一维离散数据的卡尔曼滤波模型的参数估计及自适应滤波算法的改进
发布时间：2019-03-07 14:40
【摘要】：本文综述了卡尔曼滤波的研究背景和现状,详细研究了线性卡尔曼滤波及非线性卡尔曼滤波,分析了它们的优缺点,讨论了它们的应用范围。首先,基于一维离散状态数据和观测数据,分别提出了状态方程的参数估计法(SPL法)和观测方程的参数估计法(OSL法)。第一种方法,先求出与当前状态数据相关的下一时刻状态数据的概率分布,再利用最小二乘法估计出状态方程中的参数,最后得出状态方程；第二种方法,在等分状态数据和和观测数据的基础上,在每个区间内用最小二乘法估计观测矩阵,构造出状态变量和观测矩阵之间的函数关系式,最终得到观测方程。其次,对简化的Sage-Husa自适应滤波算法进行了两点改进。第一点,用观测噪声Rk-1代替观测噪声Rk,计算出卡尔曼增益Kk,解决了原算法中的死循环问题；第二点,在原算法的基础上增加了两步,即先利用前面求得的观测噪声Rk重新计算卡尔曼增益Kk,再利用新的卡尔曼增益Kk重新计算估计值xk。接着,针对单时滞系统,给出了具体的卡尔曼滤波算法,并且在状态过程和观测过程均为平稳的情况下,提出了一种估计观测延迟时间的方法。最后,实证分析了本文提出的上述方法,估计出状态方程和观测方程的相应参数以及观测延迟时间,并利用本文提出的评价函数R(s)验证了这些方法的有效性。
[Abstract]:In this paper, the research background and present situation of Kalman filter are summarized, linear Kalman filter and nonlinear Kalman filter are studied in detail, their advantages and disadvantages are analyzed, and their application scope is discussed. Firstly, based on one-dimensional discrete state data and observation data, the parameter estimation method of equation of state (SPL method) and the parameter estimation method of observation equation (OSL method) are proposed respectively. In the first method, the probability distribution of the next state data related to the current state data is obtained first, then the parameters in the state equation are estimated by the least square method, and finally the state equation is obtained. In the second method, on the basis of the equal state data and the sum observation data, the observation matrix is estimated by the least square method in each interval, and the function relation between the state variable and the observation matrix is constructed, and finally the observation equation is obtained. Secondly, two improvements are made to the simplified Sage-Husa adaptive filtering algorithm. Firstly, the Kalman gain Kk, is calculated by using observation noise Rk-1 instead of observation noise Rk, to solve the dead loop problem in the original algorithm. Second, two steps are added on the basis of the original algorithm, that is, the Kalman gain Kk, is recalculated by the observation noise Rk obtained before and the estimated xk. is recalculated by the new Kalman gain Kk. Then, for the single time-delay system, a specific Kalman filter algorithm is given, and a method to estimate the observation delay time is proposed under the condition that both the state process and the observation process are stationary. Finally, the above-mentioned methods are empirically analyzed, the corresponding parameters of the state equation and observation equation and the observation delay time are estimated, and the effectiveness of these methods is verified by using the evaluation function R (s) proposed in this paper.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN713
本文编号：2436202
[Abstract]:In this paper, the research background and present situation of Kalman filter are summarized, linear Kalman filter and nonlinear Kalman filter are studied in detail, their advantages and disadvantages are analyzed, and their application scope is discussed. Firstly, based on one-dimensional discrete state data and observation data, the parameter estimation method of equation of state (SPL method) and the parameter estimation method of observation equation (OSL method) are proposed respectively. In the first method, the probability distribution of the next state data related to the current state data is obtained first, then the parameters in the state equation are estimated by the least square method, and finally the state equation is obtained. In the second method, on the basis of the equal state data and the sum observation data, the observation matrix is estimated by the least square method in each interval, and the function relation between the state variable and the observation matrix is constructed, and finally the observation equation is obtained. Secondly, two improvements are made to the simplified Sage-Husa adaptive filtering algorithm. Firstly, the Kalman gain Kk, is calculated by using observation noise Rk-1 instead of observation noise Rk, to solve the dead loop problem in the original algorithm. Second, two steps are added on the basis of the original algorithm, that is, the Kalman gain Kk, is recalculated by the observation noise Rk obtained before and the estimated xk. is recalculated by the new Kalman gain Kk. Then, for the single time-delay system, a specific Kalman filter algorithm is given, and a method to estimate the observation delay time is proposed under the condition that both the state process and the observation process are stationary. Finally, the above-mentioned methods are empirically analyzed, the corresponding parameters of the state equation and observation equation and the observation delay time are estimated, and the effectiveness of these methods is verified by using the evaluation function R (s) proposed in this paper.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN713
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