Statistical properties of a novel recursive estimation algorithm with information-dependent updating

Statistical analysis of a recursive parameter estimation algorithm is performed. The algorithm has been used for the estimation of parameters of autoregressive processes with auxiliary inputs and bounded disturbances (ARX processes) with bounded noise. Previous analysis of algorithms used in the bounded-noise situation have been essentially deterministic. Unbiasedness of the estimates is shown under the assumption that the noise is white and zero mean. An upper bound on the covariance of parameter estimates is derived. An improved version of the algorithm is proposed which yields smoother estimates and greater resistance to outliers