Coherent summation of multiple short-time signals for direct positioning of a wideband source based on delay and Doppler

We consider identifying the source position directly from the received source signals. This direct position determination (DPD) approach has been shown to be superior in terms of better estimation accuracy and improved robustness to low signal-to-noise ratios (SNRs) to the conventional two-step localization technique, where signal measurements are extracted first and the source position is then estimated from them. The localization of a wideband source such as a communication transmitter or a radar whose signal should be considered deterministic is investigated in this paper. Both passive and active localization scenarios, which correspond to the source signal waveform being unknown and being known respectively, are studied. In both cases, the source signal received at each receiver is partitioned into multiple non-overlapping short-time signal segments for the DPD task. This paper proposes the use of coherent summation that takes into account the coherency among the short-time signals received at the same receiver. The study begins with deriving the Cramér–Rao lower bounds (CRLBs) of the source position under coherent summation-based and non-coherent summation-based DPDs. Interestingly, we show analytically that with coherent summation, the localization accuracy of the DPD improves as the time interval between two short-time signals increases. This paper also develops approximate maximum likelihood (ML) estimators for DPDs with coherent and non-coherent summations. The CRLB results and the performance of the proposed source position estimators are illustrated via simulations.