Addressing the problem of being easily interfered by false targets such as chaff and corner reflector when selecting missile targets, a multifeature multimodel target selection method based on the technique for order preference by similarity to ideal solution (TOPSIS) is proposed if only singletarget characteristics such as target position or radar cross section (RCS) size is used in the selection of missile targets. The target selection problem under the comprehensive utilisation of multiple features is regarded as a problem in decisionmaking based on multiple attributes. The BP network based on the target RCS frequency domain statistical features, the radial basis network based on the target polarisation feature and the radial size feature based on highresolution range profile (HRRP) are realised. The comprehensive utilisation of Csupport vector machine (SVM) and other target recognition methods and the comprehensive sorting of target selection, to a certain extent, enable antiship missiles to make the correct target selection more accurately. The simulation results display that the effective selection of ship targets can be achieved in the case of passive interference by surface ships.
Keywords
 vector machines
 neural networks
 TOPSIS
 target recognition
Given a certain capability of target selection, the forcedistributecode method could effectively perform target selection and force distribution during the collective attack of antiship missiles at the enemy formation, which prevents the simultaneous attack of several missiles at the target with larger radar cross section (RCS). Modern naval battle involves a complicated electromagnetic environment, causing a noticeable role of passive interferences including chaff and corner reflector in the protection against missile attacks. The problem of being easily interfered by false targets such as chaff and corner reflector is encountered if only singletarget characteristics such as target position or RCS size are used in the selection of missile targets. Because of the rapid development, the terminal guidance radar technology has not only revealed the RCS frequency sequence of targets, but also collected the highresolution features of targets including polarisation and radial length of highresolution range profile (HRRP). Therefore, a variety of classifiers (e.g. BP neural network, RBF, Csupport vector machine (SVM), etc.) could be established for different target features in the process of recognition. The recognition results could be further converted into the posterior probability under maximum likelihood estimation by employing sigmoid function mapping and other methods [1]. Subsequently, the problem of antiship missile target recognition and selection under the background of real and false targets is equal to a multiattribute decisionmaking problem. The posterior probabilities generated by diverse classifiers with different features are utilised to construct the decisionmaking matrix. Eventually, the technique for order preference by similarity to ideal solution (TOPSIS) is employed for decisionmaking with multiple attributes to comprehensively sequence the types of target and support for decisionmaking on the preset targets of antiship missiles.
TOPSIS is a method for making a decision involving multiple attributes [2]. It is mainly employed to resolve the problem of decisionmaking on the best alternative with multiple attributes or indexes [3]. Multiple attribute indexes may restrict or contradict each other, so that there is normally not the best solution, but it is possible to obtain ideal solution and negative ideal solution. TOPSIS utilises such two solutions simultaneously to sequence the alternatives in terms of quality. In the meanwhile, these two solutions are used for the following reason: when the distance of two alternatives to the ideal solution is the same, priority is given to the alternative that is farthest away from the negative ideal solution [4].
TOPSIS has the basic principle as shown in Figure 1. Among them,
Ruck, Richard and Kenichi et al. [5, 6] have proved that, if the class coding of ‘1 out of C’ is adopted by network output, and minimum meansquare error is taken as the training target, the outputs of all feedforward neural networks correspond to the posterior probabilities of training sample categories. In this case, ‘1 out of C’ means that the expected output of feedforward neural network must be:
If neural network estimation is quite accurate, the sum of its outputs for each class should be 1. If inaccuracy is taken into account, the sum will not be 1. In this case, normalisation should be conducted as follows:
For the training sample (
Clearly, SVM could not output the posterior probability, but the classification result of sample data, that is, 1 or −1. Platt [7, 8] utilised the sigmoid function to realise the mapping between SVM output and probability. The transformation is in the form of following equation:
The principles of TOPSIS target selection method with support of target recognition posterior probability is presented in the Figure 2. RCS frequency statistical feature, polarisation feature and the HRRP mirror size are selected for classified target recognition by employing BP neural network, RBF network, and SVM, respectively. The recognition results are transformed into the posterior probability as detailed in Sections 3.1 and 3.2. Subsequently, TOPSIS is adopted to comprehensively evaluate and determine the sequence of target types. The steps are detailed as follows:
Let
where
The posterior probability of target recognition classification is a benefit attribute, so that the ideal solution
The distance of target class
The distance from target class
Based on the analysis in Reference [9], a warship normally places chaffs in the form of missile axis symmetric ‘four targets’ when it detects an incoming antiship missile, as shown in Figure 3 [10]. In the meantime, it also rapidly deploys corner reflector, and then moves fast to create a complicated interference situation involving many types of false targets, which confuses the incoming missile and makes it select a false target. Under such situation, if the target selection method of the antiship missile is defined as ‘selecting the right side’, the antiship missile is very likely to select the chaffer or corner reflector when only RCS size is taken as the basis for type judgement.
