Mobile localization estimation is a significant research topic in the fields of wireless sensor network (WSN), which is of concern greatly in the past decades. Non-line-of-sight (NLOS) propagation seriously decreases the positioning accuracy if it is not considered when the mobile localization algorithm is designed. NLOS propagation has been a serious challenge. This paper presents a novel mobile localization method in order to overcome the effects of NLOS errors by utilizing the mean shift-based Kalman filter. The binary hypothesis is firstly carried out to detect the measurements which contain the NLOS errors. For NLOS propagation condition, mean shift algorithm is utilized to evaluate the means of the NLOS measurements and the data association method is proposed to mitigate the NLOS errors. Simulation results show that the proposed method can provide higher location accuracy in comparison with some traditional methods.

Wireless localization is one of the technologies in the fields of the intelligent robot, national security, and health surveillance [

In the WSN-based localization approaches’ design, the location of the beacon nodes and the measurements between the beacon nodes and unknown node are assumed to be the known prior information. Generally, there are four measurement methods: time of arrival (TOA) [

In this paper, we propose a novel location algorithm which can solve the NLOS errors. This paper is structured as follows: related works are introduced in Section

In order to solve the NLOS errors, researchers proposed numerous methods. These methods can be generally divided into two types [

There are many approaches proposed to realize the accurate location without any prior knowledge of statistical information of the NLOS measurements. These methods are termed as nonparametric methods. In [

Most of the nonparametric methods mentioned above were designed with the assumption that the obstacles are fixed. But, in the practical and complicated environments, the positions of the obstacles may be changed dynamically. These nonparametric methods cannot provide desirable position estimation in mixed LOS/NLOS environments where some obstacles are always moving. This paper presents an efficient mobile node localization approach which is termed as improved Kalman filter (IKF) based on mean shift [

In this section, we consider the scenario with

The LOS/NLOS propagation.

At time

In the LOS propagation environment, the probability density function (PDF) of

In the NLOS propagation environment,

The prior knowledge of the NLOS errors cannot be obtained in practical environment. The mean shift method is employed to approximate the probability density. It is assumed that there are

This kernel function is used to determine the weights of the neighborhood data to re-estimate the mean. In the practical application, there are many initial estimates required to obtain the desirable results. The weighted means can be obtained through an iteration process. This method always sets the initial estimates

The range measurements play the significant roles in the whole process of mobile localization. We adopt the high-frequency measurements [

We define the following state vector of the unknown node relative to the

The corresponding state model is

The measurement equation in the mixed propagation environment is

Figure

Structure of the improved Kalman filter.

(Kalman predication). It is assumed that

The measurement residual is defined by the following:

The innovation covariance matrix is expressed as follows:

The Kalman gain is expressed as follows:

(NLOS detection). We employ the hypotheses and alternatives [

The following hypotheses and alternative are utilized to identify the propagation condition:

(mean shift-based data association). In the NLOS condition, the mean shift method is employed to compute the weighted means of the measurements

The output result

If

The output of the mean shift-based data association is expressed as

(Kalman update). In the LOS environment,

The covariance can be updated as follows:

After obtaining the state estimation vector

(ML-based location). We use the ML method to realize the final localization estimation. As mentioned above, the coordinates of the beacon nodes are

The final position of the moving target can be obtained as follows:

The location ability of the proposed approach in the mixed LOS/NLOS environments is tested through the following simulations in this section. The proposed improved Kalman filter (IKF) algorithm is compared with the maximum likelihood (ML) algorithm, the residual weighting (Rwgh) algorithm, and the Kalman filter (KF) algorithm to validate its effectiveness. We consider a 100 m × 100 m square area. There are seven beacon nodes in this area. The target is moving in this field with the velocity of 1 m/s. The obstacles are distributed randomly, and their positions are always changed dynamically. Figure

Diagram of the simulation environment.

The location ability of these four approaches is evaluated by the average location error:

Firstly, we discuss the location ability of these four methods in the case of Gaussian distribution, in which the NOLS error

We illustrate the variance of NLOS errors versus the average location error of these four approaches as shown in Figure

Secondly, we discuss the location ability of these four methods in the case of uniform distribution, in which the NOLS error

_{max} versus ALE.

Finally, we investigate the performance of the four approaches with the assumption that the NLOS errors obey the exponential distribution

We investigated the mobile localization in rough environments and presented a novel IKF algorithm which can realize the accurate mobile node localization. The proposed IKF algorithm is independent of prior information. In the whole location process, the NLOS errors are completely unknown. In the simulation, the proposed method is compared with three traditional algorithms. The simulation results illustrate that the proposed IKF approach has the best performance. It has higher localization accuracy than KF, Rwgh, and ML methods about 32.8%, 17.19%, and 13.07%, respectively. In the future, we will focus on the robust localization method with the mobile beacon nodes in the mixed LOS/NLOS environments.

The authors declare that there is no conflict of interests regarding the publication of this article.

This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61701101, 61603080, 61603415, and 61503274 and the Fundamental Research Fund for the Central Universities of China (N162610004, N160404003, and N150503009).