有色噪声下的不敏卡尔曼滤波器

Unscented Kalman Filter with Colored Noise

有色噪声干扰情况下非线性系统的状态估计是许多实际工程需要解决的问题。通常的方法是利用扩展卡尔曼滤波方法将非线性系统线性化后,再利用线性系统的方法对有色噪声系统进行估计。然而,模型的线性化误差往往会严重影响最终的滤波精度,甚至导致滤波发散。为了避免此类误差,先通过对测量方程进行变换的方法,将观测方程的有色噪声转换为白噪声后,再利用不敏卡尔曼滤波方法,对系统的状态进行估计。虽然,该方法也需要对观测方程进行线性化,但是由于此线性化过程是在求解新量测方程的测量误差中进行,因此对系统的误差影响不是很大。仿真结果表明新方法能够有效地对有色噪声环境下系统的状态进行估计,性能要优于现有的一些基于EKF的方法。

In the real world, it is a common problem how to estimate the state of nonlinear systems with colored noise. The Extended Kalman Filter （EKF） is generally used to linearize the state or measure equations of the nonlinear system, and the linear method can be used. However, the performance of the EKF may not be always good due to the linearization error. In this paper, a new method is proposed. Firstly, the method transforms the measure equation of the system, so the colored noise of the equation can be changed into white noise. Then, the Unscented Kalman Filter （UKF） can be used to estimate the state of the system. Although, the linearization of the equations is also needed in this method, it will not affect the precision of the method, because the linearization is performed during the course of computing the error of the new measure equation. The results of the simulation show that the new method can effectively get the precision state estimation of the nonlinear system with colored nois.