無線傳感網(wǎng)中的迭代加權(quán)最小二乘定位算法

聞建剛; 馮文淑; 馮曉斐; 華驚宇; 余緒濤

doi:10.11999/JEIT250203

無線傳感網(wǎng)中的迭代加權(quán)最小二乘定位算法

doi: 10.11999/JEIT250203 cstr: 32379.14.JEIT250203

1.
浙江工商大學(xué)信息與電子工程學(xué)院杭州 310018
2.
東南大學(xué)移動(dòng)信息與科學(xué)工程學(xué)院南京 210096

基金項(xiàng)目: 國(guó)家自然科學(xué)基金(62271445)

詳細(xì)信息

作者簡(jiǎn)介:
聞建剛：男，講師，博士，研究方向?yàn)闊o線通信中的信號(hào)處理

馮文淑：女，碩士生，研究方向?yàn)橥ㄐ排c網(wǎng)絡(luò)

馮曉斐：女，副教授，碩士，研究方向?yàn)橥ㄐ排c網(wǎng)絡(luò)

華驚宇：男，教授，博士，研究方向?yàn)闊o線定位、通信信號(hào)處理

余緒濤：女，教授，博士，研究方向?yàn)橥ㄐ排c網(wǎng)絡(luò)

通訊作者:
華驚宇　eehjy@163.com

中圖分類號(hào): TN929.5
計(jì)量
- 文章訪問數(shù): 66
- HTML全文瀏覽量: 23
- PDF下載量: 14
- 被引次數(shù): 0
出版歷程
- 收稿日期: 2025-03-25
- 修回日期: 2025-05-29
- 網(wǎng)絡(luò)出版日期: 2025-06-14
- 刊出日期: 2025-03-10

Iterative Weighted Least Square Localization Algorithm in Wireless Sensor Networks

1.
College of Information and Electronic Engineering, Zhejiang Gongshang University, Hangzhou 310018, China
2.
National Mobile Communication Research Laboratory, Southeast University, Nanjing 210096, China

Funds: The National Natural Science Foundation of China (62271445)

