Introduction

As I said in my first internship report, for an engineer, it is not enough to have theoretical background, but also we need to see how this theoretical information is applied to the real world. When I started Elec 291 internship, I had limited theoretical background on some topics. For this reason, Elec 291 internship can be thought as a general topic internship. For Elec 391 internship, I increased and gained my theoretical background especially on signal topics. Signal can be defined as the most important area of electronics. Signal applications are required not only to produce a product, but also to create background of a product. To see both of the processes, the most suitable place for me a factory which has high standard R&D department. To satisfy all conditions that I mentioned, I started my internship at Aselsan Company that is one of the best companies to see and understand how signal theory is created and applied to the production in Turkey. To understand what is the main function of signals in the real world, a project called “Target Tracking for Maritime Surveillance “was given to me. As I will mention later, Aselsan is a military products producer, so assignment of important and new projects is risky for national security. For this reason, the project given to me is a chance for me to increase information about radar systems and general known applications; however, the project does not work for me to learn new applications on military systems. To be an engineer, it is not enough just to know information, but also it is required to create new processes for the world. This project helped me to understand what the signal is exactly, how signal applications are applied to the real world and how I can convert noisy information to the usable information. In this report, at company description part, general information about Aselsan Company can be found. At project part, information about the internship project will be explained. In addition, detailed information about my internship department can be found at project part because knowing what is produced and which methods are used, is required to apply my project.

Company Description

Aselsan can be described as the best military and defense company in Turkey. Unlike everyone knows, Aselsan is not a military company. It is a private company. Aselsan is a company of Turkish Armed Forces Foundation. It is a company that produces products for mostly military facilities and some non-military facilities. According to Aselsan web site, vision of Aselsan can be defined as the following: “Being a national technology company that maintains its sustainable growth by creating value in the global market; preferred due to its competitiveness, trusted as a strategic partner, and caring for the environment and people.” As most of Turkish citizens know, in 1974 which is the year of Cyprus Peace Operation, Turkish Army understood that they need local produced defense and military systems. For this reason, Aselsan was founded in 1975 to supply communication tools of Turkish Armed Forces. Mission of Aselsan is defined by Aselsan web site as “By focusing primarily on the needs of the Turkish Armed Forces; to provide high-value-added, innovative and reliable products and solutions to both local and foreign customers in the fields of electronic technologies and system integration; continuing activities in line with global targets as well as increasing brand awareness and contributing to the technological independence of Turkey.” Aselsan has 5000 employees whose 60% is engineer, 4 facilities in Turkey and 10 affiliates. These 10 affiliates can be listed as the following:

ASELSAN BAKÜ ŞİRKETİ

ASELSANNET LTD. ŞTİ.

MİKROELEKTRONİK LTD.ŞTİ.

ASELSAN HASSAS OPTİK A.Ş.

ASELSAN BİLKENT MİKRO NANO TEK. A.Ş.

IGG ASELSAN (IAIS LLC)

KAE LLP

ASELSAN MIDDLE EAST PSC

ROKETSAN A.Ş

ASPİLSAN A.Ş.

Since 1975, Aselsan has made many successful operations, processes, applications. However, some of them can be listed as the milestone for the company. According to Aselsan, these milestones can be listed as the followings:

In 1978, the first premises in Macunköy Facility were completed and the manufacturing operation started.

In 1980, the first man pack and tank wireless radios were delivered to the Turkish Armed Forces.

In 1983, the first export was realized.

In 1987, ASELSAN was included in a common project attended by 4 NATO countries for the manufacturing of Stinger Missile and started the required investment for the thick film hybrid circuit production.

In 1988, ASELSAN produced the first avionic appliance for the F-16 program.

In 1991, a Radar Technology Center was established in Aselsan with the SSIK 91-3 decision.

In 1992, an Electro-Optical Technology Center was established in Aselsan with the SSIK 92-4 decision.

In 1996, the TASMUS agreement was executed.

In 2002, the Project for MWS-TU Missile Warning System and Leopard Volkan Fire Control System to be used in the Turkish Armed Forces Air Platforms was executed.

