A differential geometric approach to nonlinear filtering: theprojection filter

Brigo D.; Hanzon B.; LeGland F.

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A differential geometric approach to nonlinear filtering: theprojection filter

机译：非线性滤波的差分几何方法：投影滤波器

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This paper presents a new and systematic method of approximating exact nonlinear filters with finite dimensional filters, using the differential geometric approach to statistics. The projection filter is defined rigorously in the case of exponential families. A convenient exponential family is proposed which allows one to simplify the projection filter equation and to define an a posteriori measure of the local error of the projection filter approximation. Finally, simulation results are discussed for the cubic sensor problem

机译：本文提出了一种新的系统方法，采用差分几何方法对统计数据进行精确的非线性滤波器与有限维滤波器的逼近。对于指数族，必须严格定义投影滤镜。提出了一种方便的指数族，其允许简化投影滤波器方程并定义投影滤波器近似的局部误差的后验度量。最后，讨论了立方传感器问题的仿真结果

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来源
《IEEE Transactions on Automatic Control》 |1998年第2期|p.247-252|共6页
作者
Brigo D.; Hanzon B.; LeGland F.;
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正文语种 eng
中图分类自动化系统;
关键词
differential geometry; filtering theory; nonlinear filters; probability; statistical analysis; cubic sensor; differential geometry; exponential families; finite dimensional filters; nonlinear filtering; nonlinear filters; probability; projection filter;

机译：微分几何;滤波理论;非线性滤波器;概率;统计分析;立方传感器;微分几何;指数族;有限维滤波器;非线性滤波;非线性滤波器;概率;投影滤波器;

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1. A differential geometric approach to nonlinear filtering: the projection filter [J] . Brigo D., Hanzon B. IEEE Transactions on Automatic Control . 1998,第2期

机译：非线性滤波的差分几何方法：投影滤波器
2. A nonlinear filtering approach to changepoint detection problems: Direct and differential-geometric methods [J] . Vellekoop MH, Clark JMC SIAM Review . 2006,第2期

机译：解决变更点检测问题的非线性滤波方法：直接和微分几何方法
3. A nonlinear filtering approach to changepoint detection problems: Direct and differential-geometric methods [J] . Vellekoop MH., Clark JMC. SIAM Journal on Control and Optimization . 2003,第2期

机译：解决变更点检测问题的非线性滤波方法：直接和微分几何方法
4. A differential geometric approach to nonlinear filtering: the projection filter [C] . Brigo, D., Hanzon, . 1995

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7. A differential geometric approach to nonlinear filtering: the projection filter [O] . D. Brigo, B. Hanzon, F. LeGland 1998

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8. PDE, Differential Geometric, Algebraic, Wavelet and Parallel Computation Methods in Nonlinear Filtering [R] . Yau, S. S. 2003

机译：非线性滤波中的偏微分方程，微分几何，代数，小波和并行计算方法

A differential geometric approach to nonlinear filtering: theprojection filter

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