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In this paper, a localization scenario that the home base station (BS) measures time of arrival (TOA) and angle of arrival (AOA) while the neighboring BSs only measure TOA is investigated. In order to reduce the effect of non-line of sight (NLOS) propagation, the probability weighting localization algorithm based on NLOS identification is proposed. The proposed algorithm divides these range and angle measurements into different combinations. For each combination, a statistic whose distribution is chi-square in LOS propagation is constructed, and the corresponding theoretic threshold is derived to identify each combination whether it is LOS or NLOS propagation. Further, if those combinations are decided as LOS propagation, the corresponding probabilities are derived to weigh the accepted combinations. Simulation results demonstrate that our proposed algorithm can provide better performance than conventional algorithms in different NLOS environments. In addition, computational complexity of our proposed algorithm is analyzed and compared.

Wireless localization which can determine the position of mobile station (MS) in wireless network has received considerable attention over the past years, especially the application of the location based services (LBSs). The existing wireless localization techniques such as received signal strength (RSS) [

There are two ways to cope with the NLOS condition. The first way localizes with all NLOS and LOS measurements, but provides weighting, nonlinear optimization, or scaling to minimize the effects of the NLOS error. Residual weighting algorithm (Rwgh) [

In this paper, we investigate hybrid TOA/AOA NLOS identification with a residual test and the weighting localization approach to minimize the effect of NLOS error. Different from the residual test in [

The rest of the paper is described as follows. In Section

There are

In this section, we present the proposed NLOS identification and probability weighting localization algorithm in terms of system model shown in Section

As shown in Section

For AOA equation in (

Squaring the range equations in (

By fixing the first equation in (

The position estimate of MS

We choose

Putting (

Due to the Gaussian distribution of

In order to validate (

The hypothesis

In the above discussion, we only consider the combination that all the BSs are involved. It is easily extended to other combinations. For example, if the combination contains two range measurements and one angle measurement, there are

For our system model in Section

The final position estimate of MS is weighted as

In extreme circumstances, none of these combinations is accepted in the tests; the proposed algorithm will not output a valid position estimate of MS. If this situation happened, it means that the range measurements in neighboring BSs deteriorate significantly. The localization accuracy will be degraded if they are combined with the range and angle measurements in home BS. Thus, only home BS is reliable to provide the position estimate of MS. With the assumption of LOS propagation, the position estimate of MS is easily obtained as

In this section, we carry out some simulations to prove the performance of the proposed NLOS identification and probability weighting localization algorithm. Three BSs with a hexagonal layout shown in Figure

Simulation scenario in wireless network.

The range measurement consists of three parts, the true distance, the NLOS error, and the measurement error. The standard deviations of three range measurement errors are assumed to have the same value

Typical parameters in different environments. Table

Environments | | | |

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Bad Urban | 1.0 | 0.5 | 4 |

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Urban | 0.4 | 0.5 | 4 |

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Suburban | 0.3 | 0.5 | 4 |

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Rural | 0.1 | 0.5 | 4 |

The angle error

In this subsection, we carry out simulation results to validate the performance of NLOS identification about our proposed algorithm. In Figure

The probability of LOS combination with three BSs in different NLOS environment.

The probability of LOS combination with two BSs in different NLOS environment.

In this subsection, we present simulation results to evaluate the localization accuracy of our proposed algorithm. Three other algorithms denoted as hybrid line of position (HLOP) [_{2} or BS_{3}. It is observed that the localization performance of the proposed algorithm is better than HLOP, Rwgh-HLOP, and TS-LS in bad urban, urban, and suburban environment, whereas it is slightly better than Rwgh-HLOP and TS-LS in rural environment. Moreover, when the NLOS propagation becomes serious, the localization performance of all the algorithms is decreased. As shown in Figures

The performance comparison with one NLOS BS in different NLOS environments.

The performance comparison with two NLOS BSs in different NLOS environments.

The performance comparison with three NLOS BSs in different NLOS environments.

In this subsection, computational complexity of our proposed algorithm is analyzed and compared. The proposed algorithm is consisted of different combinations; each combination contains two main steps: HLOP algorithm and construction of a statistic. HLOP algorithm is done by least square algorithm; its computational complexity is

Computer running time of the four algorithms.

Algorithm | HLOP | TS-LS | Rwgh-HLOP | Proposed |

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Time (ms) | 0.033±0.001 | 0.095±0.01 | 0.13±0.01 | 0.18±0.01 |

In this paper, we investigate the hybrid TOA/AOA localization approaches and propose a new probability weighting algorithm based on NLOS identification. Simulation results show the following:

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

The authors declare that they have no conflicts of interest.

This research was supported by China Scholarship Council (CSC 201708505083), Foundation and Frontier Research Project of Chongqing (cstc2016jcyjA0365, cstc2016jcyjA0285), the Science and Technology Research Program of Chongqing Municipal Education Commission of China (KJZD-K201800701, KJQN201800703, KJ1705139, KJ1705121, and KJ1705115), Open Fund Project of Urban Rail Transport Vehicle System Integration and Control Chongqing Key Laboratory (CKLURTSIC-KFKT-201805), Natural Science Foundation of China (61703063, 61573076), the Scientific Research Foundation for the Returned Overseas Chinese Scholars (no. 2015-49), and Program for Excellent Talents of Chongqing Higher School (no. 2014-18).