Iterative Weighted Least Square Localization Algorithm in Wireless Sensor Networks

WEN Jiangang; FENG Wenshu; FENG Xiaofei; HUA Jingyu; YU Xutao

doi:10.11999/JEIT250203

Volume 47 Issue 3

Mar. 2025

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Article Navigation > Journal of Electronics & Information Technology > 2025 > 47(3): 582-589

WEN Jiangang, FENG Wenshu, FENG Xiaofei, HUA Jingyu, YU Xutao. Iterative Weighted Least Square Localization Algorithm in Wireless Sensor Networks[J]. Journal of Electronics & Information Technology, 2025, 47(3): 582-589. doi: 10.11999/JEIT250203

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WEN Jiangang, FENG Wenshu, FENG Xiaofei, HUA Jingyu, YU Xutao. Iterative Weighted Least Square Localization Algorithm in Wireless Sensor Networks[J]. Journal of Electronics & Information Technology, 2025, 47(3): 582-589. doi: 10.11999/JEIT250203

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Iterative Weighted Least Square Localization Algorithm in Wireless Sensor Networks

doi: 10.11999/JEIT250203 cstr: 32379.14.JEIT250203

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)

Received Date: 2025-03-25
Rev Recd Date: 2025-05-29

Available Online: 2025-06-14

Publish Date: 2025-03-10

Abstract

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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References(29)

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