Joint TDOA, FDOA and differential Doppler rate estimation: Method and its performance analysis

Abstract

Considering the estimation accuracy reduction of Frequency Difference of Arrival (FDOA) caused by relative Doppler companding, a joint Time Difference of Arrival (TDOA), FDOA and differential Doppler rate estimation method is proposed and its Cramer-Rao low bound is derived in this paper. Firstly, second-order ambiguity function is utilized to reduce the dimensionality and estimate initial TDOA and differential Doppler rate. Secondly, the TDOA estimation is updated and FDOA is obtained using cross ambiguity function, in which relative Doppler companding is compensated by the existing differential Doppler rate. Thirdly, differential Doppler rate estimation is updated using cross estimator. Theoretical analysis on estimation variance and Cramer-Rao low bound shows that the final estimation of TDOA, FDOA and differential Doppler rate performs well at both low and high signal–noise ratio, although the initial estimation accuracy of TDOA and differential Doppler rate is relatively poor under low signal–noise ratio conditions. Simulation results finally verify the theoretical analysis and show that the proposed method can overcome relative Doppler companding problem and performs well for all TDOA, FDOA and differential Doppler rate estimation.