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Aerodynamic objects are classified into various categories like fighter planes, UAV, helicopter, commercial planes etc. Only 30% of the RADARS in India can deduce automatically as to which category an identified target belongs to. Basically the Radar Cross Section(RCS) is used. The rest 70% of the Indian radars can give only the position of the aerodynamic objects.
Upgrading or Replacing these conventional radars(70%) with new ones is nearly impossible as it would cost more than half of the country's yearly budget. In this paper is presented a solution for this problem.
An artificial intelligence system which can identify the class to which an identified target belongs to is presented here. The system is a combination of a neural network and fuzzy logic. Results with 90% accuracy were obtained and this system will replace the conventional look up table classification system in the near future.
The conventional radars give the position of the aerodynamic targets. I preferred to use the Geodetic coordinates(w.r.to the centre of the earth) for reference of the position. It is required to calculate all the required parameters for classification from these coordinates. This is explained further in the data processing section(3).
After the data is processed, it is used to train a neural network. This neural network is capable of identifying to which
class the flight path of the identified target belongs to.The details of the neural network and the fuzzy logic used are given under the AI system(4) section.
The details of the classes into which aerodynamic objects are classified into , and the basic properties of the various classes are listed in the Target classes and their Attributes(2) section.
2. CLASSIFICATION OF TARGETS
The targets are basically classified into:-
â€¢ Fighter (Ftr)
â€¢ Commercial ac (civil)
â€¢ Helicopter (Heli)
â€¢ Unmanned air vehicle (UAV)
â€¢ Jammer aircraft (Jam)
â€¢ Cruise Missile (CM)
â€¢ Air to ground (AG)
â€¢ Anti-radiation missile (ARM)
They will be referred to by the above given abbreviations.
2.1. ATTRIBUTES OF DIFFERENT TARGET CLASSES.
General characteristics of each Target :
â€¢ They follow only chartered flight paths.
â€¢ They fly alone.
â€¢ They have a max. g-turn of 1
â€¢ They are very light.
â€¢ Not very fast.
â€¢ General flying altitude is around 2000 m.
â€¢ Can have straight, surveillance maneuvers.
â€¢ Hovers around the target.
Anti radiation missile:
â€¢ These are launched form fighter planes
â€¢ It seeks the source of radiation (RADAR) and strikes it.
Air to Ground Missile:
â€¢ These are launched from fighter planes.
â€¢ Once launched, these follow projectile motion.
â€¢ These are capable of doing a variety of maneuvers.
â€¢ They generally attack as a pack (In a formation).
â€¢ So, cluster testing would be useful in identifying a fighter plane.
â€¢ These are in most ways, similar to fighter planes.
â€¢ They can do all the moves a fighter plane does.
â€¢ The only differences are that it has constant velocity (i.e. 0 acceleration) and it flies alone.
â€¢ The flight has 3 stages ,
a)The initial launch stage where it goes to a very high altitude.
b)The DIP stage where it directs itself in the direction of the target and dips down to a very low altitude.
c)Te final stage where it flies low with constant velocity till it strikes the target.
3. DATA COLLECTION,PROCESSING AND PARAMETER EXTRACTION .
3.1 Data Collection.
The data necessary for the training of the neural network was simulated using a software called Flight Emitter .
The flight paths were designed considering the following parameters,
- Maximum Altitude
- Maximum Velocity
- Maximum G-turn.
- Maximum vertical turn.
- Possible maneuvers.
All extremities were considered when designing the flight path.
The output of the simulator was in the form of a text file and it contained the following details.The frequency of sampling is 1 second.
3.2 Data Formatting and Processing.
The following parameters were obtained from the simulated data,
â€¢ Velocity(x,y,z coordinates , total)
â€¢ Ground velocity.
â€¢ Jerk factor.
â€¢ Latitude, Longitude positions.
â€¢ Rate of ascent /descent.
â€¢ Radius of turn.
3.2.1 Formulae Used for finding the parameters.
(x1,y1,z1) be the position of the plane at time t1.
(x2,y2,z2) be the position of the plane at time t2.
(x3,y3,z3) be the position of the plane at time t3.
Radius of turn( R ) :
In this method , we use four points and fit it into a sphere , then we find the radius of te sphere which will be very close to the radius of the actual path taken.
