Explicit (Noniterative) Loran Solution

Abstract

The main computational requirement for LORAN navigation systems is the transformation to geographic latitude and longitude of time difference measurements made by the LORAN receiver. It is desirable to maintain a computational accuracy of less than one second of arc to avoid degradation of the inherently attainable LORAN system accuracy. It is therefore necessary to take into account the effect of a non-spherical earth (ellipticity correction) and variable velocity of propagation (secondary phase correction.) Incorporation of these corrections into the analysis results in two non-linear equations in two unknowns. This paper presents a derivation and discussion of an explicit, noniterative, LORAN mechanization of very high accuracy (approximately one second of arc). The advantages of this explicit solution are as follows: 1. No initial guess as to receiver position is required. This provides for a self-sufficient LORAN system. 2. Perfect computational repeatability is achieved. 3. With the explicit solution, it is always possible to select the proper solution of the two possible solutions. 4. The simple explicit equations lead to reduced computational time and memory storage requirements for the computer. This technique has been programmed on the RECOMP III Computer. It was tested for accuracy by comparison with the National Bureau of Standards computations [2] for the East Coast LORAN Net. Representative samples of the results are given.