Frequency difference of arrival (fdoa) for geolocation

A system for determining a frequency difference of arrival (FDOA) with respect to a pulsed waveform emanating from a remote emitter, comprising:

• at least two spaced apart sensors disposed on a moveable platform, each of the at least two sensors adapted to receive the pulsed waveform from the remote emitter;
• a respective receiver channel in communication with each of the at least two sensors, the respective receiver channel configured to provide a respective plurality of in-phase and quadrature-phase (IQ) samples indicative of a pulse envelope of the received pulsed waveform, the pulsed waveform comprising a plurality of pulses;
• a time difference of arrival (TDOA) detector configured to determine an approximation of a TDOA responsive to IQ samples indicative of a leading edge of a common sampled pulse of the pulsed waveform;
• a cross correlator configured to obtain for each pulse of the plurality of pulses, a first complex cross correlation of IQ samples at a delay (dc) closest to the approximation of the TDOA, and respective second and third complex cross correlations at least one additional delay (dc+1 and dc−1) on either side of the closest delay;
• a phase processing module in communication with the cross correlator, the phase processor configured to determine for each pulse of the plurality of pulses, a respective rate of change of cross-correlation phase (Δφ);
• and
• a FDOA processing module in communication with the phase processing module, configured to determine FDOA as a slope of a straight line approximation of the rates of change of cross-correlation phase (dΔφ/dt) determined for the plurality of pulses.

A system for determining a frequency difference of arrival (FDOA) with respect to a pulsed waveform received from a remote source by two spaced apart sensors located on a moveable platform, comprising:

• means for obtaining for each sensor, a respective plurality of in-phase and quadrature-phase (IQ) samples indicative of a pulse envelope of the received pulsed waveform, the pulsed waveform comprising a plurality of pulses;
• means for determining an approximation of a time difference of arrival (TDOA) responsive to a leading edge of a common sampled pulse of the pulsed waveform;
• means for obtaining for each pulse of the plurality of pulses, a first cross correlation of IQ samples at a delay (dc) closest to the approximation of the TDOA, and respective second and third cross correlations at least one additional delay (dc+1 and dc−1) on either side of the closest delay;
• means for refining for each pulse of the plurality of pulses, the approximation of the TDOA according to an interpolation of amplitudes of the cross-correlation;
• means for determining for each pulse of the plurality of pulses, a respective rate of change of cross-correlation phase (Δφ);
• and
• means for determining a FDOA as a slope of a straight line approximation of the rates of change of cross-correlation phase (dΔφ/dt) determined for the plurality of pulses.