Recognizing the formations of CVBG based on shape context using electronic reconnaissance data

To recognize the formation of the carrier battle group (CVBG) from passive electronic reconnaissance and location data, a shape context-based method is proposed. The proposed method treats the location data as a graph model

✉ Email: huangzhen@tsinghua.edu.cn To recognize the formation of the carrier battle group (CVBG) from passive electronic reconnaissance and location data, a shape contextbased method is proposed. The proposed method treats the location data as a graph model, and a graph matching method is used for formation recognition. The shape context and background context for each unit in CVBG is calculated and used for multi-viewpoint shape feature, which is rotation invariance and distinctive. The experimental results show that the proposed method can recognize the formation with a higher accuracy and locate the ship with electromagnetic silence.
Introduction: The formation of the carrier battle group (CVBG) varies with the task types and environment of battlefield and plays an important role in modern battles. Recognizing the formation of enemy fleets can help commanders to discover their purpose and weakness, eventually seize the opportunity to win a battle. Passive electronic reconnaissance (PER) technology can locate each unit of a CVBG using satellite-borne or airborne radar to receive electromagnetic signal transmitted by the fleet. It was widely used for war ship detection because of its wide detection range and difficulty to be found by the enemy. However, most of the current researches [1][2] focused on analysing individual unit of a CVBG, and the location of each unit in the fleet was not involved, which made it hard to recognize the formation of a CVBG. Contextbased recognition methods [3][4] treat the formation recognition as shape matching problem, and the location information is encoded by shape context.
A CVBG can be treated as a sparse target group, which can be characterized by a set of scattered points. But the traditional context-based methods were designed for continuous object, which cannot get enough feature from a CVBG for recognition, and the symmetry of CVBG formation makes it worse. Another difficulty is that the formation of a CVBG cannot be described by a fixed shape, because relative position between ships and the number of ships is not fixed. When some unit in the fleet is electromagnetic silence or more ship join in temporary, the number of units obtained by the PER system will change and which need the recognition method to be robust to the variation of units number.
Proposed method: This paper proposes a novel CVBG formation recognition method, which uses the location result from passive electronic reconnaissance to build a graph model and treats the recognition problem as graph matching. In order to obtain enough features for matching, the shape context and the background context of each unit were combined to form a multi-viewpoint shape feature for CVBG formation. And a loss function based on both square loss and cosine loss is used to measure the similarity between shape features of PER and CVBG formation diagram.
The main flow chart of the proposed method is shown in Figure 1. The shape context and background context for each unit in CVBG are extracted, which are used to form a multi-viewpoint shape feature. The shape features extracted from passive electronic reconnaissance data and CVBG formation diagram are matched based on a distant measurement to recognize the fleet formation. After matching, each ship in the fleet is recognized according to the CVBG formation diagram, even the one with electromagnetic silence. Let ,where X i is the location of a unit in CVBG, and Mis the total number of units. G = {V, E}is a fully connected graph model built from X, with nodes and edges described by V and E respectively.  All edges congregating on X i is denoted by E i , and its complementary Shape context: For a given ship located onX i , its shape context can be calculated as follows.
A polar coordinateρ − θ is built, with X i be origin and velocity reversal be the reference direction, which is rotation invariance when the angle between the fleet and the radar platform changes.
As shown in Figure 2(a), the coordinate space of ρ − θ is divided into N ρ × N θ bins, each is represented by π ρ,θ (X).
The number of ships in each bin is obtained by averagingX over each bin which was used to form the descriptorF C i = {h ρ,θ (X i )} and the fleet shape context F C = [F C 1 , F C 2 , . . . , F C M ] . The shape context uses a histogram to capture the distribution of the remaining units relative to the reference unit, thus one can obtain the globally discriminative characterization of the CVBG.
Background context: For a given ship located onX i , its background context is calculated as follows. A right-handed rectangular coordinate system x-yis obtained, with the centre of the fleet without the reference pointX i be the origin and the velocity reversal be the x coordinate axis.
In order to get a distinctive descriptor of the background context, each edge inĒ i is represented by its middle point position in x-y and the gradient of the edge. Therefore, each edge is encoded in a three-dimensional (3D) space, which is called coordination-gradient space (CGS) in [5], with one dimension be the gradient direction and the others be the coordinates of the middle point. To calculate the distribution ofĒ i , the 3D space is divided into N α × N x × N y bins, which is shown in Figure 2. Then, a histogram F B i is exploited to present the number of edges located in each bin. Unlike [5], a local coordinate system is built on each reference point whereĒ i is represented. And the velocity reversal obtained by passive electronic reconnaissance is encoded in this local coordinate system.
Multi-viewpoint shape context: The shape context F C i and background context F B i are combined to get a shape feature for each unit in the fleet, where C S (F i , H i ) = j=1 (F j,i − H j,i ) 2 is the square loss, C c (F i ,H i )is cosine loss, and λ ∈ [0, 1] is a coefficient of balance.
The best candidate match for each unit of PER is found by identify its nearest neighbour from CVBG formation diagram. However, many units from PER will not have a correct match because the symmetry of the formation. So, the k nearest neighbour is conceded as candidate matching. The similarity of multi-viewpoint shape features between PER and CVBG formation diagram is calculated from the candidate matching as where M s = min (M1, M2). We set a constraint on Equation (3) that each H i can only have a best matching.
Experimental results: The experimental results of the proposed method in this paper, in [3] (SC) and [4] (MVC), are compared with the data generated according to [4]. Shape context (SC) proposed in [3] is a traditional shape matching method, and the one in [4] is the state-of-theart method. The CVBG is composed of one aircraft carrier (CV), three cruisers (CG), four guided-missile destroyers (DD), and two frigates (FFG), totalling 10. As shown in Figure 3, three kinds of CVBG formations are used, which are proceeding formation, offensive formation and combat formation. And 900 data are generated, 300 data for each kind of formation.
For the proposed method, the number of units of CVBG is M = 10, coordinate space of ρ − θ is divided into2 × 12 bins and the CGS is divided into 6 × 4 × 4bins. The recognition results are shown in Table 1. As shown in Table 1, the recognition accuracy of the proposed method is 2% higher than MVC for the combat formation, and the same for the other formations.
In order to show the ability of the proposed method can recognize the formation of a fleet with different number of units, we randomly delete or and a DD (or CG, FFG) in the FER data. And the recognition result is shown in Table 2. In Table 2 DD+ means a DD was added to the FER data at a random location without change the formation of the fleet, and DD-means a DD was missing. From Table 2 we can see that the proposed method can recognize the formation accurately, even the number of units in the fleet is different. The inconsistent ship amount has less influence on the proceeding formation compared with the other two.
The exits of the CV are important for formation recognition, especially for the combat formation. If the CV is missing from the FER data due to the electromagnetic silence or other reasons, the recognition accuracy will drop down to 91%, 90.5% and 88% for the proceeding, offensive and combat formation, respectively.