Position equations records format

A set of records used to input a series of observations measured as a unit where the common factor is normally something like a common orbit for satellite observed from different stations at the same time.

The set is made up of a header record which defines the type of set, followed by 0 or more psuedo observation records and/or the auxiliary parameter identification records. A covariance header which describes the type and size of the matrix follows. A psuedo observation is the result of the reduction of observations and is expressed as a coordinate and associated covariance matrix.

  1. Position equation header record Code 95
  2. Position difference header record Code 91
  3. Partially reduced normal equations header record Code 93
  4. Weighted station equations header record Code 93
  5. Weighted auxiliary parameter equation header record Code 93
  6. Auxiliary parameter equivlancing equation header record Code 93
  7. Exchange format header record Code 93
  8. Doppler position equations header record (tape9) Code 95
  9. Doppler position difference equations header record (tape9) Code 91

Header record format

The header record is used to identify a group of records that are used to define a set of observations. The observations set consists of one or more observations of coordinate or auxiliary parameters along with the associated matrix. This type of set is used to input into the adjustment observations that have been reduced to a series of coordinate values alomg with the associated covaraince.

      COLUMN                           CONTENT

          1    Blank
        2:3    Code used to identify the type of data
                       91 : Coordinate difference header record
                       93 : Partially reduced normal equation header record
                       95 :  Coordinate observation header record
        4:6    Type used to identify a class of observations (Examples)
                        PRN     : identifies following observations as
                                   partially reduced observations
                Any 3 alpha-numerical characters can be used to
                identify a class of observation
        7:30   Group identification listed on output
       31:37   Alternate file name to read data
       38:40   File type - 9   Doppler tape9 format data
                         - 1   Exchange data format
                         - 3   Exchange data format (vertical)
                         - iss Inertial survey data format
                         - any other number indicates a standard observed data file
       41:45   Number of similiar sets in the file (EOF)
       46:59   Epoch of coordinates as year and decimal year or "year:doy:sod"
               where year = 4-digit year, doy = 3 digit day of year, and
               sod = 5 digit seconds of day are separated by ":"

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Observed Cartesian coordinate record format

      COLUMN                           CONTENT

           1   Blank
         2:3   Code 92 :
         4:6   Type used to identify a class of observations (Examples)
                        DOP     : doppler
                        GPS     : global positioning system data
                        LBI     : long baseline interferometry data

                Any 3 alpha-numerical characters can be used to
                identify a class of observation
         7:15   Station number used to associate the data on
                this record with data on other records for the same
                coordinates
        16:30   Station name
           31   Blank
        32:35   Observation type
        36:50   X coordinate (decimal required)
        51:65   Y coordinate (decimal required)
        66:80   Z coordinate (decimal required)

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Observed Geographic Coordinate Record Format

      COLUMN                           CONTENT

         1:2   Blank
           3   Code   96 :  geographic coordinate
         4:6   Type  DOP : Instrument type for identification
                     GPS : global positioning system data
                     LBI : long baseline interferometry data
        7:15   Station number used to associate the data on
                this record with data on other records for the same
                coordinates
       16:30   Station name
          31   Blank
       32:35   Observation type
       36:39   Blank
          40   Latitude north-south indicator (blank, N, + or S, -)
       41:42   Latitude degrees
       43:45   Latitude minutes
       46:54   Latitude seconds  (decimal required)
          55   Longitude east-west indicator (blank, W, + or E, -)
       56:58   Longitude degrees
       59:61   Longitude minutes
       62:70   Longitude seconds  (decimal required)
       71:80   Ellipsoid height (meters)

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Observed Coordinate Difference Record Format

The order of the coordinate differences must match the order of the covariance matrix.

Also refered to as a baseline observation. A series of baseline observations measured at the same time using the same satellites are refered to as a session observation.

      COLUMN                           CONTENT

           1   Blank
         2:3   Code 41 :
         4:6   Type used to identify a class of observations (Examples)
                        DOP     : doppler
                        GPS     : global positioning system data
                        LBI     : long baseline interferometry data

                Any 3 alpha-numerical characters can be used to
                identify a class of observation
         7:15   Station number used to associate the data on
                this record with data on other records for the same
                coordinates
        16:25   Station number used to associate the data on
                this record with data on other records for the same
                coordinates
        32:35   Observation type
        36:50   X coordinate difference(decimal required)
        51:65   Y coordinate difference(decimal required)
        66:80   Z coordinate difference(decimal required)

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Partially Reduced Normal Equation Record Format

The order of the terms must match the order of the partially reduced matrix.

      COLUMN                           CONTENT

           1   Blank
         2:3   Code 92 :
         4:6   Type used to identify a class of observations (Examples)
                        PRN     : Partially Reduced Normal equations

                Any 3 alpha-numerical characters can be used to
                identify a class of observation

         7:15   Station number or auxiliary parameter number used to
                associate the data on this record with data on other
                records for the same unknowns.

        36:50   X' partially reduced term (decimal required)
        51:65   Y' partially reduced term (decimal required)
        66:80   Z' partially reduced term (decimal required)

The partially reduced term can be a station unknown or an auxiliary parameter unknown. The station unknown can have from 1 to 3 terms. The associated partially reduced matrix will conform exactly to the number of terms on the records.

