Improve the accuracyof passive radar systems for monitoring airports

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This paper presents methods for analyzing and examining factors that affect the accuracy of the target position localizationina Multilateration system. A solution for accuracy enhancement of the system with a pre-defined tolerable error and an accuracy-guaranteed model for monitoring airports using passive radar systems have been proposed. Nghiên cứu khoa học công nghệ IMPROVE THE ACCURACYOF PASSIVE RADAR SYSTEMS FOR MONITORING AIRPORTS NGUYEN DUC VIET*, TRAN MANH HOANG** Abstract: This paper presents methods for analyzing and examining factors that affect the accuracy of the target position localizationina Multilateration system A solution for accuracy enhancement of the system with a pre-defined tolerable error and an accuracy-guaranteed model for monitoring airports using passive radar systems have been proposed Keywords: Passive radar, Errors, Accuracy improvement INTRODUCTION Passive radar system has been widely applied in air traffic control(ATC) systems.The main phases in an ATC system are: journey monitoring, approaching monitoring andonairport monitoring Monitoring journey phaseis called remote monitoring, the approaching andon-airport monitoring phases are considered as local monitoring Accuracy requirements are different for different phases This paper focuses on improving the accuracy in local monitoring phases Figure.1 Application of Mutilateration in Surveillance: (a)En-route Surveillance;(b) Terminal Maneuvering Area Surveillance; (c) Airport Surveillance [3] Table I shows the accuracy requirements in local monitoring phases of an ATC system [3] The requirements must be met by local monitoring systems such asprimary, secondary and passive multilateration radar systems The accuracy requirements presented in Table I will be used as the target criteria for setting up a passive radar system that aims to improve the accuracy of target position localization Table I Requirements about the Accuracy of the Local Area Supervision Equipment No Data type Requirement Update interval of receiver sec Theaircraftonthe taxiways Approaching altitude H≤ 4Km; R≤ 9Km Approach altitude km ≤ H≤ 8km; R≤ 18Km  7.5 meters; Probability of correct detection 95%; Probability of false detection 106  20 meters: Probability of correct detection 95%; Probability of false detection 104  40 meters: Probability of correct detection 95%; Probability of false detection 104 Tạp chí Nghiên cứu K H&CN quân sự, Số 36, 04 - 2015 53 Ra đa SURVEY ON FACTORS THAT AFFECT THE ACCURACY OF TARGET POSITION LOCALIZATION This section focuses on analyzing components that affect accuracy of target position localization based on time taken to transmit signals from the target to the receiving stations called hyperbolic method (TDOA - Time Difference of Arrival) The supervision system will calculate the arrival time of the signal from the target to the receiving station N to determine the location of the target Errors of TDOA are evaluated against following parameters [1,6]: - Circular Error Probability - Geometric DilutionOfPrecision - Mean Squared Error CEP error is based on the differences between evaluation times of coordinates This method performs a series of measurements GDOP error depends on the geometric position of the target and the positions of receiving stations GDOP is defined as the ratio of the RMS (root mean square), the error position with the error distance PDOP (Position Dilution of Precision), VDOP (Vertical Dilution Of Precision), HDOP (Horizontal Dilution Of Precision) are also similarly defined On the basis of analyzing the factors affecting accuracy when determining the osition of the target by TDOA method In the next section of article, we analyse a passive radar model that supervises flying targets in TDOA methods to identify the limited accuracyas the basic for building area sonable passive radar system model for monitoring airport Some problems must be identifiedin the model as followings: - The accuracy depends on the number of receiving points - The minimum berofreceiving points N required to meet the accuracy requirement spresented in Table I FACTORS AFFECTING THE ERROR OF PASSIVE RADAR SYSTEM SUPERVISING THE FLYING TARGET As to concretize the problem, we consider a system model consisting of stations: S0, S1, S2 and S3 in Figure 