%=SNX 2.10 USN 26:118:34268 USN 26:117:63010 26:117:66586 R 00001 2   E         
*
* Created on:   2026.04.28-09:31:08 local time
* Created at:   United States Naval Observatory
* Created by:    (  )
* Generated by: routine WRITE_SINEX_J , revision date 2023-01-19
*
* -----------------------------------------------------------------------------
*
+FILE/REFERENCE
 DESCRIPTION       USN
 OUTPUT            Single session VLBI solution
 CONTACT            <>
 SOFTWARE          VLBI analysis system Calc/Solve, revision date 2025.04.10
 HARDWARE          x86_64 Linux 5.14.0-611.47.1.el9_7.x86_64
 INPUT             VLBI experiment v26117, database 20260427-v26117 version 006
-FILE/REFERENCE
*
* -----------------------------------------------------------------------------
*
+FILE/COMMENT
 
 Format Description: http://gemini.gsfc.nasa.gov/solve_root/help/sinex.html
 Solution description: n/a
 
 
>>> FORMAT DESCRIPTION <<< 
>>> ################## <<< 
 
  Sinex output implementation in the VLBI Analysis software system Calc/Solve
                                       OR
                                  SINEX V2.10


                                Leonid Petrov (Original author)
                                John Gipson (CALIBRATION blocks)


                                2021.01.19


                                Abstract

   This document describes how Calc/Solve writes down a listing
of a VLBI solution in Sinex format.



Questions and comments about this guide should be sent to:

Dan MacMillan (Daniel.S.MacMillan@nasa.gov)
John Gipson   (John.M.Gipson@nasa.gov)


                                Table of contents:


1 ................ Overview


2 ................ Deviations from the SINEX 1.00 standard

   2.1 ........... New block SOLUTION/CONSTRAINT_EQUATION_INFO
   2.2 ........... New block SOLUTION/CONSTRAINT_EQUATION_MATRIX
   2.3 ........... New block SOLUTION/CONSTRAINT_EQUATION_VECTOR
   2.4 ........... New block SOLUTION/CONSTRAINT_WEIGHT_MATRIX
   2.5 ........... New block SOLUTION/NORMAL_MATRIX BLOCK
   2.6 ........... New block SOLUTION/NORMAL_VECTOR BLOCK
   2.7 ........... New block NUTATION/DATA
   2.8 ........... New block PRECESSION/DATA
   2.9 ........... New block SOURCE/ID
   2.10 .......... New block SOLUTION/NORMAL_CALIBRATION_ESTIMATE
   2.11 .......... New block SOLUTION/NORMAL_CALIBRATION

3 ................ Deviations from the SINEX 2.10 standard


4 ................ Implementation in Solve

   4.1 ........... Syntax of INCLUDE_PARAM and EXCLUDE_PARAM lists
   4.2 ........... Examples of INCLUDE_PARAM and EXCLUDE_PARAM lists
   4.3 ........... Treatment of station with discontinuous motion
   4.4 ........... Restrictions

________________________________________________________________________________

        1 Overview
        ==========

  SINEX stands for "Solution INdependent EXchange format". This format was
developed by Blewitt et al. (1994)
http://www.dgfi.badw-muenchen.de/gps/sinex.html and
http://alpha.fesg.tu-muenchen.de/iers/sinex/sinex_v2_appendix1.pdf
for facilitating the task of combining several GPS solutions. Original
design of Sinex format was made for solving this specific task. However,
later this format evolved towards to a common machine-readable form of
solution listings for other space geodesy techniques, VLBI and SLR, and
attempts were made for overcoming flaws of the original design. This
process of evolution is not yet completed, therefore, different software
systems implement a little bit different flavors of Sinex format.

  Listings in Sinex format produced by Solve contain information about
stations, sources, estimates of the parameters, their covariance matrix,
constraint equation, right-hand side of constraint equations and weight
matrix of constraint equations. In addition to these results, a portion of
the decomposed normal matrix and normal vector can be included in the
listing as well. A user has control which blocks should be included in the
listing. The current implementation of the Sinex format does not allow
to include in the listing any parameter which was solved for. Only
some type of parameters, like station position, EOP, etc can be included.
However, a user has total control which parameters among the parameters
of the supported type are to be included or not included in the listing.


        2 Deviations from the SINEX 1.00 standard
        =========================================


   Solve currently writes listing either in Sinex 2.10 format or in
Sinex 2.20 format. Deviations from the Sinex 1.00 standard are as follows:

1)  Eight new blocks were added:

   SOLUTION/CONSTRAINT_EQUATION_INFO
   SOLUTION/CONSTRAINT_EQUATION_MATRIX
   SOLUTION/CONSTRAINT_EQUATION_VECTOR
   SOLUTION/CONSTRAINT_WEIGHT_MATRIX

   The purpose of these four blocks is to overcome the flaw of original
design of Sinex format and provide complete information about all
constraints used in the solution.

Prior to January 2021 there were two blocks called
   SOLUTION/DECOMPOSED_NORMAL_MATRIX
   SOLUTION/DECOMPOSED_NORMAL_VECTOR
These were the normal equations AFTER clocks and atmospheres had been squeezed out.
The purpose of these blocks is to provide information about transformed
normal equations before applying constraints. NB: one of the three items:
covariance matrix, constraint equations and decomposed normal equations is
redundant: having two of them one can derive the third one.

Since these were not part of the SINEX standard they were renamed
   SOLUTION/NORMAL_EQUATION_MATRIX
   SOLUTION/NORMAL_EQUATION_VECTOR

   NUTATION/DATA
   PRECESSION/DATA

   The purpose of this section is to provide information about used
nutation/precession model and to define parameter "estimates of nutation
angles".

