On passive TDOA and FDOA localization using two sensors with no time or frequency synchronization

Traditional passive localization based on Time-Difference of Arrival (TDOA) or Frequency-Difference of Arrival (FDOA) usually involves several remote sensors, which require precise time-synchronization and frequency-locking among them. The need for such time or frequency alignment sometimes poses a serious operational challenge on the system. In addition, it is often desired to keep the number of sensors to a minimum. In this work we look into the operationally-simplest scenario in this context: using only two sensors, without any synchronization or locking. When at least one of the sensors, or the transmitting target, is moving at some considerable speed, it is still possible to localize the target, based on a few TDOA and / or FDOA measurements, by considering the time- and frequency-offsets as additional unknown parameters. We analyze the associated performance bound and propose a Maximum Likelihood estimation approach. The attainable accuracy and its dependence on geometry are demonstrated numerically and in simulation.