1x10-16 frequency transfer by GPS IPPP. G. Petit Bureau International des Poids et Mesures

Transcription

1 1x10-16 frequency transfer by GPS IPPP G. Petit Bureau International des Poids et Mesures

2 This follows from past work by! CNES to develop basis of the technique D. Laurichesse & F. Mercier, Proc 20 th ION GNSS, , J. Delporte et al., IJNO, Article ID , S. Loyer et al., J Geod 86: , 2012.! CNES and CLS to operate the GRG IGS analysis center and to regularly generate integer SV clocks and WSB! Amale Kanj s work at the BIPM ! Julia Leute 2-month stay at the BIPM Summer 2015! See Metrologia 2015, 52,

3 ! PPP with integer ambiguity resolution (IPPP)! IPPP for time links: developing operational procedures! IPPP and PPP vs. Fiber link! IPPP and PPP: other comparisons and conclusions

4 A new direction in GPS carrier phase frequency transfer! PPP benefits from the low noise of GPS carrier phase observables but also from its drawbacks:! Phase clock solutions are ambiguous and need to be aligned to ensure continuity Alignment on code, subject to the code noise => random errors from track to track (τ = few hours) Alignment over consecutive batches creates boundary discontinuities due to code noise.! A number of techniques (or tricks) have been proposed to solve or mitigate these problems.! Taking into account the integer nature of the ambiguities allows, in principle, to rigorously solve the problem of boundary discontinuities. For integer ambiguities solutions, such discontinuities should be integer numbers of the Narrowlane wavelength λ c (357 ps) and can be exactly determined. 4

5 PPP with Integer ambiguity resolution (IPPP)! CNES approach (basis for the products of the GRG analysis center of the IGS, see : based upon processing of a global network of GPS stations determination of wide-lane satellite biases : WSB, file grgxxxxx.wsb determination of phase clocks : clocks, file grgxxxxx.clk The user can then use these GRG products to determine integer ambiguities in the PPP solution (IPPP ), e.g. with the GINS software developed by CNES.! IPPP: Two-step procedure, where the ambiguities at the two frequencies N 1 / N 2 are determined as the Widelane N w = N 2 - N 1 and e.g. N 1 1. Zero-difference widelane identification => N w 2. Ambiguity fixing in the Zero-difference iono-free phase equation => N 1 5

6 Zero-difference widelane identification Step 1 = Determine N w (Widelane wavelength λ w = cm) integer widelane ambiguity w 4 observable Melbourne-Wübenna linear combination j ( P, P, L L ) + µ N f µ = 1 2 1, 2 i Receiver bias (variations below 0.1 N w for geodetic receivers) Transmitter bias (contained in GRG products) For details : see Delporte et al. IJNO, 2008 and Loyer et al. J. Geod, N w = N 2 N 1 Frequency 2 ambiguity Frequency 1 ambiguity

7 Ambiguity fixing method in zero-difference iono-free phase equation Step 2 = iono-free phase solution with integer N 1 (Narrowlane wavelength λ c = cm) wind-up effect frequency 1 integer ambiguity (each pass) γλ1l 1 λ2l γ 1 2 = D c + λ W c λ N c 1 + λ2 γ 1 N w + Δh ionosphere free phase combination propagation distance (model, including troposphere) L 1, L 2 λ 1,λ 2 λ c : phase measurements on the two frequencies (cycles) : wavelength on the two frequencies, γ is the squared frequency ratio γλ1 λ2 = γ 1 : equivalent wavelength for the ionosphere-free problem ~ cm or 357 ps widelane integer ambiguity receiver/emitter clock difference (each epoch)

8 ! PPP with integer ambiguity resolution (IPPP)! IPPP for time links: developing operational procedures! IPPP and PPP vs. Fiber link! IPPP and PPP: other comparisons and conclusions

9 N w and N 1 ambiguity determination difficulties Step 1 problem: Widelane ambiguity determination The widelane ambiguity N w may be affected by integer cycle errors at batch limits and other hardware variations Solution: Problems in N w can be identified through the receiver WL bias µ i.which should be continuous and constant Step 2 problem: Limitation due to the daily orbit/clocks solutions The phase clocks in the GRG solution are determined in daily batches; they are defined modulo 1 cycle (λ c ) and are all consistent within the batch. BUT there is no guarantee to have continuity over day boundaries => not possible to just assemble daily solutions with GRG (orbits/clocks) to perform a solution over many days. Solution 1: A specific procedure has been developed to reconstruct the GPS satellites clocks using internal daily orbits/clocks solutions overlaps => Aligned GRG products Solution 2: Introduce a Step 3, to be applied for each link (not at the station level) 9

