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Performance Analysis and Simulation of JTIDS Network Time Synchronization Nan Wu, Hua Wang and Jingming Kuang Dept. of Electronic Engineering Beijing Institute of Technology Beijing, China wunan@bit.edu.cn Abstract—Round Trip Timing (RTT) and PPLI message are two ways of time synchronization in the Joint Tactical Information Distribution System (JTIDS) network. The former is a kind of active time synchronization, which could make the user have high timing
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  Performance Analysis and Simulation of JTIDS Network Time Synchronization  Nan Wu, Hua Wang and Jingming Kuang Dept. of Electronic EngineeringBeijing Institute of TechnologyBeijing, Chinawunan@bit.edu.cn  Abstract   —Round Trip Timing (RTT) and PPLI messageare two ways of time synchronization in the Joint TacticalInformation Distribution System (JTIDS) network. Theformer is a kind of active time synchronization, which couldmake the user have high timing level directly. The latter iscompletely passive and could provide low level timesynchronization as a byproduct of navigation. This paper  begins with the introduction of the two timing mechanismsof JTIDS network. Models of passive and active timesynchronization are built up respectively. Two filters, one isnavigation filter and the other is RTT filter, are designed based on the models. Simulation validates the design of thetwo filters, and effects of major error sources and modeluncertainty are analyzed.I.   I  NTRODUCTION The Joint Tactical Information Distribution System(JTIDS) is a synchronous, time-division multiple-access(TDMA), spread spectrum system, with integrated ability of communication, navigation and identification [1]. All user terminals operate on the common time base which issynchronized to the network time reference (NTR). Theysend messages in the allocated slots and receive in theothers.Round Trip Timing (RTT) and Precise Position Locationand Identification (PPLI) message are two means of maintaining time synchronization in JTIDS network [2].The former is a kind of active time synchronization, whichoperates independently of Relative Navigation (RELNAV).The latter is completely passive, and which is intrinsic toRELNAV function. Superior users in JTIDS network areassigned some fixed time slots to send RTT message to keepsynchronization with NTR. However, inferior users must becapable of performing clock synchronization completely passively by receiving PPLI message.Time synchronization and navigation performance areinteractive in JTIDS network. On the one hand, RTT makesthe user have higher timing level directly, which leads to agood navigation performance. On the other hand, good position information makes the passive synchronizationmore effective. Because of the complexity of completetheory analysis, finding the relationship between timedissemination and navigation error sources in JTIDS network using computer is very important.This paper begins with the introduction of the two timingmechanisms of JTIDS network. Based on the clock model,RTT filter and navigation filter are designed for processingRTT message and PPLI message respectively. Finally, thetwo timing modules are used in a JTIDS network simulation platform to test the effectiveness of model uncertainty andthe effect of error sources on time synchronization andnavigation.II.   M ODEL OF T IME S YNCHRONIZATION  Before we start the analysis and simulation, models of the two time synchronization have to be built up first.  A.    Passive Synchronization by PPLI Message Passive synchronization is the main method for someinferior users, which often have to be radio silence, tomaintain synchronization in JTIDS network. A RELNAVuser’s clock error adds linearly and equally to the observedone-way radio ranges to all the PPLI sources. The RELNAVKalman filter of passive users minimizes this common range bias by assigning it to the clock state carried in the filter.The basic passive synchronization and rangingobservation model can be expressed by [3] 222 ()**()()() o c t c t t t  c TOA R b c b c N  X X Y Y Z Z  = = + − +  = − + − + −    where  R o   is the observed ranged to the source;  R c   is thecomputed range to the source based on the information inPPLI message and user’s own position prediction; c is