# Solution description
Agency: Norwegian Mapping Authority
Product: Daily Sinex
Software: Where (https://kartverket.github.io/where/)
Solution code: 2019a
## Input
Observations: Group delays from version 4 vgosdb files.
Apriori CRF: ICRF3 with galactic aberration (value in observation file as backup)
Apriori TRF: ITRF2014 with postseismic deformations (latest VTRF or value in observation file as backup)
Apriori EOP: IERS c04 or Bulletin A
Planet ephemerides: de430
## Models
EOP variations:
+ Ocean tides and liberation are added to the X-pole, Y-pole and UT1 (PMSDNUT2.F, ORTHO_EOP.F and UTLIBR.F from the IERS Conventions website)
Station displacements:
+ Solid Earth tide (DEHANTTIDEINEL.F from the IERS Conventions website)
+ Solid Earth pole tide (IERS 2010 Conventions) with mean pole 2015 model
+ Ocean loading (HARDISP.F from IERS Conventions website with TPXO.7.2 from http://holt.oso.chalmers.se/loading/)
+ Ocean pole tide (IERS 2010 Conventions) with mean pole 2015 model
+ Tidal atmospheric loading (IERS 2010 Conventions)
+ Non-tidal atmospheric loading (gridded 3D-displacements from http://vmf.geo.tuwien.ac.at/)
+ Eccentricity vector (file from GSFC).
Delay models:
+ Gravitational and geometric delay from IERS 2010 conventions
+ Troposphere from IERS Conventions with VMF1
+ Axis offset and thermal deformation from Axel Nothnagel:Conventions on thermal expansion modeling of radio telescopes for geodetic and astrometric VLBI
+ Cable delay and ionosphere from observation file
+ Clock polynomial reduced from the residuals
## Estimation
Where uses a Kalman filter with a Modified Bryson-Frazier Smoother to estimate parameters. The implementation is first described in Bierman2006: Factorization Methods for Discrete Sequential Estimation and later more clearly recited in Gibbs2011: Square Root Modified BrysonFrazier Smoother. Normal equations are generated using the method described in Mysen2016: On the equivalence of Kalman filtering and leastsquares estimation. The observation noise covariance used in the Kalman Filter is set to the obs_ferr^2 + (1cm)^2.
### Parameters
Parameters are modelled either as a constant (one value estimated for the entire session) or as a continuous piecewise linear parameter. The constant parameters are station coordinates, source coordinates and Earth Orientation Parameters, namely polar motion, polar motion rate, UT1-UTC, LOD, precession/nutation.
For each station there is two continuous piecewise linear parameter for the horizontal gradients (east and north), additional clock error (except the reference clock) and the zenith wet delay. By default the linear segments are 1 hour for clocks and troposphere and 6 hours for horizontal gradients.
### Estimates
The SINEX SOLUTION/ESTIMATE block is computed by solving the normal equation and by adding NNT and NNR constraints on stations from ITRF2014 and NNR conditons on all ICRF3 sources.
## Outliers
Outliers are removed in several stages. By default observations with quality flag higher than zero or ionosphere quality flag less than zero is discarded. After estimating the clock polynomial all observations with residuals higher than 8 times the rms are discarded. Then the clock polynomial is refitted to the remaining obsevations. The purpose of this outlier test is to avoid greatly distorted clock polynomials based on just a few outliers. In most cases no iterations are needed, but if quality flags are missing (which is sometimes the case for vgosDb files) several iterations are needed and the limit needs to be lowered. After estimating all the parameters a second outlier test is applied. This time residuals larger than 3 times the rms are removed and the estimation process is repeated. The process stops after the second iteration.