Stabilization of the RLS algorithm in the absence of persistent excitation

Stability problems associated with recursive least-squares (RLS) algorithms due to lack persistency exciting input data are considered. It is shown by an example that quantization of data and finite-word length computations assist each other in destroying persistent excitation. A projection operator formalism is used to interpret this effect for the square-foot factorized autocorrelation matrix estimator. This estimator is modified such that only the single dimension observed through the current input data is updated. Thereby divergence of unobserved modes is prevented. This new O(N²) RLS algorithm with selective memory is computationally simple and stable even for small values of the forgetting factor