动态EIV模型及其总体卡尔曼滤波方法

doi:10.11947/j.AGCS.2018.20170098

测绘学报 ›› 2018, Vol. 47 ›› Issue (4): 480-489.doi: 10.11947/j.AGCS.2018.20170098

动态EIV模型及其总体卡尔曼滤波方法

余航¹, 王坚², 王乐洋³, 宁一鹏¹, 刘志平¹

1. 中国矿业大学环境与测绘学院, 江苏徐州 221116;
2. 北京建筑大学测绘与城市空间信息学院, 北京 100044;
3. 东华理工大学测绘工程学院, 江西南昌 330013

收稿日期:2017-02-28 修回日期:2017-12-29 出版日期:2018-04-20 发布日期:2018-05-02
通讯作者: 王坚 E-mail:wjiancumt@163.com
作者简介:余航(1991-),男,博士生,研究方向为室内外无缝定位理论和应用。E-mail:yhecit@163.com
基金资助:
国家重点研发计划（2016YFC0803103）；国家自然科学基金（41664001）；江西省杰出青年人才资助计划（20162BCB23050）

Total Kalman Filter Method of Dynamic EIV Model

YU Hang¹, WANG Jian², WANG Leyang³, NING Yipeng¹, LIU Zhiping¹

1. School of Environment Science and Spatial Information, China University of Mining and Technology, Xuzhou 221116, China;
2. School of Geomatics and Urban Spatial Information, Beijing University of Civil Engineering and Architecture, Beijing 100044, China;
3. Faculty of Geomatics, East China University of Technology, Nanchang 330013, China

Received:2017-02-28 Revised:2017-12-29 Online:2018-04-20 Published:2018-05-02
Supported by:
The National Key Research and Development Program of China (No. 2016YFC0803103);The National Natural Science Foundation of China (No. 41664001);The Support Program for Outstanding Youth Talent in Jiangxi Province (No. 20162BCB23050)

摘要/Abstract

摘要： 针对求解动态EIV模型时未考虑状态方程中状态转移矩阵误差的问题，本文建立了一种能够同时顾及状态方程和观测方程中各量误差的动态EIV模型。推导了针对该动态EIV模型的总体卡尔曼滤波方法及其近似精度评定公式。对比分析了本文总体卡尔曼滤波方法与已有总体卡尔曼滤波方法及总体最小二乘方法的异同。算例结果表明，本文方法统计上要优于标准卡尔曼滤波方法和已有的总体卡尔曼滤波方法。

关键词: 总体最小二乘, 总体卡尔曼滤波, 动态EIV模型, 先验信息, 虚拟观测值

Abstract: For the case of the adjustment method of dynamic errors-in-variables(EIV)model ignoring the random errors in the state propagating matrix of system equations,this paper establishes a dynamic EIV model which considers the errors of each elements in both observation equations and system equations.A total Kalman filter method (TKF) and its approximated precision estimator are proposed based on this dynamic EIV model.The similarities and differences of the proposed method,the existing total Kalman filter methods and total least squares (TLS) methods are also analyzed.The results show that the proposed method is statistically superior to the standard Kalman filter method and the existing total Kalman filter methods.

Key words: total least squares, total Kalman filter, dynamic EIV model, prior information, virtual observations

中图分类号:

P207

余航, 王坚, 王乐洋, 宁一鹏, 刘志平. 动态EIV模型及其总体卡尔曼滤波方法[J]. 测绘学报, 2018, 47(4): 480-489.

YU Hang, WANG Jian, WANG Leyang, NING Yipeng, LIU Zhiping. Total Kalman Filter Method of Dynamic EIV Model[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(4): 480-489.

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动态EIV模型及其总体卡尔曼滤波方法

Total Kalman Filter Method of Dynamic EIV Model

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