Bernese GPS Software Version 5.0 - Bernese GNSS Software

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9. Combination of Solutions Both reference frames are related to each other by the 7-parameter transformation: ⎛ ⎜ ⎝ X i Y i Z i ⎞ ⎟ ⎠ = (1 + µ) ⎛ ⎜ ⎝ 1 γ −β −γ 1 α β −α 1 ⎞ ⎟ ⎠ ⎛ ⎜ ⎝ Xi Yi Zi ⎞ ⎛ ⎟ ⎜ ⎠ + ⎝ where i runs over all indices of the reference frame defining stations. ∆X ∆Y ∆Z ⎞ ⎟ ⎠ (9.31) The 7-parameter transformation may be written in this linearized form, because only small rotations α,β,γ are considered. The idea of minimum constraint conditions is based on the requirement that some of these seven parameters (computed using the Helmert method) are set equal to zero. Setting the translations to zero results in a no-net-translation condition imposed to the estimated coordinates with respect to the a priori reference frame, setting the rotations to zero results in a no-net-rotation constraint. The former is usually used for the datum definition in regional networks, the later for global networks. Eqn. (9.31) may be rewritten as ⎛ ⎜ ⎝ X i Y i Z i ⎞ ⎟ ⎠ = ⎛ ⎜ ⎝ or, in vector notation: Xi Yi Zi ⎞ ⎛ ⎟ ⎜ ⎠ + ⎝ 1 0 0 0 −Zi Yi Xi 0 1 0 Zi 0 −Xi Yi 0 0 1 −Yi Xi 0 Zi Let us introduce the vectors ˜ X,X, and the matrix B by ˜X = ⎛ ⎜ ⎝ ˜X1 ˜X2 . ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎛ ⎜ ⎝ ∆X ∆Y ∆Z α β γ µ ⎞ ⎟ , (9.32) ⎟ ⎠ ˜Xi = Xi + Bi ξ . (9.33) , X = ⎛ ⎜ ⎝ X1 X2 . ⎞ ⎛ ⎟ ⎜ ⎠ , B = ⎝ B1 B2 . ⎞ ⎟ ⎠ . If we want to compute the parameters, we can use the following “observation equation”: which results in the following system of normal equations: v = B ξ − ( ˜ X − X) , (9.34) B ⊤ B ξ = B ⊤ ( ˜ X − X) . (9.35) In our case the expression ˜ X − X is the difference between the estimated and the a priori value: ˜X − X = p . (9.36) The parameters of the 7-parameter transformation are given by ξ = (B ⊤ B) −1 B ⊤ p . (9.37) Page 194 AIUB
9.3 Manipulation of Normal Equations The free network condition thus may be imposed by adding the following fictitious observation H p = 0 , (9.38) where H = (B ⊤ B) −1 B ⊤ . (9.39) Because of the regularity of the matrix B ⊤ B it is even possible to use H = B ⊤ . (9.40) ADDNEQ2 uses the first of the two possible equations. It is not always necessary to constrain all seven parameters ξ. The number of singularities (that have to be removed using the constraints) depends on the solution type. In global solutions, when estimating orbits and/or Earth orientation parameters, it is usually sufficient to constrain the rotation parameters only (using the corresponding part of H). This is the minimum constraint for the GNSS network. Minimum constraint conditions may be applied separately for coordinates and velocities. We refer to Chapter 10 for more details. 9.3.10 Parameter Pre-Elimination and Deletion Pre-elimination of parameters in ADDNEQ2 works in the same way as in GPSEST and as described in Section 7.5.5. The different pre-elimination options implemented in ADDNEQ2 are described in Section 9.4.4. Parameters may be pre-eliminated before or after the stacking of normal equations. Before pre-elimination, the parameters may be constrained and transformed. In ADDNEQ2 it is possible to eliminate (“delete”) parameters. This action is performed by removing the rows and columns corresponding to the respective parameters from the normal equation. As a result these parameters are fixed to their a priori values. The effect is the same as if the parameters were pre-eliminated after applying infinitely heavy constraints or if they were never set up. 9.3.11 Restrictions All manipulations possible at normal equation level are based on linear transformations. Only simple model changes are, therefore, possible with program ADDNEQ2. These include setting up site velocities, geocenter coordinates, or stochastic parameters at boundaries of the normal equations, and reduction of parameters for piece-wise linear representations. Model changes that require access to the observations are not possible. In particular, in case of changing • the sampling rate, • the analyzed linear combination of observations or frequency, • the elevation cutoff, • the troposphere model or mapping function, • the satellite antenna offset or pattern group definition, or • from relative to absolute antenna phase patterns. The reanalysis of the observations with program GPSEST is required in order to get normal equation files referring to the new model. Bernese GPS Software Version 5.0 Page 195
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Bernese GPS Software Version 5.0 Ed
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Bernese GPS Software Version 5.0 As
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Contents 2.3.6.1 Ionosphere-Free Li
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Contents 6.3.3 Kinematic Stations .
