# AOA-Based Three-Dimensional Positioning and Tracking Using the Factor Graph Technique
## 1 Introduction  
Future wireless networks should not only realize communication, but also support new services, such as connected transportation systems, smart logistics, unmanned factories, etc. [1; 2; 3; 4]. As one of the enabling techniques, position detection is becoming increasingly important. Its technical evolution can be found in discussions within the Third-Generation Partnership Project (3 gpp), the Bluetooth Special Interest Group (SIG), and other standard development organizations. Such applications should not only be confined to two-dimensional (2D) planes, but also be implementable to three-dimensional (3D) spaces.Moreover, communication may also rely on positioning techniques. For example, in multiple-input multiple-output (MIMO) systems, beamforming is well utilized to focus the signal power towards a specified receiver. However, conventional approaches for deciding the beam direction may not satisfy the future requirement, especially when the target is moving. Hence, a robust and low-complexity tracking solution should be considered. To track non-linear target movement in practice, the extended Kalman filter (EFK) is used. One of the factors that influences the accuracy of EKF is the variance estimation of observation errors [5; 6]. In this paper, the observation process in EKF is realized by a specific location detector, instead of a theoretical model in many previous works [7; 8]. Usually, it is difficult to estimate the variance of detection errors in real-time scenarios. Such estimation may get even worse when the environment changes. For example, in connected car networks, car sensing may not only be performed by fixed infrastructures on the roads, but also be conducted by surrounding vehicles, which forms a simultaneous localization and mapping (SLAM) problem [9; 10]. In SLAM, the sensing environmentmay change as devices move, and the variance of detection errors may become unstable. Hence, it is a crucial challenge for the tracking system to perform accurate estimations of such variance in real time. In SLAM, multiple sensors can be used for detecting a single target. Actually, since the network density continues to grow, the utilization of multiple distributed sensing devices will become more convenient in the future. Therefore, this paper considers a scenario with distributed sensors. To perform a location detection with distributed sensors, many algorithms have been proposed. For example, in [11], the least squares (LS) method was applied for indoor positioning, and a hybrid system combining time-difference-of-arrival (TDOA) and angle-of-arrival (AOA) measurements was considered. In [12], a factor-graph (FG) method [13] was proposed for location detection using time-of-arrival (TOA) measurement. The performance was shown to achieve the maximum likelihood (ML) bound with relatively low complexity. Due to such advantages, many extensions of the FG algorithm to other applications can be found in [14; 15; 16] for received-signal-strength (RSS), TDOA, and AOA, respectively. This work will also focus on FG for both location detection and tracking. A location detection and tracking algorithm using TOA was proposed in [17]. However, the use of TOA always requires strict time synchronization, because the signal emitting time should be known. Such a limitation will increase the difficulties of implementing such a technique in practice. Moreover, for an anonymous target that may not provide any transmission information to sensors or the fusion center, TOA cannot be used. There are still some limitations for RSS-based detection [14]. For example, RSS is also regarded as a technique only for a known target, because the training of received signal strength has to be conducted before the real deployment. To deal with the drawbacks mentioned above, TDOA-based techniques can be used, which does not require synchronization between the target and sensors, as well as off-line training. However, the performances are too sensitive to the measurement errors, due to the light speed.