=============================================================================
| NOAA/NGS ANALYSIS STRATEGY SUMMARY |
| (template version 2.0, 07 Aug. 2006) |
=============================================================================
| Analysis Center | National Oceanic & Atmospheric Administration (NOAA) |
| | National Geodetic Survey (NGS) |
| | SSMC3; N/NGS2 |
| | 1315 East-West Highway |
| | Silver Spring, MD 20910 |
| | USA |
| | |
| | Analysis Center code: NGS |
| | website: http://www.ngs.noaa.gov/ |
| | phone: 301-713-3209, fax: 301-713-4322 |
|---------------------------------------------------------------------------|
| Contact people | William Kass |
| | e-mail: Bill.Kass@noaa.gov |
| | phone : 301-713-3209 ext.164 |
| | Robert Dulaney |
| | e-mail: bobd@ngs.noaa.gov |
| | phone : 301-713-3209 ext.168 |
| | Jake Griffiths |
| | e-mail: Jake.Griffiths@noaa.gov |
| | phone : 301-713-3205 ext.153 |
| | Stephen Hilla |
| | e-mail: Steve.Hilla@noaa.gov |
| | phone : 301-713-2851 ext.208 |
| | Jim Ray |
| | e-mail: jimr@ngs.noaa.gov |
| | phone : 301-713-2850 ext.112 |
| | Jim Rohde |
| | e-mail: Jim.Rohde@noaa.gov |
| | phone : 301-713-2851 ext.209 |
| | Gerald Mader |
| | e-mail: Gerald.L.Mader@noaa.gov |
| | phone : 301-713-2854 ext.201 |
| | William Dillinger |
| | e-mail: William.H.Dillinger@noaa.gov |
| | phone : 301-713-2850 ext.210 |
| | |
|---------------------------------------------------------------------------|
| Software used | "pages" developed at NOAA/NGS for the primary |
| | observations & parameter set-up; |
| | "gpscom" for the combination of reduced normal |
| | equation systems for subnetworks of observations |
|---------------------------------------------------------------------------|
| GNSS system(s) | GPS |
|---------------------------------------------------------------------------|
| Final products | ngsWWWWn.sp3 daily orbit & satellite clock files |
| generated for | ngsWWWW7.erp weekly ERP file of daily values |
| GPS Week 'WWWW' | ngsWWWW7.sum weekly analysis summary file |
| day of Week 'n' | ngsWWWW7.snx weekly SINEX file |
| (n=0,1,...,6) | ngsWWWWn.tro daily tropo estimates at 1-hr intervals |
| | |
| Rapid products | ngrWWWWn.sp3 daily orbit & satellite clock files |
| generated daily | ngrWWWWn.erp daily ERP file |
| | |
| | NOTES: |
| | * Ephemeris files use SP3c format |
| | * SP3c accuracy codes based on formal errors of orbit |
| | parameters |
| | * Clock values are extracted from Broadcast message |
| | * ERP files contain estimates for pole, pole-rate, & |
| | LOD; the initial UT1-UTC is a constrained a-priori |
| | value; subsequent UT1-UTC values are estimates |
| | consistent with the reported LOD values |
| | * Tropo files began starting week 1404 |
| | |
|---------------------------------------------------------------------------|
| Preparation date | 2006-12-05 (original updated version) |
|---------------------------------------------------------------------------|
| Modification dates| 2007-01-10: add tropo product files (from week 1404) |
| | 2007-01-14: begin using Delaunay triangulation to |
| | create double-differenced baseline networks |
| | (from Rapid week 1409-6, Final week 1410) |
| | 2007-01-28: begin using elevation-dependent obs |
| | weights (from Rapid week 1413-2, Final week 1412) |
| | 2007-03-11: begin using IGS polar motions as a-priori |
| | values (from Rapid and Finals week 1418) |
| | 2007-04-22: begin modeling lunar eclipses (from Rapid |
| | and Finals weeks 1424) |
| | 2007-06-29: change orbit model parameterization to |
| | CODE-like (Rapid week 1433-4, Final week 1433) |
| | 200?-??-??: ... |
| | |
|---------------------------------------------------------------------------|
| Effective date | 2006-11-05 (GPS week 1400) and afterwards, including |
| for data analysis | IGS reanalysis campaign |
|---------------------------------------------------------------------------|
| Instructions: Please provide as complete information as possible. The |
| template below is illustrative only; replies should reflect |
| actual analysis implementation. Please accumulate changes |
| with effective dates of usage, rather than remove earlier |
| information. |
=============================================================================
=============================================================================
| MEASUREMENT MODELS |
