============================================================================= | MEASUREMENT MODELS | |---------------------------------------------------------------------------| | Preprocessing | Static point positions to edit outliers | | | Remaining data screened for data gaps | | | Reference clock sites chosen from preferred list | | | Reference frame sites chosen from preferred list | | | Carrier Phase: Decimated to 5 minutes | | | Pseudorange: Carrier aided smoothing to 5 minutes | | | Cycle slip detection | |---------------------------------------------------------------------------| | Basic Observable | Undifferenced ionosphere-free carrier phase, LC | | | Undifferenced ionosphere-free pseudorange, PC | | |--------------------------------------------------------| | | Elevation angle cutoff: 7 degrees | | | Sampling rate: 5 minutes | | | Data weight, LC: 1 cm | | | Data weight, PC: 1 m | |---------------------------------------------------------------------------| | Modeled | Undifferenced LC and PC combinations | | observable | CA-P1 biases from CODE applied | |---------------------------------------------------------------------------| | RHC phase | Applied | | rotation corr. | | |---------------------------------------------------------------------------| | Marker -> antenna| dN, dE, dU eccentricities from IGS sinex file applied | | ARP eccentricity | to compute station marker coordinates | |---------------------------------------------------------------------------| | Ground antenna | PCV model from igs08_wwww.atx applied | | phase center cal.| Receiver antenna and radome types from IGS sinex file | |---------------------------------------------------------------------------| | Troposphere | A priori model: Pressure from GPT model | | | (Boehm et al, 2007) | | | Hydrostatic delay from Davis (1985) | | | Wet delay 10 cm | | | Mapping Function: Global Mapping Function (GMF) | | | Estimation: Zenith delay and horizontal gradients | |---------------------------------------------------------------------------| | Ionosphere | 1st order effect: Removed by LC and PC combinations | | | 2nd order effect: Not modeled | |---------------------------------------------------------------------------| | Plate motions | Station velocity model applied for apriori positions | |---------------------------------------------------------------------------| | Tidal | Solid earth tide: IERS 2010 Conventions | | |--------------------------------------------------------| | | Permanent tide: NOT removed from model, so NOT in | | | estimated site coordinates | | |--------------------------------------------------------| | | Pole tide: IERS 2010 Conventions | | |--------------------------------------------------------| | | Ocean Tide Loading: | | | Diurnal, Semidiurnal, MF, and MM Model: FES04 | | | Semiannual: Self-consistent equilibrium model | | | hardisp.f from IERS2010 | | | | | | Surface deformations computed at JPL with respect to | | | instantaneous center of mass | | |--------------------------------------------------------| | | Ocean Pole Tide Loading: Not applied | |---------------------------------------------------------------------------| | Non-tidal | Atmospheric Pressure: Not applied | | loading |--------------------------------------------------------| | | Ocean Bottom Pressure: Not applied | | |--------------------------------------------------------| | | Surface Hydrology: Not applied | | |--------------------------------------------------------| | | Other Effects: None applied | |---------------------------------------------------------------------------| | Earth Orientation| IERS 2010 Conventions for diurnal, semidiurnal, and | | Parameter (EOP) | long period tidal effects on polar motion and UT1 | | Model | | |---------------------------------------------------------------------------| | Satellite center | Phase centers offsets from igs08_wwww.atx applied | | of mass | | | correction | | |---------------------------------------------------------------------------| | Satellite antenna| PCV model w.r.t. phase center from igs08_www.atx | | phase variations | applied | |---------------------------------------------------------------------------| | Relativistic | Periodic Clock Corrections, (-2*R*V/c): Applied | | corrections | Gravity Bending: Applied | ----------------------------------------------------------------------------- | GPS Attitude | GYM95 nominal yaw rate model from Bar-Sever (1996) and | | model | yaw rates estimated for Block II satellites | ============================================================================= ============================================================================= | ORBIT MODELS | |---------------------------------------------------------------------------| | Geopotential | EGM2008 12x12 | | | C20, C30, C40, C21, S21 from IERS2010 standards | | |--------------------------------------------------------| | | GM = 398600.4415 km**3/sec**2 | | |--------------------------------------------------------| | | AE = 6378.1363 km | |---------------------------------------------------------------------------| | Third-body | Sun, Moon, and All Planets | | |--------------------------------------------------------| | | Ephemeris: JPL DE421 | |---------------------------------------------------------------------------| | Solar radiation | Block II/IIA/IIR: JPL empirical SRP model, GSPM-10, | | pressure | Bar-Sever and Kuang, (2004) | | | Sibthorpe et al, 2010 | | |--------------------------------------------------------| | | Estimate GPS "Y-Bias" and solar radiation pressure(SRP)| | | coefficient as constant with no a-priori constraint. | | | Make small time-varying (stochastic) adjustments to SRP| | | coefficients in spacecraft body-fixed X and Z | | | directions (1% process noise sigma with 1 hr 11 sec | | | updates and 4-hour correlation time.) Estimate tightly | | | constrained time-varying empirical acceleration in | | | spacecraft Y direction (0.01 nm/s^2 process noise | | | sigma with 1 hr 11 sec updates and 4-hour correlation | | | time.) | | |--------------------------------------------------------| | | Earth shadow model: conic model with oblate Earth, | | | umbra and penumbra | | |--------------------------------------------------------| | | Earth albedo: applied | | |--------------------------------------------------------| | | Attitude Model: GYM95 yaw model from Bar-Sever (1996) | |---------------------------------------------------------------------------| | Tidal forces | Solid earth tides: IERS 2010 