AN INNOVATIONS APPROACH TO LEAST-SQUARES ESTIMATION .I. LINEAR FILTERING IN ADDITIVE WHITE NOISE
AN INNOVATIONS APPROACH TO LEAST-SQUARES ESTIMATION .I. LINEAR FILTERING IN ADDITIVE WHITE NOISE
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DOI：
10.1109/tac.1968.1099025
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发表时间：
1968-01-01
影响因子：
6.8
通讯作者：
KAILATH, T
中科院分区：
文献类型：
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作者：
KAILATH, T
线性最小二乘近似问题的创新方法是首先通过因果和可逆操作来“消除”观测数据，然后处理由此产生的更简单的白噪声观测问题。这种技术被成功地用于波德和香农获得一个简单的推导经典维纳滤波问题的平稳过程在一个半无限的时间间隔。在这里，我们将扩展的技术来处理非平稳连续时间过程在有限的时间间隔。在第一部分中，我们将应用这种方法来获得卡尔曼-布西递归滤波公式的简单推导（对于连续时间和离散时间过程），以及一些小的推广。
The innovations approach to linear least-squares approximation problems is first to "whiten" the observed data by a causal and invertible operation, and then to treat the resulting simpler white-noise observations problem. This technique was successfully used by Bode and Shannon to obtain a simple derivation of the classical Wiener filtering problem for stationary processes over a semi-infinite interval. Here we shall extend the technique to handle nonstationary continuous-time processes over finite intervals. In Part I we shall apply this method to obtain a simple derivation of the Kalman-Bucy recursive filtering formulas (for both continuous-time and discrete-time processes) and also some minor generalizations thereof.