Sensor placement determination for range-difference positioning using evolutionary multi-objective optimization

• Sensor placement according to different performance measures obtained from the CRLB.
• The proposed approach is valid for different positioning technologies.
• Simulations are performed for an infrared positioning system used as example.
• The examples obtain sensor placements using two and three objectives.
• We show the relevance of the multiobjective optimization analyzing the Pareto fronts.

This paper focuses on the application of a decision support system based on evolutionary multi-objective optimization for deploying sensors in an indoor localization system. Our methods aim to provide the human expert who works as the sensor resource manager with a full set of Pareto efficient solutions of the sensor placement problem. In our analysis, we use five scalar performance measures as objective functions derived from the covariance matrix of the estimation, namely the trace, determinant, maximum eigenvalue, ratio of maximum and minimum eigenvalues, and the uncertainty in a given direction. We run the multi-objective genetic algorithm to optimize these objectives and obtain the Pareto fronts. The paper includes a detailed explanation of every aspect of the system and an application of the proposed decision support system to an indoor infrared positioning system. Final results show the different placement alternatives according to the objectives and the trade-off between different accuracy performance measures can be clearly seen. This approach contributes to the current state-of-the art in the fact that we point out the problems of optimizing a single accuracy measure and propose using a decision support system that provides the resource manager with a full overview of the set of Pareto efficient solutions considering several accuracy metrics. Since the manager will know all the Pareto optimal solutions before deciding the final sensor placement scheme, this method provides more information than dealing with a single function of the weighted objectives. Additionally, we are able to use this system to optimize objectives obtained from fairly complex functions. On the contrary, recent works that are referenced in this paper need to simplify the localization process to obtain tractable problem formulations.