Localization Performance of Arrays Subject to Phase Errors

The passive localization of radiating sources using an array subject to random perturbations in sensor phases is presented. All source signals as well as additive noises observed at the sensors are assumed to be independent identically distributed (IID) zero mean Gaussian random processes. Cramer-Rao bounds are derived for source bearings and ranges and for the phase errors at each sensor. It is shown that accurate phase calibration can be achieved when the number of sources exceeds a certain minimum. The locations of the calibrating sources need not be known a priori and need only satisfy mild regularity conditions. Finally an actual calibration procedure is proposed which uses maximum likelihood techniques.