Posterior Cramér-Rao lower bound for mobile emitter tracking based on a TDOA-FDOA multi-measurement model

Tracking a mobile radio emitter in a high clutter environment with low signal to noise ratio is a challenging task due to high miss detection and false alarm rates in the joint time difference of arrival (TDOA) and frequency difference of arrival (FDOA) estimation procedure. To increase the probability of detection, multiple TDOA-FDOA measurements from a number of peaks in the cross ambiguity function (CAF) are collected. In this paper, the posterior Cramér-Rao lower bound (PCRLB) based on such a multi-measurement model is derived. Different hypotheses are assigned to the measurement set and the prior probability of each hypothesis is defined. The Fisher information matrix (FIM) is computed based on the likelihood of a combination of all these hypotheses. As such, the proposed PCRLB is able to take the information from miss detection and false alarm as well as the target into account. It is therefore more accurate and more attainable than the bound derived from the single measurement extracted from the largest peak of the CAF. Tracking performance via particle filtering is employed to validate the derived performance bound.