自适应快速弱敏无迹Kalman滤波算法

Adaptive fast desensitized unscented Kalman filter algorithm

针对现有弱敏无迹Kalman滤波需要代数求解增益矩阵耗时长和不能实时调节敏感性权重的问题,提出一种自适应快速弱敏无迹Kalman滤波算法.该算法在弱敏控制技术的基础上,重新定义弱敏无迹Kalman滤波的敏感性权重矩阵,将状态估计误差对不确定参数的敏感性加入滤波的代价函数,并通过最小化该代价函数得到滤波增益矩阵的解析解,减少了滤波计算复杂度和计算时间.同时基于量测残差正交原理,设计敏感性权重的自适应渐消因子,实现滤波过程中敏感性权重的实时调节.典型算例的数值仿真结果表明:所提出的自适应快速弱敏无迹Kalman滤波算法能够提高计算效率和实时调节敏感性权重,有效地降低不确定参数对状态估计的不利影响;相较于传统的弱敏无迹Kalman滤波算法,所提出算法的状态估计误差和计算时间分别减少19.5%和99.9%.

Aiming at the problem that the existing desensitized unscented Kalman filter takes a large amount computational time to algebraically solve the gain matrix and the sensitivity weights cannot be adjusted in real-time,an adaptive fast desensitized unscented Kalman filtering algorithm is proposed.Based on the desensitized control technology,the algorithm redefines the sensitivity weight matrix of the desensitized unscented Kalman filter,and the sensitivity of the state estimation error for uncertain parameters is introduced to the cost function of the filter.The analytical solution of the filter gain matrix is obtained by minimizing the cost function,which reduces the computational complexity and time of the filter.At the same time,based on the orthogonal principle of measurement residuals,the adaptive fading factor of sensitivity weights is designed to realize the real-time adjustment of sensitivity weights in the filtering process.Numerical simulation results of a typical example show that the proposed adaptive fast desensitized unscented Kalman filtering algorithm can improve the computational efficiency,adjust the sensitivity weights in real-time and effectively reduce the adverse impact of uncertain parameters on state estimation.Compared with the traditional desensitized unscented Kalman filtering algorithm,the state estimation error and computational time of the proposed algorithm are reduced by 19.5%and 99.9%respectively.