Unified forms for Kalman and finite impulse response filtering and smoothing
Unified forms for Kalman and finite impulse response filtering and smoothing
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DOI：
10.1016/j.automatica.2013.02.026
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发表时间：
2013-06
期刊：
影响因子：
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通讯作者：
D. Simon;Y. Shmaliy
中科院分区：
文献类型：
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作者：
D. Simon;Y. Shmaliy
卡尔曼滤波器和平滑器在一定条件下是最优状态估计器。卡尔曼滤波器通常以预测器/校正器格式呈现，但卡尔曼平滑器从未以该格式导出。我们推导出卡尔曼平滑的预测/校正格式，从而提供了一个统一的形式卡尔曼滤波器和平滑。我们还讨论了无偏有限脉冲响应（UFIR）滤波器和平滑器，它可以提供一个次优的，但强大的替代卡尔曼估计。我们推导出两个统一的形式UFIR滤波器和平滑器，我们推导出其估计误差协方差的上下界。
The Kalman filter and smoother are optimal state estimators under certain conditions. The Kalman filter is typically presented in a predictor/corrector format, but the Kalman smoother has never been derived in that format. We derive the Kalman smoother in a predictor/corrector format, thus providing a unified form for the Kalman filter and smoother. We also discuss unbiased finite impulse response (UFIR) filters and smoothers, which can provide a suboptimal but robust alternative to Kalman estimators. We derive two unified forms for UFIR filters and smoothers, and we derive lower and upper bounds for their estimation error covariances.