Conventions | | |--------------------------------------------------------| | | Ocean tides: FES2004 to degree and order 30 | | | with convolution formalism of Desai and | | | and Yuan (2006) | | |--------------------------------------------------------| | | Solid Earth Pole tide: IERS 2010 conventions | | |--------------------------------------------------------| | | Ocean Pole tide: IERS 2010 conventions | |---------------------------------------------------------------------------| | Relativity | Applied | | | Acceleration due to point mass of Earth | | | Acceleration due to geodesic precession | | | Acceleration due to Lense-Thirring precession | |---------------------------------------------------------------------------| | Numerical | Variable high order Adams predictor-corrector | | Integration | with direct integration of second-order equations | | |--------------------------------------------------------| | | Integration step: variable | | |--------------------------------------------------------| | | Starter procedure: RKF | | |--------------------------------------------------------| | | Arc length: 30 hours centered at 12:00 of each day | ----------------------------------------------------------------------------- ----------------------------------------------------------------------------- | ESTIMATED PARAMETERS (APRIORI VALUES & SIGMAS) | |---------------------------------------------------------------------------| | Adjustment | Stochastic Kalman filter/smoother implemented as | | | square root information filter with smoother | |---------------------------------------------------------------------------| | Station | Daily free-network estimates for all sites | | coordinates | Combine free-network estimates to get weekly solution | | | Apply three rotations to weekly solution | |---------------------------------------------------------------------------| | Satellite clock | Estimate every 5 minutes relative to reference clock | | | Recompute every 30 seconds relative to reference clock | |---------------------------------------------------------------------------| | Receiver clock | Estimate every 5 minutes relative to reference clock | | | Reference clock usually USN3 or AMC2 | |---------------------------------------------------------------------------| | Orbital | Epoch state, solar pressure parameters | | parameters | | |---------------------------------------------------------------------------| | GPS Attitude | Estimate yaw rates for eclipsing spacecraft | | parameters | Yaw rates used for measurement but not dynamic models | |---------------------------------------------------------------------------| | Troposphere | Zenith delay: random walk 5.0d-8 km/sqrt(sec) | | | Horizontal delay gradients: random walk 5.0e-9 | | | km/sqrt(sec) | | |--------------------------------------------------------| | | Mapping function: GMF | |---------------------------------------------------------------------------| | Ionosphere | 1st order effects removed by LC and PC combinations | | | and 2nd order effects not modeled, | |---------------------------------------------------------------------------| | Ambiguity | Global ambiguities resolved | |---------------------------------------------------------------------------| | Earth Orientation| Estimate polar motion, polar motion rate, and LOD | | Parameters | UT1 integrated from estimated LOD | ============================================================================= ============================================================================= | REFERENCE FRAMES | |---------------------------------------------------------------------------| | Inertial | J2000 Geocentric | |---------------------------------------------------------------------------| | Terrestrial | IGS08 station coordinates and velocities | |---------------------------------------------------------------------------| | Interconnection | Precession: IAU 2006 Precession Theory | | |--------------------------------------------------------| | | Nutation: IAU 2006 Nutation Theory | | |--------------------------------------------------------| | | A priori EOPS: EOPC04 updated daily, with | | | polar motion and length of day estimated daily | ============================================================================= ============================================================================= | REFERENCES | |---------------------------------------------------------------------------| | Bar-Sever, Y. E. (1996), "A new model for GPS yaw attitude", Journal of | | Geodesy, 70:714-723 | | | | Bar-Sever, Y. E., and D. Kuang (2004), New empirically-derived solar | | radiation pressure model for GPS satellites, IPN Progress Reports | | 42-159, JPL. Available online: | | http://ipnpr.jpl.nasa.gov/progress_report/42-160/title.htm | | | | Bassiri, S., and G. A. Hajj, (1993), Higher-order ionospheric effects on | | the global positioning systems observables and means of modeling them, | | Manuscripta Geodtica, 18, 280-289, 1993 | | | | Blewitt, G., (1990), An automatic editing algorithm for GPS data. | | Geophysical Research Letters, Vol. 17, No. 3, p. 199-202 | | | | Boehm, J., A.E. Niell, P. Tregoning, H. Schuh (2006), "Global Mapping | | Functions (GMF): A new empirical mapping function based on numerical | | weather model data", Geophysical Research Letters, Vol. 33, L07304, | | DOI:10.1029/2005GL025545. | | | | Boehm, J., R. Heinkelmann and H. Schuh (2007), "Short Note: A global | | model of pressure and temperature for geodetic applications", Journal | | of Geodesy, DOI: 10.1007/s00190-007-0135-3 | | | | IERS Conventions 2003, D.D. McCarthy & G. Petit (editors), IERS Technical | | Note 32, Frankfurt am Main: Verlag des Bundesamts fuer Kartographie und | | Geodaesie, 2004. | | | | Kedar, S., G. Hajj, B. Wilson, and M. Heflin (2003), The effect of the | | second order GPS ionospheric correction on receiver positions, Geophys. | | Res. Lett., 30(16), 1829, doi:10.1029/2003GL017639 | | | | Moyer, T.D., (2000) Formulation of observed and computed values of deep | | space network data types for navigation, Deep Space Communications and | | Navigation Series, Jet Propulsion Laboratory, California Institute of | | Technology, Pasadena, CA, Chapter 4, pp, 19-28. | | | | Sibthorpe, A., J. Weiss, N. Harvey, D. Kuang, and Y. Bar-Sever, Empirical | | modeling of solar radiation pressure forces affecting GPS satellites, | | AGU Fall Meeting, San Francisco, CA, 2010. | =============================================================================