最大相关熵无迹滤波器
Maximum Correntropy Unscented Filter
摘要：
无迹变换（Unscented Transform，UT）是一种有效的非线性动态系统状态估计方法，它利用无导数的高阶近似来近似高斯分布，而不是近似非线性函数。将UT应用于卡尔曼滤波器类型的估计器导致众所周知的无迹卡尔曼滤波器（UKF）。虽然UKF在高斯噪声环境下有很好的效果，但当噪声为非高斯噪声时，尤其是当系统受到强尾脉冲噪声干扰时，UKF的性能会显著恶化。为了提高UKF对脉冲噪声的鲁棒性，提出了一种新的非线性系统滤波器，即最大相关熵无迹滤波器（MCUF）。在MCUF中，UT被应用于获得状态和协方差阵的先验估计，然后使用基于最大相关熵准则（MCC）的鲁棒统计线性化回归来获得状态和协方差矩阵的后验估计。两个算例验证了新算法的有效性。
英文摘要：
The unscented transformation (UT) is an efficient method to solve the state estimation problem for a non-linear dynamic system, utilizing a derivative-free higher-order approximation by approximating a Gaussian distribution rather than approximating a non-linear function. Applying the UT to a Kalman filter type estimator leads to the well-known unscented Kalman filter (UKF). Although the UKF works very well in Gaussian noises, its performance may deteriorate significantly when the noises are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises. To improve the robustness of the UKF against impulsive noises, a new filter for nonlinear systems is proposed in this work, namely the maximum correntropy unscented filter (MCUF). In MCUF, the UT is applied to obtain the prior estimates of the state and covariance matrix, and a robust statistical linearization regression based on the maximum correntropy criterion (MCC) is then used to obtain the posterior estimates of the state and covariance. The satisfying performance of the new algorithm is confirmed by two illustrative examples.
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