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1.College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China;2.College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China

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A Sequential Adaptive Method for Enhancing DOA Tracking Performance

YoussefFayad1,WangCaiyun2,CaoQunsheng1*

1.College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China;2.College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China

(Received 15 October 2015; Revised 6 June 2016; Accepted 5 August 2016)

A sequential processing is presented aiming at optimizing the direction of arrival (DOA) tracking performance. Firstly, current positions and Doppler frequency are estimated and a mathematical model is derived in order to clarify the effect of Doppler frequency on the estimation. The Doppler effect is employed within subspace concept in order to refine the estimation of the target position. Secondly, a renewed weight factor that depends on target maneuver is employed in order to realize more accurate association and smoothing processes. Simulation results show that the presented method has high accuracy in DOA tracking.

tracking maneuver; direction of arrival (DOA); Doppler effect

0 Introduction

Target maneuver is an important factor that affects the tracking radar performance. High performance tracking radars predict target future position with minimum errors. Some approaches have been established to obtain high performance[1,2], but the relationship between radar measurements and target maneuvers had not been discussed within these works. Also, they have not realized the integration processing within estimation and tracking stages in order to increase the ability of tracking dynamic targets. This work presents a new algorithm for enhancing tracking performance by dealing with target maneuver during estimation and tracking stages. ESPRIT[3-11]is employed in the estimation stage, which is affected by Doppler shift resulted from target maneuver[12-15]and leads to estimation errors. Doppler adaptation can decrease the maneuver effect on estimation process and increase the direction of arrival estimation (DOAE) accuracy leading to more accurate computations within the tracking stage. On the other hand, some other algorithms have been introduced to estimate Doppler frequency by using the fast Fourier transform (FFT), but it costs much computational time for a large number of samples[12]. It is noted that another method applying ESPRIT technique to compute Doppler shift via employing the rotational factor resulted from time delay sampling[16-18]. However, these methods require intensive matrix computations or iterative optimization techniques. Our algorithm includes estimating Doppler frequency with low matrix computational burden by applying technique based on measuring the change of displacement invariance (DI) to signal wave length ratio[5]due to target movement. Additionally, the new algorithm improves tracker performance by performing association and smoothing process according to a renewed factor, which depends on target maneuver. Since the maneuver processing is divided into two sequential stages, the algorithm realizes a robust tracking for dynamic targets.

1 Adapted Direction of Arrival Estimation

1.1 Observation model

Fig.1 shows the definition of a planar antenna array with elements oriented inxoyplane and indexedL,Ialongyandxdirections, respectively. For any pair of (i,l), its coordinate is (x,y)=((i-1), (l-1)), wherei=1,…,I;l=1,…,L, andi,lare reference displacements between neighbor elements alongxandyaxis. The measurement vector can be expressed as

Fig.1 Definition of planar antenna array

(2)

(3)

where ? denotes the Kroneker product, so the observation model can be rewritten as

(4)

(5)

where indexmruns asm=1, 2, …,Msnapshots. The space phase factors alongx-andy-directions are expressed as

(6)

(7)

Hence, the coarse estimation of the arrival angles can be estimated using T-ESPRIT[13]as

(8)

(9)

1.2 DOAE Doppler adaptation

(10)

(11)

(12)

(13)

Substitute Eqs. (12)—(13) into Eqs. (10)—(11), then

(14)

(15)

In general

(16)

(17)

wherecis the wave velocity in free space,αkthe angle between the direction of wave propagation and the target velocity vector . From Eqs (14)—(17), the more accurate T-ESPRIT algorithm should consider the effect of the Doppler frequency shift. Applying the Doppler frequency adaptation to refine angles estimated values as follow

(18)

(19)

(20)

(21)

Therefore

(22)

(23)

(24)

(25)

Obviously, it is clear that oncefdis chosen as 0 in Eqs. (24), (25), and the questions become a stationary target.

1.3 T-DIT for Doppler frequency estimation

For the transmitted signal, where no Doppler effect, the departure arguments is calculated as,

(26)

(27)

(28)

Table 1 Target directional judgment

As shown in Table 1 and Fig.2, the different signs forvy, and sinθkmean that the target is closing to the antenna, and the same signs of them mean that target is moving away from the antenna. Note thatvyhas a positive sign when its direction is in +ydirection, and has a negative sign when its direction is in -ydirection.

Fig.2 Target direction dependence on vy, and θk

It is clear that our main purpose is to determinevysign (the target direction). Substitute Eq. (25) to Eq. (20), then it has

(29)

So that

(30)

2 DOA Tracking

2.1 Prediction

(31)

(32)

(33)

(34)

ThetrackinggatedimensionswillbeθJ, φJ(rèn). Perrorwillbecalculatedaccordingtothedifferencebetweenthecurrentscanestimatedvalues(θε+1, φε+1)andthetrackinggatedimensions(θJ, φJ(rèn)).