   John Gipson added two blocks to allow users to 'back-out' the
effect of calibrations.
  SOLUTION/NORMAL_CALIBRATION_ESTIMATE
  SOLUTION/NORMAL_CALIBRATION
Prior to January 2021 the second was called SOLUTION/DECOMPOSED_CALIBRATION


2) SOLUTION/STATISTICS block has new items:

   WEIGHTED SQUARE SUM OF O-C    sum { y(T) * w * y }

   WRMS OF POSTFIT RESIDUALS     sum { (A*e - y)(T) * w * (A*e - y) )/Sp ( w )

   where y -- the difference between the observed time delay and theoretical;
         A -- matrix of equations of conditions;
         e -- vector of the parameter adjustments;
         w -- weight matrix;
         Sp   -- stands for the mathematical operation of computing trace of
                 a matrix: the sum of diagonal elements.

   Summing is done over all observations used in parameter estimation.

   Comment: field WEIGHTED SQUARE SUM OF O-C is not computed in global mode.

   Meaning of other parameters:

   NUMBER OF OBSERVATIONS          total number of used observables

   NUMBER OF UNKNOWNS              total number of unknowns, including those,
                                   which are not shown in the Sinex listing

   SQUARE SUM OF RESIDUALS (VTPV)  sum { (A*e - y)(T) * w * (A*e - y) )

   VARIANCE FACTOR                 sum { (A*e - y)(T) * w * (A*e - y) )}/
                                       ( N - M - Sp( Cov(A) * B(T) * z * B ) )

   where Cov(A) -- covariance matrix of the entire solution
                   (NB: Sinex listing may have only a portion of the solution)
         B -- matrix of equations of constraints;
         z -- weight matrix of constraints;
         N -- total number of equations of conditions (observables);
         M -- total number of unknowns.


3) The blocks which keep element of matrices do not have fields
   "Second Matrix Element" and  "Third Matrix Element".

   The purpose of this change is to facilitate the process of creation of
the listing and to reduce significantly the probability of errors.

4) SOLUTION/MATRIX_APRIORI is not provided. The reason is that Solve does not
operate the notion of apriori covariance matrix. And it also uses singular
constraints which cannot be reduced to the form of apriori covariance matrix.
Since full information about constraints is provided in other blocks,
SOLUTION/MATRIX_APRIORI is considered as an obsolete block.


                2.1 New block SOLUTION/CONSTRAINT_EQUATION_INFO
                ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

         ___________________________________________________________________
        |S_O_L_U_T_I_O_N__C_O_N_S_T_R_A_I_T__I_N_F_O__B_L_O_C_K_____________|
        |                |                                   |              |
        |__Field_________|______Description__________________|___Format_____|
        |                |                                   |              |
        | Constraint     | Row index for the constraint      |  1X,I5       |
        | Equation Row   | equation matrix. It must match    |              |
        | Index          | the index of the constraint       |              |
        |                | equation.                         |              |
        |________________|___________________________________|______________|
        |                |                                   |              |
        | Constraint     | Identifier of the constraint      |  1X,A8       |
        | Equation       |                                   |              |
        | Identifier     |                                   |              |
        |________________|___________________________________|______________|
        |                |                                   |              |
        | Constraint     | Index of vector constraint.       |  1X,I5       |
        | Equation       | 1 for scalar constraint.          |              |
        | Sub-index      |                                   |              |
        |                |                                   |              |
        |________________|___________________________________|______________|
        |                |                                   |              |
        | Constraint     | Description of the constraint     |  1X,A40      |
        | Equation       |                                   |              |
        | Description    |                                   |              |
        |________________|___________________________________|______________|

  This block provides description of constraint equations. Matrix of
constraint equations has dimension N_cns * N_par, where N_cns -- the number
of constraint equations, N_par -- number of estimated parameters. The first
field of the CONSTRAINT_EQUATION_INFO keeps the index of the constraint,
the second field keeps constraint identifier. Currently, the following
constraint identifiers are supported:

   NNT_POS  -- net rotation on station position. This vector constraint defines
               three equations:
               1:  sum { Delta_X } = const
               2:  sum { Delta_Y } = const
               3:  sum { Delta_Y } = const
               where Delta_X, Delta_Y, Delta_Z are X, Y and Z component of
               the adjustment to station position.

   NNR_POS  -- net rotation on station position. This vector constraint defines
               three equations:
               1:  sum { Phi_X } = const
               2:  sum { Phi_Y } = const
               3:  sum { Phi_Y } = const
               where Phi_X, Phi_Y and Phi_Z are the components of the vector
               of a small rotation defined as
               Phi = ( r x Delta r )/ |r|^2 * R_e
                   here
                     r       -- vector of station coordinate;
                     Delta r -- vector of adjustments to station position
                     R_e     -- Earth's equatorial radius.
               Units: dimensionless

   NNT_VEL  -- net rotation on station velocity. This vector constraint defines
               three equations:
               1:  sum { Delta_X } = const
               2:  sum { Delta_Y } = const
               3:  sum { Delta_Y } = const
               where Delta_X, Delta_Y, Delta_Z are X, Y and Z component of
               the adjustment to station position.

   NNR_VEL  -- net rotation on station velocity This vector constraint defines
               three equations:
               1:  sum { Phi_X } = const
               2:  sum { Phi_Y } = const
               3:  sum { Phi_Y } = const
               where Phi_X, Phi_Y and Phi_Z are the components of the vector
               of a small rotation defined as
               Phi = ( r x Delta v )/ |r|^2 * R_e
                   here
                     r       -- vector of station coordinates;
                     Delta r -- vector of adjustments to station velocity;
                     R_e     -- Earth's equatorial radius.

