基于卡尔曼滤波的含噪声小样本数据处理方法

提出一种基于卡尔曼滤波和扩展卡尔曼滤波的小样本噪声数据处理方法. 首先, 通过物理模型或经验公式建立系统模型. 然后, 利用系统模型预测模型数据. 最后, 采用观测数据修正模型数据, 达到平滑数据噪声的效果. 实验结果表明, 对于BC500耐候钢腐蚀增重数据, 用差分整合移动平均自回归(autoregressive integrated moving average, ARIMA)模型和随机森林(random forest, RF)模型进行腐蚀增重预测时, 经卡尔曼滤波降噪后, 决定系数$R^2$平均提升6.4%, 而经扩展卡尔曼滤波降噪后, $R^2$平均提升4.9%, 验证了本方法的有效性.

Kalman filter based method for processing small noisy sample data

A small sample noisy data processing method based on Kalman filter and extended Kalman filter has been proposed. The core idea was to establish a system model using physical models or empirical formula, then used the system model to predict the model data, and finally used the observation data to correct the model data and achieve the effect of smoothing data noise. Experimental results showed that when using the autoregressive integrated moving average (ARIMA) model and random forest (RF) model to predict the corrosion weight gain of weather steel BC500, the coefficient of determination $R^{2}$ was increased by an average of 6.4% after Kalman filter denoising, while the $R^{2}$ was increased by an average of 4.9% after extended Kalman filter. These results verified the effectiveness of the proposed methods.