摘要
普通卡尔曼滤波是在线性高斯情况下利用最小均方误差准则获得目标的动态估计,适应于过程和测量都属于线性系统,且误差符合高斯分布的系统。但是实际上很多系统都存在一定的非线性,表现在状态方程是非线性的,或者测量方程是非线性的。这种情况下就不能使用一般的卡尔曼滤波。解决的方法是将非线性关系进行线性近似,将其转化成线性问题。就转化为线性问题的2个方案扩展卡尔曼(EKF)和无迹卡尔曼(UKF)作出对比和分析,EKF与卡尔曼滤波原理相似,但是它将非线性函数在最佳估计点处进行泰勒级数展开,舍弃高阶分量,从而将非线性模型简单线性化;UKF是通过确定性采样,以无迹变换为基础,用卡尔曼线性滤波框架而建立起来的,对非线性系统有很好的滤波效果。最后在MATLAB平台下实验证明,与EKF相比,UKF不仅保持了系统的稳定性,而且提高了精确度。
General kalman filter estimation uses the minimum mean square error criterion to obtain the target estimation under the condition of linear Gauss. It adapts to the process and measurement belonging to linear-system, and its error is in accordance with a system of Gauss distribution. But in fact, many systems are nonlinear, it shows in the nonlinear state equations or nonlinear measurement equations. Kalman filter cannot be used in this case. The solution is to convert the nonlinear relationship into linear problem. In this paper, we introduce two schemes including extended kalman filter （EKF） and the unscented kalman filter （UKF） to make a comparison and analysis. EKF principle is similar to kalman filter. It uses the Taylor series expansion for the nonlinear function in the optimal estimation point and abandons the higher-order harmonics. So the nonlinear model can be changed into simple linearization; UKF takes deterministic sample based on unscented transformation（UT） using kalman linear filter framework. It has a good filtering performance for nonlinear system. The experiments show that not only UKF maintains the stability of the system but also improves the accuracy of system under the MATLAB platform when comparing with EKF.
出处
《沈阳师范大学学报（自然科学版）》
CAS
2015年第2期279-283,共5页
Journal of Shenyang Normal University:Natural Science Edition
基金
国家自然科学基金资助项目(60970112)