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Auxiliary Parameter Constraint Record Format

      COLUMN                           CONTENT

           1   Blank
         2:3   Code 92 :
         4:6   RHS : Right Hand Side

         7:15   Auxiliary parameter number used to associate the data on this
                record with data on other  records for the same unknowns.

        32:35   Auxiliary parameter type indicating class of parameter
                    CS
                      PR
                    TRAX
                    TRAY
                    TRAZ
                    ROTX
                    ROTY
                    ROTZ
                    SCPR

        36:50   Right hand side value computed as negative of initial value of
                auxiliary parameter (metres for translations, radians for rotations
                and ppm for scale) times the weight

                Type                  Class     Value
                ---------------------------------------------------------
                Constant scale         CS       0.0
                Proportional scale       PR     0.0
                Space system scale     SCPR     -(Initial PPM) x (Weight)
                Rotations              ROT      -(Initial Rad) x (Weight)

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Weighted Station Equation Record Format

The order of the terms must match the order of the covariance matrix.

      COLUMN                           CONTENT

           1   Blank
         2:3   Code 92 :
         4:6   Type used to identify a class of observations (Examples)
                        WSA    : Weighted station equations

                Any 3 alpha-numerical characters can be used to
                identify a class of observation
         7:15   Station number used to associate the data on
                this record with data on other records for the same
                stations.


        36:50   X Adjusted value (decimal required)
        51:65   Y Adjusted value (decimal required)
        66:80   Z Adjusted value (decimal required)

Note: X Y and Z values must be present

      COLUMN                           CONTENT

         1:2   Blank
           3   Code   96 :  geographic coordinate
         4:6   Type  WSA : weighted station
        7:15   Station number used to associate the data on
                this record with data on other records for the same
                coordinates
       16:30   Station name
       31:39   Blank
          40   Latitude north-south indicator (blank, N, + or S, -)
       41:42   Latitude degrees
       43:45   Latitude minutes
       46:54   Latitude seconds  (decimal required)
          55   Longitude east-west indicator (blank, W, + or E, -)
       56:58   Longitude degrees
       59:61   Longitude minutes
       62:70   Longitude seconds  (decimal required)
       71:80   Ellipsoid height (meters)

The weighted station unknown can have from 1 to 3 terms. The associated covariance matrix will conform exactly to the number of terms on the records.

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Auxiliary parameter identification record format

Auxiliary parameters are identified as belonging to the data set through the use of code 94 records. Parameters are defined for the 7 Helmert transformation terms of rotation(3) translation(3) and scale. Up to seven parameters can be defined for each set and each set can have a different set of parameters identified through the auxiliary parameter number. Remember auxiliary parameters are used to solve for a bias in the data set that can be defined in terms of an associated data set or sets. For example to solve for the translation parameters in a data set, the translation parameters of at least one station must be defined by some other means.

When using auxiliary parameters make sure that there is a solution in the first place. For example solving for translation for a position difference set will cause a singularity. You may have a thousand sets identified with a translation parameter but only one or two stations where the translation is actually defined. Rotations and scale are more difficult to determine. One method of determining the strength of the solution of a parameter is to examine the variance of the solution, a weak solution will have a large variance.

      COLUMN                           CONTENT

            1   Blank
          2:3   Code : 94 Auxiliary parameter

          4:6   Type - used to identify a class of observations
                        DOP - Doppler
                        GPS - Global positioning System
                        LBI - Long Baseline Interferometry
                        PEQ - Position EQuation
                        PRN - Partial reduced normal
         7:15   Auxiliary parameter number used to associate the data on this
                 record with data on other records
        16:30   Additional identification
        32:35   Type of Coordinate system parameters 
                        TRAX - Translation parallel to the X azis
                        TRAY - Translation parallel to the Y azis
                        TRAZ - Translation parallel to the Z azis
                        ROTX - Rotation about the X azis
                        ROTY - Rotation about the Y azis
                        ROTZ - Rotation about the Z azis
                        SCPR - Scale correction

                        Note: Translation parameters are not defined
                              for position difference observations

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Matrix header record format

      COLUMN                           CONTENT

           1   Blank
         2:3   Code 97 :
         4:6   Type used to identify a class of observations (Examples)
                        PDV : Position difference covariance
                        POV : Position covariance
                        PDW : Position difference weight
                        POW : Position weight
                        PRN : Partially reduced normal equations
         7:14   Used to identify the type of matrix formatting
                    UPPER : Upper triangular starting from the diagonal four
                            terms per record until end of row. New record for next row.
                    BLOCK : Matrix stored a block of data starting from the first
                            term in the row four terms for each record until end of
                            row. New record for a new row.
        15:20   Matrix size
        21:25   Block size
        26:30   Number of blocks
        31:36   Number of observation included
        37:42   Number of eliminated normal equations
        43:62   Partial sum of VtPV
        70:80   Scale factor for Matrix

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Matrix record format

Each record contains up to 4 terms in a row of the matrix. Where more then 4 terms are required to complete the row another record is written. Where less than 4 terms are required only the terms required to complete the row are read.

      COLUMN                           CONTENT

          1:20   Floating point term right justified for exponent
         21:40   Floating point term right justified for exponent
         41:60   Floating point term right justified for exponent
         61:80   Floating point term right justified for exponent

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Revised 20 Dec 98 by Mike Craymer
Revised 18 Oct 2001 by Mike Craymer
Revised 20 Apr 2013 by Mike Craymer (added epoch field to header record)