Improved technique for calibration of transponder arrays used in positioning applications

In this paper a new technique is proposed for dealing with the transponder calibration problem. The method presented determines the relative location of transponders in a three-dimensional array of transponders fixed relative to one another. The method simultaneously yields the loci of a roving interrogator (ship) relative to each of the transponders in the array. System operation is dependent upon a sequential interrogation of the array to produce relative range measurements between each transponder of the array and the roving interrogator. The method yields closed-form solutions for all transponder coordinates and all interrogator coordinates. No prior knowledge is required in terms of a predetermined interrogator path and all results are exact in as much as the range measurements used are exact. Techniques are indicated for determining the sensitivities of both transponder coordinates and interrogator coordinates to range measurement variations. Effect of interrogator path and transponder geometry on results is discussed and the concept of critical, or singular, geometries, which produce poorly-conditioned solutions, is introduced.