Fractional lower-order statistics-based ambiguity functions for differential delay Doppler estimation

The problem of estimation of differential-delay Doppler in an environment in which the signal of interest is embedded in highly impulsive interference is addressed. A signal model is formulated with wide applications in radar, sonar, communications and biomedicine and the construction of a new ambiguity function is proposed which is based on the recently-developed concepts of fractional, lower-order statistics and is, therefore, resistant to the presence of severe outliers in the observed time series. The performance of the proposed differential-delay Doppler estimators is theoretically analysed, verified via Monte Carlo simulation, and compared to the performance of traditional, second-order statistics-based estimators