加权最小二乘法与AR组合模型在极移预测中的应用研究

Joint Model of Weighted Least-squares and AR in Prediction of Polar Motion

分析了极移预测的重要性,介绍了目前极移预测的主要方法。根据目前常用预测模型中周年项和钱德勒项的时变性质,在极移预测方法上进行了一种新的尝试,即利用加权最小二乘法与AR组合模型对极移进行预测。为进一步优选模型中的加权函数,设计了3种选权方案,并通过对比,给出了极移X、Y序列各自合适的选权方案。通过实验最终验证了这种新方法对极移预测的精度提高有一定作用,可作为极移预测的一种参考方法;但该方法作为极移预测的一种新的尝试,在选权方案优选时,其物理激发上的理论依据仍需进一步探讨。

Earth rotation parameters （ERPs） include length of day and polar motion. Precise transformations between the international celestial and terrestrial reference frames are needed for many advanced geodetic and astronomical tasks including positioning and navigation on Earth and in space. To perform this transformation, accurate ERPs are necessary. However, the precise measure- ments of ERPs by space-geodetic techniques have to be pre-processed before the ERPs are available. This causes a delay of 15 to 20 hours in case of GPS and of a few days in case of very-long-baseline interferometry （VLBI） and satellite laser ranging （SLR）.Thus it＇s necessary to predict the ERPs over at least a few days. In addition, it might be interesting to look further into the future to estimate the Earth＇s rotation in the next few months. Therefore, this paper deals with short-term predictions for next 30 days, long-term predictions for 360 days. Various prediction methods have been developed, such as the joint model of least-squares and AR, joint model of least-squares and artificial neural networks（ANN）, and so on. These methods most treat the Chandler Wobble（CW） and Annual Wobble（AW） of the polar motion as constants. However, the CW and AW are of time variant characteristics as a matter of fact. This paper puts forward a new joint model of weighted least-squares（WLS） and AR, according to the time variant characteristics of CW and AW. One important issue in building the WLS^AR model is the right choice of the weight matrix P. According to the statistical properties of the polar motion series, the rule of weight choice is determined： the fitting value nearer to prediction value is given larger weight. In accordance with the rule, three kinds of weight function are built and compared in order to assess the weight function of the weighted least-squares. The more appropriate weight function for X series and Y series are suggested respectively. Finally the WLS＋AR model is compared with LS＋AR model and shown that the new models are effective for improving the accuracy of the PM prediction. The model is an interesting and new attempt in the PM prediction, and could be seen as an alternative prediction method. However, in the paper, the theoretical basis of the model is not analyzed in depth, and which will be further studied in the later research.