A cross-spectral variation of the cross-ambiguity function

We present a new cross-spectral variation of the Cross-Ambiguity Function (CAF) and demonstrate use of the CS-CAF in obtaining improved Frequency Difference of Arrival (FDOA) estimates. Unlike the conventional CAF process that estimates the FDOA of two signals received by moving receivers, as approximately constant over a short observation time, the CS-CAF models FDOA as a slowly varying continuous function. Under the CS-CAF model, we apply cross-spectral estimation methods to estimate and track the instantaneous FDOA of the received signals. This has two important advantages. The cross-spectral frequency estimation methods are extremely accurate, and by modeling the FDOA as a continuous function of time, we resolve the issue of assigning an event time to the estimated FDOA. In addition, by recovering an FDOA component from the received signals, we may apply LaGrange interpolation to track the instantaneous phase of the FDOA component, enabling an even more accurate estimate of instantaneous FDOA.