基于AR(p)的卡尔曼滤波在GPS变形监测中的应用

Application of Kalman Filter Method Based on AR(p)Model in GPS Deformation Prediction

由于AR(p)模型结构比较简单且计算比较方便,在变形分析中,目前常采用此模型建立变形模型。然而单纯的AR模型把模型参数作为定值,变形数据拟合误差及变形预测误差可能会比较大。介绍了将卡尔曼滤波引入AR模型,利用观测数据建立AR模型,即建立观测方程;以AR模型的参数为状态向量建立状态方程。从而形成动态系统的卡尔曼滤波函数模型,动态计算出AR模型的参数以便预测。此方法快速、实时,且占有较少内存,充分利用了AR模型和卡尔曼滤波二者的优点。

In GPS deformation prediction, we usually use AR（p） model to establish predict model for that the structure of AR（p） is simple and convenient in calculation. However, traditional AR（p） model put the model parameters as fixed values. Thus, the fitting errors of deformation data and the errors of deformation predict data can be comparatively large. This paper has mainly introduced the Kalman filter method based on AR（p） model. It can establish AR model by surveying data and construct the surveying equations. Then, it will build status equations using the parameters of AR model and finally form the dynamic system of Kalman filter. The parameters of AR model can be calculated in a movement in this method. The algorithm is fast and dynamic, it takes less calculation space and uses the advantages of AR model and Kalman Filter.