﻿ 一种短时序Kalman滤波决策优化预测新方法

# 一种短时序Kalman滤波决策优化预测新方法A New Decision Optimization Prediction Method Based on Short-Term Time Series and Kalman Filter

Abstract: In order to make scientific and agile decision, a new short-term prediction TS_KF (Time Se-ries-Kalman Filter) method is proposed based on the combination of time series analysis and Kalman Filter. Aiming to improve the prediction precision and decrease the calculation complexity, a prediction model is built using Kalman filter to describe the prediction process, and the auto regression for time series analysis is utilized to renew and optimize the state transfer matrix, which is the key parameter for Kalman Filter. A coal production prediction test is conducted by comparison with some typical time series prediction method, and the results show that the TS_KF prediction method in this paper has significantly enhanced the prediction precision while keeping the same low calculation complexity. The result gives a strong proof for the effectiveness of the new TS_KF prediction method.

1. 引言

2. TS_KF预测方法

2.1. 预测模型框架

TS_KF预测方法以Kalman滤波预测模型为基础，预测模型能保持Kalman滤波本身的迭代收敛特性，在使用过程中通过样本的积累实现逐步收敛。预测模型框架如图1

Figure 1. Predictive model framework

Table 1. Comparison of different prediction methods

• 不必进行前期大量样本值的训练，而将此过程融入到运行过程中，减少了模型应用过程中的前期准备工作量；

• 在使用过程中可以对样本值进行滤波，减小样本本身的误差，这是其它模型没有实现的。

2.2. 预测模型的构建

$\left\{\begin{array}{l}{x}_{{}_{k}}=A{x}_{k-1}+B{u}_{k}+{w}_{k-1}\\ {z}_{k}=H{x}_{k}+{v}_{k}\end{array}$ (1)

$\left\{\begin{array}{l}{w}_{k-1}~N\left(0,Q\right)\\ {v}_{k}~N\left(0,R\right)\end{array}$ (2)

$\left\{\begin{array}{l}{x}_{k}=a{x}_{k-1}+{w}_{k-1}\\ {z}_{k}={x}_{k}+{v}_{k}\end{array}$ (3)

${\stackrel{˜}{y}}_{t}={\varphi }_{1}{\stackrel{˜}{y}}_{t-1}+{\varphi }_{2}{\stackrel{˜}{y}}_{t-2}+\cdot \cdot \cdot +{\varphi }_{p}{\stackrel{˜}{y}}_{t-p}+\xi$ (4)

${\stackrel{˜}{y}}_{k}={\varphi }_{1}{\stackrel{˜}{y}}_{k-1}+\xi$ (5)

$\mu$${y}_{k}$ 的期望水平的情况下，将 ${\stackrel{˜}{y}}_{k}={y}_{k}-\mu$ 代入到(5)，可得AR(1)的以下等效过程：

${y}_{k}={\varphi }_{1}{y}_{k-1}+\tau +\xi$ (6)

$\left\{\begin{array}{l}\stackrel{¯}{y}=\frac{1}{S}{{\sum }_{i=0}^{S}y}_{k-i}\\ {\varphi }_{1}=\frac{{{\sum }_{i=0}^{S-1}{y}_{k-i}y}_{k-i-1}-\left(S-1\right){\stackrel{¯}{y}}^{2}}{{\sum }_{i=0}^{S-1}{y}_{k-i-1}^{2}-\left(S-1\right){\stackrel{¯}{y}}^{2}}\\ \tau =\left(1-{\varphi }_{1}\right)\stackrel{¯}{y}\end{array}$ (7)

$\left\{\begin{array}{l}{x}_{{}_{k}}=a{x}_{k-1}+\beta +{w}_{k-1}\\ {z}_{k}={x}_{k}+{v}_{k}\end{array}$ (8)

$\left\{\begin{array}{l}{\sigma }^{2}={{\sum }_{i=0}^{S}\left[{\stackrel{^}{y}}_{i}-\left({\varphi }_{1}{\stackrel{^}{y}}_{i-1}+\tau \right)\right]}^{2}\\ {R}_{k}=diag\left({\sigma }^{2}\right)={\sigma }^{2}\end{array}$ (9)

2.3. 算法描述

Figure 2. Predictive algorithm flow

3. 实验研究

Table 2. Comparison experimental parameter setting of different prediction methods

Table 3. A detailed list of predicted statistical data

Table 4. Error statistics of different prediction models

Figure 3. Comparison of forecast effect of coal yield using various predictive methods

4. 结论

1) 综述了决策中现有的典型预测方法，阐述了不同预测方法的应用场合和相互关系。统计时间序列方法主要用于短期预测，是决策敏捷性的重要支撑，因此着重对短期时间序列预测进行了研究。

2) 为提升决策的敏捷性和科学性，以短时段数据的时间序列为研究对象，提出了将时间序列模型和Kalman滤波模型相结合的TS_KF预测方法，并从预测准确性和计算复杂度上优化预测方法。TS_KF方法具有模型简洁、有效、计算复杂度低等特点。

3) 以煤产量数据作为时间序列样本，采用与典型的时间序列预测方法(MA和ES)对比的方法，设计了实验验证算例，以验证TS_KF方法的有效性。结果表明，在保持计算复杂度同水平的前提下，TS_KF方法能极大的提高预测的准确性。

NOTES

*通讯作者。

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