On the Use of a Calibration Emitter for Source Localization in the Presence of Sensor Position Uncertainty

Sensor position uncertainty is known to degrade significantly the source localization accuracy. This paper investigates the use of a single calibration emitter, whose position is known to the sensor array, to reduce the loss in localization accuracy due to sensor position errors that are random. Using a Gaussian noise model, we first derive the CramÉr–Rao lower bound (CRLB) for a time difference of arrival (TDOA)-based source location estimate with the use of a calibration source. The differential calibration technique that is commonly used in Global Positioning System through the use of a calibration source to mitigate the inaccuracy in satellite ephemeris data is analyzed. The analysis indicates that differential calibration in most cases cannot reach the CRLB accuracy. The paper then proceeds to propose an algebraic closed-form solution for the source location estimate using both TDOA measurements from the unknown and the calibration source. The proposed algorithm is shown analytically, under high signal-to-noise ratio (SNR) and small sensor position noise, or under moderate level of SNR and sensor position noise together with distant unknown and calibration sources, to reach the CRLB accuracy. Simulations are used to corroborate and support the theoretical development.