Volume 3, Issue 2

The standard reference in uncertainty modeling is the “Guide to the Expression of Uncertainty in Measurement (GUM)”. GUM groups the occurring uncertain quantities into “Type A” and “Type B”. Uncertainties of “Type A” are determined with the classical statistical methods, while “Type B” is subject to other uncertainties which are obtained by experience and knowledge about an instrument or a measurement process. Both types of uncertainty can have random and systematic error components. Our study focuses on a detailed comparison of probability and fuzzy-random approaches for handling and propagating the different uncertainties, especially those of “Type B”. Whereas a probabilistic approach treats all uncertainties as having a random nature, the fuzzy technique distinguishes between random and deterministic errors. In the fuzzy-random approach the random components are modeled in a stochastic framework, and the deterministic uncertainties are treated by means of a range-of-values search problem. The applied procedure is outlined showing both the theory and a numerical example for the evaluation of uncertainties in an application for terrestrial laserscanning (TLS).

Carrier phase multipath caused by signal reflections in the vicinity of GNSS stations is a major error source of precise differential positioning. Detection and mitigation of carrier phase multipath errors can be based on signal quality values (e.g. signal-to-noise ratio values) as provided by GNSS receivers. These values are influenced by various factors as e.g. the actual strength of the transmitted signal, space loss, atmospheric effects, and antenna gain pattern. After their removal, deviations from nominal signal quality values mainly contain multipath information which can be used to calculate carrier phase multipath corrections. The described technique is valid only for observations collected in static mode and single dominant reflectors. Practical experiences show that corrections based on signal quality observations are able to remove a large portion of the carrier phase multipath errors.

Dynamic processes are usually monitored by collecting a time series of observations, which is then analysed in order to detect any motion or non-standard behaviour. Geodetic examples include the monitoring of dams, bridges, high-rise buildings, landslides, volcanoes and tectonic motion. The cumulative sum (CUSUM) test is recognised as a popular means to detect changes in the mean and/or the standard deviation of a time series and has been applied to various monitoring tasks. This paper briefly describes the CUSUM technique and how it can be utilised for the detection of small baseline length changes by differencing two perpendicular baselines sharing a common site. A simulation is carried out in order to investigate the expected behaviour of the resulting CUSUM charts for a variety of typical deformation monitoring scenarios. This simulation shows that using first differences (between successive epochs) as input, rather than the original baseline lengths, produces clear peaks or jumps in the differenced CUSUM time series when a sudden change in baseline length occurs. These findings are validated by analysing several GPS baseline pairs of a network deployed to monitor the propagation of an active ice shelf rift on the Amery Ice Shelf, East Antarctica.

The analysis of series of offshore bathymetric surveys provides insight into the morphodynamics of the sea floor. This knowledge helps to improve resurvey policies for the maintenance of port approaches and nautical charting, and to validate morphodynamic models. We propose a method for such an analysis that is based on statistical testing theory, particularly aimed at the detection of dynamics in areas with tidal sand waves. The method explicitly considers the uncertainty of every measured depth value, resulting in parameter estimates for the sea floor dynamics, and their uncertainty. We apply the method to sea floor representations both with and without a sand wave pattern. A test scenario is set up, consisting of a survey of an existing area in the Southern North Sea, for which dynamics are simulated. The results show that the proposed method successfully detects different types of sea floor dynamics, leading to satisfactory estimates of the corresponding parameters.

The available geoid undulations on the WGS84 ellipsoid at over two hundred GPS stations are interpolated using a least-squares surface fitting technique to determine the geoid of the central highlands in Sri Lanka. However, it is not possible to interpolate these points directly to prepare a detailed map of the geoid surface as the geoid separation varies intense due to the rugged local topography making the interpolation inaccurate. The gravity potential and subsequently the undulation of the local geoid due to the topography have been calculated separately using a topographic model and removed from the available geoid undulations. This model was created using information obtained from 1:50 000 digital topographic maps provided by the Survey department of Sri Lanka. The resulting geoid separations were interpolated and three surface polynomials were employed to determine the geoid using the least-squares surface fitting technique. To avoid possible artefacts in regions without observations, an area including central highlands was selected to determine the geoid. Finally, the geoid undulations due to the topography were added back to the Bouguer co-geoid represented by three mathematical surfaces to create a detailed map of the geoid of Sri Lanka. A local positive geoid surface superimposing a large negative regional surface has been obtained and the local maximum value of the geoid undulation is about –92.05 m in the vicinity of Piduruthalagala peak.