In 2007, MILGEM war system supply project was executed.

In 2008, ATAK agreement and Multi Band Digital Common Wireless Radio (ÇBSMT) Project were executed and ASELSAN delivered the first originally developed Air Defense Radar.

In the year 2013, ASELSAN has continued its climb for the aim of being one of the top 50 defense companies, and ranked 74th according to annual sales.

According to Aselsan, operation divisions of Aselsan can be listed as the followings:

Transportation, Security, Energy and Automation Systems

Communications and Information Technologies

Defense Systems Technologies

Microelectronics, Guidance & Electro-Optics Division.

Radar, Electronic Warfare and Intelligence Systems

The last operation division that is Radar, Electronic Warfare and Intelligence Systems (REHİS in Turkish) was my division in Aselsan. As its name suggests, main aim of REHİS is to produce and provide radar systems to consumers. REHİS was located on the location of Gölbaşı/ANKARA and has an area of 350000 m2. There are more than 1000 employees in REHİS. My department under REHİS division was Directorship of Radar System Engineering. There are important people for this department that can be listed below:

Bora KARTAL (Director of the department)

Tevfik Bahadır SARIKAYA (Senior expert engineer)

Mr. SARIKAYA was my supervisor. Resources of Aselsan and with the help of Mr. SARIKAYA, I started the internship project whose details can be found in next part.

The project “Target Tracking for Maritime Surveillance “

As I mentioned before, Aselsan is a military products producer. As we know, in defense and military industry, one of the most important topics is tracking. In my opinion, tracking can be defined as the determination of some properties of an object. These properties might be location, angle, altitude, velocity, acceleration etc. The tracking process is made by an equipment that is called radar. According to Skolnik, “radar can be defined as an electromagnetic system that detects location of some objects such as aircrafts, ships by radiating energy into space and detecting echo signals reflected from an object.” In addition, there is another equipment to detect location that I learned in internship. It is called sonar. Unlike radar, it uses acoustic signals rather than electromagnetic signals for detection. However, my focus point in this internship was radar.

According to Skolnik, “radar is a combination of the words radio detection and ranging.” For real, the main aim of the radar is to detect range of an object. In internship, I learned how these detections are made with the help of my supervisor and books of Aselsan. I will mention the methods of detection later. These methods mostly were observed by MATLAB program. However, before learning radar detection, I made research on radar equations to understand mathematical background of radar systems.

As I mentioned before, radar is an electromagnetic signal. In space, all electromagnetic signals has a speed of light. For this reason, the only measured value for detection of an object is time. According to Skolnik, simple radar formulas can be written as the following:

R=c*TR/2 where R: Range, c: Speed of light, TR: Time for travel of signal to target and back

Run=c*Tp/2=c/(2*fp) where Run: Maximum unambiguous range, Tp: pulse repetition period, fp: pulse repetition frequency

According to Skolnik, “maximum unambiguous range can be defined as the range beyond

which targets appear as echoes that arrive after the transmission of the next pulse.”

Simple radar equation can be described as the following:

Rmax=[Pt*G*Ae*σ/(16*π*π*Smin)]^0.25

Pt: Transmitter power

G: Antenna gain= Maximum power density radiated by a directive antenna/(Power density radiated by a lossless isotropic antenna with the same power input)

Ae: Effective area

σ: Radar cross section

Smin: Minimum detectable signal

Rmax: Maximum range of a radar

Pr: Received signal power=[Pt*G*Ae*σ/(16*π*π*R^4)]

Rmax is found by equalizing Pr to Smin.

Until here, it seems that we can find range of an object by using these equations. However, in real world, this situation is not correct. According to Skolnik, “there are 4 important reasons of the failure of the simple radar equation which are listed as the following:

The nature of minimum detectable signal or existence of receiver noise.

Uncertainties in the target’s radar cross section.

The losses on radar system

Propagation effects caused by the earth’s surface and atmosphere.”

As we know, noises include properties of probability theorem, so “the range of radar will be a function of the probability of detection, Pd, and the probability of false alarm, Pfa.”

