In this paper a multi-static ambiguity function (AF) based on the Kullback directed divergence (KDD) and a distributed multiple-input and multiple-output radar system (DMRS) framework is introduced. Additionally a mathematical analysis is used to derive the AF in terms of signal-to-noise ratios (SNRs) and matched filter outputs. This method manages to extract an upper bound and properly define an AF bounded from 0 to 1. Moreover, this method leads in avoidance of large matrices inversions allowing less complex and more accurate computations. Finally the performance of the proposed method in localisation problems is assessed by comparing the proposed AF with the squared summation of the matched filter outputs at each receiver at different SNR scenarios.
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