GPS网平差的多元响应-非线性最小二乘模型及其解的最优化混合算法

在控制网中,用GPS测量,可以同时测得一个点的基线向量,在具有起算数据时可获得观测点的三维坐标等多个响应变量值,将这些响应变量包含的信息综合起来,可以得到参数的更精确的估计。本文针对GPS测量数据为多元响应数据的特点,建立了一个GPS网平差的多元响应-非线性最小二乘模型,针对该模型,结合拟牛顿法和信赖域算法建立了一个新非线性优化的混合算法,该算法具有全局收敛性和超线性收敛性。

Multi-response-nonlinear LS model for adjustment of GPS network and its hybrid algorithm

In GPS network, values of several response variables such as the 3-D coordinates of the observation points can be obtained at the same time.By integrating all the information in the response variables, we can get more precise estimation of response parameters. Considering the multi-response GPS data, a multi-response-nonlinear LS model for adjustment of GPS network is established in this paper. In order to solve the model,combining the quasi-Newton method and the trust region method, a new hybrid method of optimization is presented.The hybrid method possesses the properties of global convergence and superlinear convergence.