|---------------------------------------------------------------------------|
| Preprocessing | RINEX files pre-screened using TEQC metrics to reject |
| | small/incomplete files (<85%), excessive phase slips |
| | (>500), or high multipath (>1.2 m). |
| | |
| | Phase preprocessing in a baseline by baseline mode |
| | using double-differences. In most cases cycle slips |
| | are fixed automatically looking simultaneously at |
| | different linear combinations of L1 and L2. Rarely, |
| | manual editing is done on baselines showing larger |
| | than normal post-fit RMS statistics in the all- |
| | baseline combined solution. In that case, bad data |
| | points are removed or new phase bias ambiguities are |
| | estimated. |
| | |
| | 1 ms RINEX clock jumps fixed using clockprep. |
|---------------------------------------------------------------------------|
| Basic observables| Double-differenced carrier phase; code only used for |
| | receiver clock synchronization and to aid in fixing |
| | phase ambiguities using the Melbourne-Wuebbena widelane|
| | method. Double-differenced baseline network defined |
| | using optimal Delaunay triangulation algorithm (from |
| | 2007-01-14); see Renka (1997). |
| |--------------------------------------------------------|
| | elevation angle cutoff: 10 degrees |
| | sampling rate: 30 seconds |
| | weighting: (for raw obs *before* iono correction) |
| | * carrier phase = 5 cm sigma (nominally) at zenith |
| | * uniform weighting applied (no elevation-dependent |
| | scaling) before week 1412 |
| | * weighting model changed starting week 1412 to: |
| | sigma = (5 + 2/sin(elevation)) cm |
| | * parameter sigmas rescaled to give reduced chi^2 |
| | of 1 for the postfit phase residuals |
| | deweighting: a few consistently ill-behaved satellites |
| | are deweighted by a factor of 2 a-priori |
| | smoothing: no smoothing is applied |
| | code biases: C1 & P2' corrected to P1 & P2 using |
| | cc2noncc tool depending on receiver type |
|---------------------------------------------------------------------------|
| Modeled | Double-differenced carrier phase with ionosphere-free |
| observables | linear combination applied |
|---------------------------------------------------------------------------|
|*Satellite antenna| SV-specific z-offsets & block-specific x- & y-offsets |
| -center of mass | (from manufacturers) from file igs05_wwww.atx based on |
| offsets | GFZ/TUM analyses using fixed ITRF2000 coordinates |
| | [refer to IGS Mail #5189, 17 Aug 2005] |
|---------------------------------------------------------------------------|
|*Satellite antenna| block-specific nadir angle-dependent "absolute" PCVs |
| phase center | applied from file igs05_wwww.atx; no azimuth-dependent |
| corrections | corrections applied |
| | [refer to IGS Mail #5189, 17 Aug 2005] |
|---------------------------------------------------------------------------|
|*Satellite clock | 2nd order relativistic correction for non-zero |
| corrections | orbit ellipticity (-2*R*V/c) applied |
| | [NOTE: other dynamical relativistic effects under |
| | Orbit Models] |
|---------------------------------------------------------------------------|
| GPS attitude | GPS satellite yaw attitude model: applied (Bar-Sever, |
| model | 1995) based on nominal yaw rates |
|---------------------------------------------------------------------------|
|*RHC phase | phase wind-up applied according to Wu et al. (1993) |
| rotation corr. | |
|---------------------------------------------------------------------------|
|*Ground antenna | "absolute" elevation- & azimuth-dependent (when |
| phase center | available) PCVs & L1/L2 offsets from ARP applied from |
| offsets & | file igs05_wwww.atx |
| corrections | [refer to IGS Mail #5189, 17 Aug 2005] |
|---------------------------------------------------------------------------|
|*Antenna radome | calibration applied if given in file igs05_wwww.atx; |
| calibrations | otherwise radome effect neglected (radome => NONE) |
|---------------------------------------------------------------------------|
|*Marker -> antenna| dN,dE,dU eccentricities from site logs applied to |
| ARP eccentricity | compute station marker coordinates |
|---------------------------------------------------------------------------|
| Troposphere | met data input: latitude, longitude, height, & DOY |
