theoretical analysis provides performance measures in a finite precision environment. The performance measure is derived in terms of the biases that are present in steady-state along the diagonal entries of the matrix used in the approach. An analytical expression has been derived for this bias as a function of wordlength, forgetting factor, and signal statistics. This result is further used to show that the diagonal entries will not reduce to zero or become negative, thereby ensuring stability of the algorithm. All analytical results are verified by corresponding simulation results