Wideband TDOA/FDOA processing using summation of short-time CAF's

A commonly used method of calculating TDOA and FDOA is the cross ambiguity function (CAF). The narrowband model assumes that the Doppler is constant over the bandwidth of the signal. When time companding, caused by relative motion, becomes large enough, the CAF performance is degraded. One method of compensation is to resample the signal, but this can be computationally intensive, especially if there is a wide range of time companding. A second method is to reduce the time the CAF is computed over, but the processing gain is reduced. If the short-term CAFs are recombined after the time companding has been compensated, much of the processing gain can be recovered. In this paper, three novel methods of recombining short-time CAFs are developed and analyzed. The first method is to estimate the TDOA and FDOA for each short-time CAF. The second method is to compensate and noncoherently add the CAFs together. This improves the peak detection over the first method but not the TDOA and FDOA accuracy. The third method is to compensate for both time and phase and then coherently add the short-time CAFs together. This last method improves the FDOA accuracy over the first two methods. The effects of sampled data and frequency dual are analyzed. Simulation results are provided to verify analytical results.