Source localization with two dimensional array subject to uncertainty in sensor location

Uncertainty in sensor locations can seriously degrade the localization capability of an array. This paper considers array calibration procedures using auxiliary sources in locations that need not be known a priori. It calculates Cramer-Rao bounds on the attainable accuracy of array geometry as well as on source bearings and ranges. It establishes conditions under which array shape can be established with arbitrary accuracy but shows that a residual error in array orientation is irremovable. This residual error translates into an irremovable error in source bearings, but not in source ranges. The bearing error can be reduced but not eliminated by proper array design. An iterative calibration procedure is proposed which appears capable of achieving errors close to the Cramer-Rao bounds for signal to noise ratios well within the practical range.