A theoretical basis for divergence of conventional recursive least squares filters

The authors identify several specific sources of instability in the conventional recursive least squares (CRLS) algorithm. They explore why the algorithm is numerically unstable under fixed-point precision and examine how it can be stabilized. A form of the CRLS algorithm that maintains symmetry in the inverse autocorrelation matrix estimate is first presented, and divergence phenomena are discussed. Several sources of instability are identified as well as practical techniques for combating each instability source. Experimental results that demonstrate the usefulness of these techniques are presented. Initial simulation results indicate that by compensating for the source of numerical instability, it is possible to obtain numerical stability with negligible loss in performance