Poitioning, 14, 5, 1-1 Publihed Online February 14 (http://www.cirp.org/ournal/po) http://dx.doi.org/1.436/po.14.51 Multipath Error Analyi of COMPASS Triple Frequency Obervation Xuying Ma 1, Yunzhong Shen 1, 1 College of Surveying and Geo-Informatic, Tongi Univerity, Shanghai, China; Center for Spatial Information Science and Sutainable Development, Tongi Univerity, Shanghai, China. Email: voldemortpotter@ina.com, yzhen@tongi.edu.cn Received November 11 th, 13; revied December 4 th, 13; accepted December 11 th, 13 Copyright 14 Xuying Ma, Yunzhong Shen. Thi i an open acce article ditributed under the Creative Common Attribution Licene, which permit unretricted ue, ditribution, and reproduction in any medium, provided the original work i properly cited. In accordance of the Creative Common Attribution Licene all Copyright 14 are reerved for SCIRP and the owner of the intellectual property Xuying Ma, Yunzhong Shen. All Copyright 14 are guarded by law and by SCIRP a a guardian. ABSTRACT The BeiDou- atellite navigation ytem broadcat triple frequency data. In thi paper, the peudorange multipath i extracted by uing the geometry-free and ionophere-free combination of one peudorange and two phae meaurement, and the phae multipath i extracted by uing triple frequency phae meaurement, repectively. By uing everal day tatic obervation data, we exact the noiy peudorange and phae multipath of three type of atellite, GEO, IGSO and MEO atellite. Becaue of the low frequency characteritic of the multipath, the low frequency wavelet filter i further ued to recover the high-preciion low frequency multipath ignal that are pecified by their amplitude, period and phae. The reult how that the multipath period are about 8616, 86158 and 46391 for GEO, IGSO and MEO atellite, repectively, which coincide with that of the correponding atellite orbit. Then we ue the extracted multipath ignal to correct the peudorange meaurement in order to improve the accuracy of point poitioning. The poitioning accuracy in Eat-Wet direction can be ignificantly improved by uing the multipath corrected peudorange meaurement, and in the other two direction the poitioning accuracy can alo be improved to ome extent. KEYWORDS BeiDou- (COMPASS); Multipath; Wavelet Filtering; Single Point Poitioning 1. Introduction The BeiDou- (COMPASS) atellite navigation ytem will provide regional ervice in China and it urrounding area in 1. Since the multipath cannot be eliminated via combined or differential GNSS obervation, they are uually uppreed by uing choke antenna and other hardware device, or computed and then corrected to the meaurement [1-3]. In recent year, Feng et al. [1] conducted a preliminary invetigation on the multipath of BeiDou- atellite. Wu and Zhou [4] extracted peudorange multipath of GEO and IGSO atellite and corrected them to improve the preciion of ingle point poitioning. The triple frequency carrier phae meaurement can form both geometry-free (GF) and ionophere-free (IF) combination, which only contain the combined phae multipath and random obervation error [6]. Montenbruck et al. [7] ued thee combination to analyze the triple frequency phae and peudorange noie of BeiDou- atellite. After denoiing proceing of the multipath, in thi paper we will extract the multipath of peudorange and phae from peudorange and carrier phae combination and triple frequency carrier phae combination, repectively, then correct the extracted multipath to peudorange meaurement to carry out point poitioning.. Multipath Extraction Beide receiving ignal tranmitted by atellite directly, GNSS receiver alo receive the indirect ignal reflected from the obect nearby receiving antenna at the mean time. The error produced by overlapping ignal are known a multipath. A hown in Figure 1, S repreent the direct ignal received by GNSS receiver, S' the indirect ignal reflected
