1、 l : 2010-09-26Te: .(1982) ), 3,p V 3, E-mai:l bit- wj bit. edu. cn.YT: (1964) ), 3, q,p V 3 =, E-mai:l siliangw bit. edu. cn.31 7 2011 M7 vTransactions ofBeijing Institute ofTechnologyVo.l 31 No. 7Ju.l 2011 / M6s王俊1, 2, 李加琪1, 吴嗣亮1( 11 v0, 100081; 21Yv0, 100044)K 1: a ,t l | M/ o6. M 6 q$ oM.C= M, o
2、M6, . 26.YVw, 29 T._TV ,1oM6s ,o6 !9.1oM: M; ; . 26ms |: TN 953 DS : A cI|: 1001-0645( 2011) 07-0838-06TrackingErrorAnalysis of FLL-Assisted-PLLWANG Jun1, 2, LIJia-qi1, WU S-i liang1( 1. School of Information and Electronics, Beijing Institute ofTechnology, Beijing 100081, China;2. School ofElectron
3、ic and Information Engineering, Beijing JiaotongUniversity, Beijing100044, China)Abstract: To adapt the high dynamic environmen,t satellite navigation receivers often adopt frequency-locked loop (FLL) to assist the phase-locked loop (PLL) for carrier tracking. Based on the classic thirdorderPLL assi
4、sted by second order FLL, the carrier phase tracking error is investigated, which iscomposed of dynamic stress errorand thermalnoise tracking error. The formulae for calculating above twoerrors are derived. Simulation results show that the analysis of carrierphase tracking error is correct andaccura
5、te, and it is helpful to design the carrier tracking loop feather.Key words: FLL-assisted PLL; dynamic stress error; thermalnoise tracking errort l ? l 1t|,4a 1 .t Ma qaoM S4 t. ?,tl l|5T) , M qY 9.,6?|T%. , oM,Y M(PLL)/ . V t l7, /, Mi a ? 5 1.yN, M |Bn . T (FLL), Vv S, a ,.1 K1.t| l/ * | + Mo6, B=
6、 M2.6 | A i. MM M ,7/M1s . 2a q# (Z3 3. PLL V ? H,V ,yN . 2TBM. “ -, M l 4-6, . 2 T Vk. 7, / MM1s 4 , ) N5D B M ?92, 7. uY -,T| M s,w / M6 T.1 / 3 Mt|7,Bo6 m1 U2,= M.m1, P| l q; D (# ) ;N(# ) ; f0 q; fd q;UoM; n(# ) . 2, q N0;N(# )C ; fd q9; tIM HW; HPLL, noM9.m1 MFig. 1 Structure ofFLL-assisted-PLL
7、 k =s b“ v M |I(k) |Q (k) VVU8I(k) = P2D(k)R $S(k) sin P$fd(k)tIP$fd (k)tIcos $H(k) + N I(k), (1 )Q(k) = P2D(k)R $S(k) sin P$fd(k)tIP$fd(k)tIsin$H(k) + NQ (k). (2 )T: $S(k) M9, 6S,# MY; $fd (k) 9; $H(k)M;NI(k)NQ (k)sYM N. 2, PN I = PNQ = (N0 /4)tI, (3 )RN INQ (k) = 0, k I Z. (4 )D2|-k E.1HKD, O 1 pK
8、,| q1| q,TBB) . I n XBB,N ETef(k) =|PtIP. (5 )|Sc = Q(k)I(k - 1) - I(k)Q(k- 1). (6 )|Sd = I(k)I(k- 1) + Q(k)Q(k- 1). (7 )M? s b“TTM ,M,Ip(k) = I(k)cos HPLL (k) + Q(k)sinHPLL (k),(8 )Qp(k) = Q(k)cos HPLL (k) - I(k) sin HPLL (k).(9 )V NTTMkY,kY E V4 2. _ %CostaskME,iS XBB, 9 Tep(k) = sgn(IP )QPP /2 .
