The localization technology is the essential requirement of constructing a smart building and smart city. It is one of the most important technologies for wireless sensor networks (WSNs). However, when WSNs are deployed in harsh indoor environments, obstacles can result in non-line-of-sight (NLOS) propagation. In addition, NLOS propagation can seriously reduce localization accuracy. In this paper, we propose a NLOS localization method based on residual analysis to reduce the influence of NLOS error. The time of arrival (TOA) measurement model is used to estimate the distance. Then, the NLOS measurement is identified through the residual analysis method. Finally, this paper uses the LOS measurements to establish the localization objective function and proposes the particle swarm optimization with a constriction factor (PSO-C) method to compute the position of an unknown node. Simulation results show that the proposed method not only effectively identifies the LOS/NLOS propagation condition but also reduces the influence of NLOS error.

The rapid development of microelectromechanical system (MEMS) technology, sensor technology, wireless communication, and low-power embedded technology promotes the progress and development of wireless sensor networks (WSNs). WSNs consist of a large number of inexpensive microsensor nodes deployed in a monitored region. The sensor nodes are connected to each other by self-organization and multihop communications [

One of the most important issues for WSNs is localization technology [

For the TOA-based localization method, the signal velocity is known in advance. It measures the travel time of the signal from the beacon node to the unknown node, and the distance between two nodes is equal to the product of the signal velocity and the travel time. However, this method requires high-precision time synchronization between two nodes. As light synchronization error can significantly affect the ranging error. Therefore, the TOA method requires additional hardware to ensure the time synchronization. The TDOA method requires two different transceivers on a node so that the node can transmit two signals with different velocities at the same time. It estimates the distance by measuring the two signals’ arrival time difference between the beacon node and the unknown node. The requirement of time accuracy of the TDOA method is lower than the TOA method, but it still has high requirements for hardware. The RSS method is one of the least expensive ways to locate an unknown node because it does not need additional hardware. The RSS method measures the signal power loss value from a beacon node to an unknown node, and it converts the power loss value to the distance through a signal propagation model. The AOA method measures and calculates the angles between beacon nodes and an unknown node and then estimates the position of the unknown node based on the angle between two nodes.

In this paper, we investigate the TOA-based localization method in an indoor environment. Obstacles can result in NLOS propagation in harsh indoor environments, and the accuracy of localization will drop sharply. We first propose an NLOS identification method based on residual analysis. The propagation condition can be identified by it. Then, the localization objective function is established using the LOS measurements. In addition, the particle swarm optimization with a constriction factor method is proposed to find the optimal solution of the localization function. The optimal solution is the estimated position of the unknown node. The main contributions of this paper are given as follows:

The NLOS identification method does not need prior knowledge of the NLOS error. In addition, it can identify the NLOS measurements when the number of LOS measurements is larger than the number of NLOS measurements.

The proposed NLOS correction method can mitigate the effect of the NLOS error.

The proposed method not only uses TOA measurements but also uses other signal features such as TDOA and RSS easily. Therefore, it is not constrained by different physical measurement techniques.

The rest of the paper is organized as follows. Section

Compared with traditional positioning systems, WSN-based localization systems can be quickly deployed and can adapt to various harsh environmental conditions. They have the characteristics of low power consumption, low cost, and strong expansibility. In addition, the Global Positioning System (GPS) technique, which is widely used at present, has the characteristics of high energy consumption, high cost, and large volume compared with WSNs [

Because the WSN localization technology has remarkable superiority, both researchers and designers are paying more attention to it and devoting more effort to improving the positioning accuracy. In [

NLOS propagation is ubiquitous in practical indoor environments. NLOS propagation will contribute a positive additional excessive delay to the measured value. NLOS error is the main source of the localization error. To improve the positioning accuracy in practical conditions, NLOS identification and mitigation methods are widely investigated. A residual weighting algorithm (Rwgh) is proposed in [

In this section, we first analyze the TOA measurement model in LOS and NLOS propagation conditions, respectively. Then, we propose an NLOS identification method based on residual analysis, according to the characteristics of the NLOS error. Finally, we improve the existing NLOS localization method by using particle swarm optimization with a constriction factor.

