Target parameter estimation using measurements acquired with a small number of sensors

A performance prediction procedure is developed and applied to the evaluation of a passive tracking technique intended primarily for the localization of targets in the near field or vicinity of the sensors. The analysis is sufficiently general to be applied to underwater and air acoustics, passive radar, and electromagnetic direction finding systems. Since near field applications are of primary concern, localization parameter identifiability with a single pair of omni-directional sensors is established with the aid of the Fisher Information Matrix (FIM). The Fisher Information Matrix is also used to determine upper bounds on localization performance, and the corresponding uncertainty ellipses associated with target position are evaluated for various tracking scenarios and types of measurements. Emphasis is placed on the use of measurements such as time difference of arrival and frequency difference of arrival obtained with two sensors, and frequency estimates obtained with a single sensor. It is shown that under certain conditions the time difference of arrival measurements yield full localization information, even though the conditioning can be marginal. Additional measurements, such as frequency, are shown to improve localization performance significantly. Bearing measurements obtained with a closely spaced cluster of a few sensors are also considered.