An algebraic method for moving source localization using TDOA, FDOA, and differential Doppler rate measurements with receiver location errors

To weaken the effect of receiver location error on localization accuracy and make the localization model closer to the practical scenario, this paper considers the receiver location errors, usually neglected in prior studies into the measurement model, and proposes an algebraic method for locating a moving source using time difference of arrival (TDOA), frequency difference of arrival (FDOA), and differential Doppler rate measurements. The proposed method is based on the pseudo-linear set of equations and two-step weighted least square estimator. Only noise values of receiver locations and three types of positioning measurements are available for processing. In addition, a new Cramér-Rao lower bound (CRLB) combining TDOA, FDOA, and differential Doppler rate in the presence of receiver location errors is also derived in this paper. Theoretical analysis and simulation results both indicate that the proposed method can attain CRLB at a moderate noise level, avoid the rank deficiency problem efficiently, and achieve a significant improvement over the existing methods.