Approximate maximum likelihood time differences estimation in the presence of frequency and phase consistence errors

In passive location systems using time differences of arrival (TDOA) measurements, in order to digital processing, the received radio frequency (RF) signals are usually down-converted to baseband. In down-conversions, oscillators are used to mix the signals-of-interest to baseband. Frequency and phase consistence error between two oscillators degrade the performance of TDOA estimation between two sensors. Considering the oscillator consistence errors, the modified baseband data model of time delay estimation is presented. Next, the approximate maximum likelihood (AML) TDOA estimator based modified model is proposed to reduce the TDOA estimation error. Furthermore, two simplified versions of AML estimator are also developed, which include the two-dimensional (2D) search and one-dimensional (1D) search AML methods. Simulation results confirm the performance of these estimators.