Volume 7, Issue 1

The L1-norm estimation is a resistant estimation method and therefore used for the detection of gross errors in geodetic measurement data. Alternatively, other Lp-norms have been suggested in literature for resistant parameter estimation. A common numerical solution method for Lp-norm estimation is the method of iteratively reweighted least squares. Procedural manners for a successful application of this method are considered. A modification of the method is given, which reduces the number of iterations significantly. By means of a simulation the applicability of the mentioned methods and the success of different Lp-norms in the detection of gross errors are tested. It shows that solving the L1-norm numerically may be unsuccessful and that instead a resistant Lp-norm is to be recommended, which is comparably successful in the detection of gross errors and can successfully be solved numerically by the presented modification of iteratively reweighted least squares.

In Least Squares (LS), the linearized functional model betweenM observables and N unknown parameters is given. LS provides estimates of parameters, observables, residuals and a posteriori variance. To identify outliers and to estimate accuracies and reliabilities, tests on the model and on the individual residuals can be performed at different levels of significance and power. However, LS is not robust: one outlier could be spread into all the residuals and its identification is difficult. A possible solution to this problem is given by a Leave One Block Out approach. Let’s suppose that the observation vector can be decomposed into m sub-vectors (blocks) that are reciprocally uncorrelated: in the case of completely uncorrelated observations, m = M. A suspected block is excluded from the adjustment, whose results are used to check it. Clearly, the check is more robust, because one outlier in the excluded block does not affect the adjustment results. The process can be repeated on all the blocks, but can be very slow, because m adjustments must be computed. To efficiently apply Leave One Block Out, an algorithm has been studied. The usual LS adjustment is performed on all the observations to obtain the ’batch’ results. The contribution of each block is subtracted from the batch results by algebraic decompositions, with a minimal computational effort: this holds for parameters, a posteriori residuals and variance. Therefore all the blocks can be checked. In the paper, the algorithm is discussed. Two examples of ELOBO application are presented: the first testifies ELOBO reliability against classical LS tests. In the second, ELOBO numerical efficiency is analyzed.

Based on the reprocessing of a regional continuously operating reference station (CORS) network the effect of stochastic modelling on the significance of coordinate time series parameters is investigated. The aim is to identify a suitable stochastic model for the time correlated time series. It is needed as stochastic model of the time series data and to enable a realistic statement about the significance of estimated parameters like velocity, offsets, annual signal. The approach of power-law noise stochastic modelling is applied and investigated. Estimated stochastic parameters and resulting models best fitting to the time series are shown and discussed. It is found that the stochastic parameters are strongly site specific. Utilizing such a best fitting stochastic model will yield realistic statements about accuracy and significance of parameters (velocity, offsets, annual signal). The application to the assessment of the velocity field of the network concludes the paper.

One of the main scientific objectives of the Gravity field and steady state Ocean Circulation Explorer (GOCE) gravity field satellite mission is its contribution to the global unification of height systems. In this study, we compute the offsets of three height datums in North America (NAVD88, CGVD28 and Nov07) against a common equipotential surface. NAVD88 and CGVD28 are the official vertical datums for the USA and Canada, respectively. Nov07 is the latest unofficial adjustment of the first-order levelling network in Canada. This datum is only used for the validation of geoid models. The offset for each datum is determined from a combination of ellipsoidal, orthometric and geoid heights. The ellipsoidal heights on benchmarks come from the GNSS networks of Canada and the USA while geoid heights are computed from currently the best GOCE-based geopotential model in North America, i.e., go_cons_gcf_2_tim_r3. The orthometric heights of the GNSS stations are available from the adjustments of the vertical control networks of both countries. Among the various factors that contribute to the uncertainty of the computed datum offset, we investigate the effect of the omission error of the GOCE geoid by means of the EGM2008 model. In Canada, where GNSS/levelling stations are irregularly distributed over the landmass, the effect of the GOCE omission error on the computed offsets reaches one decimetre. Due to the much more densely distributed GNSS/levelling stations in the USA, the effect of the GOCE omission error on the offset of NAVD88 is 3 cm. Therefore, the effect of the omission error of GOCE-based geopotential models should be taken into account in the height datum unification on the North American continent if we aim at the one centimetre accuracy.

Bathymetric resurveying in shallow seas is a costly process with limited resources, yet necessary for adequate nautical charts and therefore crucial for safe navigation. An important factor in an efficient resurvey policy is the type and size of sea floor dynamics. We propose four indicators, which we use in a procedure to recommend changes to the resurvey policies of the Belgian and Netherlands Continental Shelf (BNLCS). These shallow regions are characterised by a sandy sea floor covered with rhythmic patterns. The proposed indicators follow from the estimates for sea floor dynamics, as given by applying the statistical method of deformation analysis. We present a concept for the shallowest likely depth surface, on which we base two of the indicators. The other two indicators may act as a warning: they quantify the potentially missed dynamics, which makes the procedure more robust in case of complicated morphology. Finally, applying our procedure to the BNLCS, we show clear differences in recommended resurvey priority between the five analysed regions, which currently have equal resurvey frequencies.

Personal navigation systems intend to provide the navigation information in any environment, indoors and outdoors, and at any time. In outdoor environments, the positioning solution is typically provided by using Global Positioning System (GPS). However, GPS is inaccurate or unavailable in most of indoor environments and therefore other externally-referenced sensing techniques are required. Inertial sensing techniques are used for pedestrian navigation in association with dead reckoning approach. Magnetometers can be used to derive the user’s heading by sensing the Earth’s magnetic field. In this paper, an efficient and robust maneuvering mode to calibrate low cost magnetometer is recommended for pedestrian navigation applications. Additionally, other maneuvering modes and errors associated with each mode to achieve best estimation for the calibration parameters in the 3D Space are also provided. Also, the effect of using different maneuvering modes (DMM) on the heading estimation for the pedestrian navigation is studied. The results show that the coordinated mode is suitable to perform the calibration process as the unit is rotated in a way to cover the whole 3D space.