Error Analysis of Airborne Fire Control System Radar via Monte Carlo Approach

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Error analysis of airborne fire control system radar via Monte Carlo approach CONFERENCE PAPER · FEBRUARY 2006 DOI: 10.1109/ISSCAA.2006.1627649 · Source: IEEE Xplore

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2 AUTHORS: Ali Karsaz

Hamid Khaloozadeh

Khorasan Institute of Higher Education

Khaje Nasir Toosi University of Technology

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Available from: Hamid Khaloozadeh Retrieved on: 04 February 2016

Error Analysis of Airborne Fire Control System Radar via Monte Carlo Approach A. Karsaz, H. Khaloozadeh

radar tracking accuracy design, and one system statistical error Abstract--The designer of the airborne defense missile system analysis and design approach is proposed [4]. is interested in defining the Fire Control System (FCS) error, and Using minimum variance estimation techniques developed a the seeker detection probability to make the defense system more model based, post-event missile trajectory and error analysis powerful. This paper develops one radar error statistical program for the National Air Intelligence Center. This paper mathematics model defense and determined the progr itS trajectory simulation ation ontelligenceeCent ........................bases on four differentThisap ..for.the. airborne physical

distribution of errors for each error, which can affect the Probability of Hit (PH). Furthermore, the errors in Radar as the

for c

alculatio th equation

ofmo

propses

tandoe

ancean re dare

determined, data. ts of from lmputing launch stoeto impact and the error ellipses plotted simulated and analysis. Then a new statistical mathematics fom

important subsystem

of fire control

system

are

approach based on Monte Carlo Method suggestion for error expected to be, powerful aids for assisting military planners and sensors in and/or over a battlefield and what types of data analysis of radar. to collect-are required for, meeting their specification for Index Terms--Error analysis, Fire control system, Monte Carlo launch site and impact point accuracies [5]. simulation, Radar sensitive analysis, Hit Probability. The method of target-position location in a bistatic system is described, and the analysis about the position error is made. I. INTRODUCTION The Root Mean Square (RMS) is used to describe the position There exist two approaches for the error analysis, Analytical accuracy, and the constant-accuracy contours are drawn to methods and stochastic simulations. The First method required show the location characteristics of the bistatic system [15]. a mathematical model for analysis. However, the stochastic All errors can belong to two large categories, random and simulations are a strong method for the complex systems systematic errors called kind of error and each of them can analysis, based on the random input variables. In many belong to three categories dynamic, disturbance and equipment applications stochastic simulations approach identify as Monte errors called type error [6]. Carlo method. In Monte Carlo techniques an actual realization A typical fire control system can be divided to the three of process is simulated on computer and, after having important subsystems in the airborne defense, as mentioned observed the simulated process for some time, estimate the before Radar subsystem, environmental and carrier subsystem. In this paper, after airborne fire control system (AFCS) stochastic parameters [1], [2]. There are many papers for computing Circular Error description in section 2, all errors in radar subsystem are determined Probability (CEP) for projectiles. [7], [8]. For example, in in section 3. Error analysis technique which used in this paper Ref.21 describes a concept for deriving information for gun are described in section 4, and finally the simulation results system calibration from projectile track data. A common shows the radar elements effect on reduce of probability of hit technique for improving the accuracy of gun fire against in section 5. surface targets which has been in use since the earliest development of gun technology is the spotting procedure. In a II. AIRBORNE FIRE CONTROL SYSTEM (AFCS) DESCRIPTION typical application of this procedure, a number of shots are fired at a specific target. The centroid of the fall of shot is A modern AFCS are composed of number of systems, each computed and incremental to the gun pointing angle are made tasked with specific functionality. Example includes aerial to move the centroid on to the target. However, the concept of radar, for target parameters tracking such as speed, range, (CEP) and this types technique are for projectiles. In this azimuth, bearing of target. Wind meter for measuring speed paper there is a missile that beyond to the large categories of and direction of wind, temperature and pressure sensors for missiles that called Fire&Forget missiles. The design of the determine the environmental temperature and pressure. And shipboard defense missile system is highly considered in the helico ptrsbyemenosfreauighdn,rl,ptc defense industry electronics, especially the missile fire control by (AHRS) height by Altimeter sensor and velocity by Doppler sensor of helicopter. Central computer that receives A. Karsaz is currently Ph.D. student at Department of Electrical each parameters of above subsystems and in the equations C)evutstw al_ka73@stu-caldMsieFrCotlDrcor(

