Exact Bayesian Inference for a Class of Nonlinear Systems with Application to Robotic Assembly

Abstract

Abstract This paper presents a new finite-dimensional Bayesian filter. The filter calculates the exact analytical expression for the posterior probability density function (pdf) of static systems with any kind of nonlinear measurement equation subject to Gaussian measurement uncertainty. The paper also extends this filter to a limited class of dynamic systems. The filter is applied to the estimation of the inaccurately known position and orientation of two mating parts during autonomous robotic assembly. The sufficient statistics of the posterior pdf are obtained by Kalman Filter formulas, making online estimation possible. Exact finite-dimensional filters exist only for a small class of systems. The best known example is the Kalman Filter for linear systems (i.e., systems for which both the process equation and the measurement equation are linear) with Gaussian uncertainties. In this case, the posterior pdf is a Gaussian represented by its mean and its covariance matrix. Other examples are the filters of Benes (1981), which requires the measurement equation to be linear, and Daum (1988), applicable to a more general class of systems with nonlinear process and measurement equations for which the posterior pdf is any exponential distribution.