Submillimetric GNSS distance determination: an account of the research at the Universitat Politècnica de València (UPV)

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1 Submillimetric GNSS distance determination: an account of the research at the Universitat Politècnica de València (UPV) Sergio Baselga Luis García-Aseno Pascual Garrigues Cartographic Engineering, Geodesy and Photogrammetry Department

2 OUTLINE 1. Motivation. GNSS for length determination initial assumptions 3. Functional model our approach 4. Study of reproducibility some results 5. Study of accuracy some results 6. Conclusions

3 3 MOTIVATION Absolute distance determination in the open air with submillimetric accuracy is a challenging task! We will focus on: Development of dedicated algorithms for submillimetric GNSS length determination applicable to the existing calibration baselines: Metrological facilities with known distances obtained by different techniques Possibly strong multipath D ~ m UPV calibration baseline: absolute scale transferred from Nummela Standard Baseline in 01 stability monitoring with a ME5000 (013 and 014 campaigns) Research funded by the Spanish Ministry of Science and Innovation (AYA011-33)

4 4 INITIAL ASSUMPTIONS (1/4) Modern receivers provide carrier phase observations with submillimetre level noise In the literature, e.g.: Bona, P.; Tiberius, C. (000). An experimental comparison of noise characteristics of seven high-end dual frequency GPS receiversets. Proc. IEEE Position Location and Navegation Symposium 000, IEEE, Piscataway, N.J., March Esteban, G. (008). Analysis of stochastic properties of GPS observables. Report No. 490, Geodetic Science and Surveying Division, Ohio State University. Our experiments (more to say later on), e.g.: Double-difference phase residuals for a zero baseline at UPV Hopefully R dd = sd φ R = R < 1mm We indeed obtain average R dd = 1.48 mm

5 5 INITIAL ASSUMPTIONS (/4) GNSS has a high scale stability at global scale (1 ppb) GNSS worldwide scale stability is maintained at the level of 1 ppb = 1x10-9 = 1 mm / 1000 km e.g. Altamimi, Z; Collilieux, X; Metivier, L (011) ITRF008: an improved solution of the international terrestrial reference frame, J. Geod. 85(8): Is this high absolute scale accuracy also applicable to short distance determination in the existing metrological infrastructures?

6 Distance may be more precisely determined than coordinates Normally we determine INITIAL ASSUMPTIONS (3/4) + + = (or Z) Y, X, Z,Y, X 6 Then we can compute Fortunately correlation normally makes that And even Z Y X D + + = ) (and Z D Y D X D, σ < σ < σ σ < σ σ Z Y Z X Y X Z Y X D D Z D Y D Z D X D Y D X D Z D Y D X σ + σ + σ + σ + σ + σ = σ Z Y X D σ + + σ σ < σ + terms +/- terms

7 7 INITIAL ASSUMPTIONS (4/4) E.g., simple example from our experiments (more to say later on): BASELINE with 1h timespan X -9,9353 Y -81,9418 Z 36,0661 D 94,4000 Covariance Matrix XYZ 4,7E-07-8E-08 1,9E-07 sigmax 0,00068 m -8E-08 1,9E-07 6,9E-08 sigmay 0,00044 m 1,9E-07 6,9E-08,8E-07 sigmaz 0,00053 m X/D -0,3171 Y/D -0,868 Z/D 0,3806 4,7E-08 1,5E-07 4,1E-08-5E-08-5E-08-5E-08 varianced 9,4E-08 sigmad 0,00031 m e -8,1168 n 46,5634 u 0,1981 D 94,4000 Covariance Matrix ENU 1,9E-07 1,1E-07 -E-08 sigmae 0,00044 m 1,1E-07 1,7E-07-5E-08 sigman 0,00041 m -E-08-5E-08 5,8E-07 sigmau 0,00076 m e/d -0,8699 n/d 0,4936 u/d 0,001 1,4E-07 4,1E-08,6E-1-9E-08 6,9E-11-1E-10 sigmad 0,00031 m 5,E-1 1,4E-11 1E-11 sigmaaz 5,5E-06 1,1 " 0,00051 m sigmazen 8,1E-06 1,66 " 0,00076 m sigmad 0,00031 m sigmaaz* 0,00051 m sigmazen 0,00076 m * linear units

