Explain the track detection of aesa radar using high end machine learning algorithm.
Active Electronically Scanned Array Radar
Active Electronically Scanned Array (AESA) Radar is an advanced technology that is currently in advancement. Both the AESA and PESA (passive) radar consists of numerous antennas and transmitter. The main variation between the AESA and PESA (Passive) radar is that AESA radar could generate its own microwave signal with its altering phase, i.e., it could be able to change its angle position (from one azimuth angle to another) . They could be able to operate at varied frequencies (around 1000 frequency in a second). The major problem arises here is occurrence of false alarm due to the sensor indication . This could be caused due to the certain unwanted object that could fall on the track giving a disturbance to the object of interest. Certain measures could be taken to control it. We know that machine learning algorithm have raised its head into every new invention and technologies since it could make a machine to learn by its own  . In this paper the particular detection of track and the classification of the track using machine learning algorithm is explained.
AESA radar is widely used in various fields especially for the military purposes. In our approach we’re going to concentrate only on Support Vector Machines (SVM). SVM is nothing but a classification algorithm . Here, for the detection of the track we could use various sensors that could follow the principle of micro-Doppler’s effect. Second the track detected should be classified based on the high-end machine learning algorithm. Normally classification could be done based on the statistics. Then these statistical data should be compared. Comparison and the classification could be either discriminative or generative . The adequacy of SVM could be used for this purpose.
SVMs are one of the supervised learning models in machine learning same employed for analysis. In SVM model the training/test samples are represented as dot/points in the space and they are mapped in such a way that the clear gap among the categories appears which separates the samples . New test samples/examples are later mapped on the Using the kernel trick SVMs are also be able to perform non-linear classification in addition to linear classification. SVMs automatically map the inputs with high dimensional feature/attribute spaces. In general SVM supports to construct hyper plane in any space and this can be employed for any tasks such as regression, prediction or classification. SVM hyper plane is the only responsible for good separation of training data with the largest distance to its nearby data . This approach is generally known as functional margin . The state of the rule is if margin is larger than the generalization error of classifier will be lower.
Detection of tracks using machine learning
The main aim of ordering the tracks is to exactly forecast the target class from the data in each case. The classifier engine process includes two steps:
1. Classifier Building: This method is to build a learning phase. The classifier, which evolved from training certain databases instances/tuples, is constructed by the classification algorithms. Individual instance/tuples that is composed of the preparation group is mentioned as a group. These tuples can also be mentioned to as data points.
2. Usage of Classifier – The training model/classifier generated employing the data set will classify test data set objects/tuples.
• Relevance Analysis: Database could consist of some unrelated attributes. Correlation analysis will identify any two given attributes are associated.
• Data Transformation and lessening: The following methods help in data transformation:
– Normalization: This transformation occupies scaling every value that will make them descend within a specific range   . This method is mainly used in the learning step when the neural networks or the methods evolving measurements are employed.
– Simplification: This is a major concept of transforming. Here we can use the hierarchy concept.
If the detected tracks of n points is given and the method of it is (−x→1 , y1 ) ........ (−x→n , yn ) and here yi is 1, this indicates the class with the sample →−xi is present. Each →−xi is a real vector of p-dimension . Our interest is detecting the “extreme- margin hyper plane” which separates the category of samples from →−xi. This is required to be definite to maximize the distance among the hyper plane as well as the adjacent sample →−xi.
It is understandable that H1 usually does not disconnect the classes. While H2 separates them by a minute margin, on the other hand H3 disconnects them with the greatest margin . The hyper plane is defined as the set of points →−x satisfying →−x * →−w - b = 0. The support vector contains the sample on the margin. The offset of the hyper plane from the origin with normal vector →−w is determined by the parameter →−w.
Hard-margin two parallel hyper planes which separate two classes of data, can be selected if the training data are linearly separable . So by this we can have the distance between them is as possible as large. The”margin” is nothing but the region bounded by these two hyper planes. The maximum margin hyper plane lies between these planes . These hyper planes can be described by the equations →−w * →−x - b = 1 and →−w * →−x - b = -1. →−w is the distance between two hyper planes, by minimizing w we can maximize the distance between the planes . By adding the constraint: for each either →−w * →−x - b ≥ 1 or →−w * →−x - b ≤ 1if yi = -1, here the data points can be prevented from falling into the margin.
Support Vector Machines
Figure 3: Classification based on linear SVM
Figure 4: Classification based on Hard SVM
According to the constraints/conditions every point of the data should be on the definite plane of the margin  . The modified equation is:
yi (→−w ∗ →−x − b) ≥ 1, f or al l 1 ≤ I ≤ n (1)
To get the optimization problem we can put all these together:
”Decrease →w subject to →−w * →−x - b ≥ 1 for I = 1, 2, 3,. N”. Completely the max margin hyper plane is determined by overright arrow(xi ) which lies at the near end. Here the →−x is named as support vectors .
Soft Margin is the loss function with the equation max (0, 1 – yi(→−w * →−x- b)). It is introduced to enhance Support Vector Machine where the data are non-linearly separable. If the constraint in (1) is satisfied then this function value is zero, which means, →−x is in the right margin side. The function with minimization is as below:
high(0, 1 – yi (→−w ∗ →−x − b)) + λ→−w (2)
Here λ increments the values of margin-size and making sure that the →−x is fall/separated with the actual side of it. Therefore, the soft margin Support Vector Machine may behave equally same as hard margin Support Vector Machine for enough small values of λ in the case when linearly classifiable test data are available.
Here we employ feature vector in order to detect the tracks  . The tracks are detected by the radar range equation given below.
Gt, Gr - Transceiver Gain
P1 – power transmitted
Σ – radar cross section
(SNR)min – Minimum signal to noise ratio
L - System loss factor
Figure 3: Flow chart representing the track estimation with machine learning process
With the help of the Radar Range equation we could able to obtain the raw data . The classification procedure starts with the raw data. This stage involves the filtering stage. Then the data is fed into the detection algorithm. At this stage the features are extracted from the data. Then the extracted targets are forwarded to classification. The various processed data is quantified before the classification. This utilizes the statistical methods and sends to the training phase after favouritism . The procedure repeats for the occurred target which is shown in the flow chart given above.
The intrusion detection algorithm could be employed at this stage. The similar detected tracks that are trained with the predefined characteristic set comes under one type where the remaining track with certain disturbances comes on the other side which is shown in the figure given below.
Figure 4: Detection of Abnormal tracks using SVM
#Import Library Line 1. This is done through jupyter notebook
import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm,data
#Load the dataset. we have to detect the data from the sensor. we take the data in the form of two #features. the two dimension data is considered to avoid the ugly slicing
iris = datasets.load_iris()
X = iris.data[:, :2]
y = iris.target
# Line 3. Plot the map
from sklearn import make_blobs
(X,y) = make_blobs(n_samples=50,n_features=2,centers=2,cluster_std=1.05,random_state=40)
#we need to add 1 to X values (we can say its bias)
XX = np.c_[np.ones((X.shape)),X]
plt.scatter(XX[:,1],XX[:,2],marker='o',c=r)# default marker is 'o'
Through our paper we have generated a solution to ignore the abnormal track and take the necessary track using high end machine learning algorithm. The advantages of AESA radar technology are many. These technologies are highly adapted in the field of air and naval forces that uses AESA radar to detect minute targets at a wider range. Electronic surveillance system finds difficult to vary in its frequencies for detecting the position. But AESA could highly vary in its frequencies with a minute pulse at a random sequence. The greatest advantage is to resist jammers. But a minor disadvantage is that since it could show variations in its frequencies, this system could no longer persist in its life time.
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