# A Robust Tracking Algorithm Based on a Probability Data Association for a Wireless Sensor Network
## 2 Problem Statement
### A Brief Introduction of Existing Methods  
The interacting multiple model (IMM) algorithm is used to track and locate in NLOS environments. In [PERSON] and [PERSON] (2018), the IMM algorithm uses two Kalman filters to smooth the TOA range measurements in both the LOS model and the NLOS model. In order to reduce the NLOS errors, the TOA range measurements smoothed by the Kalman filter is used to subtract the NLOS mean error in the NLOS model. The distance estimates between the mobile node and the beacon nodes are determined by combining the state estimate in the LOS model with the state estimate in the NLOS model, which eliminates the NLOS errors. Then, the location of the mobile node is determined using a geometric method based on the smoothed distance estimates. According to the idea of data fusion, [PERSON] et al. (2019) proposed an IMM algorithm based on TOA and RSS data fusion to find the location of a mobile node. Almost all IMM algorithms need to presuppose NLOS statistical errors to solve the NLOS interference problem, but in practice, the NLOS statistical errors are unknown. The robust IMM (RIMM) algorithm proposed in [PERSON] et al. (2019) does not need prior knowledge of the NLOS error. In the LOS model, EKF is used to estimate the location of a mobile node. In the NLOS model, REKF is used to transform the EKF equation into a linear regression problem, which is solved using robust techniques in [PERSON] and [PERSON] [31]. Then, the state vectors of the two models are weighted using likelihood function values to determine the final state vectors of the mobile node.  
EKF can achieve accurate positioning in LOS environments, but the positioning accuracy is not high in NLOS environments. Therefore, it is necessary to improve the filters of the IMM algorithm to improve the positioning accuracy. The RIMM algorithm is used to improve the filter of the NLOS model in the IMM algorithm. The MPDA algorithm in [PERSON] et al. [32] has a high positioning accuracy and can mitigate NLOS errors. The MPDA algorithm is a sub-optimal filtering algorithm based on the Bayesian formula, which divides the range measurements between the beacon nodes and the mobile node into different groups. Each group obtains the corresponding position estimation via a least-squares method and optimizes the position estimation by using the Gauss-Newton iteration method. The optimized location estimation is identified using NLOS detection, and the location estimation that does not fall into the validation gate is discarded. The location estimation that falls into the validation gate is weighted by the corresponding association probability to determine the location of the mobile node. Choosing an appropriate validation gate is a prerequisite for realizing the probability data association. The common validation gate forms are a rectangular gate, elliptic gate, sector gate, etc. Among them, the elliptic gate is the most widely used. The positioning accuracy of the MPDA algorithm is very high, but it is sensitive to outliers. These outliers often fail to locate, so it is necessary to abandon the outliers to ensure the positioning accuracy of the MPDA algorithm. Compared with the MPDA algorithm, the EKF algorithm has better robustness.