               Units: 1/yr

   NNR_SRC  -- net rotation on source coordinates
               1:  sum { Phi_X } = const
               2:  sum { Phi_Y } = const
               3:  sum { Phi_Y } = const
               where Phi_X, Phi_Y and Phi_Z are the components of the vector
               of a small rotation

   EOP_XPL  -- constraint on X pole coordinate
   EOP_YPL  -- constraint on Y pole coordinate
   EOP_UT1  -- constraint on UT1 angle
   EOR_XPL  -- constraint on X pole rate
   EOR_YPL  -- constraint on Y pole rate
   EOR_UT1  -- constraint on UT1 rate

   VEL_U    -- constraint on Up    topocentric coordinate of station velocity
   VEL_E    -- constraint on East  topocentric coordinate of station velocity
   VEL_N    -- constraint on North topocentric coordinate of station velocity
   VEL_X    -- constraint on X  coordinate of station velocity
   VEL_Y    -- constraint on Y  coordinate of station velocity
   VEL_Z    -- constraint on Z  coordinate of station velocity

   STA_U    -- constraint on Up    topocentric coordinate of station position
   STA_E    -- constraint on East  topocentric coordinate of station position
   STA_N    -- constraint on North topocentric coordinate of station position
   STA_X    -- constraint on X  coordinate of station position
   STA_Y    -- constraint on Y  coordinate of station position
   STA_Z    -- constraint on Z  coordinate of station position


   BLC_VAL  -- constraint on baseline clocks
   DCL_ORG  -- constraint on declination of the set of certain sources
   GRD_OFF  -- constraint on atmosphere path delay gradient offset
   NUT_OFF  -- constraint on offset of nutation in longitude and nutation in
                             obliquity
   OAT_RAT  -- constraint on rate of changes of atmosphere path delay
   OCL_RAT  -- constraint on clock drift
   RAS_ORG  -- constraint on right ascension of the set of certain sources
   SRC_COO  -- constraint on source right ascension and declination
   STA_ORG  -- constraint on position of certain stations
   STA_TIE  -- constraint on differences in position of several sites
   VEL_DIR  -- constraint on horizontal projection of the differences
               in velocities of two stations
   VEL_ORG  -- constraint on velocities of certain stations
   VEL_SET  -- constraint on linear combination of velocity components
   VEL_TIE  -- constraint on differences in velocities of several sites
   VEL_VER  -- constraint on vertical component of station velocity

   Constraints on segmented parameters

   STA_PWC  -- constraint on site velocity in the the case when site position
               is modeled by linear spline
   GRD_RAT  -- constraint on atmosphere path delay gradient rate
   ATM_RAT  -- constraint on atmosphere path delay rate between segments
   CLO_RAT  -- constraint on clock rate between segments
   UT1_RAT  -- constraint on UT1 rate in the case of linear spline
                             EOP parametrization
   XPL_RAT  -- constraint on X pole coordinate in the case of linear spline
                             EOP parametrization
   YPL_RAT  -- constraint on Y pole coordinate in the case of linear spline
                             EOP parametrization


   Constraint equation sub-index is 1 for scalar constraint, like EOP_XPL and
   runs over components of vector constraints, like NNT_POS (1,2,3 in this
   example).


                2.2 New block SOLUTION/CONSTRAINT_EQUATION_MATRIX
                ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


   This block keep matrix of constraint equations. Equations are organized by
   rows. Zero elements are omitted.

       _____________________________________________________________________
      |__S_O_L_U_T_I_O_N__C_O_N_S_T_R_A_I_T__E_Q_U_A_T_I_O_N__B_L_O_C_K_____|
      |                  |                                   |              |
      |__Field___________|______Description__________________|___Format_____|
      |                  |                                   |              |
      | Constraint       | Row index for the constraint      |  1X,I5       |
      | equation row     | equation matrix. It must match    |              |
      | Index            | the index of the constraint       |              |
      |                  | equation.                         |              |
      |__________________|___________________________________|______________|
      |                  |                                   |              |
      | Constraint       | Column index for the Constraint   |   1X,I5      |
      | equation         | Equation. It must match the       |              |
      | column index     | parameter index in the            |              |
      |                  | SOLUTION/ESTIMATE block for the   |              |
      |                  | same parameter.                   |              |
      |__________________|___________________________________|______________|
      |                  |                                   |              |
      | Constraint       | Matrix element at the location    |   1X,E21.14  |
      | matrix element   | (row index, column index).        |              |
      |__________________|___________________________________|______________|


                2.3 New block SOLUTION/CONSTRAINT_EQUATION_VECTOR
                ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    This block keeps the right-hand side of constraint equations.

         ___________________________________________________________________
        |__S_O_L_U_T_I_O_N__C_O_N_S_T_R_A_I_T__V_A_L_U_E__B_L_O_C_K_________|
        |                |                                   |              |
        |__Field_________|______Description__________________|___Format_____|
        |                |                                   |              |
        | Constraint     | Row index for the constraint      |  1X,I5       |
        | Equation Row   | equation vector. It must match    |              |
        |                | the index of the constraint       |              |
        |                | equation.                         |              |
        |________________|___________________________________|______________|
        |                |                                   |              |
        | Right hand     | Value of right hand part of the   |
        | side value     | constraint equation.              |   1X,E21.15  |
        |________________|___________________________________|______________|
        |                |                                   |              |
        | Sigma          | Reciprocal weight which is        |              |
        |                | ascribed to this constraint       |   1X,E21.15  |
        |                | equation.                         |              |
        |________________|___________________________________|______________|
                                                             |              |
                                                             |     48       |
                                                             |______________|

                2.4 New block SOLUTION/CONSTRAINT_WEIGHT_MATRIX
                ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    This block contains the elements of the weight matrix of constraint
    equations. Zero elements are omitted.

      ______________________________________________________________________
     |_____________C_O_N_S_T_R_A_I_N_T___W_E_I_G_H_T___M_A_T_R_I_X__________|
     |                                                                      |
     |__Field__________________Description_______________________Format_____|
     |                   |                                   |              |
     | Row index of the  | Row index for the weight          |   1X,I5      |
     | weight matrix     | constraint matrix. It matches     |              |
     | of constraint     | the index of the constraint       |              |
     | equations         | equation.                         |              |
     |___________________|___________________________________|______________|
     |                   |                                   |              |
     | Column index of   | Column index for the weight       |   1X,I5      |
     | the weight matrix | constraint matrix. It matches the |              |
     | of constraint     | index of the constraint equation  |              |
     | equations         |                                   |              |
     |___________________|___________________________________|______________|
     |                   |                                   |              |
     | Weight matrix of  | Matrix element at the location    |   1X,E21.14  |
     | constraint        | (row index, column index).        |              |
     | equations element |                                   |              |
     |___________________|___________________________________|______________|