thespeed of light; TOA is the observed time of arrival withrespect to the user’s own clock time;  X  t  , Y  t  ,  Z  t    are positioncoordinates of the transmitter;  X  , Y  ,  Z  are positioncoordinates of the user; b t  is the time bias of the source with 836 0-7803-9052-0/05/$20.00 © 2005 IEEE.  respect to system time, which is unknown to source and user; b is the time bias of the user;  N  is the sum of measurementnoises. Each user should try to minimize b by passive or active synchronization. Generally, b t  could be consideredincluded in  N  .Because the observation equation of JTIDS passivesynchronization and ranging is nonlinear, we have tolinearize the observation equation and use the extendedKalman filter (EKF) equations as follow predicted covariance: |11|1 T T k k k k   P Q − − − = Φ Φ + Γ Γ  (1) predicted state vector: |1|11|1 ˆ k k k k k k   X X  − − − − = Φ (2)gain: 1|1|1 T T k k k k k k k k   K P H H P H R −− −   = +   (3)filtered state vector: ||1 ˆˆ k k k k k O O  X X K R R −   = + −   (4)filtered covariance: [ ] ||1 k k k k k k   I K H P  − = − (5)where  H  is the linearized observation matrix which containssuch elements as ( ) ( ) ( ) , , , t c t c t c c X X R Y Y R Z Z R − − − −  Details about EKF can be found in [4], and will not becovered in this paper.Terminal users will process the equations above insequence. However, not every PPLI message received isused to update EKF equations. In consideration of systemstability and operation precision, received PPLI messageswill first be stored. Then, the optimal source will be chosenaccording to the source selection algorithm [5]. Integratedquality of source can be obtained by ( ) 12 total p t g  Q H H W H W  = + +  where,  H   p and  H  t  are source quality of position and timing;  H   g  is the quality of relative position relation of source anduser; W  1 and W  2 are two weighed coefficients. Source withmaximal integrated quality Q total    will be used to update theEKF equations, which will give new estimate about timingand position.  B.    Active Synchronization by RTT  Active synchronization by RTT is a very importantmethod in JTIDS network time dissemination. Compared to passive synchronization by PPLI message, RTT is muchmore effective. It can make the user have good time qualityafter only one slot time, which is 7.8125 milliseconds inJTIDS network, and with very high precision.Generally, the NTR transmits first in any new net andestablishes the system time to which all other unitssynchronize by the exchange of round-trip timinginterrogation (RTTI) and round-trip timing reply (RTTB)messages either directly with the NTR or with another unitalready synchronized to the NTR. RTTIs are very shortmessages containing only the addresses of the interrogator and of the desired donor. The donor responds at a fixed timelater in the same time slot with an RTTR messagecontaining the address of the interrogator and the time of arrival (TOA) of the RTTI as measured on the donor’sclock. The interrogator measures the TOA of the reply andcomputes the adjustment to its own clock necessary to makethe donor’s reported TOA equal the TOA of the reply at theinterrogator.Fig.1 illustrates the message exchange of RTT process.Observation equation of RTT can be expressed by ( ) ( ) ( ) ()2 err i TOA s TOA i t d  = − +     where, err(i) is the interrogator clock error; TOA(s) is thetime of arrival of interrogation on source clock; TOA(i) isthe time of arrival of reply on interrogator clock; t(o) is theslot start time, which is different for interrogator and source; t(d) is the standard reply delay time.A series of RTT transactions over a period of a fewminutes provides an estimate of the interrogator’s clock driftrate; i.e., the frequency error of its clock oscillator and thefrequency error estimate is then used to retune the oscillator driving the clock. The estimation of clock bias and frequencyerrors is carried out in a small Kalman filter which provideserror uncertainties in its covariance matrix.III.   