不确定噪声下基于轴对称盒空间滤波的非线性系统状态估计

针对不确定噪声下的非线性系统状态估计问题, 本文提出了一种基于轴对称盒空间滤波的状态估计方法. 首先, 利用轴对称盒空间包裹线性化过程带来的误差项, 将状态函数线性化误差轴对称盒空间与噪声轴对称盒空间求取闵可夫斯基和, 得到干扰误差轴对称盒空间; 随后, 利用状态量、线性误差和测量噪声的轴对称盒空间的闵可夫斯基和, 得到系统状态预测集; 进而, 利用轴对称盒空间边界正交的性质, 将盒空间拆分为多组超平面, 构造测量更新的约束条件并得到集员包裹. 本文所提方法相比传统的椭球滤波方法而言, 降低了算法的复杂度, 减少了包裹状态可行集和线性化过程带来的余, 获得了更加紧致精确的系统状态集. 最后, 采用非线性弹簧–质量–阻尼器系统验证了本文所提算法的有效性.

Nonlinear system state estimation based on axisymmetric box space filter under uncertain noise

A state estimation method based on the axisymmetric box space filtering is proposed for nonlinear system under uncertain noise. First, the axisymmetric box space is used to wrap the error term caused by the linearization process to linearize the state function, and the axisymmetric box space of the interference error is obtained by the Minkowski sum of the axisymmetric box space of the error and the noise axisymmetric box space; then, the Minkowski sum of the axisymmetric box space of the state quantity, linear error and measurement noise is used to obtain the system state prediction set; further using the orthogonality of the boundary of the axisymmetric box space, the box space is split into multiple sets of hyperplanes, which are converted into measurement update constraints, and a more compact set of members is obtained. Compared with the traditional ellipsoid filtering method, the method proposed in this paper reduces the complexity of the algorithm and the redundancy from wrapping feasible set and linearization, and obtains a more compact and accurate system state set. Finally, the use of a nonlinear spring-mass-damper system verifies the effectiveness of the algorithm proposed in this paper.