3, in which S0 is called the central station 3.1 Conditions - As suming that the target of coordinatesis ; - The receiving station coordinates are: Si  ( xi , yi , zi ) , with - The distance from target M to receiving stations Si corre sponding: ri and i  0,1, 2,3 - Wecalculate: r  ( x  x)  ( y  y )  ( z  z ) 0 0  2 ri  ( xi  x)  ( yi  y )  ( zi  z ) r  r  r  c.t i  i i Where, c  3.108 m / s : Speed of light Rewirte (1) as: ( xi  x0 ) x  ( yi  y0 ) y  ( zi  z0 ) z  ki  r0 ri (1) (2) with: ki   ri  ( x02  y02  z02 )  ( xi2  yi2  zi2 )  , i  1,2,3 54 N D Viet, T M Hoang, “Improve the accuracy of passive radar… monitoring airports.” Nghiên cứu khoa học công nghệ Figure Supervising system model of receiver stations [5] Establish matrix:  k1  r0 r1  x   x1  x0 y1  y0 z1  z0        A   x2  x0 y2  y0 z2  z0  ; X   y  ; F  k2  r0 r2   k3  r0 r3   z   x3  x0 y3  y0 z3  z0  Then equation (2) will equal: (3) A X  F  X  F A1 T T From (3), X depends on ( x, y, z ) ,( xi , yi , zi ) , and ri Therefore, the accuracy when identifying the target position will depend on ( x, y, z) T that is coordinates of the target and ri  cti ; ti  ri  r0 is the distance difference or time difference to stations From (1), we have: ri  ri  r0  fi ( x, y, z )  ( xi  x)2  ( yi  y )  ( zi  z )2  ( x0  x)2  ( y0  y )2  ( z0  z ) Approximated according to Taylor’sexpansionan dignoring higher-ordercomponents  x  x0 x  xi   y  y0 y  yi   z  z0 z  zi  d ri      (4)  dx    dy    dz ri  ri  ri   r0  r0  r0 With i  0,1,2,3 We found that d ri (error in measuring ri ) error on axes (dx, dy, dz) If we symbol:  df1 df1 df1   x  x0 x  x1    r  r  dx dy dz    df df df   x  x0 x  x2 H     r2  dx dy dz   r0   df3 df df  x  x0 x  x3     r3  dx dy dz   r0 is an function of the target coordinates y  y0 y  y1  r0 r1 y  y0 y  y2  r0 r2 y  y0 y  y3  r0 r3 Tạp chí Nghiên cứu K H&CN quân sự, Số 36, 04 - 2015 z  z0 z  z1    r0 r1  z  z0 z  z    r0 r2  z  z z  z3    r0 r3  55 Ra đa  d r1  x      X   y  and R   d r2   d r3   z  Then: R  H X (5) (6) 1 dR  H dX  dX  dR.H With dX  (dx dy dz )T and dR  (d r1 d r2 d r3 )T We have: Cov(dX )  E  dX (dX )T  (7) Replacing (6) in (7), we gain: Cov(dX )  E  (dR.H 1 ).(dR.H 1 )T   ( H H T ) 1 E  dR.dRT  1  ( H H T )1.Cov(dR) Result: Cov(dX )  ( H H T )1.Cov(dR) We have the covariance matrix of the range error:  n11 r1  Cov(dR)  E  d r , d r T    n21 r2r1  n31r3r1  (8) n12r1r2 n22 r2 n32r3r2 n13r1r3   n23r2r3  n33 r3  If nij is the correlation coefficient between ri and rj ;ri is the variance of ri Here, dR is a function of d r1 , d r2 , d r3 This component can be improved by increasing the sensitivity of the receiver, calculating ability, speed of transmission… In fact, the assumption that the distance among stations is far enough and not affecting to each other, so nij  0, nii  and ri is the same, which can measure with: ri  r1  r2  r3  c.t Here, we have c  3.108 m / s and when t  10ns then ri  3(m) So, we have:  r1 0    Cov(dR)  0  r2    r1   r2   r3  ri 0  r3   Replacing (9) in (10) we result: Cov(dR)  3 (m) (9) (10) (11)   x2  xy2  xz2   x2 0      Cov(dX )   yx2  y2  yz2     y2   zx2  zy2  z2   0  z2      Replacing (11) in (8), we have: Cov(dX )  3  H H T  1 (12) And the full position error will be:   Cov(dX )   x2   y2   z2 56 (13) N D Viet, T M Hoang, “Improve the accuracy of passive radar… monitoring airports.” Nghiên cứu khoa học công nghệ When ignoringthe z-axis, wecalculate theerror in the plane: (14)  R   x2   y2 On the basis of considering asystem model of stations S0, S1, S2 and S3 and error determination methods of the system with the full position error system(15) Subsequently, the article will calculate systematic airport surveillance radar errorsina small number of receiver stationsas a basis forgene ralization with a large number of N stations 3.2 Calcutating error of airport monitering passive radar system in a small number of receiver stations On the basis of analyzing theoretically above errors, we simulateto examine theerror with N  6,8,10 and 12 Systems of stationsare arranged under distribution laws as followings: - Distribution1: The system includes stationsona plane bounded by a circle with R  10km - Distribution 2: The system includes stationsona circle with R  10km The error simulation results for the survey of both allocations with receiver stations: 6,8, 10 and 12 are shown in Fig 4, 5, and Figure Error survey simulation results of