摘要
在状态估计理论的实际应用中,系统的状态向量可能受到线性或者非线性约束条件的限制,如果可以将这些约束条件有效地施加到滤波过程中,则从理论上可以获得更高的滤波精度。针对非线性状态约束滤波,可以通过泰勒级数展开将非线性约束函数线性化,该方法需求解非线性约束函数的雅可比矩阵,然而实际问题中总有雅克比矩阵不存在的情况。采用水平滑动估计算法,该算法无需求解雅可比矩阵,然而该方法需要计算非线性约束最优化问题,算法时间复杂度较高。为此,在状态向量的高斯假定下,提出了一类迭代收缩非线性状态约束滤波方法。该方法结合容积卡尔曼滤波、求积分卡尔曼滤波、中心差分卡尔曼滤波和不敏卡尔曼滤波思想,分别采用几种不同的数值方法对积分进行近似,获得了几种解决非线性状态约束的实现算法。在实现过程中,为了减小基点误差对于滤波结果的影响,采用迭代的方法,给非线性状态约束函数施加一系列噪声,使得在量测更新步骤中方差逐步收敛,使约束逐渐增强,提高了状态估计的精度。实验结果表明,该类方法的几种实现算法滤波精度较高,时间复杂度较为适中,无需求解雅可比矩阵或黑森矩阵。
In the practical application of state estimation theory,the state vector of the system may be restricted by linear or nonlinear constraints.If these constraints can be effectively applied to the filtering process,higher filtering accuracy can be obtained theoretically.For nonlinear state constrained filtering,the nonlinear constraint function can be linearized by Taylor series expansion.This method needs to solve the Jacobian matrix of the nonlinear constraint function,but there will always be situations where the Jacobian matrix does not exist in practical problems.The horizontal sliding estimation algorithm is adopted.The algorithm does not need to solve the Jacobian matrix,but the method needs to calculate nonlinear constrained optimization problems,and the time complexity of algorithm is high.Therefore,under the assumption that the state vector is subject to the Gaussian distribution,we present a class of iterative shrinkage nonlinear state constraints filter.The method combines with the cubature Kalman filter(CKF),quadrature Kalman filter(QKF),central divided differences Kalman filter(CDKF),unscented Kalman filter(UKF),respectively,and uses several different numerical methods to approximate the integrals appeared in the process.Consequently,some implemental algorithms are obtained and can be used to solve the problem of nonlinear state constraints.In the process of implementation,in order to diminish the influence of base point error in the filtering results,we apply a series of noises to the nonlinear state constraints function by using the iterative style,as a result,the variance gradually converge in the measurement update step,and the constraints are gently tighten step by step,which improves the precision of the state estimation.The experimental results show the proposed algorithms have higher precision and lower time complexity compared with the other available algorithms.Besides,they can work well without solving the Jacobian matrix or the Hessian matrix.
作者
贺姗
刘沫萌
李迎
HE Shan;LIU Mo-meng;LI Ying(School of Computer Science,Xi’an Polytechnic University,Xi’an 710048,China;Shaanxi Key Laboratory of Clothing Intelligence,Xi’an 710048,China;State and Local Joint Engineering Research Center for Advanced Networking&Intelligent Information Services,Xi’an 710048,China)
出处
《计算机技术与发展》
2022年第11期95-99,114,共6页
Computer Technology and Development
基金
国家自然科学基金项目(61902303)
陕西省自然科学基础研究计划资助项目(2020JQ-832)。
关键词
非线性状态约束
状态估计
不敏卡尔曼滤波
容积卡尔曼滤波
求积分卡尔曼滤波
中心差分卡尔曼滤波
nonlinear state constraints
state estimation
unscented Kalman filter
cubature Kalman filter
quadrature Kalman filter
central divided differences Kalman filter