Call the four points A, B, C and D. Any three of them must be non-collinear (otherwise all three could not lie on the surface of a sphere) and all four must not be coplanar (otherwise either they cannot all lie on a sphere or they define an infinity of them).
A, B and C define a circle. The perpendicular bisectors of AB, BC and CA meet in a point (P, say) which is the centre of this circle. This circle must lie on the surface of the desired sphere.
Consider the normal to the plane ABC passing through P. All points on this normal are equidistant from A, B and C and its circle (in fact it is a diameter of the desired sphere). Take the plane containing this normal and D (if D lies on the normal any plane containing the normal will do); this plane is at right angles to the ABC one.
Let E be the point (there are normally two of them) on the circumference of the ABC circle which lies in this plane. We need a point Q on the normal such that EQ = DQ. But the intersection of the perpendicular bisector of ED and the normal is such a point (and it exists since D is not in the plane ABC, and so ED is not at right angles to the normal).
Let the 4 points be (x1, y1, z1) etc. They are coplanar if and only if the following determinant is zero:
| x1 y1 z1 1 |
| x2 y2 z2 1 |
| x3 y3 z3 1 |
| x4 y4 z4 1 |
The equation of the sphere in this case has been given in a previous post, but it is worth repeating; it is given by setting the following determinant to zero:
| x2+y2+z2 x y z 1 |
| x12+y12+z12 x1 y1 z1 1 |
| x22+y22+z22 x2 y2 z2 1 | = 0.
| x32+y32+z32 x3 y3 z3 1 |
| x42+y42+z42 x4 y4 z4 1 |
The 5 co-factors are ,
| x1 y1 z1 1 |
M11= | x2 y2 z2 1 |
| x3 y3 z3 1 |
| x4 y4 z4 1 |
| x12+y12+z12 y1 z1 1 |
M12= | x22+y22+z22 y2 z2 1 |
| x32+y32+z32 y3 z3 1 |
| x42+y42+z42 y4 z4 1 |
|x12+y12+z12 x1 z1 1 |
M13= | x22+y22+z22 x2 z2 1 |
| x32+y32+z32 x3 z3 1 |
| x42+y42+z42 x4 z4 1 |
| x12+y12+z12 x1 y1 1 |
M14= | x22+y22+z22 x2 y2 1 |
| x32+y32+z32 x3 y3 1 |
| x42+y42+z42 x4 y4 1 |
|x12+y12+z12 x1 y1 z1 |
M15= | x22+y22+z22 x2 y1 z2 |
| x32+y32+z32 x3 y1 z3 |
| x42+y42+z42 x4 y1 z4 |
This can be solved by evaluating the cofactors for the first row of the determinant. The determinant can be written as an equation of these cofactors:
(x2 + y2 + z2) M11 - x M12 + y M13 - z M14 + M15 = 0
Since, (x2 + y2 + z2) = r2 this can be simplified to
r2 - x M12 / M11 + y M13 / M11 - z M14 / M11 + M15 / M11 = 0
The general equation of a sphere with radius r0 and center (x0, y0, z0) is
(x - x0)2 + (y - y0)2 + (z - z0)2 - r02 = 0
Expanding this gives,
(x2 - 2 x x0 + x02) + (y2 - 2 y y0 + y02) + (z2 - 2 z z0 + z02) - r02 = 0
Re-arranging terms and substitution gives,
r2 - 2 x x0 - 2 y y0 - 2 z z0 + x02 + y02 + z02 - r02 = 0
Equating the like terms from the determinant equation and the general equation for the sphere gives:
x0 = + 0.5 M12 / M11
y0 = - 0.5 M13 / M11
z0 = + 0.5 M14 / M11
r02 = x02 + y02 + z02 - M15 / M11
Note that there is no solution when M11 is equal to zero. In this case, the points are not on a sphere; they may all be on a plane or three point may be on a straight line.
