GPS Satellite Surveying, 4th Edition

2.5.6 Mixed Model with Conditions

A third case pertains to the role of the weight matrix of the parameters. The weight matrix expresses the quality of the information known about the observed parameters. For the adjustment to be meaningful, one must make every attempt to obtain a weight matrix that truly reflects the quality of the additional information. Low weights, or, equivalently, large variances, imply low precision. Even low-weighted parameters can have, occasionally, a positive effect on the quality of the least-squares solution. If the parameters or functions of the parameters are introduced with an infinitely large weight, one speaks of conditions between parameters. The only specifications for implementing conditions are

2.5.18

and

2.5.19

The respective mathematical models are

2.5.20

with

2.5.21

2.5.22

2.5.7 Observation Equation Model with Conditions

Similar to the previous case we have for the observation equation model,

2.5.23

with

2.5.24

2.5.25

Table 2.5.5 contains ...