Until this part, I tried to explain working principles of radar and mathematical background of radar. From here, I will try to explain how range of an object can be obtained, which models I learned and used to show route of an object, noise types and how noise affects the motion, and a little information about the methods of multi target tracking. In military area, detecting of an object is important, but to predict the motion of an object is more important. To achieve this, some models and filters are used. In my internship, I used Kalman filter and various models to observe the motion on Matlab. All codes that I wrote on Matlab can be found at appendices part of this internship report.

First, I should say that in Aselsan, I did not only learn to solve problem, but also learned to understand problem. In general, my examples on Matlab have two parts. First part is simulation and the other part is filter. Simulation part is the part where our motion and measurement are created by using demanded conditions; filter part is the part where similar of original motion from measurements is created. In the first days of my internship, I created my measurements and designed filter to achieve original route from measurements. However, later, another user created measurements and I used my filter to predict original movement. In addition, I should say that I used R-Θ coordinate system which R corresponds range and Θ corresponds angle, instead of x-y coordinate system in my all examples.

On the above paragraph, it seems that I create a measurement, then I use it to achieve original route. However, it is not simple as it seems. I had to deal with the noise problem that is the most significant problem of engineering in real world. During internship, noise was the most important topic that I focused and worked on. I learned that there are two types of noise that affect motion. The first type of noise is process noise. In my opinion, process noise can be defined as the randomness of the motion. To describe process noise, I should start to describe motion model and measurements equations. According to Blair, motion models and measurement equations can be shown as the following:

Xk+1= FkXk+Gkvk

Zk= HkXk+wk

Xk+1: State at time k+1 includes position, velocity, and maybe acceleration.

Fk: State transition matrix. Constant for motion. It defines types of motion.

Gk: Constant for system error. It connects process noise to the system.

vk: Process noise. It is white Gaussian noise.

Zk: Measurement at time k.

Hk: Observation matrix. It relates measurement to the state.

wk: Measurement noise. It is white Gaussian noise.

As it is written above, vk is process noise that defines the properties of next time state. If process noise did not exist, next state would depend on only current state and type of the motion. However, in real, there is process noise and our aim is to find original states by minimizing effects of process noise. However, in real world, we do not measure the process noise. What we measure in real life is called measurement. The second type of noise is measurement noise that can be defined as the difference between process noise and measurement. wk exists due to some reasons such as sensor errors, earth conditions etc.

Until here, I defined the properties of simulation or measurement part of the real life problems. The measurement data is the only data that we have to evaluate the problem. However, problem is not finished here. The most important work in radar tracking is to determine the time updated state estimates. These estimations are made by using measurement values, some pre-determined constant values and initial values of states. The main aim is to find original states from measurements by minimizing effects of process and measurement noise. This process is done by an operation that is called filtering. I used Kalman filter in my all examples. According to Blair, Kalman filter algorithm can be shown as the following:

Time update: Xk|k-1= Fk-1Xk-1|k-1

Time update: Pk|k-1= Fk-1Pk-1|k-1Fk-1T+Gk-1Qk-1Gk-1T

Measurement update: Kk= Pk|k-1HkT[HkPk|k-1HkT+Rk]-1= Pk|k-1HkT[Sk]-1

Measurement update: Xk|k= Xk|k-1+Kk[Zk-HkXk|k-1]

Measurement update: Pk|k= [I-KkHk]Pk|k-1

Xk|k: State estimate.

Pk|k: Error covariance of the state estimate.

Kk: Kalman gain matrix

Qk: Process noise covariance. Cov[vk]=Qk

Rk: Measurement noise covariance. Cov[wk]=Rk

Sk: Residual covariance.

As I mentioned before, I used two types of models. The first model that I used is constant velocity model. Constant velocity model can be described as the simplest model, but it was necessary for me to understand the fundamentals of Kalman filter principles. As I said before, codes for all parts are on appendices. Here, I will try to explain what I did for the design of this model.

