9.2.5 Single-Session Network Processing

SHOULD TRIVIAL BASELINES BE INCLUDED IN A SINGLE SESSION ADJUSTMENT?

The main argument against incorporation of all baselines (independent and trivial) into any adjustment, single session or multi-session, is because the resulting solution statistics are "over-optimistic", that is, the length of the axes of the error ellipses (or ellipsoids) are shorter than they should be. However, there is strong support for including so-called "quasi-independent" baselines in the single session network adjustment (section 9.4.5):

• It can be argued that all baselines reduced separately (and particularly if an ambiguity-fixed solution is obtained) are in fact independent.
  
• Including all baselines from a session, if reduced separately, would (partly) account for the between-baseline correlations that have been ignored at the single baseline reduction step.
  
• Increasing the number of observations, and hence the redundancies (or degrees of freedom), permits more reliable statistical testing.
  
• The use of all baselines, independent and quasi-independent, removes some of the arbitrariness involved in the selection of only independent baselines (different sets of independent baselines may lead to differing results). The outcome is therefore a unique solution.

Example of a Six Baseline Single Session Redundant Network Adjustment

Each baseline has been reduced separately. The VCV matrices have been modified in the manner described in section 9.4.1.

	

          BASELINE OBSERVATION DATA
          =========================
 BASELINE:   1
 "FROM" SITE: PM9920      -4579195.624    2765270.042   -3462837.303 "TO" SITE  : VALE HEAD   -4580210.441    2765452.961   -3461449.908
 VCV MATRIX : .5712100000E-05
             -.3688782947E-05   .4368100000E-05
              .2837932189E-05  -.1688775945E-05   .3027600000E-05
 BASELINE:   2
 "FROM" SITE: PM9920      -4579195.674    2765270.071   -3462837.341
 "TO" SITE  : PM43517     -4578660.700    2766320.048   -3462753.140
 VCV MATRIX : .4000000000E-05
             -.2535651540E-05   .3027600000E-05
              .2007931506E-05  -.1184518459E-05   .2160900000E-05
 BASELINE:   3
 "FROM" SITE: PM43517     -4578670.756    2766305.138   -3462754.685
 "TO" SITE  : PM43494     -4577941.012    2766364.667   -3463643.425
 VCV MATRIX : .3534400000E-05
             -.2572191966E-05   .3204100000E-05
              .1639849702E-05  -.9694237787E-05   .1690000000E-05
 BASELINE:   4
 "FROM" SITE: PM43517     -4578670.707    2766305.108   -3462754.647
 "TO" SITE  : VALE HEAD   -4580220.498    2765438.053   -3461451.453
 VCV MATRIX : .4972900000E-05
             -.3268030165E-05   .3880900000E-05
              .2473092755E-05  -.1476933645E-05   .2624400000E-05
 BASELINE:   5
 "FROM" SITE: PM43494     -4577920.320    2766368.883   -3463628.044
 "TO" SITE  : PM9920      -4579185.034    2765259.374   -3462823.502
 VCV MATRIX : .4622500000E-05
             -.3282697398E-05   .4040100000E-05
              .2170544325E-05  -.1276909785E-05   .2250000000E-05
 BASELINE:   6
 "FROM" SITE: VALE HEAD   -4580219.138    2765436.774   -3461450.389
 "TO" SITE  : PM43494     -4577939.605    2766363.360   -3463642.324
 VCV MATRIX : .8643600000E-05
             -.6053084591E-05   .7290000000E-05
              .4175140182E-05  -.2562779736E-05   .4368100000E-05

     ALTER INPUT VCV MATRICES:
     -------------------------
     CONSTANT HORIZONTAL OFFSET (m)=  .010
     CONSTANT VERTICAL OFFSET (m)  =  .010
     SCALE VCV STD.DEVS...         =1.0000
     LINE-LENGTH ERROR (ppm)       = 1.000


          APRIORI STATION COORDINATES
          ===========================
1: PM9920    FIXED X: -4579195.674  Y:  2765270.071  Z: -3462837.341
2: VALE HEAD FREE  X: -4580210.441  Y:  2765452.961  Z: -3461449.908
3: PM43517   FREE  X: -4578668.689  Y:  2766303.359  Z: -3462751.234
4: PM43494   FREE  X: -4577923.488  Y:  2766359.771  Z: -3463627.595


          PROCESSING RESULTS
          ==================
          NUMBER FREE PARAMETERS   =   9
          NUMBER PARAMETERS (TOTAL)=  12

  PARAMETER NAME            DIFF. CORR.     FINAL VALUE     ST.DV.
 *SITE 1 X  PM9920                .000     -4579195.674      .000
 *SITE 1 Y  PM9920                .000      2765270.071      .000
 *SITE 1 Z  PM9920                .000     -3462837.341      .000
  SITE 2 X  VALE HEAD            -.051     -4580210.492      .007
  SITE 2 Y  VALE HEAD             .031      2765452.992      .006
  SITE 2 Z  VALE HEAD            -.039     -3461449.947      .007
  SITE 3 X  PM43517              7.988     -4578660.701      .007
  SITE 3 Y  PM43517             16.689      2766320.048      .006
  SITE 3 Z  PM43517             -1.907     -3462753.141      .007
  SITE 4 X  PM43494             -7.470     -4577930.958      .007
  SITE 4 Y  PM43494             19.807      2766379.578      .006
  SITE 4 Z  PM43494            -14.287     -3463641.882      .007


          OBSERVATION RESIDUALS
          =====================
 BASELINE:   1     SITE 1: PM9920             SITE 2: VALE HEAD       
 VECTOR:                  -1014.817        182.919       1387.395
 RESID :                       .001          -.002           .001
 BASELINE:   2     SITE 1: PM9920             SITE 2: PM43517         
 VECTOR:                    534.974       1049.977         84.201
 RESID :                       .001           .000           .001
 BASELINE:   3     SITE 1: PM43517            SITE 2: PM43494         
 VECTOR:                    729.744         59.529       -888.740
 RESID :                       .001          -.001           .001
 BASELINE:   4     SITE 1: PM43517            SITE 2: VALE HEAD       
 VECTOR:                  -1549.791       -867.055       1303.194
 RESID :                      -.001           .001           .000
 BASELINE:   5     SITE 1: PM43494            SITE 2: PM9920          
 VECTOR:                  -1264.714      -1109.509        804.542
 RESID :                       .002          -.002           .001
 BASELINE:   6     SITE 1: VALE HEAD          SITE 2: PM43494         
 VECTOR:                   2279.533        926.586      -2191.935
 RESID :                       .000           .000           .000

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© Chris Rizos, SNAP-UNSW, 1999