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Optimal sensing matrices

Location information is of extreme importance in every walk of life ranging from commercial applications such as location based advertising and location aware next generation communication networks such as the 5G networks to security based applications like threat localization and E-911 calling. In indoor and dense urban environments plagued by multipath effects there is usually a Non Line of Sight (NLOS) scenario preventing GPS based localization. Wireless localization using sensor networks provides a cost effective and accurate solution to the wireless source localization problem. Certain sensor geometries show significantly poor performance even in low noise scenarios when triangulation based localization methods are used. This brings the need for the design of an optimum sensor placement scheme for better performance. The optimum sensor placement optimizes the underlying Fisher Information Matrix(FIM) . This thesis will present a class of canonical optimum sensor placements that produce the optimum FIM for N dimensional source localization (N ≥ 2) for a case where the source location has a radially symmetric probability density function within an N dimensional sphere and the sensors are all on or outside the surface of a concentric outer N dimensional sphere. While the canonical solution that we designed for the 2D problem represents optimum spherical codes, the study of 3 or higher dimensional design provides great insights into the design of measurement matrices with equal norm columns that have the smallest possible condition number.