Fast Kalman-Like Optimal Unbiased FIR Filtering With Applications
Fast Kalman-Like Optimal Unbiased FIR Filtering With Applications
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DOI：
10.1109/tsp.2016.2516960
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发表时间：
2016-05
影响因子：
5.4
通讯作者：
Shunyi Zhao;Y. Shmaliy;Fei Liu
中科院分区：
文献类型：
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作者：
Shunyi Zhao;Y. Shmaliy;Fei Liu
本文提出了一种最优无偏有限脉冲响应（OUFIR）滤波器，作为无偏FIR（UFIR）滤波器和卡尔曼滤波器（KF）之间的连接方案。我们首先推导出批量OUFIR估计，以最小化均方误差（MSE）的无偏约束，然后找到其快速迭代形式。结果表明，OUFIR滤波器是全时域（FH）的，其估计通过增加时域长度N收敛到KF估计。作为一个特殊功能，我们注意到FH OUFIR滤波器的运行速度几乎与KF一样快。OUFIR滤波器的其他几个关键属性的仿真和实际应用的基础上说明。与UFIR滤波器类似，与KF相反，OUFIR滤波器对初始条件高度不敏感。它比KF具有更好的鲁棒性对临时模型的不确定性。最后，OUFIR滤波器允许忽略工程师通常不太了解的系统噪声。
In this paper, an optimal unbiased finite impulse response (OUFIR) filter is proposed as a linking solution between the unbiased FIR (UFIR) filter and the Kalman filter (KF). We first derive the batch OUFIR estimator to minimize the mean square error (MSE) subject to the unbiasedness constraint and then find its fast iterative form. It is shown that the OUFIR filter is full horizon (FH) and that its estimate converges to the KF estimate by increasing the horizon length N. As a special feature, we note that the FH OUFIR filter operates almost as fast as the KF. Several other critical properties of the OUFIR filter are illustrated based on simulations and practical applications. Similar to the UFIR filter, and contrary to the KF, the OUFIR filter is highly insensitive to the initial conditions. It has much better robustness than KF against temporary model uncertainties. Finally, the OUFIR filter allows for ignoring system noise, which is typically not well known to the engineer.