                2.5 New block SOLUTION/NORMAL_MATRIX BLOCK
                ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  This block contains decomposed normal equations for the subset of
  parameters described in the SOLUTION/ESTIMATE block. In the case if the
  SOLUTION/ESTIMATE block described all parameters adjusted in the solution,
  decomposed normal matrix is equivalent to the full normal matrix. In the
  case if the SOLUTION/ESTIMATE block describes only a subset of parameters,
  then the decomposed normal matrix D_ii is defined as

  D_ii = N_ii - N_ei(T) * (C_ee + N_ee){-1} * N_ei    where

        N_ii -- the block of normal matrix which corresponds to the
                equations included in the SOLUTION/ESTIMATE list;
        N_ee -- the block of normal matrix which corresponds to omitted
                parameters;
        N_ei -- the block of normal matrix which corresponds to the product
                of equations of conditions of the omitted parameters and
                parameters included in the SOLUTION/ESTIMATE list.
        C_ee -- the block of normal matrix of constraints which corresponds
                to omitted parameters;

  Solve computes  D_ii as   D_ii = (V_ii){-1} - C_ii      where

        V_ii -- covariance matrix of the parameters mentioned in
                SOLUTION/ESTIMATE list;
        C_ii -- the block of normal matrix of constraints which corresponds
                to the parameters in SOLUTION/ESTIMATE list.

        It is assumed that C_ei = 0

        C_ei -- the block of normal matrix of constraints which corresponds
                to the product of equations of constraints of the omitted
                parameters and parameters from the SOLUTION/ESTIMATE list.


         ___________________________________________________________________
        |__S_O_L_U_T_I_O_N__D_E_C_O_M_P_O_S_E_D__N_O_R_M_A_L__M_A_T_R_I_X___|
        |                |                                   |              |
        |__Field_________|______Description__________________|___Format_____|
        |                |                                   |              |
        | Decomposed     | Row index for the normal matrix.  |   1X,I5      |
        | normal matrix  | It must match the parameter index |              |
        | row index      | in the SOLUTION/ESTIMATE block    |              |
        |                | for the same parameter.           |              |
        |________________|___________________________________|______________|
        |                |                                   |              |
        | Decomposed     | Column index for the normal matrix|   1X,I5      |
        | normal matrix  | It must match the parameter index |              |
        | column index   | in the SOLUTION/ESTIMATE block    |              |
        |                | for the same parameter.           |              |
        |________________|___________________________________|______________|
        |                |                                   |              |
        | Decomposed     | Matrix element at the location    |   1X,E21.14  |
        | normal matrix  | (row index, column index).        |              |
        | element        |                                   |              |
        |________________|___________________________________|______________|


                2.6 New block SOLUTION/NORMAL_VECTOR BLOCK
                ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  This block contains decomposed right hand parts of normal equations for
  the subset of parameters described in the SOLUTION/ESTIMATE block. In the
  case if the SOLUTION/ESTIMATE block describes all parameters adjusted in
  the solution, the decomposed normal vector is equivalent to the full
  normal vector. In the case if the SOLUTION/ESTIMATE block describes only
  a subset of parameters, then the decomposed normal vector d_i is defined as

  d_i = n_i - N_ei(T) * (C_ee + N_ee){-1} * n_e where

        n_i  -- the block of normal vector which corresponds to the equations
                listed in the SOLUTION/ESTIMATE;
        n_e  -- the block of the normal vector which corresponds to the
                omitted parameters;
        N_ee -- the block of normal matrix which corresponds to omitted
                parameters;
        N_ei -- the block of normal matrix which corresponds to the product
                of equations of conditions of the omitted parameters and
                parameters from the SOLUTION/ESTIMATE list.
        C_ee -- the block of normal matrix of constraints which corresponds
                to omitted parameters;

  Solve computes  d_i  as   d_i = D_i * e_i   where

        e_i  -- vector of the estimates of the parameters from the
                SOLUTION/ESTIMATE list.

         ___________________________________________________________________
        |__S_O_L_U_T_I_O_N__D_E_C_O_M_P_O_S_E_D__N_O_R_M_A_L__V_E_C_T_O_R___|
        |                |                                   |              |
        |__Field_________|______Description__________________|___Format_____|
        |                |                                   |              |
        | Estimated      | Index of the estimated parameter. |   1X,I5      |
        | Parameter      |                                   |              |
        | Index          |                                   |              |
        |                |                                   |              |
        |________________|___________________________________|______________|
        |                |                                   |              |
        | Element of   	 | Element of the decomposed normal  |   1X,E21.14  |
        | decomposed     | ( Row Number , Column Number ).   |              |
        | normal vector  | ( Row Number , Column Number ).   |              |
        |________________|___________________________________|______________|
                                                             |              |
                                                             |     28       |
                                                             |______________|

                2.7 New block NUTATION/DATA
                ~~~~~~~~~~~~~~~~~~~~~~~~~~~

  This block describes which apriori nutation model is used and what is the
reference model to which the nutation angles are referred.

         ___________________________________________________________________
        |_________________N_U_T_A_T_I_O_N___D_A_T_A___L_I_N_E_______________|
        |                |                                   |              |
        |__Field_________|______Description__________________|___Format_____|
        |                |                                   |              |
        | [Nutat. Code]  | Code for nutation reference       |   1X,A8      |
        |                | NONE                              |              |
        |                | REN2000                           |              |
        |                | IAU1980                           |              |
        |                | IERS1996                          |              |
        |                | IAU2000a                          |              |
        |                | IAU2000b                          |              |
        |________________|___________________________________|______________|
        |                |                                   |              |
        |  [Nut. Usage]  | Usage flag: APR or REF            |    1X,A3     |
        |                | APR means that the previous       |              |
        |                |     field kept the nutation model |              |
        |                |     used for apriori.             |              |
        |                | REF means that the previous       |              |
        |                |     field kept the nutation model |              |
        |                |     used as a reference.          |              |
        |                |     NONE means that the total     |              |
        |                |     nutation angles are presented |              |
        |________________|___________________________________|______________|
        |                |                                   |              |
        | Comments       |                                   |   1X,A66     |
        |________________|___________________________________|______________|
                                                             |              |
                                                             |     80       |
                                                             |______________|

                2.8 New block PRECESSION/DATA
                ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  This block describes the apriori precession constant which was used.

