# A Robust Tracking Algorithm Based on a Probability Data Association for a Wireless Sensor Network
## 1 Introduction  
Due to there being many obstacles, it is difficult to provide accurate localization indoors. Applying wireless sensor network technology to indoor localization can solve the problem of indoor localization. Wireless positioning systems usually use time of arrival (TOA), time difference of arrival (TDOA), angle of arrival (AOA), and received signal strength (RSS) to estimate the location information to realize the tracking and positioning of a mobile node. This paper uses the TOA method to obtain the Euclidean distance measurements between the beacon nodes and the mobile node. The principle of the TOA method is to calculate the arrival time from the mobile node to the beacon nodes, and then these measurements are multiplied by the speed of light in order to obtain the Euclidean distance measurements between the beacon nodes and the mobile node. Trilateration techniques can be used to estimate the position of the mobile node. If the channels between the mobile node and the beacon nodes have a direct path, the channels are considered to be in line-of-sight (LOS) and the TOA measurements obtained in LOS environments are perfect. The accurate position can be obtained using the extended Kalman filter to process the TOA measurements. However, the assumption of the LOS channel is ideal and impractical [1]. In practice, obstacles such as persons, furniture, or walls block the propagation path, causing diffraction and refraction. The propagation path of the signal becomes long, and the channel is in a non-line-of-sight (NLOS) environment. The NLOS factor results in a positive bias of theTOA measurements, leading to a decreased positioning accuracy. Thus, algorithms that reduce NLOS errors can achieve high-precision positioning. Many positioning algorithms have emerged based on various positioning methods. A semidefinite programming algorithm was proposed in [PERSON] et al. [2], where it transforms a TDOA model into a TOA model and uses new constraints to mitigate NLOS errors. A bisection-based approach is proposed in [PERSON] and [PERSON] [3], which can accurately solve the maximum likelihood estimation derived from the measurement model through the bisection procedure to achieve accurate positioning. [PERSON] et al. [4] proposed a high-precision and low-complexity localization algorithm based on an imported vector machine (IVM), which employs the probability output of an input vector machine, and has a higher localization accuracy than the corresponding methods, such as a support vector machine (SVM) and correlation vector machine (RVM). [PERSON] et al. [5] proposed a novel distributed consensus-based adaptive Kalman estimation algorithm. In order to estimate the states of the target more precisely, an optimal Kalman gain is obtained by minimizing the mean-squared estimation error. An adaptive consensus factor is employed to adjust the optimal gain, as well as to acquire a better filtering performance. In the filter's information exchange, dynamic cluster selection and a two-stage hierarchical fusion structure are employed to get a more accurate estimation. When all the range measurements estimation is from the LOS environments, the position estimation obtained by the least-squares method is accurate; if there is at least a range measurement estimate from the NLOS condition, the position estimation of the mobile node will be inaccurate, which will deviate from the real position. The more NLOS data that is used, the less accurate the positioning is. According to the idea of data fusion, combining different positioning methods is also a common method to improving positioning accuracy. An improved positioning method was proposed to improve the accuracy by combining TOA and AOA positioning methods [6; 7]. [PERSON] and [PERSON] [8] used semidefinite programming to solve the problem of collaborative localization. In [PERSON] and [PERSON] [9], a novel cooperative localization algorithm of source nodes is proposed.