On the eigendistribution of the steady-state error covariance matrix for the extended RLS algorithm

In an earlier work, we used transform methods from the theory of random matrices to analytically compute the asymptotic eigendistribution of the error covariance matrix of the single-measurement RLS filter. When we have a multiplicity of measurements, as happens in extended RLS filtering, the analysis is much more complicated. In this paper we study the multiple measurement case and obtain a system of two coupled equations for the Stieltjes transform of the asymptotic eigendistribution. Numerical solutions of this system very well predict the actual asymptotic eigendistribution for systems with as low as n = 10 - 20 state dimensions.