9、(10) ro T r“. 2L S| 3 9.K !9 5, 9,= 3 ro 3 Mro sYFFLL (z) = tIX1 tIX1 + 2 1- z- 1Kd, 1Kv, 1 (1- z- 1)2 , (11)FPLL (z) = (2X2 + 2X22tI + X32t2I ) - (4X2 +2X22tI)z- 1 + 2X2z- 2 /Kd, 2K v, 2 (1- z- 1)2.(12)T:K d, 1k 9m;K v, 1 e (NCO)9m; X1 1 q;K d, 2kM 9m;Kv, 2 M e 9m; X2M1 q.2 M6s211 M D 2 V, I nFF rT
10、 H, :B% fe,fe = 1360X21d3Rdt3. (13)yN, 6, M% TB% V,7 M,N HVHe U 0. (14)Y.d M ?, He = d3R /d3tX32 . (15)212 M . 26sY= s 8397 .: / M6s M , m2#m3 U.m2 Fig. 2 M ath modelof digitalFLLm2n1V U l . 2 k . 2;m3wd 1 , nFLL1 . 2, n2 MkY . 2. nFLL (k) = - 2PHFLL (z)n1(k). (16)THFLL (z) .f ,HFLL(z) = FFLL (z) /
11、1+ FFLL (z). (17)m3 / M Fig. 3 M ath modelof digitalPLL assisted by FLLn1(k) V T( 1) (2) ( 5),n1(k) U 12PtI2P D(k)NQ (k)cos $H(k- 1) + D(k- 1)NI(k- 1) sin $H(k) -D(k)N I(k) sin $H(k- 1) - D(k- 1)NQ (k- 1)cos $H(k) +2PD(k)D(k- 1) NI(k- 1)NQ (k) - NI(k)NQ (k- 1) . (18)n2(k) T( 9) (10)n2(k) U 2PD(k)N I
12、(k) sin $H(k) -NQ(k) cos $H(k) . (19)Ls, V s M E(k) U H(k) - tI1- z- 1FPLL (z) E(k) + n2(k) -tI1- z-1 wd(k) + nFLL(k) . (20)| T(16) E(k) U H(k) - tIwd(k)1- z- 1 - tI1- z- 1FPLL (z)E(k) -tI1- z- 1FPLL (z)n2 (k) -2PtI1- z- 1HFLL (z)n1(k).(21)yN, I n. 2,E(k) U-tI1- z- 1FPLL (z)1+ tI1- z- 1FPLL (z)n2(k)
13、 -2PtI1- z- 1HFLL (z)1+ tI1- z- 1FPLL (z)n1(k).(22)l.d M.f HPLL (z) =tI1- z- 1FPLL (z)1+ tI1- z- 1FPLL (z). (23)5E(k) U- HPLL (z)n2 (k) -2PtI1- z- 1 1-H PLL (z)HFLL (z)n1 (k). (24), V M6 . 2var E(k) U QtI/2-tI/2 HPLL (ej2PftI ) 2Sn2 (f)df+ QtI/2-tI/22PtI1- e- j2PftIHFLL( ej2PftI ) 1-HPLL( ej2PftI )2
14、Sn1 (f)df+ QtI/2-tI/22Re HPLL ( ej2PftI )1- HPLL ( ej2PftI ) 2PtI1- ej2PftIHFLL (e- j2PftI )Sn1, n2 (f) df. (25)T: Sn1 (f)k . 2n1 (k) q f; Sn2 (f)kM . 2n2 (k) q f ;Sn1, n2 (f) q f .Sn1 (f) = Ek= -Rn1n1 (k) e- j2PfktI, (26)Sn2 (f) = Ek=- Rn2n2 (k)e- j2PfktI, (27)Sn1n2 (f) = Ek= -Rn1n2 (k)e- j2PfktI.
15、(28)T: Rn1n1 (k). 2n1 (k)1M1f ; Rn2n2 (k). 2n2(k)1M1f ; Rn1n2 (k)n1(k)n2840 v31 (k)WM1f ,sY T(29) (31).Rn1n1 (0) U 12PtI22 2P N04tI+2 4P2 N04tI2,Rn1n1 ? 1 U 12PtI2- 2P N04tI,Rn1n1 (k) = 0, k X 0, ? 1.(29)Rn2n2 (0) = 2P N04tI,Rn2n2 (k) = 0, k X 0.(30)Rn1n2 (0) = 12PtI2PN04tI ,Rn1n2 1 = - 12PtI2PN04tI
16、 ,Rn1n2 (k) = 0, k X 0, 1.(31)z= ej2PftI var E(k) U R2E, 1 + R2E, 2 + R2E, 3 + R2E, 4. (32):R2E, 1 = N02PtI12Pj Rz = 1HPLL (z)HPLL z- 1 z- 1dz;(33)R2E, 2 = N02PtI12Pj Rz = 1(1-H PLL (z)HFLL (z) 1-H PLL (z- 1)HFLL (z- 1)z- 1dz; (34)R2E, 3 = 12 N0PtI2 12Pj Rz = 1 1-HPLL(z) HFLL (z) 1-HPLL z- 1 HFLL z-
17、 1 11- z- 111- zz- 1 dz; (35)R2E, 4 = N0PtIRe 12Pj Rz = 1HPLL (z)1- HPLL (z- 1 )HFLL (z- 1) z- 11- z(1- z- 1)dz . (36)T( 33) .d M . 2 T,RE, 1 = 3602P BnC /N0. (37)T: BnV U Mr. 2 z; C /N0V U l|.1.7 T(34) (35) (36) V = p,ZEe,9 T M, T(34) , !9 p, tIBtQ ? T( 38) UT.R2E, 2 U N02PtIt3IX21 3X51 + 6X21(X31
18、+ 2 2X21X2 + 4X1X22 + 2 2X32 ) + 2X2(4X41 + 2 2X31X2 + 5X21X22 +8 2X1X32 + 4X42) 6 2 X61 + 2 2X51X2 + 4X41X22 + 2(1+ 2)X31X32 + 4X21X42 + 2X1X52 + X62 . (38)m4 _Fig. 4 Structure of simulation programsVr TV, O ? , v,yN !9Kz 9 p.3 _Ts + MM He . 2RE,wT.C s ,M He . 2REsY_.Matlab q_, !9_ m4 U.m4, q.1 !,
