Density trees for efficient nonlinear state estimation

In this paper, a new class of nonlinear Bayesian estimators based on a special space partitioning structure, generalized Octrees, is presented. This structure minimizes memory and calculation overhead. It is used as a container framework for a set of node functions that approximate a density piecewise. All necessary operations are derived in a very general way in order to allow for a great variety of Bayesian estimators. The presented estimators are especially well suited for multi-modal nonlinear estimation problems. The running time performance of the resulting estimators is first analyzed theoretically and then backed by means of simulations. All operations have a linear running time in the number of tree nodes.