The finite impulse response (FIR) approach is known to be more robust than the Kalman approach. In this paper, we derive a batch q -lag maximum likelihood (ML) FIR smoother for full covariance matrices and represent it with an iterative algorithm using recursions for diagonal covariance matrices. It is shown that, under ideal conditions of fully known model, the ML FIR smoother occupies an intermediate place between the more accurate Rauch-Tung-Striebel (RTS) smoother and the less accurate unbiased FIR smoother. With uncertainties and errors in noise covariances, ML FIR smoothing is significantly superior to RTS smoothing. It is also shown experimentally that ML FIR smoothing is more robust than RTS smoothing against measurement outliers.

中文翻译：

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离散时间 $q$-滞后最大似然 FIR 平滑和迭代递归算法


众所周知，有限脉冲响应 (FIR) 方法比卡尔曼方法更稳健。在本文中，我们推导了全协方差矩阵的批量 q 滞后最大似然 (ML) FIR 平滑器，并通过使用对角协方差矩阵递归的迭代算法来表示它。结果表明，在完全已知模型的理想条件下，ML FIR 平滑器处于更精确的 Rauch-Tung-Striebel (RTS) 平滑器和不太精确的无偏 FIR 平滑器之间。由于噪声协方差存在不确定性和误差，ML FIR 平滑明显优于 RTS 平滑。实验还表明，针对测量异常值，ML FIR 平滑比 RTS 平滑更稳健。