Statistics of the RSS estimation algorithm for Gaussian measurement noise

The large and small sample properties of the reduced sufficient statistics (RSS) estimator of Kulhavy (1990, 1992) are derived for the nonlinear additive white Gaussian noise measurement model. The RSS algorithm recursively propagates a set of sufficient statistics for a mixture density that approximates the true posterior density of a parameter vector. The joint probability density function for the weighting coefficients of the mixture density is derived for the case of additive white Gaussian noise. Through integration of this density, the estimator bias and mean-squared error are determined. The results are applied to a scalar phase estimation problem in which the sample-averaged statistics are compared with those derived from numerical integration of the density function. The asymptotic bias and variance of the RSS estimator are also derived and compared with simulation results.