Robust optimal filters of linear stochastic systems

虽然卡尔曼滤波器在实践中已经是随机系统最流行和最广泛使用的最优滤波器，但它不是鲁棒滤波器，因此对于实际系统与其数学模型之间存在失配的系统（即，具有建模误差的系统）。Chen和Patton成功地提出了一种简单的滤波算法ODDO，该算法具有鲁棒性和最优性，甚至可以应用于具有建模误差的系统。然而，我们后来指出，ODDO是从他们不正确的基本公式推导出来的。在这个项目中，我们成功地建立了具有未知干扰的随机系统的鲁棒最优滤波器的正确理论，并发展了广泛适用于实际系统的算法（迭代法）。

Although the Kalman filter has been the most popular and widely used optimal filter for stochastic systems in practice, it is not a robust filter and so we cannot have good results often in simulations for the systems with mismatches between the actual systems and their mathematical models (i.e., the systems with modeling errors). Chen and Patton succeeded in proposing a simple filtering algorithm ODDO which is robust and optimal and can be applicable even to the systems with modeling errors. However, we later indicated that the ODDO was derived from their incorrect basic formula. In this project, we have succeeded in establishing a correct theory of robust optimal filters for stochastic systems with unknown disturbances and developing widely applicable algorithms (iterative methods) for practical systems.