一种新的鲁棒非线性卡尔曼滤波

New Kind of Robust Nonlinear Kalman Filter

Huber方法是一种基于l1/l2联合范数的估计方法,该方法可以实现估计的鲁棒性,同时尽量不损失滤波精度和效率。基于Huber估计的无味卡尔曼滤波虽提高了无味卡尔曼滤波的鲁棒性,但这种方法用统计线性回归模型来近似非线性的观测模型,损失了无味变换的精度。从Huber方法的数学意义出发,对观测信息(观测值或观测噪声)进行重新构造,然后对精确的非线性观测方程进行标准的无味卡尔曼滤波,这种新的基于Huber方法的无味卡尔曼滤波无需对非线性观测方程进行线性近似,在保持鲁棒性的前提下提高了滤波精度。通过一个具有混合高斯分布观测噪声的简明实例,验证了新算法在鲁棒性、滤波精度以及估计一致性方面的优势。

Huber method combines l1/l2 norms and provides robustness and sufficiently good precision and efficiency.In the Huber-based unscented Kalman filter,the nonlinear measurement equations are approximated by statistical linear regressed ones,but such approximation weaks the precision of unscented transformation.So,a new kind of Huber-based unscented Kalman filter is presented.Measurement information（measurements or measurements noise） are reformulated using Huber＇s cost function,and the standard unscented Kalman filter is applied to exact nonlinear measurement equation.The new method,without linear approximation,retains the high precision while the robustness is ensured.Simulation is established with a simple but evident model,and the robustness,the efficiency and the consistency of the new method are proved.