LINEAR FILTERING FOR TIME-VARYING SYSTEMS USING MEASUREMENTS CONTAINING COLORED NOISE
LINEAR FILTERING FOR TIME-VARYING SYSTEMS USING MEASUREMENTS CONTAINING COLORED NOISE
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DOI：
10.1109/tac.1965.1098063
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发表时间：
1965-01-01
影响因子：
6.8
通讯作者：
JOHANSEN, DE
中科院分区：
文献类型：
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作者：
BRYSON, AE;JOHANSEN, DE
用于连续线性动态系统的卡尔曼-布西滤波器假设所有测量都包含“白色”噪声，即与系统中感兴趣的时间相比，相关时间短的噪声。它在这里示出，如果相关时间不短，或者如果一些测量是免费的噪声，最佳的滤波器是一个修改的卡尔曼-布西滤波器，在一般情况下，包含微分器以及积分器。它也表明，在这种情况下，估计和它的协方差矩阵是，在一般情况下，不连续的测量开始时的时间。在测量中的随机偏差误差的情况下示出的例子是有色噪声的限制情况。
The Kalman-Bucy filter for continuous linear dynamic systems assumes all measurements contain "white" noise, i.e. noise with correlation times short compared to times of interest in the system. It is shown here that if correlation times are not short, or if some measurements are free of noise, the optimal filter is a modification of the Kalman-Bucy filter which, in general, contains differentiators as well as integrators. It is also shown for this case that the estimate and its covariance matrix are, in general, discontinuous at the time when measurements are begun. The case of random bias errors in the measurements is shown by example to be a limiting case of colored noise.