G-turn Value = ( A)/(9.8ã€-msã€-^(-2) )
Program for finding latitude, longitude & altitude:
/* geodetic to cartesian (latitude, longitude) */
void ECEF_To_Geodetic(double x, double y, double z, double* lat, double* lon, double* alt)
double a = 6378137.0;
double f = 298.257223563;
double b = 6356752.3142;
double e1 = 0.00669437999013;
double e2 = 0.00673949674226;
p = sqrt((x*x) + (y*y));
tan1 = (z*a)/(p*b);
tan2 = (y/x);
theta = atan(tan1);
tan3 = (z + e2*b*sin(theta)*sin(theta)*sin(theta))/(p - e1*a*cos(theta)*cos(theta)*cos(theta));
*lon = atan(tan2);
*lat = atan(tan3);
*alt = (p/cos(*lat)) - rlamda;
After the conversion of these data into desired form, we obtain data in this form:
Rate of Ascent/descent
4. ARTIFICIAL INTELLIGENCE SYSTEM : NEURAL NETWORKS.
Neural Network is a network of many simple processors ("units"), each possibly having a small amount of local memory. The units are connected by communication channels ("connections") which usually carry numeric (as opposed to symbolic) data, encoded by any of various means. The units operate only on their local data and on the inputs they receive via the connections.
Most NNs have some sort of "training" rule whereby the weights of connections are adjusted on the basis of data. If trained carefully, NNs may exhibit some capability for generalization beyond the training data, that is, to produce approximately correct results for new cases that were not used for training.
Practical applications of NNs most often employ supervised learning. For supervised learning, we must provide training data that includes both the input and the desired result (the target value). After successful training, we can present input data alone to the NN (that is, input data without the desired result), and the NN will compute an output value that approximates the desired result. In practice, NNs are especially useful for classification and function approximation/mapping problems which are tolerant of some imprecision, which have lots of training data available, but to which hard and fast rules (such as those that might be used in an expert system) cannot easily be applied.
4.1 BACK PROPAGATION NETWORK
I am planning to use this model in our project. "Backprop" is short for "backpropagation of error". The term backpropagation causes much confusion. Strictly speaking, backpropagation refers to the method for computing the gradient of the case-wise error function with respect to the weights for a feedforward network, a straightforward but elegant application of the chain rule of elementary calculus. By extension, backpropagation or backprop refers to a training method that uses backpropagation to compute the gradient. By further extension, a backprop network is a feedforward network trained by backpropagation.
Standard backprop can be used for both batch training (in which the weights are updated after processing the entire training set) and incremental training (in which the weights are updated after processing each case). For batch training, standard backprop usually converges (eventually) to a local minimum, if one exists. For incremental training, standard backprop does not converge to a stationary point of the error surface. To obtain convergence, the learning rate must be slowly reduced. This methodology is called "stochastic approximation" or "annealing".
Merits & Demerits of BPNN:
Â§ The most widely and nearly exclusively used neural network for business and technological applications is the backpropagation neural network (BPNN).
Â§ The generalized-delta learning rule affects a gradient descent search in weight space used to minimize classification error in the identification of the aircraft.
Â§ BPNNs have demonstrated their efficacy on many practical problems such as classification of objects and have been shown to be relatively easy to use.
Â§ BPNNs do self-adapt to learn from information. They thereby provide powerful models that may be used in many circumstances to transform vague data into knowledge useful for making decisions.
Â§ The weight adjustment process may be extremely slow and as in many nonlinear search methods is not guaranteed to converge to an optimal solution(only during the training).
4.2 ROLE OF FUZZY LOGIC
The fuzzy code in this network is used for preprocessing of the data. The altitude, velocity, gturn values have a great degree of variation and range. For easier training, we use the fuzzy code to normalize the processed data. Training of the neural network data is easier and quicker.
4.3 TRAINING DETAILS OF NEURAL NETWORK
Training rate: 0.01
No. of cycles: 1, 00,000
No. of hidden layers: 1
4.4 Optimization of Neural Network- Pruning :
Need for pruning:
In the neural network, certain nodes may be ineffective or may provide a constant error. Nodes of these kinds are not required. Identifying and removing such nodes will increase the accuracy of the neural network. This is nothing but the optimization of the size of the neural network.
Optimal Brain Damage Algorithm was used for this purpose and increased the accuracy of the neural network by 6%.
â€¢ Our network after training recognized Fighter Planes with almost 90% efficiency.
â€¢ An ambiguity of around 50% occurs between CM and Fighter planes in the case of much closed data but that may be removed easily by incorporating the parameter of cluster id.
â€¢ Commercial planes and UAV can be recognized by nearly 60% efficiency.
This software can be integrated with the existing centralized radar network. Each object identified will launch a new thread which is the Neural Network. The output which is the class to which the identified object belongs to is displayed.
This system will replace the conventional look up table identification method in the near future.