On the numerical stability and accuracy of the conventional recursive least squares algorithm

We study the nonlinear round-off error accumulation system of the conventio nal recursive least squares algorithm, and we derive bounds for the relativ e precision of the computations in terms of the conditioning of the problem and the exponential forgetting factor, which guarantee the numerical stabi lity of the finite-precision implementation of the algorithm; the positive definiteness of the finite-precision inverse data covariance matrix is also guaranteed. Bounds for the accumulated round-off errors in the inverse dat a covariance matrix are also derived. In our simulations, the measured accu mulated round offs satisfied, in steady state, the analytically predicted b ounds. We consider the phenomenon of explosive divergence using a simplifie d approach; we identify the situations that are likely to lead to this phen omenon; simulations confirm our findings.