Using multi-position interferometry to determine the position of objects

An accurate analytical solution for positioning technologies based on both the difference of distances from the object to reference points (TDOA) and the distances themselves (TOA) is considered. The bijection of the obtained coordinate transformation allows reducing the problem of hyperbolic positioning to the Cartesian coordinate system. It is shown that all localization systems of the same rank with different numbers of sensors reduce to a single canonical form with a fixed number of (virtual) sensors corresponding to the dimension of space plus one. The resulting solution allows us the simultaneous observation of many objects, both close and distant, with determination of the distance to them. The possibilities of using positioning systems with a reduced rank have been analyzed. The synthesis of a sensor system with a higher rank from several separate systems is considered. Algorithms for solving the problem are linear and allow direct reconstruction of the image of objects