Engineering, Ferdowsi University, Mashhad Iran (e-mail:

mail.um.ac.ir).caldMsieFrCotoDietr(FDevutstw

H. Khaloozadeh is with Department of Electrical Engineering, Ferdowsi parameters for setting in the missiles, see Fig. 1. In MFCD as

University, Mashhad Iran (e-mail:).

383

_ IF

> xismoreimportantthaty

V. SIMULATION RESULTS Because, with equal mse on the j th MFCD's arise by x,y, x There are several advantages of error analysis, as first results, hase smaller 8x than y. is determined the percentage of importunacy for each of four 0: R4 R2 radar elements that effects on the PH. For using the (10), first T e 02*4fR3A3S3] (4) by 200 iterations, mseT and msev are determined for one /Jmse,, random input variable of radar. For example, the target azimuth with specific random error (example 0.5 deg (std)) is By using the least square error criteria can obtain the efficient used. Fig. 3 shows the Tmvalues irises for this standard coefficient for IFs. deviation error of target azimuth. O* (~T.9)-].y n

0*: Efficentparameters 9: Inputmatrixeachrowscffe[8R 6A 8S y : crospondingoutputstoinputvectors

6B]3

For second step on the Missile Dynamic Equations (MDE) box

IFJ=APHI mseR R

F

395

385-

(5)

38

(6)

APH: Re duced Probability of Hit that arises by j th MFCD's output OI]*2 [TFM IFh iq]

36 5

0

20

40

Fig. 3.

60

80

100

120

No of Iterations

140

160

180

200

Tm values for 200 iterations

The ZAPH for some iterations can calculated with using stogram of circular error probability (CEP), which used in many papers for projectiles as mentioned insection2. The radius of circle is the mseT can easily calculated using (2). Same calculation is dependent on target dimensions. ZIPH directly calculated by for , dividing the outputs contact numbers of this circle to all iterations numbers. (see Fig. 6 for details) zIPH= Ni(7) N

N,: Jnsightpoints N: Iterationsnumber

385

4 30

After determined mseT

_

25 ----------

-- T--------

20 ---------r--------r------ *__.

Lr--------r

Tm

Of

----------

78

79

or

Fig. 4. Histogram of1~~~~~~~~~~~~~~~~~~~~~~~Mssl Tm Tajctr

--------

8

81

Tm (sec)E

10 so

14

333l12

14_

82

Fig. 5, 6 shows the ~/m values irises for this standard deviation 1 errorof1target.azimuthandits histogram.

8l3O...........

12

14

(km)

I-

A1 1 L14

4

76)

2U

_

,1-

20

illustrated

-

---i~~~~q~

-- ------

il4 i

40

16

]

6;0 BUNo of Iterations lO0 12U 140 1W;0 186 2W0

Fig. 5. -m values for 200 iterations 19

---

25

20

--

-

--

----

II11 5-

-

-

- - - - - - - -

60

80

r------

-

~120

100

14

Fig6 fHIstograminof

F'

-

--

120

probability hit obtained

T--t

-

-

-

-

-

- - - - -

'-

..

