An Indoor Mobile Localization Strategy for Robot in NLOS Environment

This paper deals with the problem of localization of mobile robot in indoor environment with mixed line-of-sight/nonline-of-sight (LOS/NLOS) conditions. To reduce the NLOS errors, a prior knowledge-based correction strategy (PKCS) is proposed to locate the robot. This strategy consists of two steps: NLOS identification and mitigation. We propose an NLOS identification method by applying the statistical theory. Then we correct the NLOS errors by subtracting the expected NLOS errors. Finally, the residual weighting algorithm is employed to estimate the location of the robot. Simulation results show that the proposed strategy significantly improves the accuracy of localization in mixed LOS/NLOS indoor environment.


Introduction
Indoor robot has been widely applied in health care, smart home, and emergency supporting. Location information is very important for mobile robot [1]. Due to the fact that GPS (Global Positioning System) does not work in indoor environment, so the indoor localization has motivated increased research interest. Since the Wireless Sensor Network (WSN) can be deployed quickly and �exible, so WSN is an effective application for indoor localization.
Recently, many indoor localization systems have been developed based on different wireless measurements: received signal strength (RSS) [2], time of arrival (TOA) [3], angle of arrival (AOA) [4], and time difference of arrival (TDOA) [5]. A mobile robot can estimate its location based on the wireless measurements with some beacon nodes whose locations are known prior. TDOA and AOA methods are energy-consuming resolution and they require extra hardware. TOA needs the high precision clock to achieve clock synchronization. So the above three methods are not suit for low con�gured sensor node. As an inexpensive approach, RSS has established the mathematical model on the basis of path loss attenuation with distance, and it requires relatively low con�guration and energy. In this paper, we employ RSS localization method because of its characteristics. However, due to the complex indoor environment where walls and other obstacles are present, the wireless channel will always be blocked. e NLOS environment causes the radio signal to propagate a longer path than the true distance between the beacon nodes and target (e.g., robot or unknown node) due to the re�ection and diffraction. So it induces the degradation of the localization accuracy. us, indoor localization which is robust to the NLOS environment is required [6]. In the presence of obstacles, the major positioning errors are from the measurements errors and NLOS propagation errors. And the NLOS effect leads to large localization errors if we do not consider it in the localization method.
For the purpose of realizing robust localization in NLOS environment, we propose a localization method using RSS measurement. And this method consists of four steps: NLOS identi�cation, NLOS correction, Kalman �lter, and residual weighting algorithm.
Several previous works have been investigated the localization algorithm in NLOS environment. e localization methods in NLOS environment can be categorized as nonparametric method and parametric method. For the nonparametric method, Chen [7] proposes a residual weighting algorithm to alleviate the NLOS errors in the location estimate. is method employs the least squares on all possible combinations of distance measurements and then calculates the �nal position as a weighted combination of these intermediate estimates. e computational complexity of this method grows exponentially with the number of measurements. A robust multilateration algorithm [8] is introduced in NLOS environment. is algorithm is robust in comparison with traditional least squares multilateration. However, the performance of this method is severely affected by the number of NLOS measurements. Least squares support vector machine [9] classi�er is employed to distinguish LOS/NLOS propagation and further mitigate the ranging errors in NLOS conditions. For the parametric method, the additive noise in the range measurement is characterized by different noise distributions corresponding to LOS and NLOS errors. In [10], Borras et al. propose a binary hypothesis test method to identify the NLOS measurements. In [11], Mazuelas et al. propose a prior NLOS measurements correction method to correct the measurements from NLOS propagation. Most of above works focus on the UWB system. But this system is not suit for WSN which consists hundreds of sensor nodes in the monitoring �eld.
Since the relatively low con�guration and cost, RSS-based localization techniques have drawn considerable research interest [12]. An environment-adaptive method is investigated [13] that is tolerant to parameter variations caused by environmental variations. A sigma-point Kalman smoother-(SPKS) based location and tracking algorithm is proposed [14] for RSSI-based positioning and tracking. However, all of the above methods only consider the LOS environment. Fewer papers investigate the RSS-based localization method in NLOS environment.
In this paper, we �rstly investigate the RSS-based NLOS identi�cation method using the recorded measurements. en the ratio of NLOS present in the record of measurements and the expectation of the NLOS errors are used to mitigate the NLOS errors. Kalman �lter is employed to improve the estimated range. Finally, we use the residual weighting algorithm to estimate the location of the robot. is paper is organized as follows. In Section 2, we introduce range estimation model. NLOS identi�cation, NLOS mitigation, and localization method are presented in Section 3. Some simulation results present in Section 4. e conclusions are given in Section 5.

