噪声相关条件下Unscented卡尔曼滤波器设计

Design of unscented Kalman filter with correlative noises

针对传统Unscented卡尔曼滤波器(UKF)在噪声相关条件下非线性滤波失效的问题,研究了一类带相关噪声的非线性离散系统UKF设计方法.文中基于最小均方误差估计准则,给出了系统噪声和量测噪声相关时UKF滤波递推公式,并采用Unscented变换(UT)来计算系统状态的后验均值和协方差.所设计的噪声相关条件下UKF有效克服了传统UKF必须假设系统噪声和量测噪声为互不相关高斯白噪声的局限性,拓展了UKF的应用范围.仿真实例验证了其可行性和有效性.

An Unscented-Kalman Filter（UKF） for a class of nonlinear discrete-time systems with correlated noises is designed to deal with the problem of nonlinear filtering failure in conventional UKF when system noise is correlated with measurement noise. Recursive filtering equations of UKF with correlated noises are given based on the minimum meansquare-error estimation; and unscented transformation（UT） is applied to the calculation the posterior means and covariances of the nonlinear system states. The proposed UKF breaks through the limitations on the conventional UKF that the system noise and measurement noise must be uncorrelated Gauss white noises, thus extending the applications of the conventional UKF. A simulation example shows its feasibility and effectiveness.