Multipath Error Analyi of COMPASS Triple Frequency Obervation 13 Figure 1. BeiDou- multipath generation mechanim. from the urrounding urface feature. θ i the angle between reflecting obect and indirect ignal and D i the ditance between reflecting obect and receiver antenna. An indirect ignal ha longer than a direct ignal by ( ) D 1 co θ inθ ; thereby thee indirect ignal will contaminate the direct peudorange and carrier phae meaurement and reduce the poitioning accuracy of BeiDou- atellite navigation ytem [4,5,8]. The obervation equation of peudorange and carrier phae read: ( t + t ) P = ρ + t dt d + T L + + + ε I f M p ( t t t + t ) = ρ + δ δ + + + + ε I f m N where, P i and L i repreent the peudorange and carrier phae of frequency fi ( i = 1,, 3), repectively, ρ i the ditance between GNSS receiver and atellite ; Δt and Δt are the receiver and atellite clock error; δt and δt denote the frequency-dependent receiver and atellite hardware biae for phae, while dt and dt for code; T and I repreent the tropophere and ionophere delay; λ and N repreent the phae wavelength and ambiguity including the initial phae biae of receiver and atellite, M and m repreent multipath of peudorange and phae, repectively, ε p and ε ϕ repreent the peudorange and carrier phae meaurement error repectively. It i emphaized that all term in (1) are in unit of meter. To exact the peudorange multipath, one need to eliminate all geometric and ionopheric term. In general, the geometry-free and ionophere-free combination i formed uing one peudorange and two phae. With lo of generality, let u form the geometry-free and ionopherefree combination by uing the ith frequency peudorange ϕ T (1) and the th and kth frequency phae, the combination i a follow: ( α βk ) M = P L + L () i i k Here, according to the condition that the combination i both geometry-free and ionophere-free, the coefficient are olved: ( ) ( ) ( ) ( ) f f + f f f + f α = = f f f f f f i k k i, β k i k i k Obviouly, α + βk = 1. Subtituting (1) and (3) into () yield M i = Mi + δ N k + m k + ε p αε βε (4) k where m = α m + β m k k k k = α + βk k N N N t ϕ ϕk ( d dt ) ( t ) k ( k tk) δt = t α δt δ β δt δ It i well-known that the inter-frequency hardware biae are very table in time for both receiver and atellite. Thereby, δ t can be deemed a contant. Moreover N k i contant a well if there i no cycle lip happen. Conidering the multipath i periodic and can be average out over a period of n epoch. Therefore the contant can be etimated a M i = M i ( t) n. Then the etimated peudorange multipath i M = M M (6) i i i Auming that the preciion of phae i unique for different frequencie, i.e., σϕ = σ ϕ = σ k ϕ and alo conidering the effect of phae multipath ( σ m ϕ ), then the preciion the exacted peudorange multipath i ( + )( + ) Mi pi k ϕ mϕ (3) (5) σ = σ + α β σ σ (7) In thi paper, we ue the above method to exact the peudorange multipath of triple frequency. The phae multipath cannot be aeed uing triple carrier phae meaurement [4,7]. We firt form two ionophere-free combination from two pair of carrier frequencie, then ubtract the reult from each other and obtain the geometry-free and ionophere-free (GF-IF) combination a follow [6,7,1]: f f DIF ϕ ϕ ϕ ϕ ϕ 1 3 1 = 1 f1 f f1 f f1 f3 ϕ 1 ϕ 3 f1 f3 f1 f3 (,, ) = M M + N N 1 13 1 13 (8)
14 Multipath Error Analyi of COMPASS Triple Frequency Obervation where, DIF denote the GF-IF combination. M 1 and M 13 are multipath combination of B 1,B and B 1,B 3. N 1 and N 13 are ambiguity combination of B 1,B and B 1,B 3. The combination in (8) are formed by carrier phae meaurement, o we hould detect cycle lip before ubequent analyi. If cycle lip were found, we mark it and make thee data a a egment. In a data egment of no cycle lip, the GF-IF combination mainly conit of receiver meaurement error and multipath on the repective frequencie plu a contant determined by the carrier phae ambiguitie. In the cae of no cycle lip the ambiguity i a contant and eay to handle [11]. Therefore the combination (8) can be ued to evaluate the phae multipath. The carrier phae meaurement error and phae multipath are with the ame order, and linear combination will amplify meaurement error, o denoiing proceing can be utilized to extract more accurate phae multipath. 3. Characteritic of Multipath Experimental data are collected by BeiDou- multi-frequency receiver at 3 tation, CCHU, CKUN and CWUQ, the ampling interval i 1. In thi paper we utilize conecutive day meaurement from October 11, 11 to October 13, 11 and from July 4, 1 to July to carry out analyi. 