        ___________________________________________________________________
       |_________________N_U_T_A_T_I_O_N___D_A_T_A___L_I_N_E_______________|
       |                |                                   |              |
       |__Field_________|______Description__________________|___Format_____|
       |                |                                   |              |
       | [Prec. Code]   | Code for nutation reference       |   1X,A8      |
       |                | NONE                              |              |
       |                | IAU1980                           |              |
       |                | IAU2000                           |              |
       |________________|___________________________________|______________|
       |                |                                   |              |
       | Comments       |                                   |   1X,A70     |
       |________________|___________________________________|______________|
                                                            |              |
                                                            |     80       |
                                                            |______________|

   Nutation angles can be presented either as nutation in obliquity and
   nutation in longitude in accordance to Newcomb-Andoyer formalism or
   as nutation X, nutation Y in accordance to Ginot-Capitaine formalism.
   Contrary to claims of Dr. Capitaine, both approaches are equivalent.

                2.9 New block SOURCE/ID
                ~~~~~~~~~~~~~~~~~~~~~~~

       ___________________________________________________________________
      |_____________R_A_D_I_O___S_O_U_R_C_E___D_A_T_A___L_I_N_E___________|
      |                |                                   |              |
      |__Field_________|______Description__________________|___Format_____|
      |                |                                   |              |
      | Source Code    | Call sign for a source            |   1X,A4      |
      |________________|___________________________________|______________|
      |                |                                   |              |
      | IERS name      | IERS name of the radio source     |   1X,A8      |
      |________________|___________________________________|______________|
      |                |                                   |              |
      | ICRF name      | ICRF name of the radio source     |   1X,A16     |
      |________________|___________________________________|______________|
      |                |                                   |              |
      | IAU name       | IAU J2000.0 name of the radio     |   1X,A10     |
      |                | source                            |              |
      |________________|___________________________________|______________|
      |                |                                   |              |
      | IVS name       | IVS name of the radio source      |   1X,A8      |
      |________________|___________________________________|______________|
      |                |                                   |              |
      | Comments       | Comments or other names of the    |   1X,A29     |
      |                | radio source                      |              |
      |________________|___________________________________|______________|
                                                           |              |
                                                           |     80       |
                                                           |______________|


                2.10 New block SOLUTION/NORMAL_CALIBRATION_ESTIMATE
                ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The purpose of this block is to allow users to 'back-out' the effects of a
calibration. The format is almost identical to the SOLUTION/ESTIMATE block.

Suppose that the normal equations without the calibration are:
    N A = B
The effect of the calibration is to modify the RHS of this to give:
    N A' = B+ del_B
When the normal equations are inverted we get:
    A'  = N^-1 B + N^-1 del_B =  A + del_A

The solution contribution block gives the values for the 'del_A' term.

The format of this block is almost identical to SOLUTION/ESTIMATE block.
The first few lines  look look something like this:

+SOLUTION/NORMAL_CALIBRATION_ESTIMATE LOADING_EFFECT
*Index TYPE__ CODE PT SBIN Ref_epoch___ Unit S   value
 1 STAX   7641  A    1 19:155:16735 m    2  1.12094296576514D-05 0.00000D+00
 2 STAY   7641  A    1 19:155:16735 m    2 -1.64886779400689D-04 0.00000D+00
 3 STAZ   7641  A    1 19:155:16735 m    2 -7.99174504030867D-04 0.00000D+00
 4 STAX   7297  A    1 19:155:14114 m    2 -1.28824231979959D-03 0.00000D+00
 5 STAY   7297  A    1 19:155:14114 m    2  1.26091351520643D-03 0.00000D+00
 6 STAZ   7297  A    1 19:155:14114 m    2 -6.42471735486039D-04 0.00000D+00
....
-SOLUTION/NORMAL_CALIBRATION_ESTIMATE

The sigmas are 0 because it is assumed there is no uncertainty in
the calibration.

Suppose we have two solutions in sinex format.
   Solution 1  does not include the effect of the calibration.
   * There will only be SOLUTION/ESTIMATE block.

   Solution 2 includes the effect of the calibration, and we have
   included the CALBIRATION information.
   * Then there will be a SOLUTION/ESTIMATE block
   * There will also be a SOLUTION/NORMAL_CALIBRATION_ESTIMATE block.

The relation between Solution 1 and Solution 2 is:
   SOLUTION/ESTIMATE(1) =
   SOLUTION/ESTIMATE(2)-SOLUTION/NORMAL_CALIBRATION_ESTIMATE(2)



                2.11 New block SOLUTION/NORMAL_CALIBRATION
                ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
   This block is similar to the SOLUTION/NORMAL_VECTOR block. It
provides a means of backing out the effect of a calibration.

Suppose that the normal equations without the calibration are:
    N A = B
The effect of the calibration is to modify the RHS of this to give:
    N A' = B+ del_B

The NORMAL_VECTOR block gives the effective B vector after the
nuisance parameters have been squeezed out.
The CALIBRATION block gives the value of the effect del_B vector
after the nuisance parameters have been squeezed out.

The format of the first few lines look like:
+SOLUTION/NORMAL_CALIBRATION LOADING_EFFECT
* Ind1  vector(ind1)
     1 -9.08414333456434D+06
     2 -2.78630680723758D+07
     3  1.27314635010659D+07
     4  7.21652034185454D+06
     5  8.03838945195598D+07
     6 -1.02827125834327D+08
     7 -4.42092453014595D+07
....
+SOLUTION/NORMAL_CALIBRATION

Suppose we have two solutions in sinex format.
   Solution 1  does not include the effect of the calibration.
   * There will only be SOLUTION/NORMAL_VECTOR block.

