Date of Award

Summer 2005

Document Type


Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)


Mathematical Sciences

First Advisor

Manish Chandra Bhattacharjee

Second Advisor

David Madigan

Third Advisor

Sunil Kumar Dhar

Fourth Advisor

Eliza Zoi-Heleni Michalopoulou

Fifth Advisor

Thomas Spencer


Several approaches for indoor location estimation in wireless networks are proposed. We explore non-hierarchical and hierarchical Bayesian graphical models that use prior knowledge about physics of signal propagation, as well as different modifications of Bayesian bivariate spline models. The hierarchical Bayesian model that incorporates information about locations of access points achieves accuracy that is similar to other published models and algorithms, but by using prior knowledge, this model drastically reduces the requirement for training data when compared to existing approaches. Proposed Bayesian bivariate spline models for location surpass predictive accuracy of existing methods. It has been shown that different versions of this model, in combination with sampling/importance resampling and particle filter algorithms, are suitable for the real-time estimation and tracking of moving objects. It has been demonstrated that "plug-in" versions of the bivariate Bayesian spline model perform as good as the full Bayesian version. A combination of two Bayesian models to reduce the maximum predictive error is proposed. Models presented in this work utilize MCMC simulations in directed acyclic graphs (DAGs) to solve ill-posed problem of location estimation in wireless networks using only received signal strengths. Similar approaches may be applied to other ill-posed problems.

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Mathematics Commons