receiver stations according to ditribution and Figure Error survey simulation results of receiver stations according to allocation and Figure Error survey simulation results of 10 receiver stations according to distribution and Tạp chí Nghiên cứu K H&CN quân sự, Số 36, 04 - 2015 57 Ra đa Figure Error survey simulation results of 12 receiver stations according to distribution and The simulation results ofthe systematic error survey with a number of stations and distribution of other stationsin Fig 4, 5, 6, are summarized in Table II Table II The Survey of Systematic Errors with Receiver Station N and Distribution of Different Stations Number of receiver Parameters Distribution Distribution station (N) 8.9491 10.0504 * N 5.9206 7.1067  y* N 6.7107 7.1067  x* N 0.0294 0.0102 GDOP * N  y* N  x* N GDOP 10 * N  y* N  x* N GDOP 12 * N  y* N 5.5997 4.0197 3.8986 0.0280 10.0504 7.1067 7.1067 0.0088 5.4769 3.7586 3.9836 0.0272 10.0504 7.1067 7.1067 0.0079 4.6095 3.1824 3.3346 0.0250 10.0504 7.1067 7.1067 0.0072  x* N GDOP After surveying systematic errors with number of N stations and different distribution of stations presented in Table II,we find that: - When number of stations N increase, general errors as well as component error sreduces according to N with certain ratio, GDOP of distribution is larger than that of distribution - The value of  * N ,  y * N ,  x * N is always aconstant number for each different distribution, in other words,the error is ratewith / N As a basis for concluding the dependence of the positioning error of the system upon number of stations N and the distribution law of the receiving station, the next section of the article will examine systematic errors with enough number ofstations N to make the general case 58 N D Viet, T M Hoang, “Improve the accuracy of passive radar… monitoring airports.” Nghiên cứu khoa học công nghệ 3.3 Calculating errors of the system with a large number of receiver stations (general case) According to the model shown in Fig without losing the generalization of the system, we consider the station S0 ( x0 , y0 , z0 ) placed at the origin of coordinates, which is similar to: x0  0; y0  0; z0  0; and r0  r , matrix A (called position matrix) will have form:  k1  r r1   x1 y1 z1    A   x2 y2 z2  and F   k2  r r2   k3  r r3   x3 y3 z3  Equation (3) will be equivalent as follows: A X  F  X  F A1 dF  A.dX  dX  dF A1 With dX  (dx dy dz)T and dF  (dF1 dF2 dF3 )T We have: (15) (16) Cov(dX )  E  dX (dX )T  Combining (16) and (7): Cov(dX )  E  dF A1  dF A1   ( A AT )1.E  dF (dF )T  T 1 Cov(dX )  ( A AT )1.Cov(dF ) (17) In equation(17), component matrix   ( A AT )1 characterizes the effects on location of stations to the error of the system Matrix Г is called Error Magnification Matrix Then equation (17) can be written Cov(dX )  .Cov(dF ) or   ( c)2   xx   yy   zz  GDOP     xx   yy   zz  c (18) (19) Component  xx   yy   zz in expression (19) is called GDOP (geometric dilution of precision) Expanding matrix L (with  x1 T L  A A   x2  x3   L1 ) by the following expression: y1 z1   x1 x2 x3  y2 z2   y1 y2 y3  y3 z3   z1 z2 z3  (20) If only examining in the plane (X0Y), missing effects of the height of receiver stations means that: z1  z2  z3  And:   N x2   N  j 1 j 1 L  N 1 N   j 1 x j y j N   N x y   j 1 j j N    N  y  j 1 j N  (21) Considering the calculation of GDOP for two distributions in section 3.2 with: - Distribution 1: Stations in a plane with the area bounded by circ le C, radius R Tạp chí Nghiên cứu K H&CN quân sự, Số 36, 04 - 2015 59 Ra đa - Distribution 2: Stations on a circle C, radius R With distribution 1, we have result:  4 R2  N 0   R2  1 4   2 4 NR R  R N With distribution 2, we have result: GDOP   2 R2  N (22)   R2  (23) After surveying systematic errors with small number of receiver stations (3.2) and the general case with a large number of stations N(3.3) we conclude: - The positioning accuracy of airport surveillance system depends on the location of the target compared with receiver points and coordinates of points in the monitoring system - The positioning error of the system rates with the score / N (when the number of receiver stations in the systemis large enough) Above conclusion is appliedon system model for airport passive surveillance radar if the supervision area of the airport is (20 kmx20km) and the error requirement meets
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