3.1. Multipath of Different Station Different receiver urrounding lead to the numerical difference of multipath. By proceing 4 hour (Oct 11, 11) meaurement of 3 tation, we have extracted the multipath of B 1, B and B 3 frequency peudorange and geometry-free and ionophere-free phae combination for the GEO atellite C1 from each individual tation. Figure demontrate 4-hour peudorange multipath of C1 atellite of B 1, B and B 3 frequencie for three tation. Figure 3 demontrate 4-hour phae multipath of C1 atellite for three tation. A illutrated in Figure, the peudorange multipath i in meter-level variation. It i alo oberved that the peudorange multipath differ ignificantly from the different frequencie, epecially at CKUN tation. Moreover, the peudorange multipath time erie i tation (location) dependent. Their behavior i completely different from the tation. For intance, the peudorange multipath at CCHU tation i motly within.5 m, while at CKUN tation the peudorange multipath are larger and the maximum error can be up to m. The multipath can alo reflect the quality of obervation data for each tation indirectly. A illutrated in Figure 3, the phae multipath i in centimeter-level variation. Comparing Figure and Figure 3, phae multipath i ignificantly mall and can be neglected compared to peudorange multipath. 3.. Peudorange Multipath of Different Type of Satellite BeiDou- navigation atellite contellation conit of three different type of atellite: GEO, IGSO and MEO atellite. A we know, the multipath i affected due to the reflection of the environment nearby the receiver. The atellite contellation i periodic uch that after a certain period time, the receiver can uffer the baically ame obervation environment. A a reult, the imilar multipath can be introduced. To addre thi iue latter from our exacted peudorange multipath, we firtly compute the theoretical period of the different type of atellite. The theoretical period i computed baed on the mean motion velocity n a T = π n, where n i computed a 3 n = GM a + n. (9) where GM i the Earth, a and n are the emimaor axi of orbit ellipe and the perturbation of mean velocity, both of them come from broadcat ephemeri [15]. The orbital period of thee three different atellite type are about 86164, 86164 and 4639, repectively. We have extracted the peudorange multipath of GEO, IGSO and MEO atellite at CCHU tation uing the data oberved from Oct. 11, 11 to Oct. 13, 11 and Jul. 1 to Jul. 3 1, repectively. The reult are hown in Figure 4, Figure 5 and Figure 6 for GEO, IGSO and MEO, repectively. A illutrated in Figure 4, the peudorange multipath of GEO atellite ha ignificant periodic characteritic. In Figure 5, the periodicity characteritic of IGSO atellite are not a obviou a GEO atellite. In Figure 6, ince the unique orbital period of MEO atellite, the viible time i potponed about hour related to yeterday, we extracted the multipath of relative time of three conecutive day. The periodicity characteritic of three type atellite are different, becaue the repeatability of multipath i contingent on the repeatability of geometric relationhip between the atellite, receiving antenna and the urrounding environment. Thee three figure alo certificate the concluion mentioned in [4] that: The multipath of GEO atellite preent low-frequency change, while the IGSO and MEO atellite preent highfrequency change. With an appropriate time hift to align geometric repeatability the contructed multipath correction profile can be applied to correct the meaurement for another day [1]. We preent two program for dicovering the repeat time, one uing the pectrum analyi and the other the cro correlation of adacent day multipath time erie. Both method how that the repeat time i highly
Multipath Error Analyi of COMPASS Triple Frequency Obervation 15 B1 B B3 CCHU C1-6 1 18 4 CKUN C1-6 1 18 4 CWUQ C1-6 1 18 4 Figure. Daily peudorange multipath of three frequencie B 1 (green), B (blue) and B 3 (red)..5 CCHU C1 -.5 6 1 18 4.5 CKUN C1 -.5 6 1 18 4.5 CWUQ C1 -.5 6 1 18 4 Figure 3. Daily phae multipath. Oct 11, 11 Oct 1, 11 Oct 13, 11 C1-6 1 18 4 C3-6 1 18 4 C4-6 1 18 4 Figure 4. Time erie comparion of three day B 1 frequency multipath of GEO atellite.
