基于最小均方误差估计的噪声相关UKF设计

Design of UKF with correlative noises based on minimum mean square error estimation

传统Unscented卡尔曼滤波器(UKF)要求系统噪声和量测噪声必须是互不相关的.针对此局限性,研究了一类带相关噪声的非线性离散系统UKF设计方法.基于最小均方误差估计和正交变换,给出了噪声相关UKF滤波递推公式,并采用Unscented变换(UT)来计算系统状态的后验分布.所设计的UKF有效解决了传统UKF在噪声相关条件下非线性滤波失效的问题,拓展了UKF的应用范围.最后,仿真实例表明了所设计UKF的有效性.

Unscented Kalman filter（UKF） for a class of nonlinear discrete-time systems with correlative noises is designed to overcome the limitation that the conventional UKF calls for system noise and measurement to be irrelative. Recursive filtering equations of UKF with correlative noises are given based on minimum mean square error estimation and orthogonal transformation, and unscented transformation（UT） is applied to calculation the posterior distribution of the nonlinear system state. The proposed UKF solves the problem of nonlinear filtering failure in conventional UKF when system noise is correlated with measurement noise, so it expands the applications of the conventional UKF. A simulation example shows the effectiveness of the designed UKF.