Research on the optimization design of GPS control network Liu Lilong, Lin Wenjie (Civil Engineering College, Guilin, Guangxi 541004), the reliability index, accuracy index and funding index, the criterion matrix of the optimization network is constructed, and the control network optimization design is established Mathematical models, including cost, unknowns and eigenvalues ​​as objective functions. By optimizing the design of a control network and using Monte Carlo method, in the design of GPS control network, the mixed mode of edge points is an ideal model.
Fund Project: The optimization design of the control network funded by the National Natural Science Foundation of China (49771066) is an ancient proposition. Many surveyors have conducted useful exploration and research on this, but due to the limitation of computing tools, it once stagnated. With the rapid development of computer technology, EWGrafaiend put forward the optimization problem of measurement control network (conventional network) in the 1980s, which caused widespread concern in the measurement industry. It was one of the hot topics in the measurement industry and made some important research results. . However, there are many differences between the GPS network and the conventional network. This article will discuss the optimal design of the GPS control network.
1 Design index of GPS control network Efficiency index 112. If the total number of GPS network points is n and m receivers are used for synchronous observation, then the minimum number of observation periods of the network is R if repeated station setting rate, and the minimum number of observation periods is set The actual number of observation periods is S, and the efficiency index of the GPS network is defined as the following total efficiency.
Reliability indicators. For n points in the network, the necessary observation baseline vector parameter is n-1, and the total number of independent observation baseline vectors observed in m receivers during the period, then the redundant observation baseline vector parameter in the network is therefore the average reliability index of the entire network can be defined as follows Accuracy index. The weighted average value of a network's observation before and after network adjustment can reflect the accuracy benefit brought by GPS network strength. Therefore, the following precision index funding indicators can be defined. The cost depends on the total number of midpoints in the network and the rate of repeated stations. If the average cost of a receiver's observation period is 1, the total cost is 2 criterion matrix. The actual error in the construction of GPS receivers can be expressed by the following formula. The median error is%, then the weight of the baseline edge is an indirect adjustment as an example, then the observation error equation is the point accuracy matrix. If there are n points in the network, the possible edges of the entire network are n (n ― 1) / 2, then N on (symmetry) and Pj is the weight of the side length from point i to point j. At that time, Pj = 0. 3 The mathematical model for optimal design was established with the cost as the objective function . When the control network has proposed accuracy requirements for network construction, the cost of network construction should be used as the objective function. If the cost of observing a baseline is Ci, the total cost should be the smallest with cost as the objective function, that is, it should be expressed as an optimization variable.
Take the unknown function as the objective function. In engineering control networks, accuracy requirements are usually imposed on certain quantities in the network, which are functions of unknown numbers.
If the unknown function is set, the cofactor of the unknown function is set to Qxx, and the objective function of the covariate of the unknown function with the weight as the optimization variable is generally required in the construction of the network. The unknown function cofactor Qff When the unknown cofactor is used When used as an objective function, use the following formula to calculate q. * ③ Take the eigenvalue as the objective function. The eigenvalues ​​of the coefficient matrix of the adjustment parameter method equation as digital indicators reflect the overall nature of the control network. Let the size of the feature values ​​be arranged as: Vl>; V2>,> The arithmetic mean variance is the geometric mean variance is the intrinsic variance is the variance width is 1 to 1 /, the variance ratio is when Da = 0 or Dc = 1 The accuracy of all unknown parameters is absolutely uniform. The larger the value, or the smaller the Dc value, the more uneven the accuracy of the unknown parameters. Zhou Zhongmo, Yi Jiejun and Zhou Qi. GPS satellite measurement and application.
Beijing: Surveying and Mapping Press 1997. Beijing: Surveying and Mapping Publishing House 1995. Yu Laifa. On the optimization of GPS precision engineering measurement technology. Surveying and Mapping Bulletin Gao Beichen. Two optimization methods for GPS baseline network observation schemes. Zhou Qiusheng, Sichuan. Optimized design of measurement control network. Beijing: Surveying and Mapping Press, Zhou Chenggao, Liao Yuan. Optimization methods and program design. Beijing: China Railway Press 1989.
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