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首页> 外文期刊>Mathematical Problems in Engineering: Theory, Methods and Applications >Performance Analysis of Parameter Estimator Based on Closed-Form Newton Method for Ultrawideband Positioning
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Performance Analysis of Parameter Estimator Based on Closed-Form Newton Method for Ultrawideband Positioning

机译：基于闭式牛顿法的超宽带定位参数估计器性能分析

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摘要

Ultrawideband (UWB) is considered as a promising technology in indoor positioning due to its accurate time resolution and good penetration through objects. Since the functional model of UWB positioning is nonlinear, iterative algorithms are often considered for solving the nonlinear problem. With a rough initial value, we can obtain the optimal solution by the way of continuous iteration. As an iterative descent method of high efficiency, the Gauss-Newton method is widely used to estimate the position. However, in the UWB indoor positioning, since the location information of the user is rather limited, it is not easy to get a good initial value for iteration. Besides, the positioning system is prone to become ill-posed. These factors make the Gauss-Newton method not easy to converge to a global optimal solution or even diverge, especially under ill-conditioned positioning configuration. Furthermore, the linearization of the positioning functional model results in biased least-squares estimation. The Gauss-Newton method only includes the first-order Taylor expansion of distance equations. The bias comes from neglected higher order terms. In this study, the closed-form Newton method which considers the high order partial derivatives is introduced and proposed. The simulation and measurement experiments are implemented to analyze the performance of the closed-form Newton method in UWB positioning. Both the initial value factor and geometric configuration factor are discussed. Experimental results are given to demonstrate that the closed-form Newton method can converge to the global optimal solution with better convergence and higher efficiency regardless of whether the initial iteration value is reasonable or not. Meanwhile, the closed-form Newton method can improve the accuracy of positioning results, particularly when the anchors are not uniformly and symmetrically distributed, or the ranging error is relatively large. The study shows that closed-form of the Newton method has better convergence and positioning performance than the Gauss-Newton method, especially under ill-conditioned positioning configuration or relatively low measurement precision, even though it adds a little computational cost.
机译：超宽带（UWB）因其准确的时间分辨率和良好的穿透性而被认为是室内定位中一种很有前途的技术。由于UWB定位的函数模型是非线性的，因此通常考虑使用迭代算法来解决非线性问题。有了粗略的初始值，我们可以通过不断迭代的方式得到最优解。作为一种高效率的迭代下降方法，高斯-牛顿方法被广泛用于估计位置。然而，在UWB室内定位中，由于用户的位置信息相当有限，因此不容易获得良好的迭代初始值。此外，定位系统容易出现姿势不正常的情况。这些因素使得高斯-牛顿方法不容易收敛到全局最优解，甚至发散，特别是在条件不良的定位配置下。此外，定位泛函模型的线性化导致了偏置最小二乘估计。高斯-牛顿方法仅包括距离方程的一阶泰勒展开。这种偏差来自被忽视的高阶项。本文介绍并提出了考虑高阶偏导数的闭式牛顿方法。通过仿真和测量实验，分析了闭式牛顿方法在UWB定位中的性能。讨论了初始值因子和几何配置因子。实验结果表明，无论初始迭代值是否合理，闭式牛顿方法都能收敛到全局最优解，收敛性更好，效率更高。同时，闭合式牛顿方法可以提高定位结果的精度，特别是在锚点分布不均匀、不对称或测距误差较大的情况下。研究表明，与高斯-牛顿方法相比，封闭式牛顿方法具有更好的收敛性和定位性能，特别是在定位配置条件不佳或测量精度相对较低的情况下，尽管增加了一点计算成本。

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    Wang Chuanyang; Ning Yipeng; Wang JianYao GuobiaoZhang LongpingYang Haichao;

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    China Univ Min & Technol CUMT, NASG Key Lab Land Environm & Disaster Monitoring, Xuzhou 221116, Jiangsu, Peoples R China|China Univ Min & Technol CUMT, Sch Environm Sci & Spatial Informat, Xuzhou 221116, Jiangsu, Peoples R China;

    Shandong Jianzhu Univ, Sch Surveying & Geoinformat, Jinan 250101, Peoples R China;

    Beijing Univ Civil Engn & Architecture BUCEA, Sch Geomat & Urban Informat, Beijing 100044, Peoples R ChinaPiesat Informat Technol Co Ltd, Beijing 100195, Peoples R ChinaCUMT Geotech Engn & New Technol Dev Co Ltd, Xuzhou 221116, Jiangsu, Peoples R China;

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