For constant velocity (CV) model, first of all, I created my Xoriginal matrix. Xoriginal is a 4xt matrix. t is time length that is defined as 1000 for that example. In each column, there are 4 elements. First one is for range position, second is for range velocity, third is for angle position and last one is for angle velocity. I create a suitable transition matrix (phi) for that example to keep velocity constant. Then, I define Gama matrix. Gama is for system error. It helps us to add the process noise to the system. Then, I create process and measurement noise covariance and observation matrix. In this example, also in all example, observation matrix is set up for to measure only range and angle position. For this reason, our measurement matrix Z is a 2xt matrix. To create measurement, first, Xprocess matrix is created from Xoriginal then, Z matriz is created from Xprocess matrix. Now we have 3 matrices. They are used in RMSE measurement to measure the error rates. RMSE is the most valid measurement method for me to measure errors in all examples. Now I completed simulation part. As I said before, in real life, measurement is given to me from environment and I have no information about it. However, this is one of the first examples and to understand easily, it was created by me with the help of my supervisor. I have to say that I have another example which measurement or simulation is created by another user. I will tell this example later.

For CV model, I created simulation part. Now, the most important part filter will be created. For filter part, I will use Kalman filter algorithms. As I wrote above, prediction is shown as Xk|k-1 and state estimation is shown as Xk-1|k-1. Let me explain what Kalman filter makes step by step. It takes X0|0 value to predict X1|0 value. Also, it takes covariance P0|0 value to predict P1|0 value. Then, using these, it creates X1|1 state estimate and P1|1 covariance values. Then, it uses these values to continue next steps. Now, it seems that system has some problems. What are the X0|0 and P0|0 initial values? Also, what are the Gama and phi constants? For Gama and phi values, I used the Gama and phi values that are written on simulation part. You can ask me that you use same values, so what are you doing for the solution of problem extra. In these first examples, I use same Gama and phi values to estimate correctly. However, in next examples, these values will be entered by user. As I said before, Gama and phi are constants that depend on the type of the motion. I should say that in the first examples, I know the types of the motion, so to create Gama and phi was not hard for me. However, in real life, we cannot know the motion type. For this reason, systems that are mixture of various types of Kalman filter are used. In this internship, I made an interacting multiple model estimator (IMM) which will be mentioned later.

After finding Gama and phi values, the next problem is the initial values of state estimate and covariance. For initial state estimate, I create a 4x1 matrix. First and third elements are Z (1,1) and Z (2,1) respectively. I used first elements of measurement values as initial. Second and fourth elements correspond to initial range velocity and initial angle velocity. I used the range and angle velocity values of Xoriginal matrix as second and fourth elements. In this example, I used same values, but in the next examples these values will be entered by user. You can ask me that how we can enter initial velocity values while we have no information. Actually, in real world, we make estimates depending on environment. For example, I mostly designed simulation for maritime systems. For this reason, estimated initial velocities are the close values that ships have. If our radar becomes for air systems, we should use more suitable values for initial values. After determining initial state estimate values, I entered initial covariance value by using the 2 point initialization rule.

After applying these values to the Kalman filter, I found state estimate as X. Range graph of X and Xoriginal matrix can be seen on figure 1. Angle graph of X and Xoriginal matrix can be seen on figure 2. In figure 3, one can see that the result of measured data found on Matlab.

Figure 1: Graph of state estimated range(X) and original range (Xoriginal) for CV model

Figure 2: Graph of state estimated angle (X) and original angle (Xoriginal) for CV model

Figure 3: Results of measured data on Matlab

By looking results, I can say that Kalman filter achieved its mission. RmseRANGE is the Rmse range value of Kalman filter by comparing with Xoriginal. We can see that it is lower than RMSEmeasurementnoiseRANGE and higher than RMSEprocessnoiseRANGE. I can say that Kalman filter tried to correct measurement values to the original values and achieved this in the acceptable Rmse rate. For ANGLE part, we have similar results. Kalman filter tried to make correct estimates and achieved this in the acceptable Rmse rate.

As I mentioned before, I used two types of models. The second model that I used is constant acceleration (CA) model. For real, there is not much difference between CA and CV model. For this reason, I will try to explain design process only saying differences.

