# A Robust Tracking Algorithm Based on a Probability Data Association for a Wireless Sensor Network
## 1 Introduction
Based on the interrelation of multiple source nodes, the novel extended Kalman filter (EKF) integrated with semidefinite programming method is used for localization. It not only solves the problem of the cooperative localization using multiple source nodes, but also improves the localization performance compared with the classic EKF. In addition, it can also be used for traditional non-cooperative localization. In the localization algorithms, many algorithms are studied to mitigate the interference of NLOS factors [10; 11; 12; 13; 14; 15; 16; 17]. [PERSON] [10] proposed a residual weighting (RWGH) algorithm, which can mitigate NLOS errors to a certain extent, but the computational complexity is high. The algorithm proposed by [PERSON] and [PERSON] [11] also uses a residual weighting method.Jiao and coworkers [12; 13] used a method that selects the smallest normalized residual combination using different methods, and then performs weighted summation, which reduces the complexity of the residual weighting algorithm. The introduction of iterative ideas in the NLOS algorithms and the optimization of the calculation results are also effective methods for reducing the NLOS errors. [PERSON] [15] proposed an iterative minimum residual algorithm, which iteratively selects the minimum residual combination as the final estimated position of the mobile station (MS) by iterating the residual size in each combination whose value is less than the predetermined threshold. [PERSON] and coworkers [16; 17] used a TOA/AOA hybrid positioning method to improve the performance of the iterative minimum residual algorithm by selecting the appropriate iterative minimum residual criterion. In References [18; 19; 20], the NLOS mitigation algorithms proposed by the authors can reduce the NLOS errors without prior knowledge of the NLOS errors. The NLOS identification methods can effectively eliminate the influence of NLOS errors on the positioning accuracy. [PERSON] and [PERSON] [1] proposed a method for judging whether the range measurements contain NLOS errors based on the measurement variance (standard deviation). Location spoofing is an important factor for producing NLOS errors, and [PERSON] et al. [21] eliminated NLOS errors by identifying location spoofing. [PERSON] proposed a probabilistic position selection algorithm [22], which is based on the received signal strength indication (RSSI) and pedestrian dead reckoning (PDR) in the mixed LOS environment and NLOS environment for low-complexity identification. In the case of an unknown LOS/NLOS propagation prior probability, NLOS propagation can be identified by examining whether the range measurements obey a Gaussian distribution [23; 24; 25]. In recent years, Kolmogorov-Smirnov (K-S), Aderson-Drling (A-D), chi-square, Gruss test, skewness test, and kurtosis test have appeared successfully [26; 27; 28]. If the LOS/NLOS propagation prior probability is known, the NLOS can be identified using a generalized likelihood ratio test based on the statistical distribution of the different probabilities of the error. Large outliers sometimes occur in the range measurements. These outliers can seriously interfere with the positioning result, resulting in a positioning failure, thus we need to discard the outliers. In this paper, we propose a robust tracking algorithm based on an improved modified probabilistic data association (MPDA) and an interacting multiple model (IMM). In this paper, the improved probabilistic data association filter is used in the NLOS model. Through NLOS recognition, the position estimation with the NLOS error is discarded, and the correct position estimation is weighted with the corresponding correlation probability to obtain the final position estimation to reduce the NLOS error. The proposed algorithm in this paper has the following advantages:  
(1) The traditional MPDA algorithm is used for the NLOS recognition, where there may be continuous incorrect position estimation, resulting in inaccurate positioning.