Multiradar Tracking System Using Radial Velocity Measurements

Transcription

1 Multiradar Tracking System Using Radial Velocity Measurements A. FARINA S. PARDINI Selenia S.p.A., Italy Abstract Multiradar tracking using both position and radial velocity measurements is discussed. The measurement of two or more different radial velocity components allows the calculation of rectangular velocity components. The measurement noise of the velocity components is filtered using a Kalman filter in the same way as the Cartesian position components. Before the conversion of velocity components from radial to Cartesian coordinates, the radial velocities are aligned on a time scale to account for the time shift of the radar measurements. In order to compare multiradar tracking system performance with and without radial velocity, some simulation tests have been performed for typical paths. The simulation results show a significant improvement when radial velocity is used for tracking. Manuscript received August 15, 1978; revised February 13, Authors' address: Selenia S.p.A., Via Tiburtina Km , Rome, Italy / $ IEEE Nomenclature a,, / = 1, L A A D dx, dvr, etc. g(tk) G H i,i= 1, L '4) N p(t) PA~ QK, QK R(O) Ri') SK S S T AK V v i) ARK VR(t) 7(i) a AK =tk+ K (PK, OK TI, T QX,y Ca - tk (X,, (XMl, y11) (X(), Y()) ZK (i) (i), YK x, y Parameters of the polynomi; p(t). Set of the a, parameters. Least square estimate of A. Distance between the two radars. Differentials of X, VR, etc. Measurement noise on VR. Set of the g(tk) samples. Matrix of the measurement equation. Index for the ith radar. Degree of the polynomial p(t). Measurement noise vectors. VR,K sample number for A estimation. Polynomial in time of VR estimation. A covariance matrix. Covariance matrices of the dynamic noise. Target range measurements. Covariance matrices of the measurement noises. State vector. Vector with the measurements VRK- Time. Matrix of the times. Forcing noise of the dynamic model. Target velocity vector. Target radial velocities. Radial velocity estimation. Measurement vectors. Inverse of acceleration correlation time. Time interval between two measurements. Discrete time. Transition matrices of dynamic model. Radar scan periods. Parameters of acceleration model. Azimuth measurements of the target. Coordinate systems. Target Cartesian coordinates. Cartesian components of the target velocity. St. deviations of polar measurements. IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. AES-15, NO.4 JULY

2 (X-Y):MAIN COORDINATE 5YSTEM (X1-Y1),(X-Y):RADAR COORDINATE Si-STEM,TARGET PAT W 10D Fig. 1. Radar measurements. RADAR I RK Iii RK+1 K+ Tz -I I~~X r + A, R E(K?I K+i VRKJ)Lv+1 1 K (+1 T XRAtDAR a Fig.. Acquisition time of measurements. 0 zataw 1 X RAOAA Z (1) VR,K+1 EXTRAPOLATION (1) 051$ TI-E VR HEASUREHEN15,NTIL THE TIHE K K ki- TIHE Fig. 3. Extrapolation of radial velocity measurements coming from one radar. 1. Introduction The problem of multiradar tracking (MRT) arises when target tracking is performed by track-while-scan (TWS) techniques using plots coming from two or more radars having overlapping coverage. Therefore, MRT involves 1) the overlapping of radar coverage area, in which radars are considered two at a time; and ) the measurements coming from all radars are processed by only one processing system. Because of inherent principles, MRT has the following advantages over monoradar system: 1) a target may be tracked along a surface wider than the coverage of each radar; ) there is track continuity during the hand-over of a target between two adjacent radars; 3) there is higher precision in the estimation of track parameters, due to a data rate higher than that of a single radar; 4) there is lower probability of false correlation in the cluttered surfaces due to gate dimensions smaller than ones of a single radar system; 5) there is higher detection