Instantaneous Cycle-Slip Detection and Repair of GPS Data Based on Doppler Measurement

Transcription

1 Intantaneou Cycle-Slip Detection and Repair of GPS Data Baed on Doppler Meaurement Zhoufeng Ren, Liyan Li, Jie Zhong, and Minjian Zhao Abtract In GPS receiver, carrier phae meaurement can be ued to improve the receiver poition accuracy. In order to maintain the accuracy, cycle-lip mut be detected and repaired intantaneouly and accurately. Thi paper firt analyze the implementation cycle-lip detection and repair method of GPS data baed on Doppler meaurement. Then introduce a implified ocillator model. Baed on the ocillator model, a modified method i propoed, which avoid the influence of the local ocillator bia. Data tet how that the root mean quare error of the time-difference meaurement reidual baed on the propoed method i mall enough for detecting and repairing the cycle-lip intantaneouly. Index Term Cycle-lip, Doppler meaurement, GPS data, intantaneou. I. INTRODUCTION GPS i rapidly replacing mot of the traditional urveying technique and i widely ued in daily life. Thi i due to the great flexible condition of uing thi ytem, lie no time limitation, un-neceity of inter-viibility and un-limitation for the eparation between urveyed point, free of charge etc. With the continuou progre of GPS Modernization, the economy, high preciion and high reliability of the GPS receiver ha become more and more popular. In order to obtain accurate poitioning, carrier phae meaurement i uually ued in poitioning. In addition to the initial integer ambiguity of the carrier phae meaurement, cycle-lip i till a big challenge compared with the peudo-range meaurement. Cycle-lip i dicontinuity of an integer number of cycle in the meaured carrier phae reulting from a temporary lo-of-loc in the carrier tracing loop of a GPS receiver. The caue of the cycle-lip are lited a below []: ) Cycle-lip i caued by obtruction of the atellite ignal due to tree, building, bridge, mountain, etc. ) Cycle-lip i a low ignal-to-noie ratio (SNR) or alternatively carrier-to-noie-power-denity ratio (C/N0) due to bad ionopheric condition, multipath, high receiver dynamic, or low atellite elevation angle. 3) Cycle-lip i a failure in the receiver oftware which lead to incorrect ignal proceing. The occurrence of cycle-lip affect not only the current meaurement, but alo the following epoch. It eriouly degrade the poitioning accuracy. In order to attain contant Manucript received January, 0; revied February 9, 0. The paper i upported by the Fundamental Reearch Fund for the Central Univeritie. Z. Ren, L. Li, J. Zhong and M. Zhao are with the Department of Information Science and Electronic Engineering of Zhejiang Univerity, China( longgo00@gmail.com; zhongjie@zju.edu.cn; erilee@zju.edu.cn, mjzhao@zju.edu.cn). high-preciion poioning reult, cycle-lip mut be detected and repaired or handled with carrier phae meaurement at the data proceing tage. Currently, many method are ued to detect and repair cycle-lip, uch a polynomial fitting, high-order difference method, combination method of peudo-range and carrier phae, ionophere reidual method and o on[]. But thee method have their own diadvantage: Polynomial fitting can be ued for ingle or dual frequency meaurement in pot-proceing, but it can t be ued in real-time cycle lip detection. High-order difference method can t detect mall cycle-lip, which i fit for pot-proceing. The ionophere reidual method mut be ued in dual-frequency receiver and cannot indicate on which channel the cycle-lip tae place. The combination method of peudorange and carrier phae depend on the preciion of peudorange completely which can t identify mall cycle-lip. Doppler meaurement i the intantaneou change rate of carrier phae. It i a very robut meaurement. Therefore, Doppler meaurement i an alternative way to detect and repair cycle-lip. However, in practice, the ocillator i a non-ideal cloc ource. The deviation in ocillator may reult in Doppler meaurement error. The intantaneou cloc deviation etimation i not an eay wor. The ocillator error of the receiver will be appeared in the Doppler-aided cycle-lip detection and repair method (DCDRM). Baed on the relationhip between Doppler meaurement and carrier phae meaurement, thi paper propoe a new method called modified Doppler-aided cycle-lip detection and repair method (Modified DCDRM), which avoid uing the corrected Doppler meaurement and actual integration time to detect and repair the cycle-lip. II. INSTANTANEOUS CYCLE-SLIP DETECTION TECHNOLOGY A. Doppler-Aided Cycle-Slip Detection and Repair Method The carrier phae meaurement equation can be written a[3]: Φ = Φu Φ + N ( r I + T) c = + ( δtu δt) + N + εφ λ λ Φ i the meaured carrier phae; Φ u i carrier phae generated by receiver; Φ i carrier phae arriving from atellite; λ i the carrier wavelength; r i the geometry range from receiver to GPS atellite; () 9

