Nonadjustable measured variable

In practice, the adjustment problem as formulated in Subsection 8.5.2 (see (8.5.11)) is most frequently a reconciliation problem some measured values (vector ) are adjusted (reconciled) so as to make the model solvable. The classification of variables gives one an idea of what can be expected from the reconciliation. Thus, first, the degree of redundancy H informs us on the number of independent constraints (scalar equations) the adjusted value x has to obey, thus how many measured variables are redundant in the manner that having deleted their measurement, they will be still determined by the remaining measured values. In particular if // = 0 then all the / measured values are necessary (none is redundant). If it happens that H = I then the whole measurement is redundant because the constraints determine the I variables uniquely. Generally, not any H measured variables are determined by the other values, thus redundant-, some of them can be nonredundant thus not subject to the constraints (solvability conditions), hence their measurement cannot be deleted. Under frequent hypotheses adopted by the statistical model of measurement, the nonredundant values remain unadjusted by the reconciliation so they are also called nonadjustable. 

In the case (b) above, in a neighbourhood of the possible rare points, the variable will be almost nonadjustable if an estimate falls into this neighbourhood, the estimated will only slightly differ from the measured x even if subject to a gross error. Such case can occur in the reconciliation and cannot be avoided by the a priori classification. See later Section 10.5, Remark. 

In particular, this is the case when the variable JTh has been classified as nonadjustable see Subsection 8.5.4. In the latter case, the property (10.3.14) is a property of the system of measurement and it will occur at any measurement in a series more generally, it can also occur (rather unlikely) only incidentally. Then, by (10.3.11b) thus (10.3.10) with (10.3.7), the h-th adjustment... 

The theoretical concepts of redundancy/nonredundancy are more tricky see Chapter 8, Section 8.5, finally Subsection 8.5.4. In practice, assuming the covariance matrix F diagonal, the concepts can be replaced by those of redundancy (adjustability)/nonadjustability. So if, in a series of measurements, a variable Xh is found nonadjustable (10.3.14) then it is, almost certainly, nonadjustable in the whole admissible region. Otherwise, at some points a variable can be also almost nonadjustable see Remark to Section 10.5 below. 

At least if the problem is linearized in a neighbourhood of the point, we conclude that variable is observable, / and unobservable, and no measured value is nonadjustable (all are redundant). 

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