RSS室内定位信号经验模型重构研究
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摘要
介绍低秩矩阵填充理论,结合RSS室内信号图的特点,借鉴地形图中的地物特征点概念,提出RSS欧氏空间信号特征点概念;提出RSS室内定位信号经验模型的具体重构算法和流程。最后,分析RSS几何空间特征点构建指纹库的精度分析和RSS欧氏空间信号特征点信号模型重构的精度分析,对不同类型的特征点赋予不同的权值,并将这些特征点用在RSS室内定位信号经验模型的重构中。实验结果表明,在数据采样量略高于位置指纹(约为1.37倍)的情况下,利用RSS室内定位信号经验模型的定位精度显著高于位置指纹的定位精度(约为2倍),特别是0.5m以内的定位精度。
This paper introduces the theory of low rank matrix filling,and uses the theory of low rank matrix to fill the RSSI sample data.Then,based on the characteristics of RSSI indoor signal map,the concept of RSSI Euclidean space signal feature points is proposed by using the concept of feature points in topographic maps.Finally,this paper proposes an empirical model of RSSI indoor positioning signal reconstruction algorithm.According to their respective accuracy,different types of feature points are given different weights,and those feature points are used in the reconstruction of the RSSI indoor positioning signal empirical model.Based on the experimental results,the positioning accuracy of the empirical model of the RSSI indoor positioning signal is significantly higher than that of the location fingerprint(about 2 times)in the case of data sampling is slightly higher than the location fingerprint(about 1.37 times),especially the positioning accuracy within 0.5 meters.Therefore,the empirical signal model of RSSI indoor positioning has some research significance and application prospects.
This paper introduces the theory of low rank matrix filling,and uses the theory of low rank matrix to fill the RSSI sample data.Then,based on the characteristics of RSSI indoor signal map,the concept of RSSI Euclidean space signal feature points is proposed by using the concept of feature points in topographic maps.Finally,this paper proposes an empirical model of RSSI indoor positioning signal reconstruction algorithm.According to their respective accuracy,different types of feature points are given different weights,and those feature points are used in the reconstruction of the RSSI indoor positioning signal empirical model.Based on the experimental results,the positioning accuracy of the empirical model of the RSSI indoor positioning signal is significantly higher than that of the location fingerprint(about 2 times)in the case of data sampling is slightly higher than the location fingerprint(about 1.37 times),especially the positioning accuracy within 0.5 meters.Therefore,the empirical signal model of RSSI indoor positioning has some research significance and application prospects.
引文
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[2]陈晓雷.面向WLAN室内AP部署的衰减因子传播模型参数校正研究与实践[D].湖南湘潭:湖南科技大学,2013.
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[4] CANDES E J,ROMBERG J,TAO T.Robust uncertainty principles:exact signal reconstruction from highly incomplete frequency information[J].IEEE Transactions on Information Theory,2006,52(2):489-509.
[5] Donoho D L.Compressed sensing[J].IEEE Transactions on Information Theory,2006,52(4):1289-1306.
[6]赵玉娟,郑宝玉,陈守宁.矩阵填充及其在信号处理中的应用[J].信号处理,2015(4):423-436.
[7]王红亮,王帅,刘文怡.压缩感知实现方法及应用综述[J].探测与控制学报,2014,6(4):53-61.
[8]石光明,刘丹华,高大化,等.压缩感知理论及其研究进展[J].电子学报,2009,37(5):1070-1081.
[9]彭义刚,索津莉,戴琼海,等.从压缩传感到低秩矩阵恢复:理论与应用[J].自动化学报,2013,39(7):981-994.
[10]朱更明,周星岚,谢井雄,等.基于压缩感知的无线传感网数据收集研究进展[J].西北大学学报(自然科学版),2015,45(4):560-567.
[11]李珅,马彩文,李艳,等.压缩感知重构算法综述[J].红外与激光工程,2013,42(增1):225-232.
[12]王强,李佳,沈毅.压缩感知中确定性测量矩阵构造算法综述[J].电子学报,2013(10):2041-2050.
[13]万莎,徐彪,段洪涛.压缩感知技术综述[J].中国无线电,2013(2):60-62.
[14]马晓慧.矩阵填充理论方法分析[D].杭州:浙江大学,2012.
[15]袁淦钊.矩阵的低秩近似算法及其应用[D].广州:华南理工大学,2013.
[16]RECHT B,FAZEL M,PARRILO P A.Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization[J].Siam Review,2007,52(3):471-501.
[17]李雷,刘盼盼.压缩感知中基于梯度的贪婪重构算法综述[J].南京邮电大学学报(自然科学版),2014,34(6):1-8.
[18]王蕴红,谭铁牛.基于奇异值分解和数据融合的脸像鉴别[J].计算机学报,2000,23(6):649-653.
[19]Nakayama T.On Frobeniusean algebras.I[J].Annals of Mathematics,2010,40(1):611-633.