| a priori model | climate model from Boehm et al. (2007) |
| | (GPT version 2006June16); |
| | rel. humidity set to 50% for all sites |
| (parameter |--------------------------------------------------------|
| estimation is | zenith delay: Saastamoinen (1972) "dry" + "wet" using |
| below) | synthesized input met data |
| |--------------------------------------------------------|
| | mapping function: GMF (Boehm et al., 2006) for dry & |
| | wet zenith delays individually |
| |--------------------------------------------------------|
| | horiz. grad. model: no a priori gradient model is used |
|---------------------------------------------------------------------------|
|*Ionosphere | 1st order effect: accounted for by dual-frequency |
| | observations in linear combination |
| |--------------------------------------------------------|
| | 2nd order effect: no corrections applied |
| |--------------------------------------------------------|
| | other effects: no other corrections applied |
|---------------------------------------------------------------------------|
|*Tidal |*solid Earth tide: IERS 2003 (dehanttideinel.f routine, |
| displacements | based on Ch. 7.1.2) |
| |--------------------------------------------------------|
| |*permanent tide: zero-frequency contribution left in |
| (IERS Conventions| tide model, NOT in site coordinates |
| 2003, Ch. 4, eqn |--------------------------------------------------------|
| 11 contributions)|*solid Earth pole tide: IERS 2003; mean pole removed |
| | by linear trend (Ch. 7, eqn 23a & 23b) |
| |--------------------------------------------------------|
| |*oceanic pole tide: no model is applied |
| | [IERS Conventions updated, Ch. 7, |
| | eqn 27] |
| |--------------------------------------------------------|
| |*ocean tide loading: IERS Conventions 2003 (updated |
| | Ch. 7, 2006) using site-dependent |
| | amps & phase for 11 main tides from |
| | Bos & Scherneck website for FES2004 |
| | model; NEU site displacements computed |
| | using hardisp.f from D. Agnew; CMC |
| | corrections applied to station tidal |
| | coefficients and to SP3 orbits. |
| | (See also NOTES below.) |
| |--------------------------------------------------------|
| |*ocean tide geocenter: site-dependent coeffs corrected |
| | for center of mass motion of whole |
| | Earth; CMC corrections also applied |
| | to SP3 orbits. (See also NOTES below.) |
| |--------------------------------------------------------|
| | atmosphere tides: corrections for S1 & S2 tidal |
| | pressure loading not applied (no model |
| | available yet) |
| | [IERS model under development] |
|---------------------------------------------------------------------------|
|*Non-tidal | atmospheric pressure: not applied |
| loadings |--------------------------------------------------------|
| | ocean bottom pressure: not applied |
| |--------------------------------------------------------|
| | surface hydrology: not applied |
| |--------------------------------------------------------|
| | other effects: none applied |
|---------------------------------------------------------------------------|
|*Earth orientation| ocean tidal: diurnal/semidiurnal variations in x,y, & |
| variations | UT1 applied according to IERS 2003 (ortho_eop.f)|
| |--------------------------------------------------------|
| (near 12 & 24 hr | atmosphere tidal: S1, S2, S3 tides not applied |
| only; longer | [no IERS model specified yet] |
| period tidal |--------------------------------------------------------|
| corrections | high-frequency nutation: prograde diurnal polar motion |
| should not be | corrections (IERS 2003, Table 5.1) applied |
| applied) | using IERS routine PMsdnut.for |
| |--------------------------------------------------------|
| |
| [NOTE: effects are included in observation model as well as in the |
| transformation of orbits from inertial to terrestrial frame] |
=============================================================================
=============================================================================
| REFERENCE FRAMES |
|---------------------------------------------------------------------------|
| Time argument | GPS time as given by observation epochs, which is |
| | offset by only a fixed constant (approx.) from TT/TDT |
| | |
| | [NOTE: Please specify which general relativistic |