(35)

(36)

2.2 Association and smoothing

(37)

(38)

(39)

Thus,thelearningfactorcanbecalculatedas

(40)

(41)

Afterassociation,thealgorithmimplementsthenextsmoothingprocess[1, 21]

(42)

(43)

(44)

(45)

Alsoitisadaptedaccordingtothetargetvelocitywhichisrenewedateachscan.Therefore,thepredictioninputsinEqs.(28)—(29)aresmoothedto

(46)

whichdecreasesthepredictionerrorofthenextperiod,leadingtoreductiondimensionsofthe″acceptancegate″thatincreasestheassociationprocessaccuracy.

Thenewalgorithmrealizesarobusttrackingbecauseitreactswithtargetsmaneuveronlineandintwostages.ThefirststageistheDOAE,whichisthecreatorofthetrackinggatedimensions,andthesecondstageisthetrackingfilterwhichistomaketheassociationandsmoothingprocessesmoredynamicandcompatiblewithtargetmaneuver.

3 Validations and Simulation Results

For the second stage validation, Table 2 lists the errors for the proposed method results and the method used in Ref.[2] withhigh maneuver and without maneuver. For maneuvering case, the error of the algorithm is compared at the point that target course starts to change with min. error of Ref.[2]. Fig.5 displays comparison between the non-maneuver target azimuth trajectory computed by the proposed algorithm and the real one and also its counterparts of Ref.[2].

Fig.3 The proposed algorithm

Table 2 Comparison of tracking errors

Fig.4 The first stage RMSEs for the proposed algorithm

Fig.5 Azimuth trajectory of non-maneuver target

Fig.6 introduces a three-dimensional tracking trajectory compared to a real trajectory. From Table 2 and Fig.5, it is found that the errors of the proposed algorithm are less than those of Ref.[2], and the trajectory is more close to the real one. Also， the advantage of the sequential adaptation exists that the tracking accuracy is upgraded when the weight factor is employed in addition to first stage adaptation (Doppler adaptation). Fig.6 indicates the ability of the proposed algorithm to track a maneuver target with high accuracy. This improvement is because the method deals with target in two consecutive stages which realizes robust tracking. For more validation, this algorithm has been applied to two targets moving with different courses with initial values ofθ1=15°,θ2=10° andφ1=30°,φ2=10°, The first target movs away from the antenna then turns toward it； on the contrary， the second target starts to move toward the antenna then movs away from it. The maximum maneuver of both targets isga=6g. Comparison of the real tracking elevation and azimuth values of two moving targets are showed in Figs.7， 8, respectively. The RMS error of the first target is about 1.19 and for the second one is 0.51, which is almost close to the data in Ref.[1] which ranges from 0.21 to 1.85.

Fig.6 Three-dimensional maneuvering target tracking trajectory

Figs.7， 8 show the proposed algorithm can realize a robust track for two targets with different maneuvers.

Fig.7 Elevation angles of moving targets during the flight

Fig.8 Azimuth angles of moving targets during the flight

4 Conclusions

A new DOA tracking method is introduced to reduce the target maneuver effect. It deals with target maneuver in both of estimation and tracking stages. Doppler effect is embedded in the T-ESPRIT technique to refine the moving DOAE. Then, a weight factor adapted with target maneuver is used for accurate association and smoothing. A robust tracking has been achieved using this algorithm. Tracking errors have been reduced about 52% to 89%. Also, the proposed method can track two targets with high accuracy. This approach achieves robust tracking with low computational load, which can help to improve the tracking performance of radar system.

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Dr. Youssef Fayad was born in Alexandria, Egypt, in 1975. He received the B.S. in electronic engineering and the M.S. in communications and electronics from faculty of engineering, Alexandria University, Egypt, in 1997, 2010 respectively. He obtained his Ph.D. degree in radar system in the College of Electronic and Information Engineering, Nanjing, in 2016. He is an IAENG Member, and a Student Member of IEEE. He also works as an Assistant Lecturer in Air Defense College, Egypt. Dr. Fayad research interests are antenna and radar signal processing.

Dr. Wang Caiyun was born in Shanxi, China, on September 30, 1975. She graduated in 1996 with a B.S. degree and in 1999 with a M.S. degree. She received her Ph.D. degree in signal and information processing from Beihang University, Beijing, China, in 2008. She is currently an associate professor in the College of Astronautics, Nanjing University of Aeronautics and Astronautics (NUAA). Her major research interests are radar automatic target recognition (RATA), radar signal processing, and adaptive signal processing, and pattern recognition.

Prof. Cao Qunsheng received his Ph.D. in electrical engineering from the Hong Kong Polytechnic University. He is now a professor of electrical engineering at Nanjing University of Aeronautics and Astronautics (NUAA). His current research interests are computational electromagnetics, antenna and microwave technology and the radar signal processing. Prof. Cao has published more than 160 academic papers in refereed international journals and conference proceedings.

(Executive Editor： Zhang Bei)

TN925 Document code:A Article ID:1005-1120(2016)06-0739-09

*Corresponding author, E-mail address: qunsheng@nuaa.edu.cn. How to cite this article: Youssef Fayad, Wang Caiyun, Cao Qunsheng. A sequential adaptive method for enhancing DOA tracking performance[J]. Trans. Nanjing Univ. Aero. Astro., 2016,33(6):739-747. http:∥dx.doi.org/10.16356/j.1005-1120.2016.06.739