CORS站高程非线性速度场及方差波动模型构建方法

本文描述了CORS站高程时间序列采用固定周期项建立线性速度场的基本概念,指出给定周期与实际周期存在偏差的问题。为此,提出了CORS站高程时间序列非线性速度场建模方法。该方法以线性最小二乘解作为迭代初值,利用高斯-牛顿迭代算法求解非线性速度场模型的未知参数,实现了CORS站高程时间序列数据的非线性建模;给出了拟合模型残差平方序列异方差特性的检验方法,阐述了建立GARCH(p,q)模型反映CORS站高程非平稳序列波动情况的基本准则。本文以国内外6个CORS站20余年的高程时间序列为研究对象,建立非线性速度场运动模型。结果表明:CORS站高程运动并不存在严格的整年或半年周期项,近似年周期运动最为明显,近似两年周期运动占比最小,年周期估计偏差达到12%,半年周期偏差18%,两年周期偏差6%,非线性建模精度和效果整体优于线性模型。利用ARCH检验法得到CORS站高程非线性模型的残差平方序列存在异方差性,即残差平方序列具有非平稳特性,引入GARCH(p,q)模型对CORS站高程分量非平稳残差平方序列建模,反映了残差平方序列的非平稳波动。验证了GARCH(p,q)模型对CORS站高程非平稳残差平方序列建模的可行性,为今后利用GARCH(p,q)模型对CORS站高程非平稳噪声序列建模和非线性速度场重构提供了思路。

Height nonlinear velocity field and variance fluctuation model construction method for CORS stations

The basic concept of establishing linear velocity field with fixed period term in CORS stations height time series is described, and the problem of deviation between given period and actual period is pointed out. Therefore, this paper proposes a nonlinear velocity field modeling method for CORS stations height time series. This method takes the linear least squares solution as the initial value of iteration, and uses the gauss-newtoni-teration algorithm to solve the unknown parameters of the nonlinear velocity field model, realizing the nonlinear fitting of height time series data of CORS stations. The test method for the heteroscedasticity of the residual square sequence of the fitting model is given, and the basic criteria for the establishment of GARCH (p, q) model to reflect the fluctuations of non-stationary sequence are expounded. The six CORS stations at home and abroad more than 20 years as the research object, the height of time series nonlinear velocity motion model is set up, the results show that the CORS stations height movement does not exist strict year or half year cycle, the approximate periodic motion is most obvious, the approximate period of two years than the minimum, cycle in deviation of 12%, half year cycle is 18%, two year period is 6%, nonlinear modeling accuracy and effect is better than the linear model as a whole. The ARCH test method is used to obtain the heteroscedasticity of the residual square sequence of the nonlinear model of CORS stations height, that is, the residual square sequence has non-stationary characteristics. GARCH (p, q) model is introduced to model the non-stationary residual square sequence of the height component of CORS stations, which reflects the non-stationary fluctuation of the residual square sequence. The feasibility of GARCH (p, q) model in modeling non-stationary residual square series of CORS stations height is verified, which provides an idea for future modeling of non-stationary noise series of CORS stations height and reconstruction of nonlinear velocity field with GARCH (p, q) model.