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The Dependence of Aggregation in the Determination of Optimal Sensor Configurations for Source Localization

The focus of this article is to study methods for information-based planning of sensor configurations for use in source localization. Given a bounded region of interest, for each individual (plausible) source location, we define a performance measure as a scalar function (determinant) of the Fisher information matrix, which depends on the sensor-source geometry. This has been shown to be a useful measure of the localization performance of a given configuration of sensors. To establish a scalar numerical objective for optimizing the sensor configuration (for deployment of sensors), these measures must be aggregated over all the possible source locations. In this article, we study a variety of potential aggregation approaches through the generalized mean family of functions, which subsumes all common means, such as geometric, arithmetic, and harmonic means. We construct several examples, and show for bearings-only sensor schemes that there is a strong relationship between the choice of aggregation function and the structure of the optimal configurations, even with the assumption of a range-independent covariance structure. However, for two other sensor schemes for source localization, range-only and time difference of arrival, there is little or no effect on the optimal configuration as the aggregation is varied, when the covariance is range independent.