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Contents 9.4.4 Pre-Elimination Opti
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Contents 13.2 How to Correct P1-P2
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Contents 18.3.2 Command Bar . . . .
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Contents 20.4 Description of the Pr
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Contents 22.8.2 Station Abbreviatio
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Contents Page XVI AIUB
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List of Figures 5.1 Flow diagram of
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List of Figures 13.3 P1-C1 code bia
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List of Figures 22.20 Tabular orbit
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List of Tables 12.2 Influences of t
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1. Introduction and Overview • bu
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1. Introduction and Overview Table
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1. Introduction and Overview • Th
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1. Introduction and Overview The Be
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1. Introduction and Overview for Ca
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2. Fundamentals 2.1.1 GPS System De
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2. Fundamentals Table 2.2: Componen
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2. Fundamentals Clock correction [n
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2. Fundamentals Figure 2.5: GLONASS
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2. Fundamentals Table 2.6: GLONASS
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2. Fundamentals In contrast to the
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2. Fundamentals 2.2 GNSS Satellite
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2. Fundamentals 2.2.2.1 The Kepleri
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2. Fundamentals Table 2.9: Perturbi
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2. Fundamentals R.A. of Ascending N
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2. Fundamentals where aROCK is the
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2. Fundamentals By taking the deriv
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2. Fundamentals δi error of satell
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2. Fundamentals Ionospheric refract
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2. Fundamentals 2.3.6.1 Ionosphere-
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2. Fundamentals Table 2.10: Linear
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3. Campaign Setup variable to the f
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3. Campaign Setup Figure 3.1: Examp
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3. Campaign Setup In this section w
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3. Campaign Setup 3.5 Processing Ov
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4. Import and Export of External Fi
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5. Preparation of Earth Orientation
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6. Data Preprocessing Preprocessing
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6. Data Preprocessing (a) AS turned
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6. Data Preprocessing 6.2.4 Code Sm
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6. Data Preprocessing is set to 2.
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6. Data Preprocessing 6.3.2 Preproc
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6. Data Preprocessing RMS of kin. s
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6. Data Preprocessing The ambiguiti
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6. Data Preprocessing no loss of si
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6. Data Preprocessing This epoch-di
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6. Data Preprocessing result in lar
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6. Data Preprocessing (e.g., from C
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6. Data Preprocessing The second pa
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6. Data Preprocessing GAR small pie
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6. Data Preprocessing -------------
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6. Data Preprocessing automated pro
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6. Data Preprocessing 6.6.2 Generat
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6. Data Preprocessing 6.6.3 Detect
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6. Data Preprocessing (6) If the to
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6. Data Preprocessing Page 138 AIUB
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7. Parameter Estimation p u × 1 ve
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7. Parameter Estimation The two bas
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11. Troposphere Modeling and Estima
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12. Ionosphere Modeling and Estimat
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13. Differential Code Biases Promin
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13. Differential Code Biases Figure
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13. Differential Code Biases Figure
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13. Differential Code Biases ======
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13. Differential Code Biases Page 2
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14. Clock Estimation τ (BRUS-PTBB)
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14. Clock Estimation Here the limit
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14. Clock Estimation to zero. All c
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14. Clock Estimation #OBS : Number
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14. Clock Estimation 14.3 Clock RIN
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14. Clock Estimation cessed if CCRN
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14. Clock Estimation RINEX files th
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14. Clock Estimation the clock valu
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14. Clock Estimation SINGLE POINT P
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15. Estimation of Satellite Orbits
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16. Antenna Phase Center Offsets an
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17. Data Simulation Tool GPSSIM 17.
