A Study on the Effects of Sensor Position Error and the Placement of Calibration Emitter for Source Localization

Modern applications use mobile or randomly deployed sensors whose positions are not precise when locating a signal source. An estimator would require statistical knowledge of the sensor position errors to reach the optimum localization performance. Further accuracy improvement necessitates a calibration emitter whose position is known exactly to correct the sensor positions. Under Gaussian error model, this paper shows that when the covariance matrices of the sensor position errors and the measurement noise satisfy certain relation, taking the sensor position errors into account is not necessary and a simpler estimator that pretends the sensor position uncertainties are absent is sufficient to reach the optimum performance. The performance gain from a calibration emitter depends on where it is placed. We derive the optimum calibration position by improving the Fisher information matrix of the source location estimate. The optimum position is of theoretical interest and may not be practical. A suboptimum criterion for realistic calibration emitter placement is then proposed. We shall use TOA, TDOA, and AOA localizations to illustrate the derived results. Simulations support very much the theoretical developments and performance analysis.