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On the linear and nonlinear observability analysis of the SLAM problem

机译：关于SLAM问题的线性和非线性可观性分析

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Research in simultaneous localization and mapping (SLAM) has been progressing for almost two decades. Although several researchers attempted recently to investigate its observability (mostly without proofs for the general cases) the established facts have often been left unnoticed or ignored by the research community. In this paper rigorous proofs have been provided as an enlightenment for the observability properties of the general two dimensional SLAM problem incorporating a car like kinematic model in the context of piece-wise constant systems theory and non-linear Lie derivative theory. Observable and unobservable states of the general n landmark SLAM problem have been established with proofs. A comparison of linear and non-linear techniques to evaluate the observability of SLAM is provided using simulations.

机译：同时定位和地图绘制（SLAM）的研究已经进行了近二十年。尽管最近有几位研究人员试图调查其可观察性（大多数情况下没有针对一般情况的证据），但确定的事实常常被研究界忽视或忽略。在本文中，已经给出了严格的证明，以启发一般二维二维SLAM问题的可观测性，该问题在分段常数系统理论和非线性Lie派生理论的背景下结合了类似汽车的运动学模型。已经证明了一般n个界标SLAM问题的可观察和不可观察状态。通过仿真比较了线性和非线性技术，以评估SLAM的可观察性。

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《Mechatronics, 2009. ICM 2009》|2009年|1-6|共6页
会议地点 Malaga(ES);Malaga(ES)
作者
Perera L.D.L.; Melkumyan A.; Nettleton E.;
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Australian Centre for Field Robot., Univ. of Sydney, Sydney, NSW;

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关键词
SLAM (robots); mobile robots; nonlinear control systems; observability; piecewise constant techniques; SLAM problem; car like kinematic model; linear observability analysis; nonlinear Lie derivative theory; nonlinear observability analysis; piecewise constant systems theory; simultaneous localization and mapping; SLAM;

机译：SLAM（机器人）;移动机器人;非线性控制系统;可观测性;分段常数技术; SLAM问题;类运动学模型;线性可观测性分析;非线性李导数理论;非线性可观测性分析;分段常数系统理论;同时定位和映射; SLAM;

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1. Ship Hull Slamming Analysis with Nonlinear Boundary Element Method [J] . 中国海洋工程（英文版） . 1997,第004期

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2. AN APPROACH TO THE ANALYSIS OF OBSERVABILITY AND CONTROLLABILITY IN NONLINEAR SYSTEMS VIA LINEAR METHODS [J] . Alexey ZHIRABOK, Alexey SHUMSKY International Journal of Applied Mathematics and Computer Science . 2012,第3期

机译：用线性方法分析非线性系统中的可观性和可控性的方法
3. An approach to the analysis of observability and controllability in nonlinear systems via linear methods [J] . Alexey Zhirabok, Alexey Shumsky International journal of applied mathematics and computer science . 2012,第3期

机译：通过线性方法分析非线性系统中的可观测性和可控制性的方法
4. On the Linear and Nonlinear Observability Analysis of the SLAM Problem [C] . L.D.L. Perera, A. Meikumyan, E. Nettleton IEEE International Conference on Mechatronics . 2009

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5. Noise-Enabled Observability of Nonlinear Dynamic Systems Using the Empirical Observability Gramian. [D] . Powel, Nathan D. 2016

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6. Observability Analysis and Observer Design for a Nonlinear Three-Tank System: Theory and Experiments [O] . Santiago Rúa, Rafael E. Vásquez, Naveen Crasta, 2020

机译：非线性三箱系统的可观察性分析与观测器设计：理论与实验
7. On the transformation of nonlinear dynamical systems into the extended nonlinear observable canonical form [O] . Boutat, Driss, Busawon, Krishna 2011

机译：关于将非线性动力学系统转换为扩展的非线性可观测典范形式
8. On the Observability of Nonlinear Systems with Applications to Nonlinear Regression Analysis. [R] . fitts,john m. 1971

机译：非线性系统的可观性及其在非线性回归分析中的应用。

On the linear and nonlinear observability analysis of the SLAM problem

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