# Multiple Extended Target Tracking Algorithm Based on Spatio-Temporal Correlation
## 1 Introduction  
In the traditional multi-target tracking (MTT) [1] scenario, a single target generates, at most, one measurement at a time. In this case, the target can be regarded as a point target and its shape can be ignored. However, with the development of modern high-resolution sensors, the target will occupy multiple resolution cells of the sensor, so the point target model is no longer applicable. Instead, the target should be modeled as an extended target (ET), where a single target generates multiple measurements at each time. In the past few years, the extended target tracking problem has attracted a lot of attention; the references [2, 3] summarize the extended target tracking problem. At present, the measurement model of the extended target is mostly based on the non-uniform Poisson process measurement model proposed by [PERSON] and [PERSON] [4], which assumes that the measurement sources of the extended target are randomly distributed around the center of mass of the extended target, and the measurements received by sensors about the target and clutter at the same time all follow Poisson distribution. The extended target cannot be modeled by the point target model, and its shape model should be considered. At present, the modeling methods of extended target shape mainly include random matrix (RM) [5, 6], random hypersurface model (RHM) [7], and Gaussian process (GP) [8]. The RM method assumes that the shape of the target is approximately an ellipse, while the RHM and GP methods no longer limit the shape of the target to an ellipse, but a more irregular shape; however, these two modeling methods also result in more computational complexity. In recent years, the extended target tracking method based on random finite set (RFS) has received extensive attention. Since the target tracking framework based on RFS has a strict Bayesian theory foundation, it can simultaneously estimate the number of targets and the state without considering the data association. Therefore, it is particularly suitable for multiple extended target tracking problems. The RFS framework for MTT proposed by [PERSON] [9], driven by the inherent combinatorial characteristics of Bayesian multi-objective filters, has led to the utilization of probability hypothesis density (PHD) [10], cardinalized PHD (CPHD) [11], and multi-Bernoulli filters [12; 13] to approximate optimal Bayesian filtering. Based on the extended target Poisson model proposed by [PERSON], [PERSON] derived the measurement update equation of the PHD filter. However, the measurement update equation remains intractable. [PERSON] proposed a tractable extended target Gaussian mixture PHD filter algorithm (ET-GM-PHD) [14], and proposed a distance partition (DP) method to partition the measurement set. The Gaussian-inverse-Wishart PHD (GIW-PHD) filtering algorithm [6], which combines RM with the ET-PHD framework, can not only estimate the motion state of the target, but also estimate the extended state of the target. How to partition the measurement set accurately and effectively is one of the main tasks of extended target tracking. In multiple extended target tracking, a single target generates multiple measurements, and with the interference of clutter, it is difficult to establish the correspondence between the measurements and the target. The ET-GM-PHD filtering algorithm needs to consider all partitions of the target measurement set, which is computationally difficult in practical applications. In application scenarios with a large number of targets and measurements, the DP algorithm has high computational complexity. In addition, it is essentially a hierarchical single-chain clustering algorithm, which lacks robustness and is sensitive to noise. In addition to DP, K-means++ clustering [15], spectral clustering [16], and expectation maximization (EM) [6] partitioning algorithms are also included. It is difficult to deal with measurement set partition in complex scenes using single partition method.