Optimal Filters for Bilinear Systems with Nilpotent Lie Algebras.

机译：具有幂零李代数的双线性系统的最优滤子。

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The authors consider a bilinear signal process driven by a Gauss-Markov process which is observed in additive, white, Gaussian noise. An exact stochastic differential equation for the least squares filter is derived when the Lie algebra associated with the signal process is nilpotent. It is shown that the filter is also bilinear and that it satisfies an analogous nilpotency condition. Some special cases and an example are discussed, indicating ways of reducing the filter dimensionality. (Author)

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作者
chikte, shirish d. ting-ho lo,james;
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年度 1978
页码 1-33
总页数 33
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Lie groups; Mathematical filters; Optimization; Nonlinear analysis; Gaussian noise; Markov processes; Least squares method; ITO processes; Stochastic differential equations;

机译：李群;数学滤波器;优化;非线性分析;高斯噪声;马尔可夫过程;最小二乘法; ITO过程;随机微分方程;

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1. Bilinear systems with nilpotent lie algebra: optimal finite-dimensional filtering of their state vector [J] . M. E. Shaikin Automation and Remote Control . 2000,第2aPta1期

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2. Free nilpotent and H-type Lie algebras. Combinatorial and orthogonal designs [J] . Furutani Kenro, Markina Irina, Vasilev Alexander Journal of pure and applied algebra . 2015,第12期

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3. Optimal Finite-Dimensional Filtering of the State Vector for Linear Systems with Nilpotent Lee Algebras [J] . Shaiakin M. E Автоматика и Телемехелемех . 2000,第2期

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4. On the reachable set of nonlinear control systems with a nilpotent Lie algebra [C] . Margaliot Michael European Control Conference . 2007

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5. Finite order automorphisms and a parametrization of nilpotent orbits in p-adic Lie algebras. [D] . Portilla, Ricardo. 2011

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7. Optimal Filtering Scheme for Bilinear Discrete-Time Systems:a Linear Matrix Inequality Approach [O] . Shaker, Hamid Reza 2012

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Optimal Filters for Bilinear Systems with Nilpotent Lie Algebras.

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