10 Step 3: Remove discontinuities between batches for a link (1/2) When forming a link, problems with the GRG reference vanish and receiver clock differences are defined up to an overall unknown number of cycles of λ c. Discontinuities between batches should be integer multiples of λ c. If batches are overlapping the connexion should be easy as the only errors in the difference are from the models (troposphere). Making overlapping solutions requires Aligned GRG products λ c If batches are not overlapping there are other boundary effects and the connexion is not necessarily straightforward. 10

11 Step 3: Remove discontinuities between batches for a link (2/2) Two techniques to connect non-overlapping batches; Extrapolation, assuming the stability of the compared clocks is sufficient Bridging, assuming another time link solution exists to bridge the discontinuity. Advantage: Step 3 takes care of all discontinuities: between daily batches but also due of other interruptions (not breaking the phase continuity), if they are recognized! 11

12 ! PPP with integer ambiguity resolution (IPPP)! IPPP for time links: developing operational procedures! IPPP and PPP vs. Fiber link! IPPP and PPP: other comparisons and conclusions

13 Test of IPPP vs. 420-km fiber link! UTC(AOS)-UTC(GUM) fiber link reported to the BIPM since 04/2013; Rinex files also reported.! Fiber link technology developed at AGH University! Instability ~10-17 τ =1 day reported from spooled fibers or through urban network. 13

14 IPPP and PPP vs. 420-km fiber link (1/3)! IPPP analysis for ~6 months of AOS-GUM link by Amale Kanj; close to 100% success at solving integer λ c boundaries over ~6 months! A 41-day period (longest continuous operation for all systems): Stability of IPPP better at few hours and at long term : 7.1 days PPP apparent slope of order 1x10-16, IPPP has no significant slope Blue = IPPP Fiber link Red = NRCan Fiber link 1 NL ambiguity 14

15 IPPP and PPP vs. 420-km fiber link (2/3)! Another 22-day period: PPP has apparent slope of order several 10-16, IPPP has no significant slope Stability of IPPP better at few hours and at long term : 3.6 days Blue = IPPP Fiber link Red = NRCan Fiber link 1 NL ambiguity 15

16 IPPP and PPP vs. 420-km fiber link (3/3)! IPPP is now operated in automatic mode and all recent data (7 intervals, 330 days) has been looked at. However success in this mode is not (yet) automatic. When successful, same conclusions for IPPP performances : 5.7 days Blue = NRCan Fiber link Red = IPPP Fiber link 1 NL ambiguity 16

17 ! PPP with integer ambiguity resolution (IPPP)! IPPP for time links: developing operational procedures! IPPP and PPP vs. Fiber link! IPPP and PPP: other comparisons and conclusions

18 Test of IPPP on ITOC data (J. Leute)! ITOC aims at comparing optical clocks in Europe using all available techniques (fiber, broadband TW, GNSS). See e.g. (Riedel et al, EFTF 2015)! Test campaign in October 2014, main campaign in June 2015 (3+ weeks).! 20-day link between two masers at OP and PTB: IPPP vs. PPP with NRCan IPPP seems to τ = 2 days and above, may be limited at 3x10-16 by maser No τ = few hours, may be limited by tropo parametrization in IPPP. 18

19 Some conclusions! GPS PPP is operational ; typical uncertainty stated at 1x10-15 at 1-day averaging to a few at many-day; can be optimized to provide ~5x10-16 at 1-day averaging.! Integer ambiguity resolution (IPPP) looks promising to improve PPP, in principle, for averaging time of several hours and above: day demonstrated for a few hundred km link. Stability should decrease as 1/τ as long as data continuity can be ensured.! Advantages Only weak continuity is required: short gaps can be overcome as long as the hardware set-up remains continuous. Stability decreases as 1/τ, compared to 1/ τ when phase cannot be connected from interval to interval (e.g. TW phase so far).! Drawbacks Continuity of clocks to be compared is also required; OK for fountains but not yet fulfilled for optical clocks! => account for dead time with flywheel.! Uncertainty: Will it work for very long links? 19

20 THANK YOU Acknowledgements: AOS and GUM for providing fiber link data to the BIPM NRCan for continuous support