Kalman Filtering in Levelling: An Application

Abstract

The present study deals with the analysis of repeated levelling networks set up to control geological deformation (such as subsidence or landslide phenomena). Vertical movements are determined by comparing repeated measurements in subsequent epochs on the area under study. For large networks, this comparison is not easy. The measurements can require a great deal of time, to the extent that this may be compared to the interval of time between two repetitions. This may lead to problems of loop closure in areas of fast movement and the obtained results would in this case be of very difficult interpretation. Moreover, even though the measurements involve the same area, they may concern a network that gradually modifies according the new data acquired. This means that in subsequent repetitions there are entire areas for which no data on movements are available. It is therefore essential to define a model which takes these additional characteristics of variability into consideration, so as to identify the evolution of the phenomenon correctly (VANICEK, 1979). The knowledge of the kinematic parameter i.e. velocity and acceleration is very important for the physical interpretation of the phenomena.