Multiple disjoint sources localization with the use of calibration emitters

Sensor location uncertainty is known to degrade significantly the source localization accuracy. This paper considers the problem of multiple disjoint sources localization with calibration emitters using time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements. The TDOAs and FDOAs are from unknown sources and calibration emitters. Using a Gaussian noise model, we first derive the Cramér-Rao lower bound (CRLB) for multiple disjoint sources localization with the use of calibration emitters whose locations are also not known exactly. By modeling the calibration location errors as additive Gaussian noise, the amount of reduction in localization accuracy due to calibration location errors is derived through CRLB analysis. The paper then proposes an algebraic closed-form solution for multiple disjoint sources localization using TDOA and FDOA measurements, which are both from unknown sources and calibration emitters. Finally, the algorithm is proved analytically to reach the CRLB accuracy when the sensor and calibration location errors are small. Simulations corroborate the theoretical results and the good performance of the proposed method.