Analytical solution of the Time Difference Of Arrival method with known target altitude

This article is focused on analytical solution of the target position computing in passive systems using the Time Difference Of Arrival (TDOA) method where the altitude (or Height) above the see is known (TDOAH). Passive surveillance systems using TDOA may be divided into 2-D three positional and 3-D four positional where analytical solution are known. Despite this fact the most task solved in practice is TDOAH in both cases especially for long range electronic intelligence (ELINT) where the target height measuring by 3-D TDOA is inaccurate. This task may be solved with using of iterative method but using of analytic method gives direct solution, the number of solutions and all possible solutions. Direct solution is free of errors given by iterations and possible divergences. Analytic solution gives better conditions for position error estimation and singularity analysis. In this paper is TDOAH method derived and presented on example.