probability in the overlapped surfaces; and 6) there is a capability of reconfiguration in the case of failure of one or more radars. These advantages give a higher reliability for MRT than a single radar system. Because of its inherent performance, the MRT has been widely studied [1-6] from the standpoint of algorithms and system configuration. The algorithms previously studied involve essentially the processing, through a linear Kalman filter, of the position measurements obtained with a variable data rate. In this paper, which considers only the algorithm aspect of the MRT, an algorithm using both the position and radial velocity measurements is analyzed. The radial velocity may be measured by coherent processing of the radar echo [10]. Its application has proved useful for single radar systems in cluttered and clear environments [7-9]. In the case of MRT, the measurement of two or more different radial components of the velocity permits calculation of the Cartesian components of the total vector velocity. The total vector velocity measurement, if appropriately utilized, represents useful information in order to improve the tracking performance of the MRT. The measurement noise of the velocity components may be filtered, in the same way as the Cartesian position components, using a Kalman filter. We only refer to the case of two radars being located on two-dimensional paths and on two different sites. No conceptual problems are involved in the extension to more general cases. Let us consider the geometrical situation, shown in Fig. 1 where (X"'l, Y(l)) and (X"', Y()) are the reference coordinate systems for radar 1 and, respectively. Consider (X"1', Y1l)) as the main reference system.' This is the system to which all the measurements being processed are referred. The target velocity V is resolved into two radial components 1R4) and 14), usually measured by the two radars at different times K and K + 1. A typical time sequence of both position and radial velocity measurements from radars 1 and is shown in Fig.. In order to obtain the Cartesian components (x, y) of the velocity V, it is necessary to know the radial components referred to the same time. Because of the time displacement of the two radars (time difference between the measurements of the same target, performed by the two radars), whenever the velocity measurement of one radar is acquired, it is necessary to extrapolate to the same time the measurement previously acquired by the other radar. For example, in order to obtain the components (x, y) for time K + 'The adopted reference system allows equations to be easily obtained and it may always be used as reference system for processing purposes. In the case that another reference system is required (as for display, etc.) it is possible to do a coordinate conversion aftr the data processing. The tracking performance is, of course, independent of the coordinate reference system. 556 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. AES-15, NO.4 JULY 1979

3 1, the measurement j4) (obtained directly at time K + 1) is utilized and the estimation V,,) extrapolated to time K + 1. The extrapolation of j"1) is performed using the measurements previously acquired by radar 1 with T, and also by means of the last measurement VRK (Fig. 3). The errors (due to noise and estimation) of the radial velocity components generate equivalent errors on the Cartesian components x and y. The error increment depends on the entire geometrical condition and is higher when the radial velocity directions are more nearly parallel. As a consequence, it may be convenient to limit the estimation error due to the time alignment, especially if the estimation error is biased. This bias is due to VR extrapolation on accelerating targets. Therefore, it is better to perform the time alignment by interpolation (instead of extrapolation), which