测站坐标时间序列随机模型的解析表达

Analytical Expression for Stochastic Model in Station's Coordinate Time Series Analysis

利用最大似然估计法分析测站坐标时间序列时,需根据时间序列的噪声特性构造相应的协方差阵。由于幂律噪声除包含白噪声,闪烁噪声和随机漫步噪声等谱指数为整数的噪声外,还包含谱指数为实数的噪声,且其统计特性各不相同。除白噪声和随机漫步噪声外,已有研究并没有详细给出其它幂律噪声随机模型的构造方法。本文针对有色噪声中幂律噪声类型的时间相关特性,基于分数阶差分的理论和性质,详细给出了时间域上平稳和非平稳幂律噪声的随机模型的解析表达式,并给出了相应元素之间的递推关系。该解析表达式对于研究幂律噪声时间相关性或模拟相应特征的有色噪声有一定的参考价值。

The co-variance matrix of chosen noise model is required when using maximum likelihood estimation to analysis the station’s coordinate time series.The power law noise model is one of colored noise with different stochastic processes ran-ging from white to random walk,including flicker and fractional noise.However,in current research,the specific procedure to generate co-variance matrix of power law noise is often not prescribed in sufficient detail.In this paper,an analytical expres-sion is proposed for creating stochastic model of power law noise based on fractional differencing theory in time domain.With this expression,the element of co-variance matrix can be calculated in a recursive algorithm if the power law noise process is stationary.This analytical expression would be of help for investigating the characteristic of the noise process or for the simula-ting the desired colored noise.