2 I and T are the delay of L carrier phae due to ionophere and tropophere repectively; c i the peed of light; δt u i the bia in receiver cloc; δt i bia of the GPS atellite cloc; N i the initial integer ambiguity; ε Φ i phae noie. Mae difference between adjacent epoch. The time-difference meaurement of carrier phae i decribed a: ( dr di + dt ) c ( dδtu dδt ) dφ = + + dn + dε Φ λ λ () dφ i the time-difference meaurement between adjacent epoch; di and dt are the variation of ionophere and tropophere delay repectively; dδt u, dδt i the variation of local, atellite cloc bia; dr i the variation of geometry range from receiver to GPS atellite; dn i the cycle-lip. Doppler meaurement i immune from cycle-lip. So dr can be derived from Doppler meaurement at adjacent epoch. ˆ f ( ) + f ( ) dr = λφ ( ) = λ f dt λt d0 d0 d d0 a Φ ˆ ( ) d i the variation of geometry range from receiver to GPS atellite in the form of phae; f d0 i the true Doppler frequency; T a i the true integration time in GPS time. A revealed in (), the dr hould be removed to etimate the ize of the cycle-lip. Uing the (3), the time-difference meaurement reidual (TDMR) δφ can be repreented a: δφ = Φ = + ε ' dφ ˆd dn Φ ' dr ˆ ( di + dt ) c εφ = Φd + ( d δ t u d δ t ) + d ε λ λ λ Φ (4) (3) (5) E(.) and Cov(.) are mathematical expectation and variance-covariance operator, repectively. Since there i no redundancy to carry out tatitical teting in real-time operation for () and (7). They have to be calculated through adaptive etimation. The mean value of TDMR δφ and it root mean quare error (RMSE) σ i δφ = δφ + ( δφ δφ ) (8) σ = ( ) σ δφ δφ + (9) δφ i the mean value of δφ from epoch to ; σ i the covariance of TDMR at epoch. The detection of cycle-lip i baed on (0) δφ δφ p σ (0) p i a cale factor of the threhold value which can define the ability to detect the cycle-lip. When cycle-lip i detected, the next tep i to determine it ize. Cycle-lip can be repaired by the implet way when the ampling interval i hort enough. That i dn = round( δφ δφ ) () round( ) i a mathematical function which get the nearet integer of the variable. B. Ocillator Model A the local cloc ource i non-ideal, it will introduce the ocillator error into TDMR, maing it much tougher to detect and repair mall cycle-lip. An ocillator model ha to be introduced into the modified DCDRM to avoiding the ocillator error. The performance of frequency ource i decribed by it accuracy and tability. Ideal ocillator tay at it nominal frequency in the life cycle. In fact, due to reonator aging, environmental influence uch a vibration, temperature, preure and humidity, will bring ytematic bia and random error to frequency ource. It can modeled a [4] The variation of atmopheric delay, atellite orbit bia, multipath, and receiver ytem noie are to be more or le below a few centimeter a long a the obervation ampling interval i relatively hort, which i much le than one cycle-lip. Once the TDMR of current epoch i much maller or larger than the average of TDMR, we can ay that there i a cycle-lip at current epoch. Conider the firt two moment of TDMR in (4): ' E( δφ ) = dn + E( ε Φ ), =, ' Cov( δφ ) Cov( εφ ) () = (7) f () t = f +Δ f + ( t t ) f + f () t () 0 0 f 0 i the nominal frequency; Δf i the frequency bia; f i a frequency drift; f i a random frequency. Reference [5]-[7] point out that ordinary ocillator ha good tability in a hort time. And the main error of the ource i frequency bia. The ocillator model can be implified a 97

