Optimal triangulation in the presence of range errors

Abstract

This paper is essentially a subset of the report NPS-53-84-0008 by I.B. Russak and A. A. Goldstein with modifications made to the proof of the optimality of the three dimensional triangulation. The problem of determining the location of a fixed point using range only data occurs in a variety of areas including military applications. An example is outlined below and formed the incentive for the work herein. The application consisted of precisely locating hydrophones placed on a ship's hull for the purpose of receiving acoustic signals to be used in calculating torpedo positions during a test. In this paper a method is developed which under the assumption of fixed system error input (in range data) produces the smallest possible error in locating the hydrophones.