A Forecasting Framework Based on Kalman Filter Integrated Multivariate Local Polynomial Regression: Application to Urban Water Demand

  • Guoqiang Chen
  • Tianyu Long
  • Yun BaiEmail author
  • Jin Zhang


In this study, a forecasting framework for daily urban water demand has been proposed. It was developed based on the extended Kalman filter (EKF) which consists of state estimation, forecasting and error correction. The forecasting and error correction models can be substituted. As an example, a multivariate local polynomial regression (MLPR) was used to linearize the complex system which is essential for EKF. A correctional prediction of residual based on relevance vector regression was employed to update and substitute error estimation value in the EKF. To improve the precision of the forecasts, the historical data series was decomposed into low- and high-frequency subseries using discrete wavelet transformation. Five category forecasts with the lead time of 1-day were assessed in comparison of the proposed model: MLPR, multi-scale relevance vector regression, autoregressive moving average, Back Propagation neural network and multiple linear regression. According to the performance criteria, the MLPR is slightly beneficial in capturing the basic dynamics of the daily urban water demand in the short term, but the state estimation and error correction can greatly improve the results. The proposed model obtains better forecasting performances than existing models, which is attributed to good state estimation from the Kalman transmission gain and favorable feature learning performance using MLPR.


Kalman filter Multivariate local polynomial regression Water demand Forecast Relevance vector regression 



This work is supported by the Natural Science Foundation of China (71801044), the Humanities and Social Science Foundation of Ministry of Education of China (17YJC630003), the Natural Science Foundation of Chongqing (cstc2018jcyjAX0436), and the Research Start-Up Funds of CTBU (1756012). In addition, the authors would also like to thank the editors/reviewers for their valuable suggestions and comments that have helped improve this paper.

Author Contributions

TL and YB conceived and designed the experiments; GC performed the experiments, analyzed the data and wrote the paper; JZ contributed to the scientific discussion and editing. The authors thank JX for supplying the dataset.

Compliance with Ethical Standards

Conflicts of interest

The authors declare no conflict of interest.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Urban and Rural Construction Committee of Beibei DistrictChongqingChina
  2. 2.Faculty of Urban Construction and Environmental EngineeringChongqing UniversityChongqingChina
  3. 3.National Research Base of Intelligent Manufacturing ServiceChongqing Technology and Business UniversityChongqingChina
  4. 4.Institute of Groundwater and Earth SciencesJinan UniversityGuangzhouChina

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