First, for constant acceleration (CA) model, I created Xoriginal matrix. However, this time Xoriginal is a 6xt matrix. In each column, there are 6 elements. First one is for range position, second is for range velocity, third is for range acceleration, fourth is for angle position, fifth is for angle velocity and last one is for angle acceleration. I create a suitable transition matrix (phi) for that example to keep acceleration constant. By making similar things made in CV model, I completed simulation part.

For filter part, I made same things as I did in CV model. Having initial acceleration values in state estimate matrix, different phi and Gama values and suitable covariance matrix are the only differences of this system.

After applying the values to the Kalman filter, I found state estimate as X. Range graph of X and Xoriginal matrix can be seen on figure 4. Angle graph of X and Xoriginal matrix can be seen on figure 5. In figure 6, one can see that the result of measured data found on Matlab.

Figure 4: Graph of state estimated range(X) and original range (Xoriginal) for CA model

Figure 5: Graph of state estimated range(X) and original angle (Xoriginal) for CA model

Figure 6: Results of measured data on Matlab

By looking results, I can say that Kalman filter achieved its mission. RmseRANGE is the Rmse range value of Kalman filter by comparing with Xoriginal. We can see that it is lower than RMSEmeasurementnoiseRANGE and higher than RMSEprocessnoiseRANGE. I can say that Kalman filter tried to correct measurement values to the original values and achieved this in the acceptable Rmse rate. For ANGLE part, we have similar results. Kalman filter tried to make correct estimates and achieved this in the acceptable Rmse rate.

After first examples, my supervisor wanted me to create a simulator function. Codes are on appendices, but I will say here a bit information about function.

My simulator function creates measurement and Xoriginal values. In next examples, this function helped me a lot to create measurement and original routes. This function uses some user inputs. These inputs are state transition matrix (phi), Gama matrix, process and measurement noise covariance, observation matrix, time, initial values and selection value. Selection value defines the type of the motion. 0 is for CA model, 1 is for CV model. I should give you a bit information. In next examples, mostly we created models by using similar phi and Gama values, so I updated function that does not require phi and Gama inputs from user. However, this updated version is not on appendices part.

After that, I created my Kalman filter function. This function takes measurement (Z) values and some other inputs from user. These inputs are initial range velocity, initial range acceleration, initial angle velocity, initial angle acceleration, standard deviation for range, standard deviation for angle, process noise covariance, time change interval, observation matrix and selection. You can ask that how user can enter initial values while he has no information. However, as I said before, user should have information about what he will estimate. For example, in maritime environment, he can use typical properties of typical ships. Initial value should not be exact correct. Kalman filter will update itself in each step using measurement value. Selection defines how filter should evaluate the system. Selection is 0 for CA model, and 1 is for CV model. CA model filter means filter will evaluate measurement as CA model. In below figure 7 and 8, you can see the results of evaluations made on Matlab. I made 4 evaluations. In figure 7, I used a CV model measurement and filtered it with both CA and CV models. In figure 8, I used a CA model measurement and filtered it with both CA and CV models.

Figure 7: CV model measurement evaluated with both types of models

Figure 8: CA model measurement evaluated with both types of models

As you can see on figure 7, if a CV model is filtered by CV model filter, Rmse of range and angle of this situation becomes lower than Rmse of range and angle of the situation that CV model is filtered by CA model filter.

Reverse of this is valid. As you can see on figure 8, if a CA model is filtered by CA model filter, Rmse of range and angle of this situation becomes lower than Rmse of range and angle of the situation that CA model is filtered by CV model filter.

From above, we can reach the result that if measurement and filter model is same, error becomes lower. However, in real world, we cannot know the motion type exactly. For this reason, we need such mechanism that makes filtering in both type. As I said before, there are such systems that are mixture of various types of Kalman filter. This is called interacting multiple model estimator (IMM) and from now, I will try to explain what I did for IMM filter.

In my opinion, the fundamental principle of IMM is to combine many filter to obtain suitable result. There is no limit for number of filter in IMM, but I will use 2 filters in my example.