Range Estimation Model
e robot carries a sensor node which is used to communicate with the beacon nodes in the WSN. e beacon nodes emit signal continually. e robot estimates the distance between beacon node and the robot through received signal strength. e most widely applied signal propagation model is the lognormal shadowing model. e received signal strength of the robot from th beacon node [15] is PL = PL 0 − 10 los/ los log 10 0 + los/ los , where PL 0 is the received signal strength at reference distance of 0 meters. 0 is assumed to be 1 m, and is the path loss exponent. Generally line-of-sight of indoor environment shows around 1.6 to 1.8, and around 4 to 6 in the presence of obstacles. los ∼ 0, 2 los ) is the LOS measurement noise modeled as zero mean white Gaussian with variance 2 los . los ∼ los , 2 los ) is the measurement noise in NLOS environment. And los > los . ese parameters could be obtained in an environment through simulation or experiment.
= − ) 2 + − ) 2 is the true distance between the th beacon node and the robot. ( , ) is the coordinate of th beacon node, and ( , ) is the position of the robot.
From (1), the estimated range between the th beacon node and the robot can be expressed as = 10 10 los/ los log 10 + los/ los )/10 los/ los = ⋅ 10 los/ los /10 los/ los = + 10 los/ los /10 los/ los − 1 . ( We can approximately obtain that [16] los = 10 los /10 los − 1) ∼ 0, 2 1 ) under LOS environment, and los = 10 los /10 los − 1) So the estimated range can be rewritten as Based on this range estimation model, we investigate NLOS identi�cation when the obstacles present and propose a prior knowledge-based correction strategy (PKCS) to mitigate NLOS errors. e proposed method can be used to localize the mobile robot in indoor environment. is strategy will improve the localization accuracy.

�. ���� �denti��ation and Mitigation
e propagation conditions can change from LOS to NLOS when the robot is moving in the indoor environment. e NLOS propagation generally leads to a positive bias in the estimation range and causes a serious error in location estimation. So we should �rstly identify the propagation conditions and then to mitigate the NLOS errors.
We make the following assumptions in the study. ere are beacon sensors and one robot in the �eld. e beacon nodes emit radio signal which attenuates inside the area under observation. e intensity of a signal emitted omnidirectionally. e robot receives the radio and estimates the distance between the beacon node and the robot according to (3).
In this section, we propose a strategy for robot localization in NLOS environment. We �rstly employ the polynomial �t to smooth the measurements, and then the average deviation between the smoothed curve and measurements and the standard deviation of the LOS noise are used to identify the NLOS measurements. Secondly, we estimate the NLOS ratio in the measurements to determine which measurements contain the NLOS errors, and then mitigate the NLOS measurements errors through subtracting the expectation of NLOS errors. Kalman �lter is introduced to improve the estimated range. Finally we use the residual weighting (Rwgh) algorithm to estimate the location of the robot. e �owchart of the proposed algorithm is given in Figure 1.

3.�. NLOS ���nti��ation.
In order to identify the NLOS measurements, we consider the historical measurements from each beacon node individually. Based on the measurements of beacon node during a period of time and the standard deviation of the LOS noise, we determine whether the measurements contain the NLOS errors. We select a short period of time 1 -, is the number of sampled measurements from the th beacon node, and the environment parameters are constant in the period. e estimated distance between the th beacon node and the robot at time is called ( ). e standard deviation of the measurements of th beacon node can be expressed as [17]  (4) We can determine that the data have affected by NLOS if the standard deviation is much larger than the standard deviation of the LOS noise. But the value of ( ( )) is unknown, so we will employ a smooth version of the measurement records which we have stored to estimate the value of ( ( )). For this purpose, we will use a smooth cubic regression of the measurements. e polynomial �t is used to estimate the deviation of the measurements.
is the thirdorder polynomial that best �ts the available measurements minimi�ing its curvature. e third-order polynomial ful�lls the objective of estimating the value of ( ( )) with a high accuracy.
At th beacon node, the measurements are smoothed as So the standard deviation of the measurements can be rewritten as Because the NLOS errors are uncorrelated in time, so the measured data will have a signi�cantly larger average deviation from the smoothed curve when the NLOS errors present. e algorithm requires comparison of the deviation and the standard deviation of the LOS noise. If 1 , then the measurements contain the NLOS errors. Otherwise the propagation path of the measurements is LOS.

NLOS Mitigation.
When the NLOS is present, the measured data will deviate from the smoothed curve largely. In order to mitigate the NLOS errors, we must know which measurements are affected by NLOS. We �rstly estimate the percentage of measurements in our records which are corrupted by NLOS errors during the sample period. en we determine which measurements are corrupted by NLOS errors. Finally, an NLOS mitigation algorithm is proposed in this subsection.
If the measurements are affected by NLOS, where and represent the measurements taken at time coming from LOS and NLOS, respectively.
is the percentage of measurements corrupted by NLOS errors. So From (9), it can be seen that the and follow noncentral chi-square distribution: erefore the expectation of the deviation can be presented as When the number of sample is large, (10) can be rewritten as: e variance of 2 is given by where Var( ) = 2( ) + 4 ( ) ( ) and Var( ) = 2 + 4 ( ) √ . When is relatively large, variance of 2 is very small in (12). So we can assume that 2 ≈ ( 2 ). We can obtain 2 as 2 ≈ ( ) 2 ( ) + 2 ( ) .
e percentage of measurements corrupted by NLOS errors is given by en we estimate which measurements are corrupted by NLOS errors aer the percentage of measurements which have NLOS errors is obtained.
As we know, los > (3/2) } = 0.0668. It means that the probability of LOS errors which larger than one and half its standard deviation is very low. So the large errors are mainly from the NLOS environment. And we assume that = los > (3/2) }, so the number of NLOS measurements is pNK. We sort the standard deviation of the measurements from large to small. e largest pNK measurements may contain the NLOS errors. We calculate the mean of these standard deviations of the pNK measurements, and it can be expressed as NLOS . Since the NLOS errors are the positive bias. We correct the pNK measurements which contain the NLOS by substracting the expected NLOS errors NLOS . e corrected range can be expressed as