13020

---------T---- -----

T-

- - - - -

-

-

fti---r---aleteerraayi pormeeue lutrtdi of missile n t E ig. 8.h Ee nd points adtre Fpcsa

-c

a

--

- - - - - - --

r-~~~~~~1---

~~~~~ 30~ ~~ ~(dg ~~~~~~8

I

I~ ~

n

7

3

q

24

by equation (9), the mse of MFCD's outputs and the ~~~~~~percentage of importance by using equation (10). These 22 are ranked by the PIs of each For obtain results one raw of this table the error analysis program executed 200 Table ilutrae th Tuc misl cnroadTbe1 epochs as illustrated in the fig. 9. The end points of missile respect to target are easily obtained from Fig. 6, as illustrated at Fig. 8. In this figure the circle, which defined the target are shows with specific radius.

3°~~~~~~~~~~~~~~~~~~~~~~~~~~1 -250-----------------[ -----12. --0 20 40

22

Fig. 7. Missile and target trajectories for 200 iterations

T

8-

1E;

whchdfneshetretaeghwswtrseifcrais The end p oints of missile respect to target are easily obtained \\hich --1_______Lreut0y from ilt:gasus Fig. 7, the tratedri~ ate8... Fig.In. this figure the cir ~ prmtr

zmt and it

f agt 16o

by using the (4) all-internal parameters in

0 is obtained. Therefore, for using (10), only IFhT IFhV are unknown and ---------must be calculated independently. By using (5), and deferent mse for both Tm, Vm, as variable inputs the corresponding output (i.e. APH) obtained from (7), for example 200 iterations (see Fig. 7). Fig. 7, shows the missile and target trajectories for 200 iterations with specific mean square error

15

~ . . .10. 71T

,msel,

11

in

11

-

1?

13V,

-----

1l_

I --------

--

__

----T , -----

__ IS __

--------------

---- ---

------

-- -- -- ---

-----* -----

- -- -

A ___ L __ --

-----------------

--------

,2

@

5

VIII. BIOGRAPHIES AliKarsazreceived the B.S. degree in Electrical Engineering from the Amirkabir Un,versity of Technology, his nMISc. d r in Eectrical Engineering in 2004 at Ferdowsi University of Mashhad. He is currently as a Ph.D. student in Control Engineering at the Ferdowsi University of Mashhad,, Mashhad, Iran. Hamid Khaloozadeh, received the B.S. degree in

VI. CONCLUSIONS in this paper, a analysis technique for a typical radar of airborne FCS was illustrated. This method based on Monte Carlo approach that deals with input random variables and its statistical momentums. All errors of radar by executed of this technique are ranked at the Table II. From this table it is clear that which parameter in radar catalog is most important and which is not. This table can help the designer of FCS to choice the efficient radar with proper price too.

control engineering from Sharif University of technology (Tehran, .Iran), in 1990, the M.S. degree

VII. RiEFERENCES [1] Papoulis, A. M., "Probability Random Variables and Stochastic Processes", McGraw-Hill 1965.

in control engineering from K.N.Toosi university of technology Tehran, Iran), in 1993, and the Ph.D. degree in control engineering from Tarbiat

Moddaress university (Tehran, Iran), in 1998. Since 1998 to 2004 he was a faculty member at Ferdowsi University of Mashhad. He is currently an assistant Professor teaches in the Department of Electrical Engineering in K.N.Toosi University of Technology (Tehran, Iran). His interest area is Digital Control, Nonlinear Modeling, System Identification, Optimal Control, Adaptive Control, Stochastic Estimation and Control, Neural Networks and Time Series Analysis.