To explain you the IMM more detailed, I should explain the IMM algorithm. According to Bar-Shalom and Li, IMM algorithm can be defined as the following:

Calculation of the mixing probabilities: µi|j(k-1|k-1)= (1/ )*pijµi(k-1) i,j=1,2, …,r

Calculation of the mixing probabilities: =∑_(i=1)^r'▒'〖'pijµi(k-1)'〗' j=1,2,…,r

Mixing: x0j(k-1|k-1)= ∑_(i=1)^r'▒' xi(k-1|k-1) µi|j(k-1|k-1) j=1,2,….,r

Mixing: P0j(k-1|k-1)= ∑_(i=1)^r'▒' µi|j(k-1|k-1){Pi(k-1|k-1)+[xi(k-1|k-1)-x0j(k-1|k-1)] [xi(k-1|k-1)-x0j(k-1|k-1)]’} j=1,2,…,r

Mode-matched filtering: Λj(k)= N[z(k);zj[k|k-1;x0j(k-1|k-1)],Sj[k;P0j(k-1|k-1)]] j=1,..,r

Mode probability update: µj(k)= (1/c)* Λj(k) j=1,…,r

Mode probability update: c= ∑_(j=1)^r'▒'〖'Λj(k) '〗'

Estimate and covariance combination: x(k|k)= ∑_(j=1)^r'▒' xj(k|k) µj(k)

Estimate and covariance combination: P(k|k)= ∑_(j=1)^r'▒' µj(k) {Pj(k|k)+[xj(k|k)-x(k|k)] [xj(k|k)-x(k|k)]’}

µi|j: Mixing probability

: Normalizing constant

pij: Markov chain transition matrix between models

x0j(k-1|k-1): Mixed initial condition

P0j(k-1|k-1): Mixed initial covariance

Λj(k): Likelihood function

x(k|k): Combined state estimate

r: Number of filters

P(k|k): Combined estimated covariance

As I said before, I used 2 filters for IMM. Filter 1 is modeled as CV and filter 2 is modeled as CA Kalman filter. What I next is to create my IMM function on Matlab. Function takes measurement (Z) and some inputs from user. These are initial range velocity, initial range acceleration, initial angle velocity, initial angle acceleration, standard deviation for range, standard deviation for angle, process noise covariance, time change interval and observation matrix. I should notice that to prevent errors, my filter 1 (CV) state estimate designed as 6xt matrix. I set up acceleration values as 0. Filter 2 state estimate designed as what I did in CA model Kalman filter. The initial probabilities which are µ1(1) and µ2(1) are thought as 0.5. The remaining parts are same as what I did in previous Kalman filter designs. However, in the end of each step, using mixing probabilities, I found my state estimate X and covariance estimate P. For this example, I used CA model measurement. In figure 9, one can see the mixing probabilities with respect to time and in figure 10, one can see the result of measured data of IMM on Matlab.

Figure 9: Mixing probabilities of 2 filter. u1 is for filter 1 (CV) and u2 is for filter 2 (CA)

Figure 10: Results of IMM

As seen on the figures, IMM function for CA model measurement seems working. Let me explain more detailed. In figure 9, we see that at the beginning both of the mixing probabilities are 0.5. However, when it goes steady state situation, value of mixing probability of filter 2 (CA) goes

to 1. We can say that IMM function understood the measurement is CA modeled and updated its mixing probabilities in each step to supply better result.

In figure 10, we can say that IMM shows the properties of 2 filters. Because, if we apply CA model measurement to the IMM, we see that Rmse of range and angle of IMM is between the Rmse of CAtoCA and Rmse of CAtoCV. One can say that using only CA model Kalman filter is better than IMM. However, as I said before, in the real world, we cannot know the type of a measurement. For this reason, we should include and measure all conditions and try to reach an optimum solution. Also, I should say that in real life, CV and CA are not only models. There are other models. For this reason, number of filter can go to a huge number to satisfy the best optimum solution of a random measurement.

