Optimal placement of multiple sensors for localization applications

Indoor localization systems are usually based on distributed sensors. The sensor output is thereby converted into a distance or angle measure in order to estimate a target´s position via triangulation or trilateration. For such systems, the localization error on the one hand depends on the quality of the sensor measurements and on the other hand on the sensor placement. In this paper, the problem of optimally placing a minimum number of distributed sensors to fulfill and optimize task requirements is addressed. It is shown how adequate task requirements can be stated for different types of sensor systems by exploiting the Geometric Dilution of Precision (GDOP). Using these requirements, the problem can be formulated in a discrete and continuous search space. The discrete formulations are presented and evaluated using Binary Integer Programming (BIP) and Mixed Integer Programming (MIP) solver. In contrast, the continuous formulation is briefly described and evaluated using Nonlinear Programming (NLP) methods. Both approaches are evaluated with respect to their solvability, runtime and quality. To find solutions for the NP-hard placement problem in reasonable time even for large problem sizes, a new approximation heuristic is introduced. Its worst case solution quality is derived and its solutions are compared to the optimal placements. All evaluations are done using the properties of a visual sensor system that exploits the thermal infrared radiation of humans for indoor localization.