引用本文:吉浩日,席裕庚,李德伟,薛蕾.线性离散随机系统输入和状态的多步估计方法及应用[J].控制理论与应用,2017,34(1):54~60.[点击复制]
KIL Ho-Il,XI Yu-geng,LI De-wei,XUE Lei.A multi-step input and state estimation for the linear discrete-time stochastic system and its application to the anaerobic digestion process[J].Control Theory and Technology,2017,34(1):54~60.[点击复制]
线性离散随机系统输入和状态的多步估计方法及应用
A multi-step input and state estimation for the linear discrete-time stochastic system and its application to the anaerobic digestion process
摘要点击 2508  全文点击 1837  投稿时间：2016-04-04  修订日期：2016-12-28
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DOI编号  10.7641/CTA.2017.60187
  2017,34(1):54-60
中文关键词  卡尔曼滤波  状态估计  未知输入估计  厌氧消化过程
英文关键词  Kalman filtering  state estimation  unknown input estimation  anaerobic digestion process
基金项目  国家自然科学基金项目(61374110, 61333009, 61521063, 61590924)资助.
作者单位E-mail
吉浩日 上海交通大学自动化系 khi2012@sjtu.edu.cn 
席裕庚 上海交通大学自动化系  
李德伟* 上海交通大学自动化系 dwli@sjtu.edu.cn 
薛蕾 上海交通大学 自动化系  
中文摘要
      具有未知输入的系统的状态估计问题已经在过去几十年里引起了相当的关注. 本文对于线性离散随机系 统提出了一种基于多步信息的输入和状态同步估计方法. 首先, 采用多步信息的最小方差方法来获得未知输入. 由 于引入了包含多个时间步骤的扩张状态和测量向量而计算多步信息, 使估计结果与一步估计相比减少了对噪声的 敏感性. 其次, 利用输入估计值和卡尔曼滤波估计过去和当前的状态. 该方法在未知输入维数等于状态维数时仍然 有良好的估计效果. 数值仿真验证了提出的估计方法的有效性. 最后, 该方法应用于厌氧消化过程反应罐中的溶解 甲烷和二氧化碳的浓度估计以验证方法的实用性.
英文摘要
      The problem of state estimation for systems with unknown inputs has received considerable attention during the past decades. This paper proposes a simultaneous estimation method for inputs and states of linear discrete-time stochastic systems based on multi-step innovation. Firstly, the unknown input is obtained from the multi-step innovation with weighted least square estimation. The extended states and measurement vector which consist of multi-step variables are introduced and used to calculate the multi-step innovation. This novel approach can reduce the impact of the noise on estimation performance. Secondly, the past and current states are estimated from the input estimate and the Kalman filter. This method still performs well when the dimension of the unknown input vector is equal to that of the state vector. The effectiveness of the proposed method is demonstrated through the numerical example. Finally, the method is applied to an anaerobic digestion process to estimate the concentration of the dissolved methane and the carbon dioxide in the anaerobic digestion reactor.