   Solution 2 includes the effect of the calibration, and we have
   included the CALBIRATION information.
   * There will be a SOLUTION/NORMAL_VECTOR block.
   * There will also be SOLUTION/NORMAL_CALIBRATION block.

Note that:
   SOLUTION/NORMAL_VECTOR(1) =
   SOLUTION/NORMAL_VECTOR(2)-SOLUTION/NORMAL_CALIBRATION(2)


        3 Deviations from the SINEX 2.10 standard
        =========================================


   Sinex listing in 2.20 format has different names for parameters
in accordance to an anonymous document circulated in 2008 known as
"Proposal 2".


        4 Implementation in Solve
        =========================

   Solve normally produces the listing in its own so-called "spool-format".
In addition to the spool listing, Solve has a limited ability to generate
listings in Sinex format. It can write the listing in Sinex format when it
runs in batch mode. Description of the keyword Sinex in the control language
can be found in
http://gemini.gsfc.nasa.gov/solve_root/help/solve_guide_03.html#section3.13

   When a user requests to apply specific constraints, Solve does not modify
normal matrix immediately. Procedures of imposing constraints collect all
constraint equation coefficients, weights, right hand part equations as well
as constraint description in an intermediate data structure. After collecting
all information about constraints Solve "applies" constraints by modifying
normal matrix and normal matrix. If a Sinex output option is specified, then
Solve passes this intermediate data structure to the routine which writes
listing down and, thus, this subroutine has access to full information about
the constraints.

   Solve allows a user to specify which items among ESTIMATES, COVARIANCES,
CONSTRAINTS, NORMAL_EQUATIONS or all of them are to be included
in the listing together with mandatory blocks. Solve allows a user to
specify which parameters are to be included in the output. Currently, Solve
does not allow to include any parameter in the listing, but only one from
the pre-defined list of supported parameter.

                4.1 Syntax of INCLUDE_PARAM and EXCLUDE_PARAM lists
                ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

INCLUDE_PARAM and EXCLIDE_PARAM files contain the parameter lists.
List consists of one or more lines with Solve intrinsic 20-characters
long parameter names. The lines which starts from # are considered as
comments. Wild-card symbols * and ? can be included.

  Solve check the name of each estimated parameter against INCLUDE_PARAM
list. If the name matches with at least one line (except comment) then
the name is flagged as "included". After that Solve check each parameter
against EXCLUDE_PARM list. If it matches with at least one line (except
comment) then it is flagged as "excluded". All parameters which are
flagged as "included" and are not flagged as "excluded" will be included
in the Sinex output.

The list of intrinsic parameter names:

Parameters which can be put in the listing in Sinex format:

ssssssss X COMPONENT   X-coordinate of station position at reference epoch
ssssssss Y COMPONENT   Y-coordinate of station position at reference epoch
ssssssss Z COMPONENT   Z-coordinate of station position at reference epoch
ssssssss X VELOCITY    X-coordinate of station velocity
ssssssss Y VELOCITY    Y-coordinate of station velocity
ssssssss Z VELOCITY    Z-coordinate of station velocity
ssssssss Xyymmdd-COO   X-coordinate of station position at epoch yymmdd
ssssssss Yyymmdd-COO   Y-coordinate of station position at epoch yymmdd
ssssssss Zyymmdd-COO   Z-coordinate of station position at epoch yymmdd
ssssssss Xyymmdd-POS   X-coordinate of station position at epoch yymmdd
ssssssss Yyymmdd-POS   Y-coordinate of station position at epoch yymmdd
ssssssss Zyymmdd-POS   Z-coordinate of station position at epoch yymmdd
ssssssss AXIS OFFSET   axis offset of the ssssssss station
X WOBBLE 0yymmddhhmm   X-coordinate of pole position at epoch  yymmddhhmm
X WOBBLE 1yymmddhhmm   Time derivative of X pole coordinate at yymmddhhmm
Y WOBBLE 0yymmddhhmm   Y-coordinate of pole position at epoch  yymmddhhmm
Y WOBBLE 1yymmddhhmm   Time derivative of Y pole coordinate at yymmddhhmm
UT1-TAI  0yymmddhhmm   UT1 angle at epoch yymmddhhmm
UT1-TAI  1yymmddhhmm   First time derivative of UT1 angle at epoch yymmddhhmm
LONGITUDE NUTATION     Nutation in longitude
OBLIQUITY NUTATION     Nutation in obliquity
qqqqqqqq RIGHT ASCEN   Right ascension at J2000.0 epoch
qqqqqqqq DECLINATION   Declination at J2000.0 epoch
qqqqqqqq RIGHT ASC V   Proper motion in right ascension
qqqqqqqq DEC VELO      Proper motion in declination

Other parameters which the current version of Solve cannot put in the
listing in Sinex format:

ssssssssA0yymmddhhmm   Atmosphere path delay at epoch  yymmddhhmm
ssssssssa0yymmddhhmm   Atmosphere path delay at epoch  yymmddhhmm
ssssssssC0yymmddhhmm   Global clock offset at epoch  yymmddhhmm
ssssssssC1yymmddhhmm   Global clock rate at epoch  yymmddhhmm
ssssssssC2yymmddhhmm   Global clock rate drift at epoch  yymmddhhmm
ssssssss--ssssssss C   baseline dependent clocks
ssssssssNGyymmddhhmm   Atmosphere gradient in north direction
ssssssssEGyymmddhhmm   Atmosphere gradient in east  direction
X WOBBLE 2yymmddhhmm   Second time derivative of X pole coordinate at yymmddhhmm
Y WOBBLE 2yymmddhhmm   Second time derivative of Y pole coordinate at yymmddhhmm
UT1-TAI  2yymmddhhmm   Second time derivative of UT1 angle at epoch yymmddhhmm
Gamma                  Relativistic PPN parameter gamma


where
"ssssssss"    stands for the IVS station name
"qqqqqqqq"    stands for the IVS source name
"yyddmmhhss"  stands for time epoch like 980729113459 -- July 29, 1998 11 hours
              34 minutes 59 seconds.