| | timescale is the underlying basis for the time |
| | argument used in the analysis. For instance, |
| | geocentric time, TCG, is recommended by the IAU but |
| | is not generally used in practice; see NOTES below.] |
|---------------------------------------------------------------------------|
| Inertial | geocentric; mean equator and equinox of 2000 Jan 1.5 |
| frame | (J2000.0) |
|---------------------------------------------------------------------------|
| Terrestrial | ITRF2005 reference frame realized through the set of up|
| frame | to 130 station coordinates and velocities given in the |
| | IGS internal realization IGS05.snx (aligned to |
| | ITRF2005). Some reference stations may be excluded |
| | based on significant non-linear motions or |
| | discontinuities. |
| | The datum is specified tightly for Rapid solutions by |
| | fixing the orientation and origin to IGS05 using |
| | NNR+NNT constraints wrt IGS05 coordinates. |
| | The datum for Finals is specified only for orientation |
| | using NNR constraints wrt IGS05 coordinates. |
|---------------------------------------------------------------------------|
| Tracking | use all available stations of the 132 IGS05 set, plus |
| network | add others based mostly on geometry up to a total of |
| | ~ 315 stations; data are processed in double-difference|
| | subnets and combined at the normal equation level; |
| | a core net ensures interconnection of the subnets. |
| | Double-differenced baseline network defined using |
| | optimal Delaunay triangulation algorithm (from |
| | 2007-01-14); see Renka (1997). |
|---------------------------------------------------------------------------|
| Interconnection | precession: IAU 1976 Precession Theory |
| |--------------------------------------------------------|
| (EOP parameter | nutation: IAU 1980 Nutation Theory, with daily offset |
| estimation is | corrections applied from IERS Bulletin A. |
| below) | |
| |--------------------------------------------------------|
| | a priori EOPs: UT1 interpolated from IERS Bulletin A, |
| | updated weekly. Polar motion interpolated |
| | from IGS Rapid and Ultra-rapid realizations, |
| | updated every six hours. |
=============================================================================
=============================================================================
| ORBIT MODELS |
|---------------------------------------------------------------------------|
| Geopotential | GEM-T3 model up to degree and order 8; |
| (static) | C21 & S21 modeled according to polar motion variations |
| | (IERS 2003, Ch. 6) |
| |--------------------------------------------------------|
| | GM=398600.4415 km**3/sec**2 (for TT/TDT time argument) |
| | [NOTE: see Relativity Notes below.] |
| |--------------------------------------------------------|
| | AE = 6378136.3 m |
|---------------------------------------------------------------------------|
| Tidal variations |*solid Earth tides: C20,C21,S21,C22, and S22 as in IERS |
| in geopotential | (1992); n=2 order-dependent Love numbers & frequency |
| | dependent corrections for 6 (2,1) tides from Richard |
| | Eanes (private comm., 1995) |
| |--------------------------------------------------------|
| | ocean tides: no model applied |
| |--------------------------------------------------------|
| |*solid Earth pole tide: no model applied |
| |--------------------------------------------------------|
| | oceanic pole tide: no model applied |
|---------------------------------------------------------------------------|
| Third-body | Sun & Moon as point masses |
| forces | |
| |--------------------------------------------------------|
| | ephemeris: Generated from the MIT PEP program |
| |--------------------------------------------------------|
| | GM_Sun 132712440000.0000 km**3/sec**2 |
| | GM_Moon 4902.7989 km**3/sec**2 |
|---------------------------------------------------------------------------|
| Solar radiation | a priori: Berne 9-parameter SRP model with D,Y,B |
| pressure model | scales plus once-per-rev sines & cosines; |
| | a priori values from fit to prior day's |
| | orbit & weak constraints applied to the |
| | 6 periodic terms. (thru wk 1432) |
| | |
| | From wk 1433 the CODE operational version of |
| | their SRP model is applied, which adjusts |
| | the D,Y,B offsets plus once-per-rev sine & |
| | cosine only for the B direction (orthogonal |
