基于混沌时间序列的Volterra自适应滤波极移预报方法

A Volterra Adaptive Filtering Method for Polar Motion Prediction Based on Chaotic Time Series

针对极移复杂的时变特性,根据混沌相空间坐标延迟重构理论,提出一种基于Volterra自适应滤波的极移预报方法.首先,利用最小二乘拟合算法分离极移序列中的线性趋势项、钱德勒项和周年项,获得线性极移、钱德勒极移和周年极移的外推值;其次,通过C-C关联积分法对最小二乘拟合残差序列进行相空间重构,并利用小数据量法计算残差序列的最大Lyapunov指数验证其混沌特性,在此基础上,构建Volterra自适应滤波器对残差序列进行预测;最后,将线性极移、钱德勒极移和周年极移的外推值以及最小二乘拟合残差的预测值相加获得极移最终预报值.利用国际地球自转服务局(International Earth Rotation and Reference Systems Service,IERS)提供的极移数据进行1-60 d跨度预报,并将预报结果分别与国际地球定向参数预报比较竞赛(Earth Orientation Parameters Prediction Comparison Campaign,EOPPCC)结果和IERS A公报发布的极移预报产品进行对比,结果表明:对于1-30 d的短期预报,该方法的预报精度与EOP PCC最优预报方法相当,当预报跨度超过30 d时,该方法的预报精度低于EOP PCC最优预报方法,优于参与EOP PCC的其他方法;与IERS A公报相比,该方法的短期预报效果较好,当预报跨度增加时预报精度低于IERS A公报.预报结果表明该方法更适合于极移短期预报.

In consideration of the complex time-varying characteristics of polar motion(PM),this paper takes PM as chaotic time series.A Volterra adaptive filter is employed for predicting PM based on the state space reconstruction of delay-coordinate embedding of dynamic system.This method first uses the Least Squares(LS)technology to estimate the harmonic models for the linear trend,Annual and Chandler Wobbles(AW and CW)in PM.The selected LS deterministic models are subsequently used to extrapolate the linear trend,AW and CW and obtain the LS residues(the difference between the LS model and PM data themselves).Secondly,the phase space and largest Lyapunov exponent of the LS residues is reconstructed and calculated by means of the C-C and small data-set algorithm,respectively.Further,a Volterra adaptive filter is designed for generating the extrapolations of the LS residues.The extrapolated LS residues are then added to the LS deterministic models in order to obtain the predicted PM values.The EOP C04 time series released by the International Earth Rotation and Reference Systems Service(IERS)are selected as data base to generate the PM predictions up to 60 days in the future.The results of the predictions are analyzed and compared with those obtained by the Earth Orientation Parameters Prediction Comparison Campaign(EOP PCC)and IERS Bulletin A.The results show that the accuracy of the predictions up to 30 days is comparable with that by the most accurate prediction techniques participating in the EOP PCC for PM,but worse than that by those most accurate techniques beyond 30 days in the future.The results also illustrate that the short-term predictions are better than those published by the IERS Bulletin A.However,the errors of the predictions rapidly increase with the prediction days.It is therefore concluded that the proposed method is a potential technology for short-term PM prediction.