involves lower bias errors. In this case, the measurements are processed with a certain delay (shorter than the scan period), as shown in Fig. 4. The radial velocity measurements, following time alignment, are converted into the Cartesian components x and y by a nonlinear memoryless conversion. The Cartesian component relevant to position (x, y) and velocity (x, y) may be processed through a linear Kalman filter in order to reduce noise measurements. The block diagram of the overall algorithm is shown in Fig. 5. It includes the polar-to-cartesian conversion of coordinates from the reference system (X(', Y()) to the main reference system (X(l), Y(l)), where all the subsequent processing is performed. In the following sections all the problems thus far considered are thoroughly examined. The results of simulation tests for typical paths are discussed in Section VI where we compare multiradar tracking with and without the use of the radial velocity. 11. Mathematical Model of Target Motion In order to develop a mathematical model of the target motion, we consider the state vector SK (6 x 1) SK = [XK XK XKYK PK YK] (.1) where XK, YK are the Cartesian coordinates of the target motion on the ground plane. We consider a planar path for the sake of simplicity. The state vector s is asynchronously sampled every AK seconds, where AK is the interval between the time measurements K + 1 and K. The following mathematical model is derived [8]: SK+1 = 4)K SK +,AK (.) where the matrix 4,(6 x 6) is O AtEAR 1 X CAAR z k+1 K+Z Fig. 4. Interpolation of radial velocity measurements coming from one radar. V(RT) DATA-TIT EME R ALIGcMENT FItTER EVAWATION OF PSEUDO MEASU)RE= ALIGNMT ENT kalma FLTER FILTER APERIODIC 9 ~~~~~~~~~~~~WITH, Rkl) _sdat.4 RAZTE ESTIMAT109i F() SYSTEM Fig. 5. Outline of multiradar tracking filter. (I)K o/ T (.3) If aa, <E ½/, where a is the correlation time of the target acceleration, OK (3 x 3) is 1 AK AK/ =' [ 1 AK ] (.4) O 0 1 The vector IAK (6 x 1) is a white Gaussian sequence with zero mean and covariance matrix QK (6 X 6) QK= aaa I Q' Q., Q' QXY Q' Q' (.5) where aa is the variance of the acceleration process and Q,. is the correlation coefficient between the x and y components of the acceleration. If aak < ½/, the matrix QK (3 x 3) is [13] AKX/0 A4/8 AK/6 QK AK/8 AK/6 AK/ (.6) [AK/6 A/ AK The K Sequence takes into account the random characteristics of the target acceleration. By examining the simulation results of the tracking algorithm, we can select the covariance aa to account for the uncertainties in the dynamic system. Ill. Measurement Equation The sampled radar measurements are the polar FARINA/PARDINI: MULTIRADAR TRACKING SYSTEM USING RADIAL VELOCITY MEASUREMENTS 557

4 coordinates of position (R"', 0(l), (R11, 0()), and radial velocities (R1), 4)) (Fig. 1). They are affected by mutually independent additive white Gaussian noises, with zero mean standard deviation given by (R), ', and a(,), with i-1,. From the polar measurements (R('", 0`i)) we can obtain the Cartesian measurements (x(i), y(i)), which are the state components. If the noise is not too high, compared with the above measurements, the noise sequences affecting (x(i), y(1)) are still zero mean, white, but dependent on each other. The variances and covariances are a.( = [R(i)] cos 0(i) + [R(i) sin ' (i)1 [yi ]= [a()1 sin 0(i) + [R(i) X, y= sin 0C') cos 0(i) [(R] cos 0(L) (i)1 - [R' j,010] sin 0Oi) cos 0(i) (i = 1, ). (3.1) The G` measurements may be expressed by means of the state components. jr4) is the projection of velocity V (x, y) on the radar's target directions, which have = components x)i/rz)i), y(')/r(). Then we have GI ) = (X, X(i) + y(i) y(i))/ (X(')) + y(i)) + noises (i = 1, ). (3.) To obtain x, P from the J4*) measurements, we consider first (3.) without noise. Then we consider the effect of noise upon x and jy. Solving the (3.) without