大地控制網最佳化設計

Abstract

本文主要在求解大地控制網一、二級最佳化設計問題，以推導之數學模式 同時來求解網形結構(一級網設計)及網形觀測計劃(二級網設計)之最佳化 設計。經由輸入網形點位座標最大可能位移範圍和所有觀測量(含距離、 方位角)最大有效精度，利用目標函數■，所推導之數學模式來求出最佳 之A、P矩陣，而得到網形點位最佳位移量，及觀測量最佳觀測權，以便於 野外選點之參考及各種測量儀器選用之標準。可在外業未施行前，先預知 網形之結構及作為各項觀測工作計劃之依據，以節省人力、物力，而能達 到最佳化之網形精度要求。 This paper deals with the optimization design of geodetic networks. The developed mathematical modelling solves for both an optimal network configuration(First Order Design) and an ptimal observational plan(Second Order Design)simultaneously. The input information includes amount of the maximum possible coordinate shifts for each network point, and all the possible observables together with the maximum available observational precisions. We can derive mathmatical modelling which to solve for both A and P matrix of optimization from objective function ■. The optimally solved for coordinate shifts and observational weigrts of network are used as a guide-line for the choice ofnstrumentation and field operation procedures. The results of optimization enable us to make decisions on which instruments should be selected from the various geodetic instruments should be selected from the various geodetic instruments and where they should be located in order to estimate the unknown parameters and achieve the desired precision derived from and determined by the purpose of the network.