| | to the Direct and Y-axis directions). In |
| | addition, the velocities of all SVs are |
| | allowed to change at noon each day subject |
| | to a constraint of 10^-6 to 10^-5 m/s. No |
| | other constraints are applied. A priori |
| | values continue to come from fit to prior |
| | day's orbit. |
| | |
| | Shielding from solar radiation by the earth |
| | and moon is handled by scaling the SRP |
| | acceleration according to the fraction of |
| | the shielding (e.g., 0 <= lambda <= 1). |
| (parameter |--------------------------------------------------------|
| estimation is | Earth shadow model: umbra & penumbra included |
| below) |--------------------------------------------------------|
| | Earth albedo: not applied |
| |--------------------------------------------------------|
| | Moon shadow model: umbra & penumbra included (from |
| | wk 1424) |
| |--------------------------------------------------------|
| | satellite attitude: model of Bar-Sever (1995) applied; |
| | using nominal yaw rates |
| |--------------------------------------------------------|
| | other forces: none applied |
|---------------------------------------------------------------------------|
|*Relativitic | dynamical correction: not applied |
| effects | (see IERS 2003, Ch. 10, eqn 1) |
| |--------------------------------------------------------|
| | gravitational time delay: IERS 2003, Ch. 11, eqn 17 |
| | applied |
| |--------------------------------------------------------|
| |
| [NOTE: see NOTES ON RELATIVISTIC EFFECTS below.] |
|---------------------------------------------------------------------------|
| Numerical | variable (high) order Adams-Moulton predictor-corrector|
| integration | with direct integration of second-order equations |
| |--------------------------------------------------------|
| | integration step-size: variable |
| |--------------------------------------------------------|
| | starter procedure: Runge-Kutta Formulation; initial |
| | conditions taken from prior orbit solution at 12:00 |
| |--------------------------------------------------------|
| | arc length: 24 hours (00:00:00 - 23:59:30 GPS time) |
=============================================================================
=============================================================================
| ESTIMATED PARAMETERS (& APRIORI VALUES & CONSTRAINTS) |
| |
| Note on NGS parameter estimation: PAGES uses batch weighted least-squares |
| estimation. Time-varying quantities can be modeled using offset |
| parameters for specified intervals. Offset parameters at boundaries |
| between fitting intervals can be constrained to be equal, which gives |
| a piecewise linear, continuous model. Otherwise, piecewise linear step |
| offsets are estimated. In general, a priori constraints can be applied |
| for any parameter. |
| |
| For efficiency, the processing of large networks is usually done by first |
| processing suitable subnetworks down to reduced normal equations, which |
| are then combined to determine global parameters. |
| |
|---------------------------------------------------------------------------|
| Adjustment | weighted least squares and Helmert blocking to |
| method | process subnetworks separately (pages) and then |
| | combined (gpscom). |
|---------------------------------------------------------------------------|
| Data span | 24 hours used for each daily analysis |
| | (00:00:00 - 23:59:30 GPS time) |
|---------------------------------------------------------------------------|
|*Station | all station coordinates are adjusted, relative to the |
| coordinates | a priori values from IGS05.snx; a no-net-rotation |
| | condition is applied wrt the IGS05 frame using up to |
| | 132 reference frame stations; apriori sigmas for non- |
| | reference frame stations are 1 m for each component. |
|---------------------------------------------------------------------------|
| Satellite clocks | not estimated but eliminated by double-differencing; |
| | Broadcast values reported in SP3 files. |
| |--------------------------------------------------------|
| | sp3,clk files: Broadcast values inserted |
|---------------------------------------------------------------------------|
| Receiver clocks | not estimated but eliminated by double-differencing; |
| | observations are adjusted in the preprocessing using |
