非线性系统中心差分集员估计方法

Central difference set-membership filter for nonlinear system

中文关键词  非线性系统  集员估计  状态估计  参数估计  有界噪声  计算复杂度  中心差分

英文关键词  nonlinear system  set membership estimation  state estimation  parameter estimation  bounded noise  computational complexity  central difference

中文摘要

      用于非线性椭球估计的扩展集员算法在实际应用中存在着实现性差、边界估计相对保守等缺陷. 本文提出了一种用于非线性系统状态估计的中心差分集员估计方法, 以改善传统非线性集员滤波算法的估计性能. 为克服泰勒展开的固有缺陷, 采用低阶多维Stirling内插多项式代替泰勒展开实现非线性模型的线性化处理; 利用半定规划方法对线性化误差进行外包定界并将其融入过程噪声和量测噪声中, 以降低误差定界的保守性; 量测更新中, 为提高算法的实时性, 将量测椭球松弛为多个带的交, 依次参与状态椭球的更新, 从而实现状态定界椭球的次优估计; 同时, 对椭球-带交集迭代过程中椭球中心到超平面的归一化距离的计算方法进行了改进, 使当前时刻每次迭代的椭球均参与计算并选取最优值, 以减小累计误差. 仿真结果表明了本文所提出算法的有效性和改进性能.

英文摘要

      The extended set-membership filter for nonlinear ellipsoidal estimation has some shortcomings such as poor implementation and relatively conservative estimated boundary. In this paper, a central difference set-membership filter for nonlinear system state estimation is proposed to improve the estimation performance of traditional nonlinear set-membership filter. To overcome the inherent defect of Taylor’s formula, a low-order multi-dimensional extension of Stirling’s interpolation formula is used to realize the linearization of nonlinear models. Then the semi-definite programming method is utilized to outer-bound the linearization error, which is incorporated to the process noise and observation noise, to reduce the conservativeness of the estimated boundary. At observation updating stage, each observation noise bounding ellipsoid is replaced by a parallelotope formed by several strips to improve the real-time performance. Then a sub-optimal algorithm is designed based on consecutive intersection of the time-updated ellipsoid by each strip. Furthermore, the computing method for normalized distances from the centre of ellipsoid to each hyperplane is improved to reduce the accumulative error, which makes the ellipsoid at each iteration of the current moment participate in the calculation and the optimal value is selected. Simulation results have shown the effectiveness and improved performance of the proposed algorithm.