Kalman Filter.
e KF is one of the popular �ltering methods developed and it, as well as its descendants, has been the dominate �lter type for the past 4� years. �ost localization systems use Kalman �lter for state estimation. Kalman �lter produces optimal estimates when measurement noise is Gaussian and stationary. It can be executed within a computer and iteratively without any extensive modi�cation or special hardware. We perform the Kalman �lter for the measurements in LOS and the corrected measurements in NLOS. e state equation of th beacon node under LOS/NLOS environment can be expressed as follows: e measurement equation of sensor under LOS/ NLOS environment can be expressed as follows: where is the corrected range according to (15) in NLOS or the measurements in LOS.
We can obtain the predicted state and prediction covariance as follows: where is the covariance matrix of measurement error. e Kalman gain is as follows: en we can obtain the updated state estimate and updated estimate covariance as follows: e ranging estimation in Kalman �lter is expressed as: 3.4. Location Estimation. e outputs of Kalman �lter are the estimated distances between the robot and beacon nodes. According to the estimated distances, we can locate the robot in the �eld. In this section, we introduce residual weighted localization method to estimate the location of the robot. e Conventional Residual Weighting algorithm can be described as follows [7]. (b) For each beacon node index set, we employ the maximum likelihood method to estimate the location of the robot which can be represented as = , . en we compute the average of Res (residual) as follows:

Performance Evaluation and Analysis
In this section, we evaluate the performance of the NLOS localization method described in the previous sections through simulations. Table 1  In this section, we compare the proposed algorithms (PKCS-ML and PKCS-Rwgh) with the naïve ML and Rwgh algorithms. All of the four algorithms employ the Kalman �lter to improve the estimated range.
In Figure 2, we compare the localization results between the Rwgh and PKCS-Rwgh algorithm. Figure 2(a) shows the sight state with respect to all the beacon nodes in sample points. We can see that the sight states vary with time. A mobile localization is shown in Figure 2(b). is �gure compares the true trajectory between the estimated one obtained by Rwgh and another obtained by our method. e localization errors can be appreciated by looking at the lines that connect the true and the estimated positions. In Figure  2(c), we can obtain the detailed localization errors in each sample point. It can be observed that the proposed method has better performance in comparison with Rwgh in most of the sample points. In Figure 3, the number of beacon nodes is varied from 4 to 8. e MLE and Rwgh methods with the prior knowledgebased correction strategy are called PKCS-MLE and PKCS-Rwgh, respectively. e results show that the effect of increasing the number of beacon nodes is higher using MLE method in comparison with the Rwgh method. However, the PKCS-MLE and PKCS-Rwgh methods have higher localization accuracy compared with MLE and Rwgh methods. Figure 4 shows the average localization error versus the standard variance of LOS noise. e PKCS-MLE and PKCS-Rwgh methods demonstrate similar robustness against the standard variance of LOS noise. e localization errors of the MLE are always larger than 4 m and increase signi�cantly as the standard variance of LOS noise increases. Due to the PKCS, the performance of PKCS-MLE and PKCS-Rwgh methods outperforms the MLE and Rwgh methods.
To investigate the robustness of the proposed method, we evaluate it under different standard variances of NLOS noise. In Figure 5, it is obvious that the average localization error increases with the increment of standard variance of NLOS noise. We can see that the localization accuracy of PKCS-MLE is improved signi�cantly in comparison with MLE. �nd the PKCS-Rwgh has 6.87% higher localization accuracy than Rwgh.
In Figure 6, we show the average localization error versus mean of NLOS noise. e accuracy of all methods is decreased with the increase of mean of the NLOS noise. We can see that the proposed method can signi�cantly    improve the location estimation accuracy by subtracting the expectation of NLOS errors. And the average localization error of MLE and Rwgh methods are worse without prior knowledge-based correction strategy.

Conclusion
An NLOS correction approach has been proposed to locate the position of mobile robot in order to alleviate the NLOS errors which arise in clustering environment. We consider the prior knowledge of the errors to identify the NLOS and then remove the NLOS errors by subtracting the expectation  of NLOS errors. is method could mitigate the NLOS propagation effect. Simulation results show that the PKCS has much better performance than those methods without the correction method and signi�cantly improves the localization accuracy.