| | receiver clock offsets derived from the pseudoranges |
| | (to ensure that all obs are aligned to the same time |
| | scale) but no receiver clocks are truly estimated. |
|---------------------------------------------------------------------------|
| Orbits | thru wk 1432: |
| | Geocentric position and velocity, solar radiation |
| | pressure scales and once-per-revolution perturbation |
| | terms. Radiation pressure scaling factors and |
| | perturbation terms are estimated for each of the |
| | orthogonal directions: satellites - sun, body centered |
| | Y, and orthogonal third directions estimated as |
| | constant offsets for each one-day arc; plus once-per- |
| | rev sine/cosine terms are estimated with apriori values|
| | from the prior day, and weak apriori constraints |
| | |
| | from wk 1433: |
| | Geocentric positions and velocities, solar radiation |
| | pressure scales in 3 directions and once-per-rev terms |
| | in 1 direction, & noon velocity breaks in 3 directions.|
| | Radiation pressure scale factors estimated for each |
| | orthogonal direction: satellite-sun, body-centered Y, |
| | & orthogonal 3rd component, estimated as constant |
| | offsets for each one-day arc; plus once-per-rev sine & |
| | cosine terms estimated only for 3rd component. |
| | Geocentric velocity breaks adjusted in all 3 |
| | components with change constraints of 10^-6 to |
| | 10^-5 m/s. No apriori applied on estimates. |
| |--------------------------------------------------------|
| | sp3 files: orbits transformed to crust-fixed (rotating)|
| | frame accounting for geocenter motions due |
| | to ocean tides and for subdaily tidal EOP |
| | variations |
| | [NOTE: see NOTES below for details] |
|---------------------------------------------------------------------------|
| Satellite | no attitude parameters are adjusted |
| attitude | |
|---------------------------------------------------------------------------|
| Troposphere | zenith delay: residual delays are adjusted for each |
| | station assuming mostly dominated by |
| | "wet" component; before Rapid week 1420-1|
| | and Final week 1416, the zenith delay was|
| | parameterized by a piecewise linear, |
| | continuous model with 1-hr intervals. |
| | Now, the delay is parameterized by a |
| | piecewise-constant, discontinuous model. |
| |--------------------------------------------------------|
| | mapping function: GMF (Boehm et al., 2006) wet function|
| | used to estimate zenith delay residuals |
| |--------------------------------------------------------|
| | zenith delay epochs: each integer hour |
| |--------------------------------------------------------|
| | gradients: one N-S & one E-W gradient parameter at the |
| | beginning and end of each day for each |
| | station, with continuous linear variation|
| | during the day; no a priori constraints |
| | are applied (see Bar-Sever et al, 1998) |
|---------------------------------------------------------------------------|
| Ionospheric | not estimated |
| correction | |
|---------------------------------------------------------------------------|
| Ambiguity | real-valued double-differenced phase cycle ambiguities |
| | adjusted except when they can be resolved confidently |
| | (<4.5 cm uncertainty), in which case they are fixed; |
| | roughly 95% of all ambiguities are fixed using modern |
| | network data |
|---------------------------------------------------------------------------|
|*Earth orientation| daily x & y pole offsets, pole-rates, and LOD at noon |
| parameters (EOP) | epochs; x and y pole estimated as piece-wise, linear |
| | offsets from IERS Bulletin A a prioris and IGS ERP |
| | a prioris over each 1-day segment; estimates then |
| | transformed to equivalent offsets and rates at noon |
| | epochs to be consistent with IGS conventions; UT1 not |
| | adjusted |
|---------------------------------------------------------------------------|
| Other | none |
| parameters | |
=============================================================================
=============================================================================
| NOTES ON RELATIVISTIC EFFECTS |
|---------------------------------------------------------------------------|
| Here is a brief summary of the relativistic effects involved in modeling |
| satellite orbits to determine a terrestrial reference frame (TRF), etc: |
