Direct positioning maximum likelihood estimator using TDOA and FDOA for coherent short‐pulse radar

Abstract

The intra-pulse phase change caused by frequency difference of arrival (FDOA) is very little and even omitted due to extremely short duration of emitter pulses that the joint location using time difference of arrival (TDOA) and FDOA cannot be realised. To solve this problem, a multi-pulse coherent accumulation algorithm of direct position determination (DPD) using the TDOA and FDOA is proposed in this study. Through establishing coherent signal model of short pulses which is deterministic but unknown, the maximum likelihood estimator for localisation of a stationary emitter using multiple moving receivers is derived by taking the DPD approach under additive Gaussian white noise environment. This study also derives a signal-specific Cramer-Rao lower bound (CRLB) of DPD, modelling the signal as a deterministic unknown. The CRLB is more applicable to some specific (non-stationary, non-Gaussian) signals, especially electromagnetic signals. Simulation results show that the proposed method achieves a significant performance improvement in locating accuracy over the existing methods and its accuracy is close to the CRLB in normal signal-to-noise ratio.