Geodetic positioning at sea

Recent accuracy requirements for navigational positioning at sea are such as to require the refinements of recent and past geodetic methods. The computational adjustment method, of this paper, is the technique of variation of parameters. All computations are performed directly on the surface of a reference ellipsoid, so as to preclude any distance restrictions. The methods presented are primarily for use with observations from electronic positioning systems of ranging (circular), and time or phase difference (hyperbolic) type. A new type of observation equation is presented which, when used with a hyperbolic system, results in the first non-iterative solution to the positioning problem. When redundant observational data is obtained, as is frequently the case, full use should be made of the data by using weighted observation equations. Through the use of the new equations, all electronic surveying observations can be processed simultaneously, in real time, with an electronic computer. A continuing error analysis, in the form of a variance-covariance matrix for both the observed and adjusted values, provides system error analysis and diagnoisis.