19、3 .2 |; 3B H,i N H|T ;| E,T ,yNi ;“ H es b“;s b“TTk ) ,kYTT ro) , q9fd (k),fd(k)YVNCOCo|T/M ) ,LC ;s b“TTM;MTTkM,|kMT ro , 8417 .: / M6s MNCO q3,NCO 3M9s b“T, LC M. d9vl, !B v l| LMH(k), MM F,i kMTT , d9MW,QM6 ?.311 s_ !FF ,10g/s;F. 2; MT, z !5Hz, M z !18Hz, V m5 U6T.m5 6 T wLFig. 5 Tracking curve o
20、f the loopm5 Vn, h“ vs , :4HzP q , MN$ ?6M, O :M0,7 MT, T(15)9 M14b.312 . 26s_ !% q, O S ;.1 !35 51 dB# Hz,.1/ . 26; MT, z !5Hz, M z !18Hz.m6 U.1M . 21“ wL,m6 Vn,_ wL w wL, .1 H Y, NS =T H ,kY . 2+? 3M.yN,?TS =,1FLL+PLLo6 . 2s .6,? . 26sS /_: !% q, O S ;.1!41 dB# Hz; MT, z%5Hz, M z !5 60m6 .1M . 21“
21、 wLFig. 6 Influence of inputCNR on the thermalnoisetracking errorHz, M z . 26Y,m7 M zM . 21“ wL.m7 M zM . 21“ wLFig. 7 Influence ofPLL bandw idth on the thermalnoisetracking errorm7 Vn: _ wL w wL; 6 “ M z9M t ,i“l.sCly T( 25)C 1-HPLL (# ),yNM . 2 M. 2 zhl7B. . 26sS /_: !% q,7 O S ;.1 !41 dB#Hz; MT,
22、M z%18Hz, z !2 20Hz, z .26Y, m8 U.m8 zM . 21“ wLFig. 8 Influence ofFLL bandw idth on the thermalnoisetracking errorm8 Vn,_ wL w wL,6 “ zM9 t ,842 v31 y T(25)iHFLL (# ).4 o6 Z 7,s M He . 2RE,w T,_w T .yN, T Vt loM6 !9#4 I, 1 N Llil. ID: 1 W ard P W. Performance comparisons between FLL, PLLand a novel
23、 FLL-assisted-PLL carrier tracking loop underRF interference conditions C M Proceedings of The 11thInternationalTechnicalM eeting of The SatelliteD ivision ofThe Institute of Navigation. Nashville, USA: s. n. ,1998: 783-795. 2 Kaplan E D. GPS M . i,r.:0, 2006.Kaplan E D. Understanding GPS, principle
24、s and applica-tions M . Kou Yanhong, trans.l Beijing: PublishingHouse ofElectronics Industry, 2006. ( in Chinese) 3. GPS l !9M .:0, 2008.X ieGang. Principles ofGPS and receiver designM . Be-ijing: PublishingHouse of Electronics Industry, 2008. ( inChinese) 4 V iterbiA J. Phase-locked loop dynam ics
25、in the presence ofnoiseby Fokker-Planck techniques J. Proceedings of theIEEE, 1963, 51( 12): 1737-1753. 5 W. M #M .:a , 1990.Cheng Shiwe.i Principles and application of PLLM . Be-ijing: O rdnance Industry of Publishing House, 1990. ( inChinese) 6 ZhuangW. Performance analysis ofGPS carrier phase ob-
26、servable J. IEEE Transactions on Aerospace and Electron-icSystems, 1996, 32( 2): 754-767. 7 PratapM israP E. o“d:|a ?M ., ,oa,r.:0, 2008.PratapM israP E. G lobal positioning system, signa,l meas-urements, and performanceM . LuoM ing, Cao Chong,X iao Xiongbing, trans.l Beijing: PublishingHouse ofElec
27、-tronics and Industry, 2008. ( in Chinese) 8 Julien O. Design of Galileo L1F receiver tracking loops D. Calgary, Canada: University ofCalgary, 2005. 9 . . r|) E D.: v, 2005.Jin Junkun. Researches on the signalprocessor of a dockingand rendezvous radar w ith PN code modulated continuouswaveD. Beijing: School of Information Engineering, Be-ijing Institute ofTechnology, 2005. ( in Chinese)(责任编辑:刘芳)8437 .: / M6s
