Ambiguity Analysis for Multitarget Estimation Using Random Permutated Frequency Diverse Arrays

For multitarget estimation using a frequency diverse array with a random permutated frequency increment (RP-FDA), ambiguity occurs when targets are located at specific locations and the frequency increment vector is not properly designed. To provide guidance for the design of a frequency increment vector to avoid ambiguous estimation, ambiguity analysis, including the principle of ambiguity, the relationship among ambiguity types, the relative target location, and the frequency increment vector, is necessary. In this paper, a relation matrix that describes the targets' relative location is established and analyzed to reveal the principle of ambiguity, that is, the rank deficiency of the relation matrix. Then, a law of relative target locations causing the rank deficiency of the relation matrix and the categories of the relative target locations are developed. Moreover, two cases of the relative target locations causing ambiguity are proposed, which are transformed based on the relative target locations causing rank deficiency. By employing the law of relative target locations causing ambiguity in a frequency increment vector pre-evaluation, more ambiguous frequency increment vectors can be identified compared with the identification using single-target criterion, which improve the unambiguous probability of a multitarget estimation. Numerical simulations verify the effectiveness of the proposed law of a relative target location causing ambiguity and of the rank deficiency examination to avoid ambiguity.