一种新的基于保证定界椭球算法的非线性集员滤波器

基于未知但有界噪声假设的集员滤波器为传统的概率化滤波方法提供了一种可行的替代选择, 然而其潜在的计算负担和保守性考虑制约了该方法的实际应用. 本文提出一种新的基于保证定界椭球近似的改进集员滤波方法, 用于解决针对非线性系统的状态估计问题,在保证实时性的前提下降低了算法的保守性. 首先,对非线性模型进行线性化处理,采用DC (Difference of convex)规划方法对线性化误差进行外包定界, 并通过椭球近似将其融合到系统噪声中; 在此基础上提出了一种结合了椭球直和计算和基于迭代外定界椭球算法的椭球--带交集计算 所构成的经典预测--更新步骤来估计得到状态的可行椭球集. 与常规的非线性扩展集员滤波方法的仿真比较表明了本文所提出算法的有效性和改进性能.

A New Nonlinear Set Membership Filter Based on Guaranteed Bounding Ellipsoid Algorithm

The framework of set membership filter (SMF) with unknown-but-bounded noise assumption provides an attractive alternative for probabilistic filters. However, the potential computational burden and conservation consideration may seriously limit the usage of this filter in practical applications. In this paper, based on guaranteed bounding ellipsoid approximation, a new enhanced set membership filter with better real-time property and reduced conservation is proposed for state estimation problem of nonlinear systems. The nonlinear model is firstly linearized and the DC programming method is used to outer-bound the linearization error, which is incorporated to the model noise with ellipsoidal approximations. A classical two-step prediction-correction procedure consisting vector sum computation between ellipsoids and an iterative outer-bounding ellipsoid algorithm to intersect ellipsoid with strip is presented to compute the ellipsoidal feasible set of the estimated states. Simulation results with comparisons to the nonlinear extended set membership filter are given to demonstrate the effectiveness and improved performances of our proposed algorithm.