Source localization and calibration using TDOA and FDOA measurements in the presence of sensor location uncertainty

Source localization accuracy is very sensitive to sensor location error. This paper performs analysis and develops a solution for locating a moving source using time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements with the use of a calibration emitter. Using a Gaussian random signal model, we first derive the Cramér-Rao lower bound (CRLB) for source location estimate in this scenario. Then we analyze the differential calibration technique which is commonly used in Global Positioning System. It is indicated that the differential calibration cannot attain the CRLB accuracy in most cases. A closed-form solution is then proposed which takes a calibration emitter into account to reduce sensor location error. It is shown analytically that under some mild approximations, our approach is able to reach the CRLB accuracy. Numerical simulations are included to corroborate the theoretical developments.