It is assumed that the terminal guidance radar could gather the RCS frequency statistical feature, polarisation feature and HRRP radial size feature of targets. TOPSIS is employed to comprehensively sequence the classification results of these features, in a bid to rule out the interferences by chaff and corner reflector. As shown in Table 1, the decision matrix reveals that if single RCS frequency domain feature is employed, false target 1 (corner reflector) is mistakenly considered as the real warship; If single BP neural network mode is employed, false target 5 (chaff cloud) is mistaken as the real warship; if single polarisation feature or single RBF radial basis network model is employed, false target 1 (corner reflector) is mistakenly considered as the real warship; if single radial size feature is employed, false target 2 (chaff cloud) is mistakenly considered as the real warship, and if single SVM model is employed, false target 3 (chaff cloud) is mistakenly identified as the real warship. When the multifeature and multimodel comprehensive classification model based on TOPSIS is adopted, and the weighted standard matrix is set as
Decision matrix
Real warship  Warship  0.4642037  0.607021  0.401691 
Chaff cloud  0.1075953  0.1135784  0.379228  
Corner reflector  0.428201  0.2794006  0.219081  
False target 1 (corner reflector)  Warship  0.412431  0.4401453  0.1364145 
Chaff cloud  0.120652  0.146565  0.1177154  
Corner reflector  0.466917  0.4132897  0.7458701  
False target 2 (chaff cloud)  Warship  0.312082  0.2197485  0.438642 
Chaff cloud  0.561797  0.6395  0.340408  
Corner reflector  0.126121  0.1407515  0.22095  
False target 3 (chaff cloud)  Warship  0.317219  0.2038501  0.486033 
Chaff cloud  0.559468  0.664808  0.302723  
Corner reflector  0.123313  0.1313419  0.211244  
False target 4 (chaff cloud)  Warship  0.316303  0.2121808  0.330903 
Chaff cloud  0.520689  0.647954  0.454883  
Corner reflector  0.163008  0.1398652  0.214214  
False target 5 (chaff cloud)  Warship  0.477049  0.2406688  0.379228 
Chaff cloud  0.40926  0.63095  0.401691  
Corner reflector  0.113691  0.1283812  0.219081 
RCS, radar cross section; SVM, support vector machine.
Distance of each class to the ideal spot and negative ideal spot





Real warship  Warship  0  0.6356  1.0000 
Chaff cloud  0.6092  0.1601  0.2082  
Corner reflector  0.3768  0.3610  0.4893  
False target 1 (corner reflector)  Warship  0.6119  0.4143  0.4037 
Chaff cloud  0.7750  0.0000  0  
Corner reflector  0.0269  0.7653  0.9661  
False target 2 (chaff cloud)  Warship  0.4884  0.2970  0.3781 
Chaff cloud  0.0982  0.6729  0.8726  
Corner reflector  0.6971  0.0000  0.0000  
False target 3 (chaff cloud)  Warship  0.5207  0.3440  0.3978 
Chaff cloud  0.1833  0.6951  0.7913  
Corner reflector  0.7418  0.0000  0.0000  
False target 4 (chaff cloud)  Warship  0.4970  0.2058  0.2928 
Chaff cloud  0.0000  0.6663  1.0000  
Corner reflector  0.6663  0.0000  0.0000  
False target 5 (chaff cloud)  Warship  0.3909  0.4127  0.5135 
Chaff cloud  0.0678  0.6110  0.9001  
Corner reflector  0.6465  0.0000  0.0000 
CST computing software is used with the CPU/GPU heterogeneous parallel computing method to determine the scattering characteristics of extremely large electric size targets including warship and corner reflection in the highperformance computing cluster. The calculation process in this paper involves eight computing nodes. Each computing node is provided with two 16core and 64 GB CPUs, and the IB network with transmission speed up to 56 GB/s for data exchange. The parameters of CST simulation software are as follows: incident horizontal angle 30°, pitch angle 5.1°, central frequency 10 GHz, bandwidth 400 MHz, and 10,001 sampling points. After all, 178 pieces of data (including 89 pieces of training data and 89 pieces of test data) were obtained for the RCS frequency statistical feature, polarisation feature and radial size feature of warship, corner reflector and four chaff clouds. The classification recognition outcome is as shown in Table 3. TOPSIS has significantly improved the recognition accuracy up to 97.75%.