[2] J. Endrenyi, "Reliability Modeling in Electric Power Systems", Research Division Ontario Hydro, Toronto. [3] Hammersley, I. M., Handscomb, D. C., "Monte Carlo Methods", Wily, 1964. [4] Li-Wei Fong, Jhu-Shi Dai, Cheng-Chiian Liu, Analysis and Design of Shipboard Defense Missile System via Statistical Error Approach, System Development Center, Republic of China.

[5] Ball Aerospace and Technologies Corporation, "Minimum Variance

Missile Launch and Impact Estimation by Fusing Observations From Multiple Sensors", IEEE 1997.

[6] F. C. Schweppe, "Uncertain Dynamic Systems", Prentice-Hall. 1973. [7] "Computation of Circular Error Probability Integral", IEEE Transaction on aerospace and electronic systems VOL, 29,NO. 3july 1993.

[8] He, Lixing, "Location Error Analysis and a Tracking Algorithm in a Bistatic Systems", in Proc. 1992, IEEE National University of defense Tech.

Pamnet Ptrarameter values 900 Fly height (m) Helicopter aimuth fly

10

TABLE I. MISSILE LAUNCH SCENARIO Parameter valus| Paraenteir

38.44

Wind speed (m/sec)

Target Azimuth (deg) Target speed (m/sec)

13.0023 13.0023

Wind direction (deg) Air pressure (mbar)

35.979

Air temperature

(d

Helicopter roll fly

3

(deg)

Helicote pitch fly eC

l_

2-

Parmete

Target range (km)

Target bearing (deg)

_l_l_ _l_ _l_

387

(0c)

Paramttr values 8.5 100 1009 32.437

6 TABLE II. OUTPUT RESULTS OF RADAR ERROR ANALYSIS

elements

errors

. . Missile angel correction Ur .

bias4

mseT. inseT

2.42

0.74

2.6984

1.22

1.10

42.3

95.488

2.92

0.19

1.7

6.76

.038

2.6

20.6

97.653

3 m/s

1.2725

0.25

1.1

4.50

0.3

2.1

9.5

98.901

5 deg

0.7489

.33

.8

6.012

0.23

0.85

6.9

99.181

0.1 deg

0.8302

0.9

0.1423

0.0389

0.17

0.1

5.2

99.431

2g 9ms

0.6574

0.8

0.132

0.0377

0.16

0.11

4.3

99.549

rms

isew

d

Target azimuth measurement Target range measurement Targetspeed measurement Target bearing

0.6 deg

6.404

350 m

Radar antenna zero setting

measurement

vHeicopter

Installation of

error

PH

0.5248

0.72

0.08

0.0181

0.1

0.09

3.4

99.640

0.4289

0.65

0.08

0.0410

0.17

0.11

2.6

99.70

0.05 deg

0.4158

0.64

0.079

0.0125

0.05

0.1

2.5

99.715

0.121

0.33

0.11

0.13

0.3

0.2

.8

99.910

0.0554

0.23

0.05

0.9344

0.4

0.88

0.8

99.914

0.005 deg

0.0125

0.11

0.02

0.0265

0.11

0.12

0.1

99.990

5 - 10 usec

0.0029

0.05

0.02

0.0544

0.12

0.2

0.05

99.995

0.033 deg

0.0017

0.04

0.01

0.0829

0.1

0.27

0.05

99.995

DC motor error

.03 deg 1.5

error Windfluctuation error Aliment of the installation area

biasr

deg

Resolution error Radar antenna production error Enternal circuit

.

200 ms

0.01

radar antenna Delay of transaction radar informations Radar encoder

~~~~~~~~~~~~~~~~~~Probability Hit of

Time of missile seeker turn on Tm

deg,

0.02

Shock error

deg

20g

0.001

0.03

0.01

0.0743

0.08

0.26

0.05

99.995

0.0000

0.02

0.02

0.0481

0.09

0.2

0.05

99.996

Figure 1. a

Figure 1. c

Figure 1. b

Missil

Targ-jet

46

2~~~~~

1

13

12

15

t

F|

5

16

-10 0

Figure 1. d

6 5

14 X (km)

~~

1

M~issile

Ta rget

X

10

(kim)

--

23

|'

15

20

6

~~~~~~0

4~

100 150 No. of Iterations

-0

0

200

-10

-5

0

4-I (degree)

5

10

22

24

Figure 1. f

---------------_-_, __

1

[---J[---

20

CI L

0

t

11

Figure 1. e

------

22 ~ 216

'I

5

50

~~~~~~24

1

0

3

T9e0 | °8

50

100 150 No. of Iterations

200

41

16

16

20

Tzk (Second)

Fig. 9. (a) The end points of missile and target (b.e)-the valus of Tm, Y'm for 200 iterations (c.f) Tm, V'm histograms (d) Missile and target trajectories.

388