AN EXACT SOLUTION TO A PROBLEM IN POSITIONING

Myron C. Young

Peer Reviewed

Abstract: In this paper a new technique is developed which yields an exact solution to the position location problem in three dimensions. 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 relative to each of the transponders in the array. System operation is dependent upon a sequential interrogation of, or by, the array to produce simultaneous 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 ambiguities arise, nor need be resolved, in the course of the solution and the results are exact in as much as the range measurements used are exact. Numerical results are presented for the sensitivities of both transponder coordinates and interrogator coordinates to variations in the range measurements. 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.
Published in: NAVIGATION, Journal of the Institute of Navigation, Volume 20, Number 4
Pages: 346 - 356
Cite this article: Young, Myron C., "AN EXACT SOLUTION TO A PROBLEM IN POSITIONING", NAVIGATION, Journal of The Institute of Navigation, Vol. 20, No. 4, Winter 1973-1974, pp. 346-356.
Full Paper: ION Members/Non-Members: 1 Download Credit
Sign In