16 Multipath Error Analyi of COMPASS Triple Frequency Obervation 1-1 Oct 11, 11 Oct 1, 11 Oct 13, 11 C7-4 6 8 1 1-1 C8-4 6 8 1 Figure 5. Time erie comparion of three day' B 1 frequency multipath of IGSO atellite. 1.5 1 July 1, 1 July, 1 July 3, 1 Station:CCHU Satellite: C11.5 -.5-1 -1.5 -..4.6.8 1 Figure 6. Time erie comparion of three day B 1 frequency multipath of MEO atellite. correlated with atellite orbital period. Carrying out the fat Fourier tranformation (FFT) to the B 1 frequency multipath time erie of C1, C3 and C4 atellite at CCHU tation for three conecutive day (Oct. 11, 11-Oct. 13, 11), the pectrum of thee time erie are obtained. The pectrum of C1 i hown in Figure 7. The period correponding to maximum amplitude are 8616, 86164 and 8616 for C1, C3 and C4, repectively, which are baically conitent with the theoretical orbital period (86164). The IGSO atellite are not tracked over a full day, we cannot exact the multipath erie for 4 hour. Therefore, we determine the period of multipath by mean of calculating cro correlation of different day multipath error [1,13]. The reult of cro correlation i plotted in Figure 8 for day of Oct. 11, 11 to Oct. 1, 11. The correlation lag t a well a it aociated maximum correlation coefficient i preented in Table 1 for IGSO atellite (C8). The cro correlation peak between the firt day and the econd day i centered at 4, the econd and the third day i centered at 4, the firt day and the third day i centered at 483, which i le than the um of the two adacent day. With the increaing number of day between the maximum correlation will gradually decreae. So the multipath of IGSO atellite appear a period ahead of time 4 every day, namely the period i about 86158 and it i baically conitent with the orbital period (86164). The multipath period of MEO atellite i determined imilar to IGSO atellite. BeiDou- MEO atellite orbital period i about 1.9 hour [9]. Thi pecial orbital period characteritic lead to a fact that the viible time i potponed about hour related to the day before, therefore
Multipath Error Analyi of COMPASS Triple Frequency Obervation 17.14.1.1 T=8616 Station:CCHU Satellite: C1 Amplitude [m].8.6.4. 1.e-4.e-4 3.e-4 4.e-4 Frequency [Hz] Figure 7. Spectrum analyi of GEO atellite multipath..88.86 Station:CCHU Satellite:C8 Oct 11,11 - Oct 1, 11 Normalized Correlation.84.8.8.78.76.74 1 3 4 5 6 7 8 hift-econd relative to one day Figure 8. The correlation curve of multipath for IGSO atellite. Table 1. IGSO atellite (C8) peudorange multipath related delay tatitic. Relevant date Max. correlation Correlation lag() Oct 11 - Oct 1, 11.87 4 Oct 1 - Oct 13, 11.933 4 Oct 11 - Oct 13, 11.847 483 we can hardly determine the multipath period imply by analyzing the cro correlation of adacent day multipath. Since the MEO atellite will appear at nearly the ame time after a week, we compute the cro correlation of MEO multipath uing the data of adacent week in order to get a more accurate period. The reult of cro correlation i plotted in Figure 9 for day of Jul. 5, 1 to Jul. 1, 1. Other related delay tatitic of MEO multipath are lited in Table. From the above tatitic in Table, we can conclude that the MEO multipath appear a period ahead of time about 17 every week compared to the week before. That i, it appear a period ahead of time about 45 every day. MEO atellite orbit around the earth 13 cycle every week, taking the 17 hift-econd relative to one week into account, a week time erie i 638. Namely the period i about 46391 and it i baically conitent with the orbital period (4639). 3.3. Carrier Phae Multipath of Different Type of Satellite We will extract the multipath of GF-IF combination. Since linear combination will amplify meaurement error, the meaurement error of GF-IF combination are a large a multipath. The high-preciion phae multipath of GF-IF combination can be extracted according to their low-frequency characteritic related to the high fre-
18 Multipath Error Analyi of COMPASS Triple Frequency Obervation Figure 9. The correlation curve of multipath error for MEO atellite. Table. MEO atellite (C11) peudorange multipath related delay tatitic. Relevant date Max. correlation Correlation lag() July 5 - July 1, 1.679 1718 July 1 - July 19, 1.688 176 July 5 - July 19, 1.39 346 quency characteritic of meaurement error by uing 7 layer wavelet de-noing of db8 wavelet. We can ee that the phae multipath are eriouly contaminated by meaurement error in Figure 1, but in Figure 11 high-preciion time erie of phae multipath are obtained after wavelet de-noiing proceing. By uing the foregoing pectrum analyi method, we depict GEO atellite (C1) phae multipath pectrum and calculate the period correponding to the maximum amplitude peak a hown in Figure 1. The period i about 8616 and i conitent with the period of peudorange multipath. Similarly, we determine the period of IGSO and MEO atellite phae multipath by mean of calculating cro correlation tatitic in Table 3 and Table 4. By comparing the figure of Figure 7 and 1 and the table of Table 1-4, we can conclude that the period of phae and peudorange multipath are baically the ame. Both tatitic how that the repeat time i variable acro the contellation, at the few-econd level for mot atellite o the multipath period of thee three kind of atellite are baically conitent with the orbital period of each kind atellite. 