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A method for nonlinear conjugate scales in a multi-position radar system with ambiguous range measurements

In this work, a two-dimensional analytical model of a multi-position radar system with ambiguous range measurements is elaborated and tested. In the proposed analytical model, properties of ambiguous measurements of fractional parts of relative unambiguity intervals in each radar are determined. Theorems are formulated defining the conditions of the unambiguous mapping of a target’s coordinates onto the aforementioned fractional parts, as well as a reverse unambiguous mapping of those fractional parts onto a two-dimensional vector of integers. The vector contains ranges from the target to pairs of radars composing the considered system. The theorems are based on a principle of mapping the measurements of fractional parts onto a multidimensional unit cube, and the interpretation of the total set of measurements as a multilayer structure of this cube. Moreover, each layer is a multidimensional hypersurface bounded by the cube faces, and the unambiguity conditions are reduced to the conditions that these layers do not intersect with each other. Based on the developed model and the formulated theorems, an algorithm is proposed for disclosing the ambiguities of the fractional parts mentioned, as well as for obtaining unambiguous estimates of the target coordinates. An example of a multi-position radar system and results of modeling chosen elements of the algorithm for disclosing ambiguities are also presented. The aims of further research are formulated, particularly regarding the synthesis of multiposition radar systems and the elaboration of an analytical model for systems for the localization of emission sources of periodic radio signals.