Minimum Variance Estimator Design for Scalar Quadratic Maps

机译：标量二次图的最小方差估计器设计

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In this paper, we consider the state estimation problem for scalar discrete-time nonlinear systems with second degree polynomial nonlinearities. A novel state estimator is proposed where the Extended Kalman filter structure is generalized to include quadratic terms and two consecutive measurements. The unbiased minimum variance estimator for the given structure is derived. It is shown both mathematically and by simulations that the new estimator achieves lower mean square estimation error than the Extended Kaiman filter. It is also shown in simulations that the new estimator fares well in performance with the recently developed current output filter.

机译：本文考虑具有二阶多项式非线性的标量离散时间非线性系统的状态估计问题。提出了一种新颖的状态估计器，其中扩展卡尔曼滤波器结构被概括为包括二次项和两个连续的测量值。得出给定结构的无偏最小方差估计量。数学和仿真均表明，新的估计器比扩展的Kaiman滤波器实现了更低的均方根估计误差。在仿真中还显示，新的估算器与最近开发的电流输出滤波器相比，性能良好。

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《Annual Allerton Conference on Communication, Control, and Computing; 20040929-1001; Monticello,IL(US)》|2004年|P.348-356|共9页
会议地点 MonticelloIL(US)
作者
Tongyan Zhai; Edwin E. Yaz; Huawei Ruan;
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作者单位

Department of Electrical and Computer Engineering Marquette University, Milwaukee, WI 53201, USA;

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原文格式 PDF
正文语种 eng
中图分类通信;
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2. Minimum variance quadratic unbiased estimators as a tool to identify compound normal distributions [J] . Rolle Jean-Daniel Journal of Computational and Applied Mathematics . 1999,第2期

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3. Quadratic subspaces and construction of Bayes invariant quadratic estimators of variance components in mixed linear models [J] . Mariusz Grządziel Statistical Papers . 2008,第3期

机译：混合线性模型中二次子空间和方差分量的贝叶斯不变二次估计的构造
4. Unbiased Minimum Variance Estimator Design for Scalar Quadratic Maps [C] . Tongyan Zhai, Edwin E. Yaz, Huawei Ruan American Control Conference . 2005

机译：标量二次图的无偏见最小方差估计设计
5. A comparison of estimators in hierarchical linear modeling: Restricted maximum likelihood versus bootstrap via minimum norm quadratic unbiased estimators. [D] . Delpish, Ayesha Nneka. 2006

机译：分层线性建模中估计量的比较：通过最小范数二次无偏估计量来限制最大似然与自举。
6. An Approximation of the Minimum-Variance Estimator of Heritability Based on Variance Component Analysis [O] . M. Grossman, H. W. Norton 1981

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7. Minimum variance quadratic unbiased estimators as a tool to identify compound normal distributions [O] . Rolle Jean-Daniel 1999

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8. On the Uniformly Minimum Variance Unbiased Estimators of the Variance and its Reciprocal of an Inverse Gaussian Distribution [R] . Korwar, R. M. 1979

机译：关于逆高斯分布的方差的一致最小方差无偏估计及其倒数

Minimum Variance Estimator Design for Scalar Quadratic Maps

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