Set-theoretic estimation based on a priori knowledge of the noise distribution

A new algorithm for estimation of a linear-in-parameters model is developed and tested by simulation. The method is based on the assumption of independent, identically distributed noise samples with a triangular density function. Such a noise model well approximates the symmetrically distributed sources of noise frequently encountered in practice, and the inclusion of a distribution assumption allows the computation of a pseudo-mean estimate to complement the set solution. The proposed algorithm recursively incorporates incoming observations with decreasing computational complexity as the number of updates increases. Simulations demonstrate that the algorithm has very favorable convergence rates and estimation accuracy and is very robust to deviations from the assumed noise properties. Comparisons with other set-theoretic algorithms and with conventional RLS are given.