3 f = f +Δ f = ( + β ) f (3) a n n f n i the nominal frequency; f a i the actual frequency; β i a cale factor of the frequency bia. The relationhip of ampling interval T n which i timing at the nominal frequency and the actual time T a i lited: T = T /( + β ) (4) a n So the true Doppler frequency will be f = ( + β)( f + δf + f ) f d0 R0 i0 d R0 According to (), TDMR can be expreed a dφ( ) = Φ( ) Φ( ) = ( Φ ( ) Φ ( )) ( Φ ( ) Φ ( )) u u = T f ( Φ ( ) Φ ( )) a R0 (7) (8) f = f + f R R0 d0 f l0 f Φ u (), Φ () are carrier phae generated in receiver and carrier phae arriving from atellite at epoch ; T a i the actual ampling interval. From (3) and (7), Φ ˆ ( ) can be repreented a d f d f i f i0 δ f i0 ˆ fd0( ) + fd0( ) Φd() = fd0dt Ta = [( + β)( f + δf + ( f ( ) + f ( ))) f ] T = ( fr 0+ δ fi0+ ( fd( ) + fd( ))) Tn+ fr 0 Ta R0 i0 d d R0 a (9) According to (8) and (9), we have Fig.. Generic receiver functional bloc diagram. C. Modified DCDRM Sytem level functional bloc diagram of a generic receiver i hown in Fig.. The generic receiver conit of the following 8 function bloc[8]: antenna, preamplifier, reference ocillator, frequency yntheizer, down-converter, an intermediate frequency (IF) ection, ignal proceing and navigation proceing. The radio frequency ignal down-convert to intermediate frequency ignal. And then in the digital ignal part, the intermediate frequency convert to bae band ignal. Conider an ideal ocillator model, which mean f = f n, then the ocillator correction will be zero. Then the Doppler meaurement will be f = f f f = f f = f (5) d R l0 i0 R R0 d0 f d i the Doppler meaurement baed on f n ; f R i the received atellite ignal frequency, which contain the atellite ending frequency f R0 and the true Doppler frequency f d0, and they atify f R = f R0 +f d0 f l0 and f i0 are the local ocillator frequency ued to down-convert the atellite ignal, the relationhip i f l0 + f i0 = f R0. When the frequency ource i not an ideal frequency ource, according to (3), there will be a mall deviation Δf, and f = ( + β)f n. All the frequency baed on f n will be biaed. The relationhip between the atellite ignal and the local ignal will be: f = f + f = ( + β)( f + f + δ f + f ) () R R0 d0 l0 i0 i0 d δφ = dφ Φˆ d = ( fr0+ δ fi0+ ( fd( ) + fd( ))) Tn ( Φ( ) Φ( )) (0) From (0), we find that in the calculation of TDMR, it ue the raw data of carrier phae arriving from atellite, Doppler meaurement baed on f n obtained from the ignal proceing bloc and the nominal ampling interval. It avoid correcting the local ocillator. And alo it avoid introducing the ocillator error into the TDMR. It implifie the computation and obtain a higher accuracy TDMR.. III. DATA TEST In order to illutrate the performance of our approach, we have teted it with data et in tatic and inematic mode. Static mode tet i carried out in May 7, 0 at Yuquan Campu of Zhejiang Univerity, uing a dual frequency receiver. Kinematic mode tet i baed on a ignal imulator and the dual frequency receiver. Three dataet are collected in the tet. The characteritic of the dataet i hown below: ) Group one: It i a Static mode tet. The receiver i fixed to place. ) Group two: It i carried out in a uniform linear motion with a relative peed of -500 m/. 3) Group three: It i carried out in a linear motion with a contant acceleration m/. In tatic mode tet, we choe PRN and PRN9 to analyze the performance of thi approach. The SNR of PRN i about 40 db-hz, while the SNR of PRN9 i 49 db-hz. The mean value and the RMSE of TDMR are hown 98

4 in Table I. In inematic mode tet, we choe PRN and PRN to analyze the performance. The SNR of thi two atellite are both 4 db-hz. The mean value and the RMSE of TDMR are hown in Table II. TABLE I: THE TDMR IN STATIC MODE TEST Sampling interval () PRN PRN 9 ( ( of the noie of TDMR i in 3 time σ. So we can et p to 3 in (0) to detect and repair the carrier phae cycle-lip. And then we found that the ampling interval mut be maller than econd to detect and repair one cycle-lip according to Table I Table II and Table III. And the mall the ampling interval i the accuracy to detect and repair one cycle-lip i. TABLE II: THE TDMR OF THE GROUP TWO DATASET Sampling interval () ( PRN PRN ( (a) The ditribution of TDMR in group one. TABLE III: THE TDMR OF THE GROUP THREE DATASET Sampling interval () ( PRN PRN ( (b) The ditribution of TDMR in group two. Table I how that the horter the ampling interval i, the maller the RMSE of the TDMR i. That i becaue time-difference meaurement i not a linear function of Doppler frequency. It i an integration of the Doppler frequency. While in thi method, an approximation i made by uing the trapezoidal integration method, which mae the RMSE of TDMR increae larger a ampling interval increae. It alo hown that the RMSE of PRN9 i maller than the RMSE of PRN at the ame ampling interval, which i due to the larger SNR of PRN9. Compared with Table I, Table II and Table III how that the noie of TDMR in inematic mode i ignificantly larger than in tatic mode at the ame ampling interval. The ame SNR of the different atellite almot have the ame TDMR at the ame ampling interval. The ditribution of TDMR without cycle-lip i hown in Fig., there are 5000 ample at 0. ampling interval in each graph. Fig. how that the TDMR of the three tet atify none-zero mean Gauian ditribution. Over 98.% (c) The ditribution of TDMR in group three. Fig.. The ditribution of TDMR in tatic and inematic mode. (a) TDMR of PRN in Group one at the ampling interval of

