The impact of acoustic signal models on time-difference-of-arrival/frequency-difference-of-arrival 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 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 paper 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: WSS Gaussian process is widely used as a valid model in the acoustic case, but is not usually appropriate in the electromagnetic case. Although the received signal equations may look identical (showing delay and Doppler shift), the resulting Fisher information, Cramer-Rao bound, and maximum likelihood estimator (MLE) are fundamentally different for the two signal scenarios. Thus, we show that there are distinct structures in processing and bounds that arise specifically due to using models appropriate for acoustic signals.