基于容积变换的平滑变结构滤波及应用

Smoothing variable structure filter based on cubature transform and its application

针对非线性系统状态估计中,平滑变结构滤波(smoothing variable structure filter,SVSF)算法要求系统是连续可微的且需要计算系统Jacoby矩阵的问题,提出了基于球面径向基容积规则的平滑变结构滤波(cubature-smoothing variable structure filter,C-SVSF)算法,该算法避免了对非线性系统Jacoby矩阵的计算;同时受计算机计算字长的限制,算法会有一定的舍入误差,误差的积累有时会导致协方差矩阵失去非负定性和对称性,从而使得滤波计算发散。因而进一步提出了C-SVSF的平方根形式,即平方根容积平滑变结构滤波算法。最后在动力定位船状态估计仿真实验中,说明了算法的有效性。

In order to solve the problem that the smoothing variable structure filter requires that the system is continuous and differentiable,and the Jacoby matrix needs to be calculated for the state estimation of nonlinear systems,a cubature-smoothing variable structure filter(C-SVSF)is proposed.The algorithm avoids the computation of Jacoby matrix.Meanwhile,the algorithm will have some rounding error because of the computer word-length.The accumulation of errors can sometimes make the covariance matrix loss of positive definiteness and symmetry which would make the filter divergence.Thus,the square root C-SVSF is proposed.Finally,the simulation results show that the algorithm is effective in the simulation experiment of the dynamic positioning ships.