Reilly, W.I. 1980 Three-dimensional adjustment of geodetic networks with incorporation of gravity field data. : . Report / Geophysics Division 160 46 p.
Abstract: The result of making comprehensive measurements on geodetic networks is the determination at each network point of seven geodetic coordinate parameters: a geocentric position vector (3 parameters), the gravity potential (1 parameter), and the gravity gradient vector (3 parameters). In particular, we choose as the seven scalar quantities to be determined, the Cartesian components (x,y,z) of the geocentric position vector, the gravity potential W, the intensity of gravity g, and the (astronomical) latitude phi and longitude omega. Information on the differential geometry of the gravity fields is introduced in the form of the values of the five independent curvature parameters of the field, calculated at each network vertex from surrounding observations of the intensity of gravity, astronomical latitude and longitude, etc., by the method of least-squares collocation. Expansions are developed for calculating changes in gravity potential W, intensity of gravity g, latitude phi and longitude omega along sides of the network, as functions of the curvature parameters. These expansions are incorporated in the adjustment as pseudo-observation equations along the sides of the network, thus introducing additional gravity field information, and enabling, for instance, the calculation of gravity potential (and thus height) at all network vertices. (auth)
