 
Summary: MAP Estimation in NonLinear NonGaussian Dynamic
Systems
Hans Driessen and Yvo Boers
THALES NEDERLAND
Hengelo, The Netherlands
{hans.driessen,yvo.boers}@nl.thalesgroup.com
keywords: MAP Estimation, Nonlinear Systems, Particle Filtering
Abstract
In nonlinear dynamic estimation problems the minimum variance (MV) and maximum a posteriori (MAP) point
estimates do not coincide in general. Particle Filtering is one of the few techniques wellsuited for keeping track of the
complete posterior density in such nonlinear systems. The MV estimate is easily approximated as the weighted sum of
the particles, until now no fair MAP estimator is available, which hinders any further exploration. This paper presents
the first fair particle based MAP estimator that is applicable in nonlinear systems. It is proven that its estimate
converges to the true MAP estimate for infinitely many particles. The results are illustrated by means of a simulation
example.
1 Introduction
Recursively estimating the state of a stochastic dynamic system is important in many practical problems. Applications
include object tracking, process control, mobile telecommunication and financial market analysis. The Bayesian approach
to this problem is computing the posterior probability density function based on the observed measurements. However
in many applications a point estimate is required for output purposes instead of the complete density. Two commonly