noise with respect to x, y and using the following equations: y(l) = y() X(1) =X() +D we obtain X= g4j) R~'1/D - R) R(I/D (3.3) )= I (R()/D) cot 0S) -R 1) (R(1)/D) cot 0(). (3.4) From the second equation of (3.4), we note that y is indeterminate when 0(l) and 0() are equal to + Kn (K = 0, 1,,...). When the target is near the x axis, the y component of the target velocity is not measurable. To evaluate the noise on x and y, the assumption The A estimation can also be obtained with a recursive estimation procedure instead of the measurements batch processing. However, the performances are the same. is made that the measurement noise on R('i, 0(i), and small with respect to the true values of the VW) is measurements. Thus the measurement noises are to be considered as differential quantities with respect to the evaluation of their mean values and standard deviations. In the Appendix are shown the detailed calculations of the covariance matrices R") of the noise measurements nflk their mean value is zero) relative to the measurements ZK'' (4 x 1 [ZK ]T= [XK XK YK YKI. (3.5) As a consequence, the measurement equations are ZK= HSK + nk (3.6) where H (4 x 6) is IV O O Time Alignment of VR Measurements (3.7) We consider now the problem of time alignment, i.e., the extrapolation (Fig. 3) or the interpolation (Fig. 4) of V(R) using the measurements already acquired with constant period Ti'. The time function VR(t) (for both (V1R4(t) and V,'(t)) can be represented as a polynomial in time of L degrees p(t) = a,t' = ta (4.1) where t(1, L + 1) is: t = [ 1 t, t, tli and A(L + 1, 1) is (4.) AT= [ao, a,,..., all. (4.3) If g(tk) denotes the measurement error associated with VR(tK), then (4.1) can be replaced by VR(tK) = tka + g(tk) (4.4) where tk = TK and g(tk) is white Gaussian, zero mean, and with dvr standard deviation. The VR estimation at time tk ± A (tk + A is extrapolation, tk - A is interpolation) is based upon the N measurements 558 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. AES-15, NO.4 JULY 1979

5 [VR(tK-N+l), VR(tKN+l),..., (4.5)( WNVR(K.1 W = (VR IMN (4. 14) where I'NN is the identify matrix (N x N). As a consequence, A estimation becomes which are used for the least square estimation A of the coefficients vector A. The estimation of VR at the time tk + A then is: A= (Th7) ThS (4.15) VR(tK A+ = tk+ A. (4.6) If the A estimation is unbiased and with covariance matrix Pi, the VR estimation is also unbiased and with the following variance: OVR = tk±a PA ttk±a (4.7) This equation will provide the measurement variance when VR is not actually measurable, but is available only with an estimation process. The estimation of the polynomial parameters A is performed by evaluating the average least square bias between p(tj) and VR(yj), where j = K -N + 1,..., K. It is convenient to collect the measurements (4.5) in a vector S(N x 1) ST = [ VR(tK-N+1), VR(tK N+),..., VR(tK)l (4.8) and the measurement errors g in a vector G(N x 1): G = [g(tk N+I), g(tk-n+),..., g(tk)] (4.9) which has the covariance matrix W(N x N). We can also define a transfer matrix T[N x (L + 1)], which includes the time vectors (4.): [tk-n 1 tk-n+1 T= tk-n+l 1 tk-n+ tk L' tk tk-n+ 1 tk-n+ tk L *-* tk-n+ 1 L *K- tk-n+ L *-0 tk j By these definitions, the N equations (4.4) may be replaced by a matrix equation: S=TA+G. (4.11) The minimum variance estimation A of A is [11] A^3 (TSW1T[1 ThW'S (4.1) with the covariance matrix: P=(TW'TW-1 1 (4.13) The estimation A, which is simply a linear combination of the previous N data points, is unbiased and efficient if the model (4.1) is a good approximation of the VR behavior. As the VR measurement errors are independent and their variances may be assumed equal to each other, W becomes: and its covariance matrix becomes = OvR(Th7). (4.16) As the measurements for the target are equally spaced in time, the T matrix may be