8 8 FUNCTIONAL MODEL OUR APPROACH (1/) Only L 1 DDs + no iono + no tropo + no ambiguity determination L 1 carrier phase observables are less noisy than L or L 5 observables, or any combination of them e.g. Xu, G. (003) GPS: Theory, Algorithms and Applications (Berlin: Springer) Additionally, L 1 observations have a considerably better signal to noise ratio Ionospheric and tropospheric corrections are not needed For very short horizontal baselines (<1 km) we assume that ionospheric and tropospheric delays are the same in both baseline ends so that they cancel out when forming double differences (DDs) We use the most recent ATX file (absolute antenna calibration)

9 9 FUNCTIONAL MODEL OUR APPROACH (/) Only L 1 DDs + no iono + no tropo + no ambiguity determination An ambiguity free approach reduces the number of unknowns to determine thus strengthening the model (REQUIRES approx. coord. ~ 1 cm) and is not affected by cycle slips Double-differenced L 1 carrier phase observation equation for subtractions with the order i λφ = ρ + λn + ε i i i l l k k l l k k ( φ φ ) ( φ φ ) = φ φ φ φ φ = + i i i i i Expanding around X,Y,Z (i held fixed) ρ i ρ i ρ i λφ i ρi = dx 0 + dy + dz + λni + ε X Y Z λφi ρi ρ 0 i 1 ρ i 1 ρ i 1 1 = dx + dy + dz + Ni + εi λ X λ Y 0 λ Z If coordinates are accurate 0 λ λ 0 enough* (say 1 cm) we have e.g /0.19*(-0.008) -0.37/0.19*(0.005) 0.857/0.19*(0.004) /0.19 *Baselga S 014 Ambiguity-free method for fast and precise GNSS differential positioning J. Surv. Eng λφ i ρ λ i 0 λφ Int i ρ λ i 0 ρ = X i 0 1 λ = dx ρ + Y i λ dy ρ + Z i λ dz + 1 λ ε i i

10 10 STUDY OF REPRODUCIBILITY (1/11) The consistency of GNSS-derived lengths over short baselines has not been studied for a considerably long period of time. The existing studies are limited to hours or a few days (e.g. Koivula et al 01, four campaigns of two 4 h GPS sessions) Baselga S, García-Aseno L and Garrigues P (013) Submillimetric GPS distance measurement over short baselines: case study in inner consistency Meas. Sci. Technol We used data from IGS, EPN, CORS Most stations may not be stable at the 0.1 mm level (roofs) We chose pillars and masts with concrete foundations that form a short, approximately horizontal, baseline with clear surroundings (as far as we could deduce from the available images) to minimize multipath We obtained solutions for every 1 h span of observations (10 epochs) during the entire year 011 (also 010): 4 x 365 = 8760 baselines per year

11 11 STUDY OF REPRODUCIBILITY (/11) A clearly repeated (one hour advanced) pattern! BAY5-BAY6 day 14 Sidereal day 3 h 56 min 4 min 15 days = 1 hour Related to constellation configuration repetition multipath is known to play a maor role in short baselines Amiri-Simkooei and Tiberius (007) BAY5-BAY6 day 14 (solid) day 139 (dotted) periodic effects can be expected due to orbit mismodelling Griffiths and Ray (013) periodic effects may also arise due to errors or approximations in the antenna/radome calibration Ray et al (008)

12 1 STUDY OF REPRODUCIBILITY (3/11) BAY5-BAY6 day 14 (solid) day 139 (dotted) ENU coord.

13 13 STUDY OF REPRODUCIBILITY (4/11) CAGL-CAGZ day 38 (solid) day 53 (dotted) Same pattern!

