协方差
代表(政治)
过滤问题
微分方程
线性滤波器
噪音(视频)
偏微分方程
协方差矩阵
线性系统
应用数学
卡尔曼滤波器
滤波器(信号处理)
数学优化
数学
非线性系统
算法
计算机科学
数学分析
统计
人工智能
政治
量子力学
图像(数学)
物理
计算机视觉
政治学
法学
扩展卡尔曼滤波器
出处
期刊:Journal of Basic Engineering
[ASME International]
日期:1960-03-01
卷期号:82 (1): 35-45
被引量:28198
摘要
The classical filtering and prediction problem is re-examined using the Bode-Shannon representation of random processes and the “state-transition” method of analysis of dynamic systems. New results are: (1) The formulation and methods of solution of the problem apply without modification to stationary and nonstationary statistics and to growing-memory and infinite-memory filters. (2) A nonlinear difference (or differential) equation is derived for the covariance matrix of the optimal estimation error. From the solution of this equation the co-efficients of the difference (or differential) equation of the optimal linear filter are obtained without further calculations. (3) The filtering problem is shown to be the dual of the noise-free regulator problem. The new method developed here is applied to two well-known problems, confirming and extending earlier results. The discussion is largely self-contained and proceeds from first principles; basic concepts of the theory of random processes are reviewed in the Appendix.
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