Joint Estimation of Time Delay and Doppler Shift for Band-Limited Signals

The standard approach for joint estimation of time delay and Doppler shift of a signal is to estimate the point at which the cross ambiguity function of the original and modified signals attains its maximum modulus. Since band-limited signals can be expressed exactly by their Shannon series, we here consider approximated signals gained by truncating their Shannon series to involve only the sampled signal values. We then estimate the time delay and Doppler shift by calculating a point at which the cross ambiguity function of the approximated signals attains its maximum modulus. This cross ambiguity function has an analytic expression which allows its evaluation at any point, and we may apply Newton's method to calculate accurately and efficiently a point where the maximum modulus is attained. In the numerical experiments we conducted, our method generally outperformed other methods for estimation of both time delay and Doppler shift.