| * The dynamical formulation should be in an geocentric frame, applying |
| the relativitistic corrections listed below for the effects on signal |
| propagation and satellite dynamics. |
| * If the TDT time scale (i.e., no secular rate term included between TT = |
| TAI+32.184s and the time coordinate used for the dynamics) is used, as |
| is still common despite IAU/IUGG recommendations to use TCG, then the |
| appropriate value for GM = 398600.4415 km**3/sec**2. However, this |
| choice of modeling will result in a TRF which differs from TCG units; |
| the TRF will need to be scaled upward by (1 + L_G) = (1 + 0.69... ppb) |
| to be consistent with a TCG timescale. |
| * If the IAU-recommended TCG timescale is used (the secular rate term |
| included between TT and the TCG time coordinate used for the dynamics), |
| then the appropriate value for GM = 398600.4418 km**3/sec**2. For this |
| choice of modeling, the TRF scale will be consistent with IAU/IUGG |
| recommendations. |
| * The observation modeling should include the following relativistic |
| effects: |
| [1] The 1st-order effects on GPS satellite clocks due to time dilation |
| and gravitational potential shifts have been accounted for by offsets |
| applied in the oscillator settings aboard the spacecraft, assuming |
| nominal orbital elements. The 2nd-order effects due to non-circular |
| orbits must be handled by applying a periodic time correction: |
| -2(R V)/c^2 |
| where R is the satellite position, V its velocity, and c the speed of |
| light; see IS-GPS-200 (formerly ICD-GPS-200). |
| [2] The coordinate time of propagation, including the gravitational delay |
| ("gravitational bending"), as given in IERS Conventions 2003, Ch. 11, |
| eqn 17, for the effect of the Earth's mass. |
| [3] The "dynamical correction" to the acceleration of near-Earth |
| satellites, as given in IERS Conventions 2003, Ch. 10, eqn 1. The |
| 2004 version differs from earlier editions by the addition of terms |
| for the Lense-Thirring precession (frame dragging) and geodesic (de |
| sitter) precession, which are probably negligible for the short arcs |
| used in most GPS analyses. |
| Note that the IERS/IGS formulation for clock modeling neglects the Earth's|
| oblateness, an effect estimated by Kouba (2004) to be ~0.2 ns/day (same |
| level as IGS clock accuracy) with periodic variations at 6 hrs and near |
| 14 days. |
=============================================================================
=============================================================================
| NOTES ON HANDLING OCEAN TIDAL LOADING DISPLACEMENT EFFECTS |
|---------------------------------------------------------------------------|
| There are three main parts involved in implementing model corrections for |
| ocean tidal loading (OTL) effects in GPS analyses to be fully self- |
| consistent: |
| [1] Site-dependent tidal coefficients |
| Site-dependent amplitude & phase values for the 11 main tides (in BLQ |
| format) are generated upon request by the Bos-Scherneck OTL service at |
| http://www.oso.chalmers.se/~loading/ |
| Users are advised to select one of the more modern ocean models from the |
| list available, such as FES2004 models. |
| For the option "Do you want to correct your loading values for the [center|
| of mass] motion?" the answer should be "YES" (but the default is "NO"). |
| [Note that for users of IGS orbits (in sp3 format) it is generally *not* |
| necessary to consider the center of mass effect because this has already |
| been taken into account by the IGS (see below). That is, the IGS orbits |
| are expressed with respect to the Earth's crust as a fixed frame. So, for|
| such applications, site-dependent coefficients should be with the option |
| "Do you want to correct your loading values for the motion?" set to the |
| default "NO".] |
| [2] Site-dependent tidal displacements |
| Given previously computed site-dependent amp & phase values for the 11 |
| main tides (in BLQ format), the hardisp.f routine, written by Duncan Agnew|
| (UCSD), determines local dU, dS, dW displacements. The code can be found |
| at the IERS Conventions Update site at |
| ftp://tai.bipm.org/iers/convupdt/chapter7/hardisp.f |
| This routine considers a total of 141 constituent tides using a spline |
| interpolation of the tidal admittances, achieving a precision is about 1%.|
