Comparison of Objectives in Multi-Objective Optimization of Ultrasonic Positioning Anchor Placement

The position of anchors in an ultrasonic positioning system has a significant impact on the performance of that system. This impact on performance can be in the form of positioning error, how large of a space the system can cover, and then number of anchors required. A comparison of three different performance metrics for anchor position optimization in ultrasonic localization systems is presented. These metrics are geometric dilution of precision (GDOP), weighted GDOP (WGDOP), and simulated localization error (SLE). Each of these performance metrics is used as an objective in a multi-objective genetic algorithm. The optimal solutions found by the genetic algorithm were processed by a simulation that used a simulated received time series to localize the target position allowing a direct comparison of the three performance metrics. While the performance difference between all three metrics was small, it was found that solutions generated using WGDOP as a metric of performance outperformed those generated using the GDOP and the SLE objectives.