Compressive TDOA Estimation: Cramér–Rao Bound and Incoherent Processing

Estimation of time-difference-of-arrival (TDOA) between a signal and its time-shifted version has many applications, mostly in localization. Because compressive sensing (CS) can reduce the sampling rate and data volume, TDOA estimation from CS samples (CS-TDOA) has become a subject of interest. Generally, CS-TDOA has lower estimation accuracy, and the Cramér-Rao bound (CRB) can quantify this degradation. The first part of this correspondence derives the CRB for CS-TDOA estimation, and the second part proposes an incoherent processing scheme for CS-TDOA estimation using partial Fourier coefficients. This results in the reduction of the number of sampling channels needed to acquire those coefficients. Simulation results are given to corroborate the theoretical development.