14 14 STUDY OF REPRODUCIBILITY (5/11) Checking for a periodic pattern. Data: complete year 011 Fourier Analysis Experimental σ for a 1,, n hour processing We find the expected peak at 1/ σ = σ1 /, σ3 = σ1 / 3,..., σn = σ1 / n σ decays until 4 (we have periodic effects averaged out) σ for 10 h is already a good figure (similarly to the conclusion reached by Hughes et al (006) for coordinate determination)

15 15 STUDY OF REPRODUCIBILITY (6/11) Is the determined GPS length STABLE in the long term (say during a whole year)? BAY5-BAY6 year 011 Max. deviation from mean: 0.1 mm Monthly averages (dotted lines represent the 95% confidence level) (These were the most stable baselines) LNC1-LNC year 011 Max. deviation from mean: 0.3 mm

16 16 STUDY OF REPRODUCIBILITY (7/11) CAGL-CAGZ year 011 Max. deviation from mean: 0.38 mm (These were baselines with intermediate stability) SUTH-SUTM year 011 Max. deviation from mean: 0.74 mm

17 17 STUDY OF REPRODUCIBILITY (8/11) MEDI-MSEL year 011 Max. deviation from mean:.7 mm (This was clearly an unstable baseline length) Why? Let us inspect setups Essential to use the same antennas/radomes in both ends (or individual absolute antenna calibrations? Koivula et al 01) Absolute antenna calibration table values may be inaccurate up to 1 mm (Zeimetz and Kuhlmann, 008)

18 18 STUDY OF REPRODUCIBILITY (9/11) Results are similar for other years (Are there ~ mm seasonal effects still present?) LNC1-LNC year 010 (compare with previous plot for year 011)

19 19 STUDY OF REPRODUCIBILITY (10/11) A further refinement: use of Global Robust Estimation Robust estimation (RE) techniques permit to obtain a solution maximally resistant towards the influence of gross and systematic errors, e.g. Andrews et al (197), Yang (1999). Optimum only if computed as a global optimization problem: Global Robust Estimation (GRE), Baselga(007) RE also has been applied to GNSS positioning after the pioneer work of Wieser and Brunner (00) We have successfully made use of GRE for - single-frequency baseline determination in the presence of strong ionospheric delays, Baselga and García-Aseno (008a) - baseline determination in the presence of strong multipath, Baselga and García-Aseno (008b) Recently, we have also applied this techniques to GNSS distance determination Baselga S, García-Aseno L and Garrigues P (014) Submillimetric GPS distance measurement over short baselines: noise mitigation by global robust estimation Meas. Sci. Technol We improved results (overcoming the not-too-strong multipath) Statistics for 1h timespan vectors for the entire year 011 LNC1 LNC

20 0 STUDY OF REPRODUCIBILITY (11/11) So far we have studied REPRODUCIBILITY (or inner consistency / precision) Same antennas and radomes are preferable in both baseline ends ~ mm precision results are obtained after 4-h observation time (maybe 10-h) They may be consistent in the long term at this submillimetre level How about ACCURACY (i.e. comparison with the SI meter)? (precision+closeness to SI meter) GNSS lengths traced to the SI metre? Suggestions! We can only study if GPS lengths are close to SI meter or not?

21 1 STUDY OF ACCURACY (1/5) Comparison with the absolute SI metre should be conducted in outdoor facilities that have been proved to be stable to few tenths of a mm and whose distances have been traced to the SI metre Few test fields meet such demanding requirements (e.g. Nummela Standard Baseline, Jokela and Häi, 006) UPV calibration baseline In June 01, the Finnish Geodetic Institute (FGI) transferred scale from Nummela baseline to the existing 7 pillar calibration test field at UPV with a calibrated Kern ME5000. The resulting distances were obtained with expanded total uncertainties of mm (σ) A subsequent agreement between UPV and the Universidad Complutense de Madrid (UCM) permitted to use the only Kern ME5000 in Spain for periodically monitoring the baseline stability (013 and 014 campaigns).

