On Necessary and Sufficient Conditions of Correct Match Despite Both Measurements Noises and Biases in Target-Object Map Problem

This article rigorously studies the target-object map (TOM) problem under the radar and the seeker with measurement errors including both unknown biases and stochastic noises. First, the equivalent bias correction-based match (EBCM) method is proposed without limitations for the size of biases and the number of simultaneously visible targets. Consequently, correct match with respect to expectation (CM-E) of EBCM is rigorously defined. Second, the necessary and sufficient conditions of CM-E are presented in the case that the simultaneously visible targets of two sensors are known. Also, it is shown that CM-E can be achieved under some conditions which are easily verified in practice. In addition, CM-E of EBCM can be proved in the general case for the sets of targets, in which the simultaneously visible targets are unknown. Finally, the simulation results of some typical TOM problems show the high accuracy of EBCM in a single experiment and the significance of eliminating biases to obtain CM-E in multiple experiments.