                4.2 Examples of INCLUDE_PARAM and EXCLUDE_PARAM lists
                ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

1. daily_inc.bsc

#
# -- Include parameters which will be put in Sinex listing
#
#    The following parameters are to be included in the Sinex listing:
#
#    1) Station coordinates
#    2) pole coordinates
#    3) UT1
#    4) rate of change of pole coordinates
#    5) rate of change of UT1
#    6) daily nutation angles
#
?????????X COMPONENT
?????????Y COMPONENT
?????????Z COMPONENT
?????????X??????-COO
?????????Y??????-COO
?????????Z??????-COO
?????????X??????-POS
?????????Y??????-POS
?????????Z??????-POS
X WOBBLE 0*
X WOBBLE 1*
Y WOBBLE 0*
Y WOBBLE 1*
UT1-TAI  0*
UT1-TAI  1*
LONGITUDE NUTATION
OBLIQUITY NUTATION

2. daily_exc.bsc
#
# -- Exclude parameters which will be put in Sinex listing
#
#    Nothing to exclude
#

3. daily_esc_notigo.bsc

#
# -- Exclude parameters which will be put in Sinex listing
#
#    All parameters related to station TIGOCONC are excluded
#
#    (NB: no common constraint equations with other stations can be
#         imposed if computation of the decomposed normal matrix is required )
#
TIGOCONC*

                4.3 Treatment of station with discontinuous motion
                ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

   It is an empirical fact that some stations has a quasi-instant motion
due to seismic events, rails repair and other reasons of instability of
VLBI site positions.

  It is an analyst who determines the appropriate model for handing such
stations. In the case if an analyst trusts to results of the measurements
of such a motion by an independent technique, f.e. results of local survey
before and after rails repairing, then position of the station is modeled
by one parameter, and the motion of the station is described by the
set of eccentricity values at the epochs before and after the motion.

  If an analyst does not trust to independent measurements, or such
measurements are unavailable, f.e. in the case of seismic motion, then
coordinates of such station are described by a model

X = a1*B0(t0,t1) + a2*B0(t1,t2) + ... + b*(t-tref)

where B0 -- a basis spline of the 0-th order on the range t0, t1
            ( it is 1 at the range [t0, t1], and 0 otherwise )
      tref -- reference epoch;
      t0   -- epoch of the first observations;
      t1, t2 ... -- epoch of discontinuities.

  Parameters a1, a2 ... have the same parameter name STAX, STAY, STAZ,
but they are distinguished by sub-index 1,2... in the field SBIN
(former name SOLN). This field is used in sections
SITE/EPOCHS, SITE/APRIORI, SITE/ESTIMATES. If the station did not have
discontinuity in the motion than SBIN always has the value 1.

  The modern approach is to model non-liner site position with B-spline
or order 0,1,2,3. Sinex format does not allow to put in the listing
estimates of B-spline of order higher than 0.

                4.4 Restrictions
                ~~~~~~~~~~~~~~~~

  The current implementation (2002.10.04) cannot write the listing in
     Sinex format in several cases:

  1) Constraint NO_NET_TRANSLATION  is not supported. Use
     NO_NET_TRANSLATION_POSITION instead of that.

  2) Suppressions

     VELOCITIES         NO
     STATIONS           NO
     SOURCES            NO
     PROPER_MOTIONS     NO

  3) Solve cannot put in the listing site position modeled by linear spline.

  4) Currently, Solve can include in Sinex listing global parameters if it
     runs in global mode and local parameters if it runs in independent mode.
     It cannot include local parameters if it runs in global mode. This
     restriction may be lifted in the future.

  5) Solve cannot include in the listing in Sinex format second and higher
     order UT1 and polar motion time derivatives.

  6) Solve cannot include user parameters in the listing in Sinex format,
     but can include user constraints.

