An improved partitioning algorithm based on FCM algorithm for extended target tracking in PHD filter
Introduction
The detection of multiple maneuvering targets by radars is always a challenging problem due to the quantity of targets is unknown and time varying. With the low resolution of former radars, a target appears in one single resolution cell, while with the increased resolution of modern radars, radars are able to receive more than one measurement per time step from different corner reflectors of a single target. Then the target can be found in several pixels of radar video data, more than one detection would arise by a detector such as constant false alarm rate (CFAR) and the region grow detector in [1]. The target with several detection is called an “extended target” or “extended object” [1]. In this context, the target is no longer categorized as a point target. It is denoted as an extended target.
Various methods based on PHD filter [2], [3], [4] arise for the problem of multiple extended targets tracking (METT), including a particle implement of extended target PHD (ET-P-PHD) filter [5], the extended target Gaussian mixture PHD (ET-GM-PHD) filter [6], [7], the extended target Gaussian mixture cardinalized PHD (ET-GM- CPHD) filter [8], the extended target Gaussian inverse Wishart PHD (ET-GIW-PHD) filter [9], [10], the extended target gamma inverse Wishart PHD (ET-GGIW-PHD) filter [11], the ET-GGIW-CPHD filter [12] and the extended target multi-Bernoulli (ET-MB) filter [13]. In these algorithms, the random matrix approach [14] has been widely used in the framework for tracking an unknown number of multiple extended targets, in the presence of missed detection and clutter. The PHD filter is superior to the traditional tracking algorithms for the data association [15] is unnecessary when multi-targets are involved.
Extended target PHD filters mentioned above are capable of estimating the kinematic states and the extent of multiple targets, in scenarios where both missed detection and clutter exist. The first step of all these algorithms [5], [6], [7], [8], [9], [10], [11], [12], [13] is partitioning of the measurement set. Correct partitions are significant to achieve good tracking performance. Therefore, various partitioning methods have been proposed. [16] shows the application of distance partitioning and K-means++ [17], [18], [19] algorithms for the partitions of the measurement set in the PHD filters [6], [9], [10], [11], [12] and multi-Bernoulli (ET-MB) filter [13]. Distance thresholds are necessary to generate enough partitions for the correct partition in [16]. Increases of targets quantity make the extended target tracking process computationally intractable. Therefore, a novel fast partitioning algorithm with fuzzy ART [20] model for the ET-GM-PHD filter is proposed in [21], [22]. Then, affinity propagation clustering is introduced into the measurement partitioning for extended target tracking in [23]. The elliptical gating defined by a validation region on the basis of the set of predicted measurements is used to remove clutter measurements in [23] makes the affinity propagation clustering capable of partitioning the measurement in a densely cluttered environment with high accuracy. [24] shows an effective partition method using spectral clustering technique, where the clutter measurements are eliminated from the measurement sets by the Gaussian kernel density analysis technique. The method [24] is also superior to the method [21], [22] in a cluttered dense scene.
In [15], [21], [22], different extended target tracking scenarios, including the crossing tracks, parallel tracks, separating tracks and turning tracks are tested. Although the ART model [21], [22] and spectral clustering [16] methods reduce the computational burden, the partitioning results would become rather bad in a cluttered dense scene, and the results are also dependent on the selection of the cluster parameters [23]. However, algorithms [23], [24] have been merely performed with crossing tracks and separating tracks. A framework to partition the measurements of the extended target with clutter when various situations are involved is necessary. Various situations in this work including following four aspects are considered. Firstly, different target tracking scenarios, including crossing tracks, parallel tracks, separating tracks and turning tracks. Secondly, the size and radar cross section (RCS) of multiple extended targets are different. Thirdly, measurement noise should be different due to different sensors would be applied. Fourthly, the number of false alarm or clutter is different. Fifthly, various azimuth resolution of the radar beam is discussed. A robust partition method should work well in all five situations mentioned above. Meanwhile, measurements of one scan must be processed within a radar scanning cycle. Therefore the complexity and calculation of the method are also significant.
A framework to partition the measurements of the extended target with clutter more accurately and more effectively is presented in this context. FCM [25], [26] algorithm is introduced into the improved partition method to achieve better tracking performance. Conventional hard clustering methods classify each point of the measurements just to one set. FCM is a type of clustering technique in which points lie in two or more sets with similar membership degree is allowed. It has robust characteristics for ambiguity and can retain much more information than hard partition methods. Theoretically, the FCM algorithm is superior to partition algorithms [17], [18], [19], [20], [21], [22], [23], [24] when multiple closely-spaced extended targets are involved.
Meanwhile, lots of enhanced FCM algorithms have been developed in recent years. The pixels of an image containing separated layers are clustered by the fuzzy c-means algorithm [27]. Cluster size insensitive FCM (csiFCM) [28] and size insensitive integrity-based FCM method (siibFCM) [29] are proposed to deal with “cluster-size sensitivity” problem. The extension state which describes the target's size and shape is time-invariant. It infers that algorithms [27], [28] can provide a good solution for measurement partition when the target's size and shape are considered. Meanwhile, the size and shape can be regarded as features which are also available to improve the performance of tracker [30]. Clustering performance is especially sensitive to the selection of initial cluster centers. Therefore, some improvements in choosing the proper centers are developed in [31], [32], [33]. All these algorithms are also available in FCM algorithm for initial centers.