5 (b) TDMR of PRN in Group two at the ampling interval of 0.5. (a) TDMR of PRN repaired cycle-lip in Group one. (c) TDMR of PRN in Group three at the ampling interval of. Fig. 3.TDMR with cycle-lip at 30 0 and 370 with different ampling interval. To tet thi approach, we manually inerted, -3, 5 cycle-lip eparately into the carrier phae meaurement of PRN in Group one dataet at the ampling interval of 0. econd, PRN in Group two dataet at the ampling interval of 05 econd, and PRN in Group three dataet at the ampling interval of econd at the time of 30, 0 econd and 370 econd. The TDMR of the atellite are hown in Fig.3. Fig.3 how that large cycle-lip are abrupt. We can detect them eaily. The mall cycle-lip may be buried in the noie at large ampling interval. A hown in Fig.3 (c), we can t identify the cycle-lip at the time 30 econd. But we can find the cycle-lip in Fig.3 (a) due to the mall ampling interval. When we detect the cycle-lip, we can ue () to determine it ize. We ue the propoed method to detect and repair the cycle-lip of the PRN, PRN and PRN. The reult are lited in Table IV Table IV how that we detect and repair all the cycle-lip at the ampling interval of 0. and 0.5. While at the ampling interval of, we doen t detect one cycle-lip at the epoch of 30. It prove that if we want to detect mall cycle-lip, the ampling interval mut be maller than econd. When the cycle-lip are repaired, the TDMR of the atellite are hown in Fig.4. PR N TABLE IV: RESULT OF THE APPROACH EPOCH TDMR MEAN RMSE CYCLE-SLI P (b) TDMR of PRN repaired cycle-lip in Group two. (c) TDMR of PRN repaired cycle-lip in Group two. Fig. 4. TDMR of the atellite repaired cycle-lip. IV. CONCLUSION In thi paper, we firt analyze the implementation of DCDRM. Then a modified method i propoed baed on a implified ocillator model. In thi method, the etimation of ocillator bia i removed. The tet reult how that the mean value of TDMR i relatively robut, and it RMSE i rarely mall at high ampling rate. The cycle-lip can be detected and repaired by rounding δφ - δφ a long a ampling interval i hort enough. Tet reult alo how that the RMSE of TDMR i larger in inematic than in tatic mode. We can chooe high ampling rate when the receiver i in inematic mode. 00

6 ACKNOWLEDGMENT The author would lie to acnowledge the excellent review of the entire manucript by Zhaodi Liu. REFERENCES [] K. Donghyun and L.R. B, Intantaneou real-time cycle-lip correction for quality control of GPS carrier-phae meaurement. Vol. 49. Manaa, VA, ETATS-UNIS: Intitute of Navigation [] L. Zhenun, GPS dynamic cycle lip detection and correction with baeline contraint. Journal of ytem engineering and electronic, 0(): p [3] E. Kaplan, Undertanding GPS: Principle and Apllication, ed. S. Edition [M]. Boton: Artech Houe Inc [4] P. Mira, Global Poitioning Sytem:Signal, Meaurement, and Performance. Second Edition ed. 00. [5] W. David Allan, N. A, and C. Clifford Hodge, The Science of Timeeeping Application Note [] Y. Cao, Realization of GPS Satellite Time' Sampling and Verification of Local Time. Electronic Technology, 9(): p [7] Y. Kou, a Method for Simulating the Crytal Ocillator Error in GPS Receiver. Journal of Electronic and Information Technology, (8): p [8] W. Bradford Parinon, J. J. S, Global Poitioning Sytem: Theory and Application, Vol. I. Zhoufeng Ren wa born in Jingning, Zhejiang Province, China in 984. He received hi bachelor degree of Communication Engineering from Zhejiang Univerity in 007 China. After two year wor, he continue to tudy in college. He i currently a mater tudent in Department of Information Science and Electronic Engineering of Zhejiang Univerity, he wa doing reearch on GPS poitioning and ignal imulator. 0