A New Approach to Linear Filtering and Prediction Problems
A New Approach to Linear Filtering and Prediction Problems
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DOI：
10.1109/9780470544334.ch9
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
T. Başar
中科院分区：
文献类型：
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作者：
T. Başar
clssical切片和prediclion问题重新审查使用的随机过程的博德-香农表示和？统计转换？动态系统分析方法。新的结果是：（1）问题的公式和解法不加修改地适用于平稳和非平稳滤波器，也适用于增长记忆和无限记忆滤波器。(2)对最优估计误差的协方差矩阵，导出了一个非线性差分（或微分）方程。由该方程的解可直接得到最佳线性滤波器的差分（或微分）方程的系数。(3)填充问题应是无噪声调节器问题的对偶问题。这里开发的新方法，适用于做众所周知的问题，确认和扩展，早期的结果。讨论在很大程度上是自洽的，并从第一原理出发;随机过程理论的基本概念在附录中进行了回顾。
The clssical filleting and prediclion problem is re-examined using the Bode-Shannon representation of random processes and the ?stat-tran-sition? method of analysis of dynamic systems. New result are: (1) The formulation and Methods of solution of the problm apply, without modification to stationary and nonstationary stalistics end to growing-memory and infinile -memory filters. (2) A nonlinear difference (or differential) equalion is dericed for the covariance matrix of the optimal estimalion error. From the solution of this equation the coefficients of the difference, (or differential) equation of the optimal linear filter are obtained without further caleulations. (3) Tke fillering problem is shoum to be the dual of the nois-free regulator problem. The new method developed here, is applied to do well-known problems, confirming and extending, earlier results. The discussion is largely, self-contatained, and proceeds from first principles; basic concepts of the theory of random processes are reviewed in the Appendix.