P ERFORMANCE A  NALYSIS AND S IMULATION R  ESULTS  We have presented that time synchronization andnavigation performances are interactive. However, theaccuracy performance of navigation is a complex function of several error sources. So, the use of computer simulation for algorithm design and for performance evaluation isnecessary. Based on a TDMA message distributionmechanism, JTIDS time synchronization modules including passive mode and active mode are designed to test the performance of time dissemination, and relationship betweentime synchronization and navigation error sources isdiscussed too. Fig. 1 Message exchange of RTT process 837  In passive synchronization by receiving PPLI message,an 8 states extended Kalman filter is used. The state vector is ][ vz vyvx Z Y  X bf bt  X  T  =  where, bt  is time offset; bf  is time rate (frequency) offset;  X  , Y  ,  Z  are three relative grid coordinates; vx , vy and vz  are thevelocities in three directions. Considering the nonlinearity of the observation function, the linearized observation matrix isgiven by  −−−−= 000)()()( 0 ct ct ct   R Z  Z  RY Y  R X  X c H   The state transition matrix Φ   and plant noise transitionmatrix Γ    are given by 88 11111111 ×  =Φ T T T T    58 11111 ×  =Γ  T T T   where, T=T  k  -T  k-1 . The plant covariance matrix Q is given by 555242322212 ×  = W W W W W  Q σ  σ  σ  σ  σ    where, 21 W  σ   and 22 W  σ   are clock random walk offsetnoise and clock flicker noise respectively; 23 W  σ   , 24 W  σ    and 25 W  σ   are velocity noise in three directions. Themeasurement noise model V  is a scalar denoted by 2 TOA σ   .Compared to passive synchronization by PPLI message,active synchronization by RTT uses a small basic Kalmanfilter which has only 2 states, bf  and bt  . Other key matrixesare given by [ ] 10  H  =   101 T    Φ=      1001   Γ =      2122 W W  Q σ  σ     =     In our simulations, every terminal user had a initial timeoffset uniformly distributed on [-2ms, 2ms], the initial timerate was selected from a zero mean Gaussian distributionhaving a standard deviation (S.D.) of 10 -8 s/s.  A.    Effect of TOA measurement error  We first analyze the effect of TOA measurement error totime synchronization. Assume the measurement TOA at timek is ˆ T  , the real TOA is T  , and the error is T  ∆ , that is ˆ T T T  = +∆ . By (2) and (4), we get ||11|1 ˆˆˆˆ k k k k k k k O  X X K cT R − − −   = Φ + −     (6)The real state at time k is ||11|111 k k k k k k k k   X X W  − − − − − =Φ +Γ  (7)By (6) and (7), we can get state error at time k  ( ) ( )( ) ( ) ||||11|11|111|11|11|111 ˆˆˆˆˆ k k  kk kk kk kk k k k k k k k Okk k k k k k k k O k   X X X  X X W K cT c T R X X W K cT R K c T  − − − − − − −− − − − − − − ∆ = −=Φ − +Γ + + ∆ −   = Φ − +Γ + − + ∆     (8)In the steady state of Kalman filter, the terms in square brackets will be minimized to zero by sources with highquality level and precise TOA measurement T  . So (8) can beapproximate to | k k k   X K c T  ∆ ≈ ∆  When the sources and user distribute uniformly, and thedistances of them do not change significantly,  K  k    approximate to a constant. In this specific situation, stateerror is in proportion to TOA measurement error. In realsituation, due to the effect of source quality level, positionvariation and the other error sources, state error is not strictlyin proportion to TOA measurement error, but theapproximate proportion relationship still exists.To verify the analysis result above, we made a simulation.There were 15 terminal users in JTIDS network, 1 of themwas NTR, and 3 of them were ground sites which were position references at the same time. The TOA measurementnoise was assumed normal with zero mean, and S.D. variesfrom 10ns to 1000ns. Table I shows the simulation results of S.D. of time bias and navigation circular error probability(CEP) in different S.D. of TOA measurement error. From thedata in the table, we could see that when S.D. of TOAmeasurement error is larger than 100ns, S.D. of time bias andthe navigation CEP are almost linear with S.D. of TOAmeasurement error. When the S.D. of TOA measurementerror is smaller than 100ns, observe noise is not the major error source in timing and navigation error sources anymore,and the linearity does not exist. This simulation results verifyour analysis about the effect of TOA measurement error onthe state error.In real project, in order to have definite timesynchronization accuracy, S.D. of TOA measurement error  TABLE I. E FFECT OF TOA M EASUREMENT E RROR    S.D.TOA_Err a  10 100 500 1000S.D. of Time Bias (ns)   37.1 44.6 314.9 689.9 CEP (m) 51.5 55.0 189.5 369.4 a. Standard deviation of TOA measurement error. 