卡尔曼滤波优化的高斯过程回归模型

Optimization Model of Gaussian Process Regression Based on Kalman Filtering

  • 摘要: 为解决单个高斯过程回归无法对来自多个信息源的数据进行整体建模的问题,提出了卡尔曼滤波优化的高斯过程回归模型(Gaussian process regression model based on Kalman filtering,KF-GPR). 该模型首先根据多个传感器获取的离散样本数据分别进行高斯过程回归,预测关键参数的均值和方差,并将其视作软传感器输出的测量值和噪声. 然后利用卡尔曼滤波算法对软传感器的输出进行融合,在最小均方误差准则下,实现对多个高斯过程回归结果的融合优化,获得优化后模型的输出结果. 仿真实验将KF-GPR与平均值融合方法进行对比,结果表明KF-GPR能够获得拟合精度更高的预测曲线,验证了模型的有效性. 最后,将KF-GPR应用于温度随纬度变化的实例分析中,分季节给出了纬度−温度预测曲线.

     

    Abstract: To solve the problem, that whole modeling can not be carried out with data from multiple information sources, an optimization Gaussian process regression model based on Kalman filtering (KF-GPR) was proposed. Firstly, according to discrete sample data obtained from multiple sensors, the model carried through GPR, respectively predicted mean value and variance of the key parameters, regarding them as measurements and noise of soft sensor outputs. Then, fusing the outputs of soft sensors based on Kalman filtering algorithm, the model carried out fuse optimization for the outputs of multiple GPR under the rule of the least mean square error, achieving the outputs of the optimized model. And then, some simulation experiments were carried out to compare KF-GPR with other average value fusion methods. The results show that KF-GPR can obtain prediction curves with higher fitting accuracy, verifying the validity of the model. Finally, KF-GPR was applied to the case analysis of temperature variation with latitude, presenting the latitude-temperature prediction curves according to season.

     

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