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Target position estimation in radar and sonar means joint estimation of range and angle in the presence of noise and clutter. The global behavior of a maximum likelihood (ML) position estimator, and the clutter suppression capability of the system, can be written in terms of a range-angle ambiguity function. This function depends upon signal waveform and array configuration, i.e., upon both temporal and spatial characteristics of the system. Ambiguity and variance bound analysis indicates that system bandwidth can often be traded for array size, and direction-dependent signals can be used to obtain better angle resolution without increasing the size of the array. Wide-band direction-dependent signals (temporal diversity) can be traded for large real or synthetic arrays (spatial diversity). This tradeoff is apparently exploited by some animal echolocation systems. The above insights are obtained mostly from the properties of the range-angle ambiguity function. In general, an appropriate ambiguity function should be very useful for the design and evaluation of any ML parameter estimator. System identification methods and radio navigation systems, for example, can be optimized by minimizing the volume of a multiparameter ambiguity function.