ABSTRACT

The Kalman filter is one of the most widely used methods for state estimation and control purposes. However, it requires correct knowledge of noise statistics, which are unknown or not known perfectly in real-life applications and then they need to be identified. Considering such background, this paper introduces a new adaptive Kalman filter algorithm in order to handle the unknown process noise covariance for linear discrete-time closed-loop systems. From the closed-loop joint analysis of the system and the a priori recursive form of the Kalman filter, we adaptively estimate the process noise covariance by relating it to the observation vector covariance. The latter is then obtained from an exponential moving average technique. Lastly, we also extend our adaptive methodology for a special class of nonlinear systems. The performance of the proposed adaptive method is demonstrated through numerical examples and it has been compared to other types of adaptive filtering algorithms.

摘要

卡尔曼滤波器是用于状态估计和控制目的的最广泛使用的方法之一。但是，它需要正确了解噪声统计信息，这些统计信息在实际应用中是未知的或不完全已知的，然后需要对其进行识别。考虑到这样的背景，本文介绍了一种新的自适应卡尔曼滤波算法，以处理线性离散时间闭环系统的未知过程噪声协方差。从系统的闭环联合分析和先验作为卡尔曼滤波器的递归形式，我们通过将过程噪声协方差与观测向量协方差相关联来自适应地估计过程噪声协方差。然后从指数移动平均技术获得后者。最后，我们还为一类特殊的非线性系统扩展了我们的自适应方法。通过数值例子证明了所提出的自适应方法的性能，并与其他类型的自适应滤波算法进行了比较。