## 1 Introduction  
Target tracking techniques have been studied extensively with fruitful results and widely developed in both military and civil fields [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]. In traditional tracking applications, it is generally assumed that at most one measurement can be received by sensors per time and the target is modeled as a single point mass. However, with the increased resolution of modern sensors, multiple measurements may be originated from different unknown sources on a target. In this case, a target should be regarded as extended if its extension is much larger than the sensor resolution. Recently, multiple extended target tracking [11; 12; 13; 14; 15; 16] has been attracting attention. However, it is still a complicated problem because there are unknown and uncertain associations between targets and measurements. Especially for multiple closely spaced extended target tracking (MCETT), extended targets may have parallel or crossed tracks (such as decoys and re-entry vehicles in ballistic missiles, and groups of airplanes with close tracks in radar surveillance). It is more difficult to judge the associations between these closely spaced targets and their measurements, respectively. The random finite set (RFS) [17] and the finite set statistics (FISST) [18] have been developed over decades. They are widely applied to deal with the tracking of multiple targets with unknown and time-varying number in noise and clutter environments, because the uncertain associations between targets and measurements can be avoided. In [19; 20], the probability hypothesis density (PHD) filter was proposed. It was evolved into the extended target PHD (ET-PHD) filter [21] by assuming that the number of measurements obeys the Poisson distribution and measurements are distributed around the target based on an inhomogeneous spatial Poisson point process [22]. In recent years, many multiple extended target tracking approaches based on the ET-PHD filter and its variants have been proposed [23; 24; 25; 26], e.g., the extended target Gaussian mixture PHD filter [27], the extended target gamma GW-PHD (ET-GGIW-PHD) filter [28; 29; 30] based on the random matrix approach [31; 32; 33], and the ET-GM-PHD filter based on random hypersurface model [34; 35; 36]. In the ET-PHD filter framework, the measurement partitioning is indispensable. It divides the set of measurements into several non-empty subsets and aims at obtaining the partitions that are closest to the true partition. The multiple extended target tracking performance is affected by measurement partitioning to a large extent because the partitioning results are directly utilized to update the predicted target state. Especially for MCETT, the dense distribution of measurements may bring difficulty to the accurate measurement partitioning and even cause the cardinality underestimation problem. To deal with this problem, the traditional partitioning algorithms usually require all possible partitions. However, the number of possible partitions grows very fast with the increasing total number of measurements, which creates a heavy computational burden. Furthermore, a large number of partitions are still unreasonable and should be eliminated. To partition the measurements more effectively, a distance partitioning algorithm was proposed to make relatively accurate partitions by decreasing the distance threshold empirically. However, this approach may not be well applied for tracking closely spaced extended targets because it is very likely to cause an underestimation in the extended target number. Furthermore, there are still unreasonable and redundant measurement partitions, which are adverse to reducing a heavy computational burden. In [37], the prediction partitioning algorithm and EM partition algorithm were proposed for tracking elliptical targets. The former directly treats the predicted mean of the GIW component as the centroid of the ellipsoid target and uses the extension estimation to put the measurements belonging to the corresponding component into the same subset.