written as: 1 T() [T(i) 1 s.. [T( i)]l 1 T( i' [T( t)1... [T( i)]l. (4.17) _1 NT( i) [NT(i ) ]... [NTi,] Then the PA and (TTP`Tr matrices may be precomputed off-line; thus A may be simply computed as a predetermined linear combination of the previous N measurements. The number. of sample points (N) and the degree (L) of polynomial p(t) must satisfy the following condition: L + 1 AN. (4.18) The minimum number of samples (N) is equal to the number of polynomial parameters. The degree of the polynomial and the number of the previous measurements by which VR has been estimated must be selected. The selection depends on the acceptable values relevant to the bias and variance in the VR estimation as well as considering the maximum time extrapolation. If the VR(t) function and its derivative are smoothly varying, it is convenient to minimize the degree of the polynomial because the variance (4.7) increases as fast as the number of the polynomial coefficients. A great amount of data provides good noise filtering, but it does not follow a sharp variation of VR(t). Proper selection depends on the accuracy of measurements, on data rates, and on curvature of paths that may be encountered. Following our experience, a selection should be performed among four or five data points to be used with a second degree polynomial estimator. Finally it is noted that the A estimation can be carried out also for that radar which measures the radial velocity. In this case, the A estimation is used to reduce the noise variance of VR(t,) (in the previous equation, A is set to zero). V. Dynamic State Estimation Since the dynamic system (.) and the measure- FARINA/PARDINI: MULTIRADAR TRACKING SYSTEM USING RADIAL VELOCITY MEASUREMENTS 559

6 Y RAtAR 1 X i - K 10iYT T1 =Tz = 1Os AK= 7S, K+l=35 t,b,=1005 R X=t m. XA= 10000m' YA= 3000W ' VA= 300m/s 5CC ZO rn/gz AF Fig. 6. Target path 1. c 4 y8(z) referred to the main coordinate system. Therefore the measurements coming from radar will be transferred to the main reference (X, Y), using (3.3) with the pro- () per error covariance matrix RK VI. Simulation Results A digital simulation has been performed in order to compare the performance between the analyzed B multiradar tracking system (referring to the method of VR interpolation shown in Fig. 4) and another one without using the radial velocity measurements. The results refer to two typical trajectories shown in Fig. 6 and Fig. 7. The measurement errors have been considered as being Gaussian, uncorrelated, zero mean value, with the following standard deviations: r~~~~~~~~~~~ ID tra0ar.n.f a, (i) =loo0m (i) = rad a" = 10 m/s (i= 1, ). (6.1) The distance between the radars is 50 km. The detection probability has been assumed to be PD = 1. The scan period, which is the same for the two radars, is equal to 10 s. Therefore, the measurements related to the same target come alternatively from the two radars. In the trajectory of Fig. 6, the sequence of the intervals between two consecutive measurements is (7 s, 3 s). In the trajectory of Fig. 7, the two radars are, instead, considered symmetrically interlaced and, therefore, the time sequence of the measurement is (5 s, 5 s). The comparison has been performed on the following quantities: El,K ={[SKIK(I) - Xk] + [SK/K(4) YKI} - E=K arccot {[SK/K(4)- YKI/[SK/K(I) XK]} - E3,K = {[SK/K()] + [PK,K(5)]} {XK + YK} E4,K = arccot {SK/K(5)/SK/K()} arccot {YK/XK} (6.) Fig. 7. Target path. ment equation (3.6) are linear and the random series 1U and nk are Gaussian, the estimator of the dynamic state sk is the Kalman filter. For the sake of brevity, we omit the known formulas (1]. By applying the algorithm equations, it must be considered that the measurements come from the two different reference systems, while the state sk and its estimate 'SKIK are where E, K' E,K E3K, and E4,K represent, respectively, the displacement between