An Algorithm for the Tri-Station TDOA Location Based on local reference Coordinate System

This paper aim at the situation of many solutions and selection ambiguity in the calculation process of traditional algorithm for tri-station TDOA (time difference of arrival) three-dimensional location. The algorithm of tri-station TDOA three-dimensional location for sea level or near earth targets using aerial base platforms is studied. Based on the high precision WGS-84 earth ellipsoid model, building a local reference coordinate system based on the coverage area of the aerial base stations is presented. In this coordinate system, the unknown coordinate dimension of target in three-dimensional rectangular coordinate system in the TDOA equation is reduced by coordinate conversion and approximate process. As a result, the tri-station TDOA three-dimensional location of target can be accomplished according to the traditional TDOA location algorithm for two-dimensional target using two base stations. And the solving, judge and solution selection in this algorithm is easier compare with the traditional algorithm for tri-station TDOA three-dimensional location. Besides, the consistency of the calculation results in this algorithm can be guaranteed. And then the precision of the location calculation results can be further improved by iteration operation. The location results of target in the geocentric coordinate system can be obtained by coordinate inverse conversion (linear conversion). The problem of many solutions and selection ambiguity existing frequently in calculation process of traditional algorithm for tri-station TDOA three-dimensional location can be resolved for the target area which we concerned, owing to that solving quartic equation can be avoided in this algorithm, the geometric meaning of each coordinate component is obvious and solution selection is quite easy. Besides, this method does not need other auxiliary measurement information such as measuring azimuth. The situation of errors in solution selection does not exist in the simulation operation. And the simulation results also show that the algorithm can satisfy the demand of application.