838  has to be controlled within a certain value. Increase bandwidth of receiver and improve SNR will decrease TOAmeasurement error and improve the time accuracy.  B.    Effect of PPLI message receiving rate PPLI message receiving rate is anther important factor which will impact the performance of time synchronizationand navigation. The rate depends on PPLI message sendingrate of terminals and the number of users in the network. Ingeneral, the higher the PPLI message rate, the higher thetime and navigation accuracy.A simulation was made to test the effect of PPLI messagereceiving rate on the performance of time synchronization.The rate varies from 0.2 to 4 messages per second.Simulation results are shown in Table II. When the PPLImessage receiving rate is more than 3 messages per second,it is no longer the major error source in JTIDS timesynchronization. So S.D. of time bias will not decreasesignificantly. C.    Effect of model uncertainty It is well known that Kalman filter is vulnerable to modeluncertainty. It makes the implicitly assumption that themodel and noise character statistic is known perfectly. Sowhen we can not get the real model characteristic, solution of Kalman filter will not be optimal and even diverge.We made a simulation to test the effect of modeluncertainty on the two filters. In our simulation, there weremodel uncertainty in both state and observation equations.The observation noise was assumed zero mean Gaussiandistribution having a S.D. of 10ns, and the uncertainty were10ns. The real S.D. equaled to the sum of assumed S.D. anduncertainty. Simulation results show that the two filters werenot stable when model uncertainty exists. When the proper model can not be obtained, we can use a robust Kalman filter to minimize the effect of unknown parameters in the model[6]. However, computation of robust Kalman filter is morecomplex than the srcinal one.IV.   C ONCLUSION  Time dissemination in JTIDS network is achieved byRTT message and PPLI message. The former is an activemode and often be used by superior users in the network toget accurate time synchronization directly. The latter is more popular with inferior users who do not have enoughtransmission slots. According to the models of the twosynchronization mechanism, RTT filter and navigation filter are designed respectively for active and passivesynchronization mode. Effect of TOA measurement error and PPLI message receiving rate are analyzed and computer simulated. Results show that TOA measurement error isalmost linear with time bias and position error, and it is amajor error source that impact both active and passivesynchronization. PPLI message receiving rate impact onlythe passive mode and its effect is not as significant as TOAmeasurement error when the rate is not very low. Simulationresults show that Kalman filter is vulnerable to the modeluncertainty. A robust Kalman filter can be used at a cost of computation complexity.A CKNOWLEDGMENT The authors wish to acknowledge the contributions of Liu Qiang in providing technical information on thecomputer simulation. They also wish to acknowledge BiZhiming in analysis efforts on JTIDS navigation techniques.R  EFERENCES   [1]   Xude Liu, “Integrated systems of tactical communication, navigationand identification symposium,” Electronic Industries PublishingCompany, 1991.[2]   Myron Kayton, Walter R. Fried, “Avionics navigation systems,” Johnwiley & Sons, Inc., 1997, pp. 284-299.[3]   Walter R. Fried, “Principles and simulation of JTIDS relativenavigation,” IEEE Trans. on Aerospace and Electronics Systems, Vol.AES-14, NO.1, January, 1978, pp. 76-84.[4]   Yongyuan Qin, Hongyue Zhang, Shuhua Wang, “Theory of Kalmanfilter and integrated navigation,” Northwest Industry UniversityPublishing Company, 1993.[5]    Nan Wu, Hua Wang, Jingming Kuang, “Performance analysis andsimulation of JTIDS relative navigation,” Systems Engineering andElectronics, Vol.27, 2005, 464-466, 478.[6]   Lihua Xie, Yingchai Soh, Carlos E. S. “Robust Kalman filtering for uncertain discret-time systems,” IEEE Trans. on Automat. Contr.1994, 39(6), pp. 1310-1314. TABLE II. E FFECT OF PPLI   M ESSAGE R  ECEIVING R  ATE   PPLI rate a (message/s)0.2 b 1 2 3S.D. of Time Bias (ns) 192.1 65.4 39.6 30.5 a. PPLI message receiving rate. b. One message per five second 839
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