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17. Data Simulation Tool GPSSIM The
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17. Data Simulation Tool GPSSIM The
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17. Data Simulation Tool GPSSIM Res
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18. The Menu System 18.2 Starting t
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18. The Menu System 18.3.1 Menu Bar
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18. The Menu System 18.3.5 Panel Co
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18. The Menu System the menu the ne
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18. The Menu System Table 18.1: Pre
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18. The Menu System 18.5.3 System E
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18. The Menu System 18.7 Change Opt
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18. The Menu System 18.9 Technical
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18. The Menu System ... ! Environme
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18. The Menu System The keyword ENV
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18. The Menu System ! List of Remai
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18. The Menu System The MENUAUX-mec
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18. The Menu System Keyword values
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19. Bernese Processing Engine (BPE)
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20. Processing Examples inspect the
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20. Processing Examples 20.3.1 How
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20. Processing Examples • (option
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20. Processing Examples PID 111 PRE
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20. Processing Examples 20.4.1.4 Co
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20. Processing Examples 20.4.1.5 Ta
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20. Processing Examples 20.4.1.7 Cr
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20. Processing Examples 20.4.2.1 Co
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20. Processing Examples appears in
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20. Processing Examples PID 313 MPR
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20. Processing Examples Further rea
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20. Processing Examples # # Create
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20. Processing Examples PID 101 GPS
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20. Processing Examples The RINEX n
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20. Processing Examples # # Preproc
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20. Processing Examples the loop, d
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20. Processing Examples PID 903 CLK
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20. Processing Examples and IGS 00B
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20. Processing Examples • Save th
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20. Processing Examples PID 321 GPS
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20. Processing Examples PID 301 CLK
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21. Program Structure $C / %C% PGM
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21. Program Structure (program GPSE
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21. Program Structure continued fro
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21. Program Structure continued fro
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21. Program Structure ! -----------
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22. Data Structure "Program" Area $
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22. Data Structure Table 22.1: List
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22. Data Structure 22.4.2 Geodetic
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22. Data Structure 22.4.4 Antenna P
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Page 484 AIUB ANTENNA PHASE CENTER
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22. Data Structure 22.4.5 Satellite
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22. Data Structure 22.4.6 Satellite
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22. Data Structure DIFFERENCE OF GP
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22. Data Structure 22.4.9 Subdaily
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22. Data Structure EGM96 EGM96, VER
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22. Data Structure SINEX : OPTION I
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22. Data Structure 22.4.16 Panel Up
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22. Data Structure 22.6.2 Header an
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22. Data Structure 15 Antenna type(
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22. Data Structure SVN-NUMBER= 2 ME
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22. Data Structure -1 2 1 5 TITLE :
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22. Data Structure Used by: ORBGEN
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22. Data Structure 53064.00 53065.0
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22. Data Structure CODE’S MONTHLY
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22. Data Structure Table 22.4: Stat
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22. Data Structure (3) TYPE 003: HA
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22. Data Structure 22.8.4 Station P
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22. Data Structure Remarks: • Eac
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22. Data Structure The following st
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22. Data Structure Table 22.7: List
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22. Data Structure AJAC $$ FES2004
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22. Data Structure Station sigma fi
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22. Data Structure GOPE 11502M002 Z
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22. Data Structure 22.8.18 Receiver
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22. Data Structure CODE RAPID 3-DAY
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22. Data Structure 22.9.3 Meteo and
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22. Data Structure IONOSPHERE MODEL
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22. Data Structure 22.10 Miscellane
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22. Data Structure 22.10.4 Variance
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22. Data Structure 22.10.5 Normal E
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22. Data Structure 22.10.7 Observat
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22. Data Structure Created by: Each
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22. Data Structure ----------------
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22. Data Structure 22.10.17 BPE log
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23. Installation Guide 23.1.2 Conte
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23. Installation Guide 23.1.3.2 Ins
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23. Installation Guide BERN50 : $C
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23. Installation Guide If you have
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23. Installation Guide To make the
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23. Installation Guide List of Inst
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23. Installation Guide 23.2.4 Confi
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23. Installation Guide Configure me
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23. Installation Guide ${P}/EXAMPLE
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23. Installation Guide To recompile
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23. Installation Guide Page 574 AIU
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24. The Step from Version 4.2 to Ve
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BIBLIOGRAPHY Bock, H. (2004), Effic
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BIBLIOGRAPHY Janes, H. W., R. B. La
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BIBLIOGRAPHY Schaer, S. (1998), COD
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BIBLIOGRAPHY Page 588 AIUB
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INDEX OF PROGRAMS NEQ2ASC, 207, 541
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Index of Program Panels CODSPP 2: I
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Index of Program Panels MKCLUS 3: R
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INDEX OF KEYWORDS Antenna verificat
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INDEX OF KEYWORDS Cluster definitio
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INDEX OF KEYWORDS variance-covarian
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INDEX OF KEYWORDS orbit products, 1
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INDEX OF KEYWORDS Multi-session sol
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INDEX OF KEYWORDS Orbital elements
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INDEX OF KEYWORDS Receiver antenna
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INDEX OF KEYWORDS orbit modeling, 9
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INDEX OF KEYWORDS WGS-84, 19, 88, 2
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