測地観測量網平均汎用プログラムの改良(ΣV=0の解を可能に)

抄録

This report is a continuation of two reports[1, 2] published previously.
An arbitrary geodetic network has been adjusted strictly on the surface of a reference ellipsoid by using the Universal Program, whose program name is TO 16 G 4 for the electronic computer NEAC-2206 in the Geographical Survey Institute. It was necessary until now that the position of a station is given at least as a known station in a network.
The Universal Program has been improved so as to be available in a case such as all stations are unknown, too. In such a case Σp_iv_i² = min. is solved under conditions nΣi=1N_icosψ_iδλ = 0, nΣi=1M_iδψ_i = 0, where p_i and v_i are the weight and the small correction of individual observed value, M_i and N_i are the radii of curvature in meridian and prime-vertical at a station P_i (longitude = λ_i East +, latitude = ψ_i), δλ_i and δψ_i are the small corrections of λ_i and ψ_i. If we give known old values of the station P_i to λ_i and ψ_i, (N_i cos &psi_i;δλ_i, M_iδψ_i) is a displacement-vector V_i for a period from old survey to new survey. The solution of ΣV = 0 is found by means of another computation process that is not so elegant as the method above, too. It is the method that we give a station in a network its old known position and perform the computation of net-adjustment and find an average displacement-vector and subtract it from individual displacement-vector. Fig. 1 is a same geodetic network used in [1] for the purpose of explainning concretely the Universal Program. These two solutions are tested on the network. Input data in the latter method in that the position of a station P4 is known is shown in the first _??_, and other input data in the elegant former method by that solution of ΣV = 0 is obtained directly is shown in the second _??_. The difference between these two input data is that there are known stations or there are not known stations in them. The results of the two methods are shown in Table I. The values in the brackets in Table I are found briefly by additional manual computation. Perfect coincidence of two results proves that the Universal Program has been improved without making a mistake.