DIFFERENTIAL DELAY-DOPPLER ESTIMATION USING SECOND-AND HIGHER-ORDER AMBIGUITY FUNCTIONS

Estimation of differential delay-Doppler parameters in passive sonar a nd radar applications is addressed. Without assuming Gaussianity it is shown that the conventional ambiguity function is asymptotically chi- squared and yields consistent delay-Doppler estimates for narrowband s ignals observed in uncorrelated sensor noises. Related asymptotic cova riance expressions and their computable forms are also derived. It is further shown that the performance of the ambiguity function degrades severely when the sensor noises are correlated. To deal with such nois es a novel third-order ambiguity function is proposed and is shown to be consistent and theoretically immune to Gaussian and symmetrically d istributed disturbances. Further, to take into account the errors due to variances of sample statistics, alternative delay-Doppler estimator s are defined to minimise a cumulant matching criterion and related is sues are discussed. The case of wideband signals is also addressed and , finally, extensions to kth-order ambiguity functions are proposed. C omputer simulations are performed to confirm the theory. Throughout th e paper the analysis treats both deterministic and stochastic signals on a common framework. Connections with active sonar and radar problem s are also shown as a special case.