基于Kalman滤波的灰色模型在沉降预测中的研究

Research of Grey Model Based on Kalman Filter in Settlement Prediction

针对沉降观测数据存在各种扰动,以及GM(1,1)模型的不足,提出卡尔曼滤波GM(1,1)模型,通过卡尔曼滤波去噪后,再利用GM(1,1)模型进行预测。由实验数据可得,改进模型的后验误差比值、小误差概率以及精度等级分别为0.108 0、100%、一级,而原有的3种模型中只有3次指数平滑接近改进模型,但改进模型的后验误差比值更小;从残差看,改进模型的预测残差比原有模型都小,这表明改进模型提高了沉降预测的精度。

Based on various disturbance of Settlement Observation Data and the weaknesses of GM （1,1）,this paper presents the Kalman Filter GM（1,1）Model,which will make predictions with it after denoising. From the experimental data,under the help of GM（1,1）,the Posterior error ratio, Small error probability and the Precision grade are 0. 108 0、100%and first optimum,while exponen-tial smoothing approached the improved model＆#39;s only three times based on the previous three models, and the Posterior error ratio of improved model is more smaller. In view of the residual error,the fore-casting residual of advanced model is smaller than the previous model, which indicates that it im-proves the precise of the Settlement Prediction.