Bayesian Estimation and Tracking: A Practical Guide

16.7 Reducing the Computational Load Through Rao-Blackwellization

In many state estimation applications where the state vector is of high dimensionality, the computational load for a SIS particle filter can become extremely costly and the estimation accuracy may deteriorate rapidly. Particle filter-based methods become quite inefficient when applied to a high-dimensional state space since prohibitively large number of samples may be required to approximate the underlying density functions to the desired accuracy. When the components of the state vector can be subdivided into two classes, one that follows a linear temporal transition and is Gaussian and a second class that is non-Gaussian, then the computational load can be reduced using what is know as Rao-Blackwellization [23–25].

The key idea of the Rao–Blackwell method is a dimensional reduction that makes use of the structure of the models to split the conditional posterior into two separate parts, with the Gaussian part conditioned on the non-Gaussian part. One first uses a particle filter to generate the non-Gaussian posterior and then uses a Kalman filter on the conditioned Gaussian part. Assume that the state vector components can be divided into two groups x_n = [q, r] such that

(16.70)

In Ref. [24] it was pointed out that ...