基于滑动L2优化准则的GPS坐标时间序列重构

GPS坐标时间序列中不仅包含白噪声,还包含闪烁噪声、随机漫步噪声等有色噪声,这些噪声将影响GPS应用的可靠性,甚至可能对一些地球物理现象做出错误的解释,因此降低GPS坐标时间序列中有色噪声的影响、提高GPS精度是一个重要和基本的问题。提出了一种滑动L₂优化估计方法(ML₂),通过选取合适的窗口建立L₂优化模型,再利用交替迭代乘子法求解每段时间序列的优化问题,并逐年滑动得到整段GPS坐标时间序列的估计。实验结果表明,ML₂方法与奇异谱分析、小波分解、滑动普通最小二乘法相比具有更好的重构效果。

Reconstruction of GPS Coordinate Time Series Based on Moving L2 Optimization Criterion

The GPS coordinate time series contains not only white noise,but also colored noise such as flicker noise and random walk noise.These noises affect the reliability of GPS applications and may even misinterpret some geophysical phenomena.Therefore,reducing the influence of colored noise in the GPS coordinate time series and improving the accuracy of GPS is an important and fundamental problem.In this article,we proposed a moving L₂ optimization estimation method(ML₂),which established the L₂ optimization model by selecting appropriate windows,used the alternating direction method of multipliers to solve the optimization problem of each time series and slid it year by year,and got an estimate of the entire GPS coordinate time series.The experimental results show that the ML₂ method has better reconstruction effect than singular spectrum analysis,wavelet decomposition and movimg ordinary least squares.