多维AR序列的最小二乘建模方法

以测量数据处理中广泛应用的最小二乘原理为基础，详细阐述了多维AR序列参数估计的最小二乘算法、阶数确定的F检验法，并对清江隔河岩大坝1998年5月、6月间洪水前夕平差后的GPS观测数据进行了建模和预报，验证了多维时间序列分析应用于变形观测数据处理的可行性。

Multi-dimensional AR Series Modeled by Least Square Criterion

Being one of the modern methods of data processing,time serials analysis has a outstanding position in system identification and analysis.Based upon mutuality functions of probability statistics,traditional time series analysis can be completed only by complicated iterative method with non_linear least squares algorithm,whose theories and applications take only one factor into account at present,which is one_dimensional time series.Hence,it can not cater for dealing with practical multi_factor problems. Based on the least squares criterion widely used in surveying data processing,time_field analysis method of multi_dimensional AR series is illustrated in detail in this paper,which includes parameter estimations by the least squares algorithm and rank confirmation by routine F _test.The feasibility of the multi_dimensional time series analysis method is tested in the application of deformation observation data processing,by modeling and forecasting GPS observation adjustment data of Geheyan Dam at Qingjiang River before flood season between May and June in 1998.All the algorithms expounded is not related to non_linear estimation in this paper.