the estimation and the "true" value of the Cartesian position, the angular component of polar coordinates, the modulus of the velocity, and the direction of the velocity. For each quantity, the mean value and the standard deviation have been considered. The first quantity of (6.) (position error) has a very low mean value even during the target acceleration (maximum value is about 10 m). The standard deviation has a nearly constant value of 60 m. Without the radial velocity, the performances show 560 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. AES-15, NO.4 JULY 1979

7 04 T1 = =105 AL K= 5 S AB= 100 S tc =05$ VA= 3O rmbs b ACC m/s 41 y () 10 - WITh Vt \WIThOUT V\/ A RADAR 1L D=50 Km RADAR 0 Fig. 9. Mean filtering error on velocity direction (path 1). o- Fig. 8. Mean filtering error on velocity module (path 1). Fig Mean filtering error on velocity module (path ). little decrease. The other quantity of (6.) (angular position error) has a maximum mean value of mrad and a standard deviation of about 1.6 mrad. Without radial velocity, the maximum mean value becomes 3 mrad and the standard deviation becomes.6 mrad. However, the improvement of performance produced using radial velocity is more evident for the velocity errors (third and fourth equations of (6.)). Fig. 8 and Fig. 9 refer to the path of Fig. 6. These figures show the error mean value for the modulus and the direction of the velocity, respectively. The standard deviations are 7m/s and 1.4, respectively, when the radial velocity is used; without VR the foregoing values become 14 m/s and.50. Fig. 10 and Fig. 11 refer to the path of Fig. 7. These figures show again the error mean value for the modulus and direction of velocity. The comparison includes also the case related to the method of radial velocity extrapolation (Fig. 3). Appendix We evaluate first the mean values and the covariances of the, measurement errors on x and y. Differentiating (3.4), we obtain = dk (1/D)[v,, dr'1) + RJ1) d l4r RdR(,- R( dv~)] dy= (1/D)[R ' cot 0'1dV4)+ jr) cot 01)dR() )R()dO(l)/sin M -)R-') cot 0 )dvr -VR1) cot 0()dR(l+ (VR4)R(l)/sin 0()) do()]. (Al) If the measurement noises on R, 0, and VR are uncorrelated white Gaussian processes with zero mean value, the measurement errors on x and y are still zero FARINA/PARDINI: MULTIRADAR TRACKING SYSTEM USING RADIAL VELOCITY MEASUREMENTS 561

8 Fig. 11. Mean filtering error on velocity direction (path ). mean but dependent on each other. The variances and covariances are =x (1/D) [{[o(v R (i) 1 + [ 4i)(i) } i=l = (l/d){[r( cot 0(a) v]+ [1V) cot 0(1) ()] + [VRR' 0(/sin 0(i)1+ [R(') cot 0() C(1 1R cot 0()Co1)] + [141)R(C). /sin 0()1} _ 0;=(/){~ XY (1 ID ) [11)o(')] [VR ar Coto 0() - [R R1)0o1] a avctr Cot 0() -[V) ()] cot 0(1) [R(1o ] cot 0(1)}. (A) To evaluate the covariances between the position and velocity measurements, we have to consider the radar, which performs these measurements. The assumption is made that the measurements are coming from radar 1, i.e., x = R') cos 0') y() = R(1' sin 0(1). (A3) Differentiating (A3), we obtain dx(') = -R(1' sin 0C'1dC)'1 + cos 0(1) dr"11 dy(i) =R') cos 0'1) d0'1) + sin 0(1) dr"-). (A4) Multiplying (A4) with dx and dy, respectively, we have dx"ldx = (1 /D) VR') cos 0(1) dr(11 56 dx'1dp = (1/D) I(VR)R'1'R'l'/sin 0(1)) d0(1) + cos (1 cot 0()11) dr0l,^ dy"l)dx = (l/d) 1R1) sin 0(1)dR(') dy Mdy = (l/d) {- (VR)R(W1)/sin0(1) cos C) d0< 1 - R 1) cot 0() sin 0'"dR('1}. The covariances are obtained by averaging the forea (1) = (lid) 1) cos 0(1) [o01)1 Xy o (1). = (1/D) {(V() R WR'1)/sin 0(1))[(1)1 + cos 0(1) cot 0() V1) [r(l)j} = (1/D) 1) sin 0 R1)[o'1)] = (l/d) {- (VRR( co1)s 0co )/sin 0(1))[(o1)1 - sin 0(1) cot 0() RR1)(1)]} When the position measurements are coming from radar, we have, by a similar calculation a(). = (l/d) cos V(R R[OR] a () = (1/D) {(R''R'1' VR14/sin 0())[0')1 V) 0() cot 