| [3] Center-of-mass orbit correction |
| After the Analysis Centers determine the GPS orbits in an inertial frame, |
| taking account of the OTL effects as described above, it is necessary as |
| a final step in generating sp3 format orbit results to account for the |
| crust-frame motions due to the ocean tidal mass. This can be done by |
| computing the net crustal frame translations dX(t), dY(t), and dZ(t) |
| according to the method given by Scherneck at |
| http://www.oso.chalmers.se/~loading/cmc.html : |
| |
| dX(t) = SUM_i=1,11 { Xin(i) * cos(ANGLE(t,i)) + Xcr(i) * sin(ANGLE(t,i)) }|
| dY(t) = SUM_i=1,11 { Yin(i) * cos(ANGLE(t,i)) + Ycr(i) * sin(ANGLE(t,i)) }|
| dZ(t) = SUM_i=1,11 { Zin(i) * cos(ANGLE(t,i)) + Zcr(i) * sin(ANGLE(t,i)) }|
| |
| where ?in(i) are the in-phase and ?cr(i) are the cross-phase amplitudes |
| for the 11 main ocean tides. ANGLE(t,i) is the angular argument returned |
| by the IERS subroutine ARG(YEAR,DOY,ANGLE) for YEAR being the (current |
| year - 1900) and DOY being the day of year and fraction thereof. The ARG |
| routine is available at the IERS Conventions Update website: |
| ftp://tai.bipm.org/iers/convupdt/chapter7/ARG.f |
| Scherneck has tabulated the center of mass motion in-phase and cross-phase|
| coefficients for the various ocean models at: |
| http://www.oso.chalmers.se/~loading/CMC/ |
| Note that on each tidal constituent record, the entries are ordered as: |
| tide, model name, Zin, Zcr, Xin, Xcr, Yin, Ycr |
| using the format (a,1p,t42,3(2x,2e12.4)). |
| In order to correct the GPS inertial orbits (ORB_cm) to the moving |
| crust-fixed frame (ORB_sp3), in addition to whatever other transformations|
| are applied, the following translations should also be made: |
| ORB_cm(t) - dXYZ(t) --> ORB_sp3(t) |
| where dXYZ(t) is the dX(t), dY(t), dZ(t) vector computed above. Note that|
| this correction is exactly analogous to the rotational corrections that |
| must be applied to create sp3 orbits whenever a sub-daily EOP tidal model |
| is used in the GPS data analysis. |
=============================================================================
=============================================================================
| REFERENCES |
|---------------------------------------------------------------------------|
| Bar-Sever, Y.E., New GPS attitude model, IGS Mail #591, 1995, |
| http://igscb.jpl.nasa.gov/mail/igsmail/1994/msg00166.html |
| |
| Bar-Sever, Y., P.M. Kroger, & J.A. Borjesson, Estimating horizontal |
| gradients of tropospheric delay with a single GPS receiver, J. Geoph. |
| Res., 103(B3), 5019-5035, 1998. |
| |
| Boehm, J., A.E. Niell, P. Tregoning, & H. Schuh, Global Mapping Function |
| (GMF): A new empirical mapping function based on numerical weather |
| model data, Geophys. Res. Lett., 33, L07304, doi: 10.1029/2005GL025545, |
| 2006. |
| |
| Boehm, J., R. Heinkelmann, & H. Schuh, Short Note: A global model of |
| pressure and temperature for geodetic applications, J. Geod., |
| doi:10.1007/s00190-007-0135-3, 2007. |
| |
| Bos, M.S., & H.-G. Scherneck, website at www.oso.chalmers.se/~loading/ |
| |
| IERS Conventions 2003, D.D. McCarthy & G. Petit (editors), IERS Technical |
| Note 32, Frankfurt am Main: Verlag des Bundesamts fuer Kartographie und |
| Geodaesie, 2004. (see also updates at website) |
| |
| Kouba, J., Improved relativistic transformations in GPS, GPS Solutions, |
| 8(3), 170-180, 2004. |
| |
| Renka, R., Algorithm 772: STRIPACK, Delaunay triangulation and Voronoi |
| diagram on the surface of a sphere, ACM Transactions on Mathematical |
| Software, 23(3), 1997. available at: |
| http://orion.math.iastate.edu/burkardt/f_src/stripack/stripack.html |
| |
| Saastamoinen, J., Atmospheric correction for the troposphere and |
| stratosphere in radio ranging of satellites, in The Use of Artificial |
| Satellites for Geodesy, Geophys. Monogr. Ser. 15 (S.W. Henriksen et al.,|
| eds.), AGU, Washington, D.C., pp.247-251, 1972. |
| |
| Wu, J.T., S.C. Wu, G.A. Hajj, W.I. Bertiger, & S.M. Lichten, Effects of |
| antenna orientation on GPS carrier phase, Manuscripta Geodaetica,18, |
| 91-98, 1993. |
=============================================================================
|* = strong consistency with IERS/IGS conventions is especially important |
| for these items |
=============================================================================