This paper presents an analytical method for the filtering error evaluation of sub-optimal filters in a noisy non-linear, discrete-time system. Thea posterioriprobability density for the filtering error process conditioned upon measurement data sequence is expanded into a series of orthonormal Hermite functions and the bias of estimate obtained from sub-optimal filters is computed recursively as the mean of this probability density. Numerical example presents a comparison of the bias obtained from several sub-optimal filters.