0(1)[o) ]}. (). = - (1/D) sin 0(R 14)] y x o (1)x = (1/D) {(VR141R 1(R'/sin 0()) cos 0()[o()] - vr sin 0() cot 0 R'[a"]I}. Finally, the measurement noises n"' are Gaussian sequences, zero mean, and with R") covariance matrices [[o(i)i a (i). R'= x x Lo() ar ( i). Lxy ( i) o) (i). OXy X X 0;; a (i). Y, Y a (i)1 x y 0;; (i) y Y, i = 1,. (A8) Note that the variances and covariances concerning y increase indefinitely when the target approaches the x axis (0(i) Kr, K = 0, 1,,...). However, these noise measurements have little influence on the state estimation, since they are weighed by an inversely proportional ratio with respect to their covariances. The same behavior does not occur for biased measurements. In fact, the foregoing calculations are carried out when the VR measurements noises are zero mean. This assumption is not valid when VR is extrapolated IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. AES-15, NO.4 JULY 1979 (A5) (A6) (A7)

9 during high target acceleration. The bias on VR produces a bias on the computed measurements x and y. To reduce this bias, we have suggested the solution at the beginning of the Appendix, shown in Fig. 4, which has given good results. References [1] M. Thomas, G. Maignan, and Y. Storey, "Tracking in a multiradar environment," Proc. IEEE, vol. 13, Mar [1 D. Willner, C. Chang, and K. Dunn, "Kalman filter algorithms for a multisensor system," presented at the 1976 IEEE Conf. Decision and Control. [31 F. Smith and D. Spain, "Multisensor tracking of reentry vehicles," presented at the 1976 IEEE Conf. Decision and Control. 14] J. Miller and J. Berry, "Multisensor utilization investigation," presented at the 1977 IEE Radar Conf., London. [51 P. Casner and R. Prengaman, "Integration and automation of multiple co-located radars," presented at the 1977 IEE Radar Conf., London. [6] A. Morley and A. Wilsdon, "Multiradar tracking in a multisite environment," presented at the 1977 IEE Radar Conf., London. [7] A. Farina, S. Pardini, and G. Barontini, "Application of nonlinear filtering theory to a track-while scan problem," in Proc. Ist Internat. Conf. Information Sciences and Systems, Patras, Italy, Aug. 19-4, [8] A. A. Farina, S. Pardini, and G. Barontini, "Employment of radial velocity measurement in a track-while-scan algorithm," Rivista Tecnica Selenia, vol. 4, no. 1, [9] A. Farina and S. Pardini, "Track-while-scan algorithm in a clutter environment," IEEE Trans. Aerosp. Electron. Syst., vol. AES-14, pp , Sept [10] F.R. Castella and J.T. Miller, "Moving target detector data utilization study," presented at the 1977 Radar Conf. [1I] R. Deutsch, Estimation Theory. Engelwood Cliffs, N.J.: Prentice-Hall, 1965, pp [1] A. Gelb, Applied Optimal Estimation. Lexington, Mass.: M.I.T. Press, 1974, pp [13] R.A. Singer, "Estimating optimal tracking filter performance for manned maneuvering targets," IEEE Trans. Aerosp. Electron. Syst., vol. AES-6, pp , July [14] C.E. Muehe, "Moving target detector, an improved signal processor," presented at the AGARD Conf., June Alfonso Farina was born in Petrella Salto, Rieti, on January 5, He received the degree of Doctor in electronic engineering from the University of Rome, Italy, in In 1974 he joined the System Analysis Group of the Research Department of Selenia S.p.A., Rome, Italy, where his interests are in estimation and control theory. Sergio Pardini was born in Torre Del Lago (Lucca), Italy, on September 13, He received the degree of Doctor in Electronic Engineering from the University of Pisa, Italy, in After his military service in 1971 he joined the System Analysis Group of the Research Department of Selenia S.p.A., Rome, Italy, where he is working in the area of tracking with sampled data and in the field of air traffic control. FARINA/PARDINI: MULTIRADAR TRACKING SYSTEM USING RADIAL VELOCITY MEASUREMENTS 563

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