Aggregation Effects on Optimal Sensor Network Configurations with Distance-Dependent Noise

Optimizing sensor placement for the accurate localization of an uncertain source is crucial for a variety of distributed sensor network applications. To handle the uncertainty of the source locations, objective functions are typically written as an aggregation over a variety of plausible source locations. While prior research has explored how the resulting optimized sensor configurations correspond to the optimization over different objectives and various aggregations, the combined impact of both a complex noise environment and the choice of aggregation function for handling source uncertainty remains largely unexplored. This paper investigates this critical interplay. We demonstrate that incorporating distance-dependent environmental noise models reveals a strong dependence of the optimal sensor configuration on the aggregation method. This dependence affects diverse sensor types in differing ways, and this distinction is illustrated by examining both bearings-only and range-only sensors. We develop computational strategies for finding optimal configurations for each of these sensor types, and illustrate their distinctive features through canonical example problems for each type. The results underscore the importance of carefully considering both the environmental complexity and the aggregation approach when employing robust and reliable localization systems in practical applications.