Deformation monitoring and the maximum number of stable points method

• The question of deformation determination among epochs is revisited.
• The general problem of deformation determination has no unique solution.
• The standard method is based on the implicit assumption of small displacements for all points.
• We propose the so-called maximum number of stable points hypothesis along with a computation method.
• We show how the new method succeeds in detecting a single displacement whereas the standard one fails.

The question of determination of displacements in control networks with two or more measuring epochs is a well-known problem with broad applications to different fields of science and engineering. The standard procedure, which is computed by means of the pseudoinverse matrix, however, makes an implicit assumption that may be not convenient for the network at hand: it distributes the noticed displacement among the majority of the network points. The present paper develops what it has been named as the maximum number of stable points hypothesis and builds from the corresponding theoretical framework an applicable computation procedure. Application to a particular example will confirm its clear advantages versus the standard procedure for deformation determination in the cases where a single large deformation may be suspected.