Observability conditions for multiple signal direction finding and array sensor localization

Three observability issues, which arise in narrowband signal direction-finding in the presence of array sensor location errors are described. Necessary and sufficient conditions for the phase delay ambiguity and the rank-2 ambiguity are presented. However, the characterization of the rank-n ambiguity is still an open problem and only a conjecture is given. Barring these ambiguities, the minimal numbers of known and unknown signals required for uniquely localizing the sources and sensors are determined under the assumption of no measurement noises.<
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