Sequential Monte Carlo Methods with Applications to Positioning and Tracking in Wireless Networks
Abstract: This thesis is based on 5 papers exploring the filtering problem in non-linear non-Gaussian state-space 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 state-space 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 observation-driven sampling. The correlated sampling approach was 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 so-called optimal proposal kernel. As an illustration, the method was applied to optimal filtering in state-space models.
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