**1. Introduction**

Extended target tracking (ETT) draws lots of attention in recent years because of its wide range of applications in traffic control [1], autonomous driving [2–4], person tracking [5,6] and etc. [7–11]. Since one extended target generates more than one measurement per time step, its shape information can be obtained. Using this information, the kinematic state and extent of the target can be estimated simultaneously. The extent of the target including the size, shape, and orientation can be further used for target identification.

The difference between point target tracking and extended target tracking lies in the measurement model and hypotheses. Point target generates at most one measurement per time step, while the extended target generates multiple measurements. Many algorithms were proposed to track point target based on point target hypothesis, such as probability hypothesis density (PHD) filter [12] and cardinalized PHD (CPHD) filter [13]. Since the extended target violates one measurement hypothesis, the number of targets will be overestimated if point target tracking algorithms are directly used for tracking extended targets. To address this problem, Mahler proposed an extended target tracking algorithm based on the inhomogeneous Poisson Point Process model (PPP model) [14] in random finite sets (RFSs) frame, namely extended target probability hypothesis density (ET-PHD) [15], Jiang et al. [16] proposed a novel time-matching ET-PHD filter, a Gaussian mixture implementation of the ET-PHD, called the extended target Gaussian inverse Wishart probability hypothesis density (ET-GIW-PHD) filter, has been presented in [17]. However, ET-PHD only estimates the kinematic state of the target (such as position, velocity) and does not estimate the extent of the target. Therefore, this

method cannot extract the shape of the target. Nevertheless, the estimation of the target extent is important because it can be used to classify target and improve tracking accuracy [18–20].

Measurement partition is an important step in ETT. In ETT, measurements are partitioned into several non-empty subsets, each subset contains measurements that are all from the same source, either a single target or a clutter source, the subset is defined as cell. In ETT, the increase of measurements gives rise to the quick increase of the set partitions, thus the partition algorithm should be designed to achieve tractable computational complexity. Distance partition [17] is the most widely used method. Modified Bayesian adaptive resonance theory (MB-ART) [21] can also achieve good performance. For more details about other partition algorithms, please see [22–24].

One of the most important works in extended target tracking is how to model the target extent. To address this problem, the stick model is used for bicycle and pedestrian tracking [25,26]. The object extension is represented by a symmetric positive definite (SPD) random matrix [27], namely a random matrix (RM) model. Feldmann et al. [28] adapted the RM model for the case when the sensor error cannot be ignored. Lan et al. [29] took into account time variation and distortion of target extension in RM frame. In order to handle irregular shapes, a random hypersurface model (RHM) is introduced in [30–32]. Gaussian Processes (GP) was used to represent the target shape and achieved good performance [33–36]. Since shape estimation is similar to curving fitting, Kaulbersch et al. [37] applied a curve fitting method for shape estimation. Granstrom¨ et al. [38] proposed an extension model for specific sensor. Granstrom¨ et al. [39] proposed extended target Gaussian inverse Wishart PHD (ET-GIW-PHD) filter to incorporate widely used RM model into PHD filter and approximate the estimated PHD with an unnormalized mixture of Gaussian inverse Wishart (GIW) distributions. Later, Granstrom¨ et al. [40] proposed extended target Gamma Gaussian inverse Wishart PHD (ET-GGIW-PHD) filter to estimate the measurement rate and target state simultaneously. The combination of several RM model was used to model nonelliptic targets in [41,42]. As mentioned in [39], more experiments that test ET-GIW-PHD filters are needed, e.g., for data that contains more clutter than typical laser data does, this provides the general motivation for this paper. We found that the number of targets will be overestimated which degrades the final performance when severe clutters are partitioned into one cell in ET-GIW-PHD. More analyses are presented in Section 3. In this paper, we proposed an anti-clutter ET-GIW-PHD filter for better cardinality estimation performance.

The main contributions of this paper are twofold. First, the reason why ET-GIW-PHD overestimates the number of targets is discussed detailedly, and the probability of the measurement generated by clutter against different scenario parameters is presented. Second, in order to deal with the cardinality overestimation in ET-GIW-PHD, we proposed an anti-clutter ET-GIW-PHD filter which revises the correction step of ET-GIW-PHD with hypothesis testing. Hypothesis testing is introduced to determine the source of measurements in the cell, hypothesis testing results are integrated into the correction step in ET-GIW-PHD. In order to deal with the source of measurements correctly, the essential differences between the measurements of targets and clutter should be recognized. Since the variation of target state over time follows certain rules (motion model and shape transition model), the state of targets could be predicted while clutter could not. Then, the likelihood functions of targets and clutter are deduced. The likelihood functions are built based on not only the number of measurements but also the target state and spatial distribution of clutter. Since the likelihood ratio test statistic is proved to be subject to chi-square distribution, a threshold corresponding to the confidence coefficient is introduced, this threshold is used to determine the source of measurements in the cell. It worth note that the perfect sensor resolution is advocated as a theoretical hypothesis in this paper. In reality, the results in the Section 5 will be affected by the limited sensor resolution. Future work will tackle the sensor's limited resolution.

The rest of the paper is outlined as follows. Section 2 reviews the ET-GIW-PHD filter. Section 3 discusses the reason why ET-GIW-PHD overestimates the number of targets. Our anti-clutter ET-GIW-PHD is presented detailedly in Section 4. We conduct experiments in different simulation scenarios to demonstrate the effectiveness of our proposed approach in Section 5; Conclusion is drawn in Section 6.