4. Impact of Multipath and It Correction on Peudorange Poitioning 4.1. Poitioning Impact of Multipath and It Periodicity A illutrated in Figure 13, the peudorange point poitioning time erie of CCHU tation how that the trend Table 3. IGSO atellite (C8) phae multipath related delay tatitic. Relevant date Max. correlation Correlation lag() Oct 11 - Oct 1, 11.59 44 Oct 1 - Oct 13, 11.517 45 Oct 11 - Oct 13, 11.451 485 Table 4. MEO atellite (C11) phae multipath related delay tatitic. Relevant date Max. correlation Correlation lag() July 5 - July 1, 1.441 171 July 1 - July 19, 1.463 175 July 5 - July 19, 1.46 3457 of poitioning error at adacent day are baically the ame. Thi cycle repeatability indicate the exitence of multipath. Multipath will be recurring day after day at the ame tation [1]. The periodic trend reflect the periodicity of the multipath of GEO, IGSO and MEO atellite. Therefore, at the ame tation, under the circumtance of ame atellite ditribution, the effect of multipath are highly related with the urrounding environment. If we extract multipath and correct to the meaurement, the poitioning accuracy i looking forward to be improved. 4.. Multipath Corrected Peudorange Point Poitioning Accuracy Analyi In order to verify the effect of multipath correction we carried out ingle point poitioning uing 4 tation meaurement including CLIN, CCHU, CSHA and CKUN. Since MEO atellite ephemeride are not available currently, we only ue 3 GEO and 3 IGSO atellite contellation to carry out ingle point poitioning. Extracting the peudo range multipath and carry out poitioning before and after multipath correction. The reult are lited in
Multipath Error Analyi of COMPASS Triple Frequency Obervation 19.5.4 Oct 11,11 Oct 1,11.3 Carrier phae multipath [m]..1 -.1 -. -.3 -.4 -.5 6 1 18 4 Figure 1. Adacent two day phae multipath time erie of C1..5.4 Oct 11,11 Oct 1,11.3 Carrier phae multipath [m]..1 -.1 -. -.3 -.4 -.5 6 1 18 4 Figure 11. Adacent two day phae multipath time erie of C1 (after wavelet filtering)..18.16.14.1 T = 8616 Station:CCHU Satellite: C1 Amplitude [m].1.8.6.4. 1.e-4.e-4 3.e-4 Frequency [Hz] Figure 1. Spectrum analyi of GEO atellite phae multipath.
Multipath Error Analyi of COMPASS Triple Frequency Obervation dn [m] 3 1 October 9,11 October 3,11 4 6 8 1 1 de [m] 5-5 4 6 8 1 1 du [m] 5-5 4 6 8 1 Figure 13. Adacent two day ingle point poitioning time erie of CCHU Station. Table 5. The reult of Table 5 how that the multipath correction will reult in better poitioning accuracy, epecially in the eat-wet direction. Since the GEO atellite are located in eat-wet direction, the eat-wet direction poitioning error RMS i maller than the other two direction [14]. The GEO atellite are tatic relative to the earth and it multipath error are more eriou compared to that of IGSO or MEO atellite [4]. Therefore, eat-wet direction poitioning accuracy increaed more ignificantly than other two direction after correcting peudorange multipath. 5. Concluion Baed on the combination of triple frequency meaurement, we extract the multipath of peudorange and phae, repectively. According to the above reult and analyi, we can draw the following concluion: The multipath of peudorange and phae meaurement i at the meter level and centimeter level, repectively. The multipath of GEO atellite preent low-frequency change. The multipath error of IGSO, MEO atellite preent high-frequency change relative to GEO atellite. The period of multipath of the GEO, IGSO and MEO atellite are about 8616, 86158 and 46391, repectively. The period of multipath are baically conitent with atellite orbit period. Correcting multipath will reult in better poitioning accuracy, epecially in eat-wet direction. Acknowledgement Thi work wa mainly ponored by Natural Science Foundation of China (Proect: 417418), a well a Table 5. Poitioning accuracy uing peudorange with and without multipath-correction. Station Data type CLIN B3IA CCHU B1IA CSHA B3IA CKUN BIA Time 3 h 5 h 5 h 3 h N RMS (m) E RMS (m) U RMS (m) Original.413.49 5.4 Deduct multipath.3896.34 5.3881 Improvement proportion 5.71% 4.3%.6% Original 5.997.3193 6.1341 Deduct multipath 5.9666.356 6.56 Improvement proportion.41% 6.1% 1.7% Original 3.7371 5.751 7.843 Deduct multipath 3.664 5.7147 7.7815 Improvement proportion 1.96%.63%.79% Original 1.468.693 11.4733 Deduct multipath 1.3418.5554 11.311 Improvement proportion 8.7% 11.74% 1.41% partly upported by Kwang-Hua Fund for College of Civil Engineering, Tongi Univerity. Li Bofeng provided ueful guidance during data proceing and paper writing. Jiao Wenhai checked ome of the calculated reult. The writer thank Tang Chengpan and the anonymou reviewer for their comment. REFERENCES [1] X. C. Feng, G. P. Jin, J. J. Fan and X. L. Wu, Experimentation and Analyi of Multipath in Code-Ranged by
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