Signal models for TDOA/FDOA estimation

Much research has been done in the area of estimating time-difference-of-arrival (TDOA) and frequency-difference-of-arrival (FDOA) and their use in locating a radiating source. Early work in this area was focused on locating acoustic sources using passive sonar processing. Only later was TDOA/FDOA-based location considered for the case of passively locating electromagnetic sources. As a result of this, it is tempting to use results derived for the acoustic case when answering questions about the electromagnetic case. This correspondence shows that such borrowing can lead to incorrect results. The key factor that drives the significant differences between these two cases is the difference between the signal model assumptions for the two cases: wide-sense stationary (WSS) Gaussian process in the acoustic case and a deterministic signal in the electromagnetic case. Although the received signal equations may look identical (showing delay and Doppler shift), the resulting Fisher information, Cramer-Rao bound (CRB), and maximum likelihood estimator (MLE) are fundamentally different for the two signal scenarios.