考虑随机模型精化的精密GPS动态定位新方法(英文)

An Approach to Precise GPS Kinematic Positioning with a Refined Stochastic Model

GPS动态定位要求建立函数模型和随机模型。函数模型描述的是观测值和待估参数之间的物理和几何关系,随机模型描述了GPS观测值的统计特征,并通过观测值的方差协方差给定了每个观测值对最后的定位结果的贡献。正确给定函数模型和随机模型对于GPS定位结果的估计和观测值的粗差探测均至关重要。由于有各种误差存在于伪距和载波相位观测值中,一般GPS动态定位模型均采用双差观测值来构建函数模型。有时候,仔细地使用单差观测值,较之双差观测值有更多的优点,给出了选用单差观测值的理由。但是单差观测值给函数模型带来了接收机钟差,如果直接使用单差观测方程,设计矩阵是奇异的。为了解决这个问题,将伪距观测值中接收机钟差项和接收机延迟项合并为一个新的未知参数。至于载波相位观测值,首先选定一个参考卫星,然后在观测方程的右端同时增加一正一负的参考卫星单差整周模糊度,将正项与接收机钟差项和接收机延迟项合并为一个新的未知参数,将负项和原观测方程中的单差整周模糊度项合并为双差整周模糊度,而参考卫星观测方程的模糊度项则为零,这样无须组建双差观测值,软件实现较容易,也可以直接使用LAMBDA法求整周模糊度,最终也解决了观测方程奇异的问题。准确理解观测值的统计特征是建立GPS随机模型的基础。

GPS kinematic positioning requires the specification of the functional and stochastic models. The GPS functional model describes the relationship between the observations. The GPS stochastic model gives a specification of the noise characteristics of GPS observations and the contributions to the final solution of the individual observations. The correct definition of functional model and the proper choice of stochastic model are of importance for both adjusting and testing GPS data. We modify the functional model of single epoch, single difference (SD) kinematic positioning for short baselines by combining nuisance parameters like clock errors, GPS receiver delay and carrier phase ambiguities. We also refine on the stochastic model by considering the relationship of GPS observation quality and Signal-to-Noise Ratio (SNR). An exponential function is employed to model the relationship between SNR and the standard deviations of carrier phases. The experimental tests testify the proposed functional model and display the improvement on positioning precision by the refined stochastic model.