Analytical Solution to the Problem of Hyperboloid Intersection for the Direction Finding of Radiation Sources

An analytical approach to finding the intersection points of N hyperboloids in N-dimensional space with euclidean metric is presented, taking into account the location of their foci relative to a selected basis. An important property of hyperboloids has been identified, which allows solving the problem in the case of non-orthonormal bases, gaining significance in the direction finding of radiation sources by the time-difference-of-arrival method.