Method of adjoint particle filters in nonlinear Bayesian estimation problems with a high prior uncertainty

Abstract

A modification of the widely known scheme for solving nonlinear Bayesian optimal estimation problems in which the state vector contains a parameter not varying during the estimation process is proposed. Such problems are often solved by a technique in which the varying part of the state vector is modeled using sequential Monte Carlo methods (particle filters) and the parameter is modeled as a conditional distribution associated with a specific trajectory (implementation of the moving component). Different modifications of this scheme differ mainly in the ways of modeling the parameter. In some recent works devoted to the problem of simultaneous localization and mapping, the vector parameter which consists of coordinates of unknown reference points (landmarks) is modeled using the generalized Kalman filter, Gaussian sum filters, and more specific methods. We consider a modification in which the parameter, as well as the moving part of the state vector, is modeled using particle filters. The main recurrence relationships between weights of particle filters are derived. The proposed computational algorithm is illustrated by an application to the problem of bearing-only simultaneous localization and mapping.