Sequential Monte Carlo Methods with Applications to Positioning and Tracking
in Wireless Networks
Svetlana Bizjajeva
Centre for Mathematical Sciences
Mathematical Statistics
Lund University
2008
ISBN 9789162875732
LUTFMS10342008

Abstract:

This thesis is based on 5 papers exploring the filtering problem in nonlinear
nonGaussian statespace models together with applications of Sequential
Monte Carlo (also called particle filtering) methods to the positioning in
wireless networks.

The aim of the first paper is to study the performance of particle filtering
techniques in mobile positioning using signal strength measurements. Two
different approaches for mobile movement (polar and Cartesian) were used,
combined with two different models for the received signal strength. The
results of the simulation study showed better performance for particle filters
based on a power model with varying propagation coefficient. The filters
based on the polar model for mobile movement were found to be more precise
in terms of mean squared error, but at the same time were more computationally
intensive.

The second paper represents the results of a simulation study on mobile
positioning in multiply input multiply output (MIMO) settings. Three different
particles filters were implemented for the positioning, and simulation results
showed that all filters were able to achieve estimation accuracy required
by Federal Communication Commission (FCC). Moreover, since dimensionality
of the particle filter state space does not depend on the antenna configuration,
it is possible to apply described filters in more sophisticated MIMO setup
without changing the algorithms.

In the third paper we investigated an algorithm for particles filtering in
multidimensional statespace models which are decomposable in the states.
We demonstrated using the simulations that the algorithm effectively reduces
the computational time without a large precision loss.

It is known that the quality of sequential Monte Carlo estimation depends
on the number of particles involved. In the paper four we explored different
strategies to increase the number of particles: correlated sampling and
observationdriven sampling. The correlated sampling approach is further
investigated in the fifth paper, where we employed the idea of using antithetic
variates. We introduced a version of the standard auxiliary particle filter
and concluded, based on the theoretical developments, that the asymptotic
variance of the produced Monte Carlo estimates can be decreased by means
of antithetic techniques when the particle filter is closed to fully adapted,
which involves approximation of the socalled optimal proposal kernel. As
an illustration, the method was applied to optimal filtering in statespace
models.