The classification recognition outcome
BP neural network  69.66%  75.28%  82.02%  84.27% 
Radial basis network (RBF)  74.16%  78.65%  86.52%  88.76% 
SVM  80.09%  78.65%  87.64%  92.75% 
TOPSIS comprehensive decisionmaking  –  –  –  97.75% 
HRRP, highresolution range profile; RCS, radar cross section; SVM, support vector machine; TOPSIS, technique for order preference by similarity to ideal solution.
In general, this method includes the recognition results of multiple target features for the comprehensive evaluation and decisionmaking, so that it could overcome the defects to some extent, that is, the target selection of missile is very easily interfered by false targets including chaff and corner reflector if the missile relies only on a single target feature such as target position or RCS size.
To address the problem of being easily interfered by false targets such as chaff and corner reflector when selecting missile targets, a TOPSIS missile target selection method with support of target recognition posterior probability is proposed if only a single target feature such as target position or RCS size is used for the selection of missile targets. In the proposed method, the problem of target selection with the comprehensive utilisation of multiple features is regarded as a decisionmaking problem involving multiple attributes. Three types of features, i.e. RCS frequency statistical feature, polarisation feature and HRRP mirror size are selected to conduct the classified target recognition with BP neural network, RBF network and SVM, respectively. Subsequently, the calculation methods for posterior probability are employed to further transform the recognition results into posterior probabilities. In the end, TOPSIS is adopted for the comprehensive evaluation to determine the sequence of target types. As revealed in the simulation results, the ship targets can be effectively selected in the case of passive interference by surface ships.
The classification recognition outcome
BP neural network  69.66%  75.28%  82.02%  84.27% 
Radial basis network (RBF)  74.16%  78.65%  86.52%  88.76% 
SVM  80.09%  78.65%  87.64%  92.75% 
TOPSIS comprehensive decisionmaking  –  –  –  97.75% 
Distance of each class to the ideal spot and negative ideal spot





Real warship  Warship  0  0.6356  1.0000 
Chaff cloud  0.6092  0.1601  0.2082  
Corner reflector  0.3768  0.3610  0.4893  
False target 1 (corner reflector)  Warship  0.6119  0.4143  0.4037 
Chaff cloud  0.7750  0.0000  0  
Corner reflector  0.0269  0.7653  0.9661  
False target 2 (chaff cloud)  Warship  0.4884  0.2970  0.3781 
Chaff cloud  0.0982  0.6729  0.8726  
Corner reflector  0.6971  0.0000  0.0000  
False target 3 (chaff cloud)  Warship  0.5207  0.3440  0.3978 
Chaff cloud  0.1833  0.6951  0.7913  
Corner reflector  0.7418  0.0000  0.0000  
False target 4 (chaff cloud)  Warship  0.4970  0.2058  0.2928 
Chaff cloud  0.0000  0.6663  1.0000  
Corner reflector  0.6663  0.0000  0.0000  
False target 5 (chaff cloud)  Warship  0.3909  0.4127  0.5135 
Chaff cloud  0.0678  0.6110  0.9001  
Corner reflector  0.6465  0.0000  0.0000 
Decision matrix
Real warship  Warship  0.4642037  0.607021  0.401691 
Chaff cloud  0.1075953  0.1135784  0.379228  
Corner reflector  0.428201  0.2794006  0.219081  
False target 1 (corner reflector)  Warship  0.412431  0.4401453  0.1364145 
Chaff cloud  0.120652  0.146565  0.1177154  
Corner reflector  0.466917  0.4132897  0.7458701  
False target 2 (chaff cloud)  Warship  0.312082  0.2197485  0.438642 
Chaff cloud  0.561797  0.6395  0.340408  
Corner reflector  0.126121  0.1407515  0.22095  
False target 3 (chaff cloud)  Warship  0.317219  0.2038501  0.486033 
Chaff cloud  0.559468  0.664808  0.302723  
Corner reflector  0.123313  0.1313419  0.211244  
False target 4 (chaff cloud)  Warship  0.316303  0.2121808  0.330903 
Chaff cloud  0.520689  0.647954  0.454883  
Corner reflector  0.163008  0.1398652  0.214214  
False target 5 (chaff cloud)  Warship  0.477049  0.2406688  0.379228 
Chaff cloud  0.40926  0.63095  0.401691  
Corner reflector  0.113691  0.1283812  0.219081 
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