Ambiguity in radar and sonar

We introduce a new ambiguity function for general parameter estimation problems in curved exponential families. We focus the presentation on passive and active radar and sonar location mechanisms. The new definition is based on the Kullback (1978) directed divergence and reflects intrinsic properties of the model. It is independent of any specific algorithms used in the processing of the signals. For the active single target problem, we show that our definition is equivalent to Woodward's (1953) radar narrow-band ambiguity function. However, the new ambiguity is much broader, handling radar/sonar problems when there are unknown parameters (e.g., unknown power level in active systems), when the signals are random (e.g., passive systems), when the signals are wideband, or when there are model mismatches. We illustrate the new ambiguity in localization problems in multipath channels.