Date of Award


Degree Name

Doctor of Philosophy


Electrical and Computer Engineering

First Advisor

Dr. Ikhlas M. Abdel-Qader

Second Advisor

Dr. Bradley J. Bazuin

Third Advisor

Dr. Abiola Akanmu


Bregman divergence, PIIN, KNN, Wi-Fi, fingerprint, KLnrg


Indoor positioning systems (IPS) have been the subject of intense academic and industrial research due to the significance of such systems in a wide range of applications. Applications of IPS include indoor navigation and its associated user services, especially by users in large complex buildings, by emergency healthcare services to locate a patient, and people with vision impairments. IPS can also play an important role in other applications that require tracking and observation, such as those used in care for the elderly or security purposes. Therefore, much research has been focused on IPS methods that fingerprint the Received Signal Strength (RSS) of the wireless local area network (WLAN) in indoor environments, the outcome of which has resulted in a positioning accuracy of close to a 1 meter.

This dissertation presents a framework based on fingerprinting maps for indoor positioning systems along with the implementation and testing results. for each technique that was investigated under this framework. This work focuses on Bregman divergences, which are a generalized form of the well-known Kullback-Leibler divergence, suited for convex functions. Since the square root of averaging KL divergence (Jensen-Shannon divergence) is a metric parameter, a framework that iii incorporates the probabilistic neural network (PNN) with Jensen-Shannon Divergence (JSD) is proposed. Based on this framework, I also investigated the Jensen-Bregman Divergence (JBD). JBD is induced by a strictly convex function generator that unifies the celebrated information-theoretic Jensen-Shannon divergence with the squared Euclidean and Mahalanobis distances. JBD is used to calculate distance by focusing on dissimilarity between classes for a reliable and accurate IPS. The proposed system was implemented and simulated in the College of Engineering and Applied Sciences at Western Michigan University. To compare and allow for validation of the proposed framework, implementation and simulations of the multivariate Kullback-Leibler divergence (KLMVG) under the Probability Neural Network (PNN) scheme and under the k-Nearest Neighbors (k-NN) technique were performed.

Access Setting

Dissertation-Open Access