摘要

摘要: 物聯(lián)網(wǎng)應(yīng)用的快速發(fā)展，帶來了對(duì)無線定位的廣泛需求，但非視距(NLOS)傳輸環(huán)境對(duì)無線定位方法精度具有巨大影響。因此該文基于到達(dá)時(shí)間(TOA)測(cè)量與雙靜態(tài)節(jié)點(diǎn)組合定義了一種位置殘差，并據(jù)此提出運(yùn)用迭代加權(quán)最小二乘(IWLS)原理的無線定位算法。算法在當(dāng)前WLS定位結(jié)果基礎(chǔ)上，通過計(jì)算位置殘差獲得反映NLOS嚴(yán)重程度的權(quán)值向量，利用權(quán)值向量在下一次WLS估計(jì)中限制NLOS影響，產(chǎn)生更加精確的定位結(jié)果。在算法的執(zhí)行過程中，殘差-權(quán)值計(jì)算方式和NLOS測(cè)距數(shù)量都會(huì)影響定位性能，因此論文通過仿真分析了這些因素對(duì)于均方根誤差(RMSE)和累計(jì)概率密度函數(shù)(CDF)的影響，確定了算法的最優(yōu)參數(shù)設(shè)定。最后論文對(duì)比了IWLS算法和傳統(tǒng)定位算法的性能，仿真結(jié)果表明，在典型非視距傳輸環(huán)境下，該文提出的IWLS算法性能優(yōu)于傳統(tǒng)算法。
- 無線定位 /
- 迭代加權(quán)最小二乘 /
- TOA /
- 位置殘差 /
- 非視距誤差
Abstract: Objective Wireless positioning technology has gained increasing attention in the Internet of Things (IoT), Intelligent Transportation Systems (ITS), and Location-Based Services (LBS). However, Non-Line-of-Sight (NLOS) errors remain a major obstacle to positioning accuracy. When Line-of-Sight (LOS) propagation between mobile and static sensors is blocked by obstacles, ranging measurement errors increase substantially. Suppressing or mitigating NLOS errors is therefore essential for improving wireless positioning performance. Although existing approaches—such as Kalman filtering, hybrid Time Difference of Arrival (TDOA)/Angle of Arrival (AOA) algorithms, and reinforcement learning—have shown some effectiveness, each faces limitations. Algorithm performance can be affected by network topology, lack adaptability in complex environments, or require high computational costs. Moreover, the statistical behavior of NLOS errors remains poorly characterized, making accurate positioning difficult in large-scale settings. This study proposes an Iterative Weighted Least Squares (IWLS) algorithm based on Time of Arrival (TOA) measurements. By defining position residuals and incorporating a residual-based weighting strategy into the WLS framework, the method suppresses NLOS errors effectively. Compared with traditional approaches, the proposed algorithm achieves higher positioning accuracy and better adaptability in NLOS scenarios, while retaining the ease of implementation offered by TOA-based techniques. Methods This study defines a new position residual based on TOA measurements from two Mobile Sensors (MSs). The residual typically approaches zero under LOS conditions but tends to increase significantly under NLOS conditions. As this residual effectively reflects deviations induced by NLOS errors, it is used to assign weights to individual equations within the linear positioning system. A residual-based weighting strategy is proposed, in which each weight is computed from the corresponding position residual, and the Weighted Least Squares (WLS) method is applied to regulate the influence of each equation. The position is estimated by iteratively updating the residuals, computing the associated weights, and applying WLS, thereby progressively reducing the positioning error and yielding an accurate estimate of the MS location. Results and Discussions The performance of the proposed algorithm is evaluated through computer simulations under varying Signal-to-Diffraction Ratio (SDR) and maximum NLOS error (NLOSmax) conditions. The simulation results indicate the following: (1) When the number of NLOS-affected static nodes is two, the Cumulative Distribution Function (CDF) of positioning error for the proposed IWLS algorithm is below 92%@5m, outperforming other tested algorithms and maintaining a consistent advantage (Fig. 6). (2) In the NLOSmax scenario (Fig. 7), the IWLS algorithm achieves better positioning accuracy than conventional methods when the number of NLOS-affected nodes is small. As this number increases, the error of the proposed algorithm grows more gradually. (3) In the SDR scenario (Fig. 8), although all algorithms show degraded performance as SDR increases, the IWLS algorithm consistently yields the lowest Root Mean Square Error (RMSE) and remains closest to the Cramér-Rao Lower Bound (CRLB). Conclusions This study proposes an IWLS localization algorithm inspired by the relationship between position residuals and the reliability of localization equations. A position residual is defined using range measurements from two static sensors, and a residual-based weighting strategy is developed to suppress the influence of NLOS errors. During each iteration, the weighting vector downregulates the contribution of equations affected by large NLOS errors, thereby improving positioning accuracy. Simulation results show that the IWLS algorithm outperforms conventional localization methods under NLOS conditions and achieves RMSE values close to the CRLB. Notably, when two static sensors are affected by NLOS errors, the localization RMSE can be reduced to approximately 2 m, representing 2% of the coverage radius.
- Wireless localization /
- Weighted Least Squares (WLS) /
- Time of Arrival (TOA) /
- Position residual /
- Non-Line-of-Sight (NLOS) error

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圖 1 位置殘差示意圖

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圖 2 IWLS算法流程圖

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圖 3 不同權(quán)值計(jì)算方法的定位CDF性能

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圖 4 不同權(quán)值計(jì)算方法的定位RMSE性能

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圖 5 位置殘差均值與迭代次數(shù)關(guān)系

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圖 6 CDF性能比較：測(cè)距噪聲標(biāo)準(zhǔn)差1 m

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圖 7 RMSE性能比較：測(cè)距標(biāo)準(zhǔn)差1 m

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圖 8 不同測(cè)距標(biāo)準(zhǔn)差的RMSE比較：NLOSmax=40 m

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表 1 對(duì)比方法描述

對(duì)比方法	描述
chan	YT Chan提出的TS-WLS定位算法^[25]
$2{\text{SS-R}}$	本文提出的位置殘差倒數(shù)的1次冪
$2{\text{SS-}} {{\mathrm{R}}^2}$	本文提出的位置殘差倒數(shù)的2次冪
$2{\text{SS-}}{{\mathrm{R}}^3}$	本文提出的位置殘差倒數(shù)的3次冪

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表 2 算法對(duì)比

算法	描述
CLS	約束最小二乘法^[22]
SDP	半正定規(guī)劃算法^[23]
RWGH	殘差加權(quán)算法^[24]
TS-WLS	已知TDOA測(cè)量值情況下，使用兩步WLS算法^[26]
OptLLOP	擴(kuò)展的LLOP算法^[27]
TS-WLS-A	基于角度殘差的兩步WLS算法^[28]
CRLB	克拉默-拉奧下界(Cramer-Rao Lower Bound)
position res-2SS	本文提出的以位置殘差倒數(shù)為權(quán)值的IWLS算法

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