  7) No common constraints between included and not included parameters can
     be imposed if computation of decomposed normal matrix is required.
     Solve will issue a warning if a constraint equation has non-zero
     elements for the parameters from both groups of included and not
     included parameters in the case if computation of a decomposed normal
     matrix is required, and will issue an error message and stop if the
     decomposed normal matrix is to be included in the sinex listing.
-FILE/COMMENT
*
* -----------------------------------------------------------------------------
*
+INPUT/ACKNOWLEDGEMENTS
 USN  U.S. Naval Observatory, VLBI analysis group
-INPUT/ACKNOWLEDGEMENTS
*
* -----------------------------------------------------------------------------
*
+SITE/ID
*Code PT Domes____ T Station description___ Approx_lon_ Approx_lat_ App_h__
 7623  A 40424S010 R KOKEE12M 12-m at Kokee 200 20 06.3  22 07 35.2  1169.3
 7388  A 14201S044 R WETTZ13S Wettzell 13-m  12 52 41.8  49 08 36.3   673.6
-SITE/ID
*
* -----------------------------------------------------------------------------
*
+SOURCE/ID
*Code IERS nam ICRF designator  IAU name   IVS name
 0001 0016+731 J001945.7+732730 J0019+7327 0016+731
 0002 0059+581 J010245.7+582411 J0102+5824 0059+581
 0003 0133+476 J013658.5+475129 J0136+4751 0133+476
 0004 0202+319 J020504.9+321230 J0205+3212 0202+319
 0005 0227+403 J023045.7+403253 J0230+4032 0227+403
 0006 0234+285 J023752.4+284808 J0237+2848 0234+285
 0007 0300+470 J030335.2+471616 J0303+4716 0300+470
 0008 1617+229 J161914.8+224747 J1619+2247 1617+229
 0009 1732+389 J173420.5+385751 J1734+3857 1732+389
 0010 1758+388 J180024.7+384830 J1800+3848 1758+388
 0011 1803+784 J180045.6+782804 J1800+7828 1803+784
 0012 1823+568 J182407.0+565101 J1824+5651 1823+568
 0013 2000+472 J200210.4+472528 J2002+4725 2000+472
 0014 2007+777 J200530.9+775243 J2005+7752 2007+777
-SOURCE/ID
*
* -----------------------------------------------------------------------------
*
+SITE/RECEIVER
*Code PT SBIN T Data_Start__ Data_End____ Receiver Type_______ S/N__ Firmware_ID
 7623  A    1 R 26:117:63010 26:117:66586 ----VLBI Station---- --NM- -----NA----
 7388  A    1 R 26:117:63010 26:117:66586 ----VLBI Station---- --NM- -----NA----
-SITE/RECEIVER
*
* -----------------------------------------------------------------------------
*
+SITE/ANTENNA
*Code PT SBIN T Data_Start__ Data_End____ Receiver Type_______ S/N__
 7623  A    1 R 26:117:63010 26:117:66586 ----VLBI Station---- --NM-
 7388  A    1 R 26:117:63010 26:117:66586 ----VLBI Station---- --NM-
-SITE/ANTENNA
*
* -----------------------------------------------------------------------------
*
+SITE/ECCENTRICITY
*Code PT SBIN T Data_Start__ Data_End____ typ Apr --> Benchmark (m)_______
 7623  A    1 R 26:117:63010 26:117:66586 XYZ   0.0000   0.0000   0.0000
 7388  A    1 R 26:117:63010 26:117:66586 XYZ   0.0000   0.0000   0.0000
-SITE/ECCENTRICITY
*
* -----------------------------------------------------------------------------
*
+SOLUTION/EPOCHS
*Code PT SBIN T Data_start__ Data_end____ Mean_epoch__
 7623  A    1 R 26:117:63010 26:117:66586 26:117:64771
 7388  A    1 R 26:117:63010 26:117:66586 26:117:64771
-SOLUTION/EPOCHS
*
* -----------------------------------------------------------------------------
*
+NUTATION/DATA
 IAU2006/2000 Precession/Nutation apriori nutation modelwas used
 NONE     REF Total nutation angles are reported in estimation block
-NUTATION/DATA
*
* -----------------------------------------------------------------------------
*
+PRECESSION/DATA
 CAPITAINE2003 apriori precession constant and obliquity rates were used 
-PRECESSION/DATA
*
* -----------------------------------------------------------------------------
*
+SOLUTION/STATISTICS
* Units for WRMS: sec
 NUMBER OF OBSERVATIONS                   62
 NUMBER OF UNKNOWNS                        6
 WEIGHTED SQUARE SUM OF O-C      2.71722472868150D+14
 SQUARE SUM OF RESIDUALS (VTPV)  6.50440534641600D+01
 VARIANCE FACTOR                 1.16150095471714D+00
 WRMS OF POSTFIT RESIDUALS       2.48306223702247D-11
-SOLUTION/STATISTICS
*
* -----------------------------------------------------------------------------
*
+SOLUTION/APRIORI
*Index Type__ CODE PT SBIN Ref_epoch___ Unit S Apriori_value________ Constraint_
     1 UT1    ----  -    1 26:117:64765 ms   2 -3.69643561223452D+04 0.00000D+00
-SOLUTION/APRIORI
*
* -----------------------------------------------------------------------------
*
+SOLUTION/ESTIMATE
*Index TYPE__ CODE PT SBIN Ref_epoch___ Unit S Total_value__________ Formal_erro
     1 UT1    ----  -    1 26:117:64765 ms   2 -3.69644849431228D+04 2.83556D-03
-SOLUTION/ESTIMATE
*
* -----------------------------------------------------------------------------
*
+SOLUTION/CALIBRATION_ESTIMATE LOADING_EFFECT      
*Index TYPE__ CODE PT SBIN Ref_epoch___ Unit S   value 
     1 UT1    ----  -    1 26:117:64765 ms   2  0.00000000000000D+00 0.00000D+00
-SOLUTION/CALIBRATION_ESTIMATE
*
* -----------------------------------------------------------------------------
*
+SOLUTION/MATRIX_ESTIMATE L COVA
* Ind1  Ind2 Covariance(ind1,ind2)
     1     1  8.04039139953823D-06
-SOLUTION/MATRIX_ESTIMATE L COVA
*
* -----------------------------------------------------------------------------
*
+SOLUTION/CONSTRAINT_INFO
*Index Cns_abr  Subind Unit  Description_of_constraint
-SOLUTION/CONSTRAINT_INFO
*
* -----------------------------------------------------------------------------
*
+SOLUTION/CONSTRAINT_EQUATION_MATRIX
* IND1  runs over constraint equations
* IND2  runs over parameters to be constrainted
*
* Ind1  Ind2 Constraint_equation(ind1,ind2)
-SOLUTION/CONSTRAINT_EQUATION_MATRIX
*
* -----------------------------------------------------------------------------
*
+SOLUTION/CONSTRAINT_EQUATION_VECTOR
*Index  Right_hand_value____  Reciprocal_weight___
-SOLUTION/CONSTRAINT_EQUATION_VECTOR
*
* -----------------------------------------------------------------------------
*
+SOLUTION/CONSTRAINT_WEIGHT_MATRIX
* Ind1  Ind2 Weight_matrix(ind1,ind2)
-SOLUTION/CONSTRAINT_WEIGHT_MATRIX
*
* -----------------------------------------------------------------------------
*
+SOLUTION/NORMAL_EQUATION_MATRIX
* Ind1  Ind2 Decomposed_normal_matrix(ind1,ind2)
     1     1  1.24372054830245D+05
-SOLUTION/NORMAL_EQUATION_MATRIX
*
* -----------------------------------------------------------------------------
*
+SOLUTION/NORMAL_EQUATION_VECTOR
* Ind1  Decomposed_vector(ind1)
     1 -1.60217048102889D+04
-SOLUTION/NORMAL_EQUATION_VECTOR
*
* -----------------------------------------------------------------------------
*
+SOLUTION/NORMAL_CALIBRATION LOADING_EFFECT      
* Ind1  Decomposed_vector(ind1)
     1  0.00000000000000D+00
-SOLUTION/NORMAL_CALIBRATION
*
* -----------------------------------------------------------------------------
*
%ENDSNX