The proposed partitioning method can be divided into two stages. Firstly, the clutter is removed by elliptical gating and Gaussian kernel density analysis technique. The two techniques are used to remove the false alarm outside and inside of the gate respectively. Secondly, partition measurements by the improved FCM method. This stage consists of four steps. Step 1, partition the measurements of targets into well separate groups. Measurements of closely trajectories would be clustered in one group using spatial-temporal clustering technique. Step 2, the quantity of extended targets in each group is estimated by the measurements in the gate. Step 3, initial centers of the FCM algorithm are obtained by the predictive location of targets. Step 4, partition the measurements of each group in sub-clusters with the FCM algorithm. Each sub-cluster means the measurements of one target.
There are four major contributions in this work: (1) The extended target model of air surveillance radar is derived and it matches well with real data. (2) An improved FCM algorithm is applied for measurement partition, at the stage of initial, the measurement rate of the targets is used to estimate the number of clusters. Compared with other partition methods [16], [22], [23], inappropriate alternative partitions would be removed directly and the tracking performance is significantly improved. (3) Predictive location of targets is used to set the initial centers which is beneficial to accelerate the convergence and reduce calculation. (4) A cluster shape and quantity insensitive integrity-based FCM method is developed with the consideration of the information of targets. Compared with other cluster methods which base its principle on iteration [19], [26], much better cluster result can be obtained to improve the tracking performance for taking full merits of prior information.
The remainder of the work is organized as follows. In Section 2, models for multiple extended targets tracking are presented. Then, the detailed implementation of the proposed method is showcased in Section 3. Simulation results are shown in Section 4. The real data of nine scenarios and simulated data under various conditions are tested separately using the following six methods: distance partitioning method in [16], K-means++ algorithm [19], MB-ART partition algorithm [22], AP based partition algorithm [23], the traditional FCM algorithm and lastly the proposed method. And the advantage of the proposed method is illustrated. Finally, the study's conclusions are presented in Section 5.
Section snippets
Target model
Assume that the extended targets are randomly distributed in the x–y plane. We use to denote the number of targets at k scan. The extended target state is defined as the triple in [11]. Firstly, the random variable is the measurement rate that describes how many measurements the target, on average, generates per time scan. Real data in Section 4.2 shows that no measurements generated by the target in some frame. Therefore, the number of target generated measurements is
Partition problem
An integral part of extended target tracking with the PHD filter is the partitioning of the set of measurements. Each set is the points of one target. The PHD filters require all possible partitions of the current measurement set for its update in theory. However, the number of possible partitions grows very large as the total number of measurements increases [22]. Therefore, both the efficiency and performance should be considered in the proposed method. The partition problem has been well
Simulation
In this section, simulation experiments are performed to present the models. The simulation is to address the spatial distribution of the measurements of an airplane which is sized 20.3 m × 12.88 m. Eq. (1) and Eq. (2) infer that the spatial distribution of the measurements is related to the relative location and amplitude of the target. The simulation is presented in Fig. 3. The sub-images in the first column of Fig. 3a denote the area where an airplane exists. It assumes that radar beams are
Conclusion
In this work, an improved partition method based on FCM algorithm for PHD filter in METT problem is proposed. The algorithm can be divided into two stages. Firstly, remove the clutter inside and outside of the elliptical gating. The effectiveness of the stage has been proved by the experiment. Second stage is the improved FCM algorithm, four steps are involved here. Compared with the traditional FCM algorithm and other existing partition methods, the proposed method combines the FCM algorithm
Conflict of interest statement
No conflict of interest exits in this manuscript and the manuscript has been approved by all authors for publication.
Acknowledgements
This work was partly supported by National Natural Science Foundation of China (No. 61604116) and Fundamental Research Funds for the Central Universities (Nos. JB151304, XJS14070).
Bo Yan received his B.S. degree from the Northwest University in 2013. In 2018, he received the Ph.D. degree in XIDIAN University. He is a lecturer in XIDIAN University now. His research interests are radar data processing, multi-target detection and tracking and data fusion.
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Bo Yan received his B.S. degree from the Northwest University in 2013. In 2018, he received the Ph.D. degree in XIDIAN University. He is a lecturer in XIDIAN University now. His research interests are radar data processing, multi-target detection and tracking and data fusion.
Na Xu was born in Xian, China, 1994. She received his B.S. degree from XIDIAN University in 2015. Her research interests lie in radar signal processing and communication. Now she is working towards the Ph.D. degree with XIDIAN University.
L.P. Xu received his M.S. and Ph.D. degrees from XIDIAN University in 1986 and 1996, respectively. Since 1988 he has been with the XIDIAN University where he is currently a Professor of Navigation, Guidance and Control. He has authored over 60 journal papers and two books. His research interests include radar system, navigation, multitarget detection.
Muqing Li received his B.S. degree from the ZhengZhou University in 2014. Now he is working towards the Ph.D. degree with XIDIAN University. His research interests are image segmentation, image recognition and processing.
Pengfei Cheng received his M.S. and Ph.D. degrees from Jilin University in 2011 and 2014, respectively. Since 2014 he has been with the XIDIAN University where he is currently an Associate Professor. His research interest is the sensors and data processing.