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2.8 Set of observations

The pair tag <obs> groups together a set of observations which are somehow related. A typical example is a set of directions and distances observed from one stand-point. An observation section contains a set of

The band variance-covariance matrix of directions, distances, and angles listed in one <obs> section may be supplied using a <cov-mat> pair tag with attributes dim (dimension) and band (bandwidth). The band-width of the diagonal matrix is equal to 0 and a fully-populated variance-covariance matrix has a bandwidth of dim-1.

Observation variances and covariances (i.e. an upper-symmetric part of the band-matrix) are written row by row between <cov-mat> and </cov-mat> tags. If present, the dimension of the variance-covariance matrix must agree with the number of observations.

The following example of variance-covariance matrix with dimension 6 and bandwidth 2 (two nonzero codiagonals and three zero codiagonals) 

     [ 1.1  0.1  0.2   0    0    0
       0.1  1.2  0.3  0.4   0    0
       0.2  0.3  1.3  0.5  0.6   0
        0   0.4  0.5  1.4  0.7  0.8
        0    0   0.6  0.7  1.5  0.9
        0    0    0   0.8  0.9  1.6 ]

is coded in XML as 

     <cov-mat dim="6" band="2">
        1.1  0.1  0.2
             1.2  0.3  0.4
                  1.3  0.5  0.6
                       1.4  0.7  0.8
                            1.5  0.9
                                 1.6
     </cov-mat>

If two or more sets of directions with different orientations are observed from a stand-point, they must be placed in different <obs> sections. The value of an orientation angle can be explicitly stated with an attribute orientation="...". Normally, it is more convenient to let the program calculate approximate values of orientations needed for the adjustment. If directions are present, then the attribute station must be defined.

Optional attribute from_dh="..." enables to enter implicit height of instrument for all observations within the <obs> pair tag.

Observed distances are expressed in meters, their standard deviations in millimeters. Observed directions and angles are expressed in centigrades (400) and their standard deviations in centigrade seconds.

Height differences can be entered in the <obs> or <height-differences> section. If entered in the <obs> section, the dist="..." parameter is ignored (Height differences).

Example

     <obs from="418">
        <direction  to=  "2" val="0.0000"   stdev="10.0" />
        <direction  to="416" val="63.9347"  stdev="10.0" />
        <direction  to="420" val="336.3190" stdev="10.0" />
        <distance   to="420" val="246.594"  stdev="5.0"  />
     </obs>
     
     <obs from="418">
        <direction  to=  "2" val="0.0000"   />
        <direction  to="416" val="63.9347"  />
        <direction  to="420" val="336.3190" />
        <distance   to="420" val="246.594"  />
     
        <cov-mat dim="4" band="0">
           100.00 100.00 100.00 25.00
        </cov-mat>
     </obs>