22 STUDY OF ACCURACY (/5) GNSS observation campaigns Less favourable observation conditions than with IGS, CORS, EPN stations Surrounding trees and buildings (stronger multipath) Feasible observation times (hours rather than months) Common field working conditions We used: Leica AR5 choke-ring antennas signal splitters 4 Trimble 5700 receivers to observe on pillars 1 and 3 (no displacement detected & potentially less affected by multipath) All in all, multipath may have undermined the accuracy attained Zero baseline: avg R dd ~ 1.5 mm (< mm as expected) 1-3 baseline: avg R dd ~ 3.9 mm

23 3 STUDY OF ACCURACY (3/5)

24 4 STUDY OF ACCURACY (4/5) 013 GNSS observation campaign Only 6h of observation (epochs 15 s) If we compute baselines with h time spans we obtain: Close agreement with ME5000 distances, esp. with that obtained the next month GNSS May 3, ME5000 ME5000 UCM FGI June 5-8, May 8-June 1, Error bars represent the 95% confidence level

25 5 STUDY OF ACCURACY (5/5) 014 GNSS observation campaign 3 days each 8h of observation (epochs 15 s) If we compute baselines for each day (8h time spans) we obtain: 013 Again a close agreement Although a displacement seems to have happened! GNSS June 5-7, ME5000 UCM June 5-8, Error bars represent the 95% confidence level

26 6 CONCLUSIONS GNSS distances have a good reproducibility mm after some hours of observations consistent in the long term within this precision level pref. same antennas and radomes in both ends (or individual antenna calibrations) GNSS distance accuracy the most difficult problem to study (very stable infrastructure, known distances traced to the SI metre, periodical deformation monitoring) consistent with the absolute meter at the level of few tenths of a mm. A possible displacement (~0.7mm) has also been detected by GNSS GNSS lengths traced to the SI metre? Suggestions! FUTURE WORK The size of residuals shows that there still may be some room for improvement: e.g. use of individual absolute antenna calibrations optimum selection of measurements study of most favourable geometries for length determination in each baseline Testing our methodology in other calibration baselines

27 7 REFERENCES Altamimi Z, Collilieux X and Metivier L 011 ITRF008: an improved solution of the international terrestrial reference frame J. Geod Amiri-Simkooei A R and Tiberius C C J M 007 Assessing receiver noise using GPS short baseline time series GPS Solut Andrews D F, Bickel P J, Hampel F R, Huber P J, Rogers W H and Tukey J W 197 Robust Estimates of Location: Surveys and Advances (Princeton, NJ: Princeton University Press) Baselga S 007 Global optimization solution of robust estimation J. Surv. Eng Baselga S 014 Ambiguity-free method for fast and precise GNSS differential positioning J. Surv. Eng Baselga S and García-Aseno L 008a GNSS differential positioning by robust estimation J. Surv. Eng Baselga S and García-Aseno L 008b Multipath mitigation by global robust estimation J. Navig Baselga S, García-Aseno L and Garrigues P 013 Submillimetric GPS distance measurement over short baselines: case study in inner consistency Meas. Sci. Technol Baselga S, García-Aseno L and Garrigues P 014 Submillimetric GPS distance measurement over short baselines: noise mitigation by global robust estimation Meas. Sci. Technol Griffiths J and Ray J R 013 Sub-daily alias and draconitic errors in the IGS orbits GPS Solut Jokela J and Häi P 006 Current research and development at the Nummela standard baseline 3rd FIG Congress (Munich, Germany, 8 13 October) PS5.. pp 1 15 Koivula H, Hai P, Jokela J, Buga A and Putrimas R 01 GPS metrology: bringing traceable scale to local crustal deformation network Geodesy for Planet Earth (Int. Association of Geodesy Symp. vol 136) ed S Kenyon, M C Pacino and U Marti (Berlin: Springer) pp Ray J, Altamimi Z, Collilieux X and van Dam T 008 Anomalous harmonics in the spectra of GPS position estimates GPS Solut Wieser A and Brunner F K 00 Short static GPS sessions: robust estimation GPS Solut Xu G 003 GPS: Theory, Algorithms and Applications (Berlin: Springer) Yang Y 1999 Robust estimation of geodetic datum transformation J. Geod

28 Thanks for your attention! Sergio Baselga Luis García-Aseno Pascual Garrigues Cartographic Engineering, Geodesy and Photogrammetry Department