The TOA method measures the travel time of a signal from the beacon node to the unknown node. The true distance of TOA is modeled as follows:

Because the travel time

In practical conditions, the existence of obstacles will result in NLOS conditions. Such obstacles will admit a positive error component to the estimated distance. Considering the NLOS error, the distance between the

Figure

The CDF for measurement noise and NLOS error.

NLOS propagation is ubiquitous in practical conditions and has a large influence on measurements. To obtain more accurate measurements, approaches to reduce the influence that NLOS error admits to localization accuracy must be considered. NLOS error has distinct characteristics compared with the measuring error: (1) NLOS error is always positive. (2) The standard deviation of the distance measurement in NLOS propagation conditions is larger than that in LOS propagation conditions. (3) NLOS error exhibits high randomness.

Considering the characteristics of the NLOS error, NLOS identification methods based on residual analysis can be used to determine and eliminate the NLOS measurements. The basic approach of the residual analysis method can be expressed as follows:

There are

Use the maximum likelihood method to compute the estimated location of each combination. The estimated position of the

Accumulate the residuals of each measurement as follows:

We can obtain

Sort the cumulative residuals from large to small; the measurements with the largest residual can be regarded as NLOS measurements.

By using the above steps, we can determine the NLOS measurements, and the rest of the measurements can be regarded as measurements in LOS propagation conditions.

The probability density function of the measurement in an LOS condition can be expressed as follows [

To solve the position function directly, not only is a large amount of calculation required but the difficulty of finding an analytical solution is also encountered. Therefore, we use the particle swarm optimization with a constriction factor (PSO-C) method to determine the optimal solution. PSO is based on simulating a simplified model of social interaction. PSO is easy to implement and does not require gradient information, so it is widely used in scientific research and engineering practice.

The basic principle of the algorithm is as follows: assume that a swarm includes

The pseudocode of the PSO-C strategy is shown as follows:

1. Initialize the basic parameters of PSO-C

2. Generate an initial population

3. Calculate the fitness values of the population

4. Set S to be the

5. Set the particle with best fitness to be

6. For

7. For

8. Update the velocity of particle

9. Update the location of particle

10. Compute the fitness values of the new particle

11. If the fitness value of

12. Then, set

13. End if

14. If the fitness value of _{g}

15. Then, set _{g}

16. End if

17. End for

18. End for

The

In this section, we evaluate the performance of our proposed NLOS localization algorithms. We compare the proposed method with RANSAC [

The default parameter values.

Parameters | Symbol | Default values |
---|---|---|

Number of beacon nodes | 8 | |

The standard deviation of the measurement noise | 1 | |

The NLOS errors | ||

The NLOS errors |

First, the identification success rate of the proposed method is evaluated. Figure

The identification success rate versus the number of beacon nodes.

When the NLOS error obeys the uniform distribution (

The identification success rate versus

In Figure

The localization error versus the number of beacon nodes.

Figure

The localization error versus

Figure

The CDF of localization error.

Figure

The localization error versus

In order to verify the effective of the proposed localization method, we perform the realistic experiment in the indoor environment. As shown in Figure

The floor plan for the test bed.

Figure

The CDF of localization error in realistic experiment.

The NLOS problem is one of the most challenging problems for wireless sensor networks. It can seriously reduce localization accuracy. In this paper, the TOA measurement model is first introduced. We then proposed an NLOS identification method based on residual analysis to solve the problem caused by the NLOS error. In addition, the particle swarm optimization with a constriction factor algorithm is proposed to find the optimal solution of the location estimate of an unknown node. Simulation results show that this method can reduce the influence of NLOS error and improve the positioning accuracy, especially when the number of beacon nodes is relatively large. In future work, the proposed method could be extended to the distributed localization method. At the same time, we will modify the residual analysis method and apply it to the mobile localization to improve the effectiveness of particle filter.

In this section, we introduce the maximum likelihood localization method. We assume that the position of the beacon node is denoted as

The above equation can be represented by a linear equation

We can obtain the estimated position of the unknown node as follows:

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there is no conflict of interest regarding the publication of this paper

This work was supported by the National Natural Science Foundation of China under Grant no. 61803077, the Natural Science Foundation of Hebei Province under Grant no. F2016501080, and the Fundamental Research Funds for the Central Universities of China under Grant nos. N172304024 and N152302001.