Until here, I mentioned Kalman filter and IMM filter. Using IMM seems good to reach the original values of range and angle. Until this exercise, we assumed that at each time, there is only one measurement. However, in real life, at each time, we can measure more than one measurement. So, at the end of this internship report, I will mention about PDAF topic for which I made some applications on Matlab. According to Rodningsby, “Probabilistic Data Association Filter (PDAF) is a good tracking method to handle targets in clutter.” In my opinion, PDAF is very similar to Kalman filter principles. The only difference is PDAF has some false alarm probabilities due to having more measurement.

To work on PDAF, I used a measurement (Z) matrix. However, this time, it is not 2xt matrix. It is 2xtx4 matrix. 4 corresponds to 4 measurements at each time. To create it, I used a prepared CV model Z matrix and then I add additional 3 dimensional by randomly. To explain PDAF exactly, I should write PDAF algorithm that was prepared by Rodningsby:

Prediction: xk|k-1= Fxk-1|k-1

Prediction: Pk|k-1= FPk-1|k-1FT+Q

Prediction: Zk|k-1= Hxk|k-1

Sk= HPk|k-1HT+R

vk(i)= Zk(i)-Zk|k-1 i= 1,2,….,mk

Calculation of association probabilities: βk(i)= {ce^(-0.5* vk(i)T*Sk-1* vk(i) i=1,2,..mk

c|2πSk|0.5*mk*(1-PGPD/VkPD) i=0}

Kalman gain: Wk= Pk|k-1HTSk-1

Combined innovation: vk= ∑_(i=1)^mk'▒' βk(i) vk(i)

State estimate: xk|k= xk|k-1+Wk vk

State estimation covariance: Pk|k= βk(0) Pk|k-1 +[1- βk(0)]( Pk|k-1 - Wk Sk-1 WkT)+ Wk[∑_(i=1)^mk'▒' βk(i) vk(i vk(i)T- vk vkT] WkT

k: Time

βk(i): Association probabilities

PD: Detection probability

PG: Probability that true measurement falls inside the gate

Vk: Volume of the gate

mk: Validated measurements

βk(0): Probability that all measurements are false alarms

As I said before, I used prepared CV model measurements. I defined initial values as what I did in first example. Also, gama, phi, process noise and measurement noise covariance and observation matrix were determined by me. In this example, for each time, I used 4 different measurements. I applied my 4-dimension measurement to PDAF and obtained the range and angle estimate as X. One can see the results in figure 11 and 12. In addition, in figure 13, one can see the all measured data on Matlab.

Figure 11: PDAF estimate range (X) and original estimate range

Figure 12: PDAF estimate angle (X) and original estimate angle

Figure 13: PDAF data on Matlab

As you can see on the figure 13, Rmse of PDAF is higher than Rmse of CV model Kalman filter. In PDAF, we have 4 measurements for each step, so the PDAF system tries to find optimal solution. This finding process causes more error on the PDAF system than the system that has only one measurement at each step. Also, by developing algorithm a bit, I tried to make targeting in the presence of wakes. Wakes are similar to clutter. However, wakes have the values that depend on measurement, while clutters have independent values.

Finally, I can say that PDAF is the fundamental of tracking. Because using PDAF, we can make multitarget tracking in real life. In the end of internship, I made some fundamental research on multitarget tracking and wrote some basic Matlab codes. However, my research was at introduction level, so on appendices there is no Matlab code for multitarget tracking.

Summary and Concluding Remarks

At my internship period, a project called as “Target Tracking for Maritime Surveillance” was attended to me. About 1 month, using books of Aselsan and my supervisor’s knowledge, I tried to increase my knowledge about radar and tracking mechanisms. This research is not only for the main aim of the project, but also for learning the fundamental principles of targeting.

For the project, my solution can be seen small. However, this small effect on the result has increased my knowledge very well. The project really helped me to understand what is signal, how it is used on the real world.

This internship really helped me to learn how real life signals can be determined on the digital environment. Also, my knowledge about tracking has increased. At the end, I presented what I did during the internship period to the engineers. This helped me to understand that the important topic is not only knowing the information but also how this information is presented.

References

“Affiliates.” ASELSAN.

Accessed June 29, 2016.

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Appendixes

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