Abstract This paper presents an innovative extention of the noise wave definition to mixed mode, differential - and commonmode noise waves which can be used for noise analysis of differential microwave networks. Mixed mode noise waves are used next to define generalized mixed mode noise wave correlation matrices of microwave multiport networks. Presented approach may be used for noise analysis of microwave differential networks with differential ports as well as with conventional single ended ports.
A new method to transform from Cartesian to geodetic coordinates is presented. It is based on the solution of a system of nonlinear equations with respect to the coordinates of the point projected onto the ellipsoid along the normal. Newton’s method and a modification of Newton’s method were applied to give third-order convergence. The method developed was compared to some well known iterative techniques. All methods were tested on three ellipsoidal height ranges: namely, (-10 – 10 km) (terrestrial), (20 – 1000 km), and (1000 – 36000 km) (satellite). One iteration of the presented method, implemented with the third-order convergence modified Newton’s method, is necessary to obtain a satisfactory level of accuracy for the geodetic latitude ( σ φ < 0.0004”) and height ( σ h < 10 − 6 km, i.e. less than a millimetre) for all the heights tested. The method is slightly slower than the method of Fukushima (2006) and Fukushima’s (1999) fast implementation of Bowring’s (1976) method.
The method that is proposed in the present paper is a special case of squared M split estimation. It concerns a direct estimation of the shift between the parameters of the functional models of geodetic observations. The shift in question may result from, for example, deformation of a geodetic network or other non-random disturbances that may influence coordinates of the network points. The paper also presents the example where such shift is identified with a phase displacement of a wave. The shift is estimated on the basis of wave observations and without any knowledge where such displacement took place. The estimates of the shift that are proposed in the paper are named Shift- M split estimators.
The work presents the results of studies on dependence of effectiveness of chosen robust estimation methods from the internal reliability level of a geodetic network. The studies use computer-simulated observation systems, so it was possible to analyse many variants differing from each other in a planned way. Four methods of robust estimation have been chosen for the studies, differing substantially in the approach to weight modifications. For comparative reasons, the effectiveness studies have also been conducted for the very popular method in surveying practice, of gross error detection basing on LS estimation results, the so called iterative data snooping. The studies show that there is a relation between the level of network internal reliability and the effectiveness of robust estimation methods. In most cases, in which the observation contaminated by a gross error was characterized by a low index of internal reliability, the robust estimation led to results being essentially far from expectations.
In the recent years three-dimensional buildings modelling based on an raw air- borne laser scanning point clouds, became an important issue. A significant step towards 3D modelling is buildings segmentation in laser scanning data. For this purpose an algorithm, based on the multi-resolution analysis in wavelet domain, is proposed in the paper. The proposed method concentrates only on buildings, which have to be segmented. All other objects and terrain surface have to be removed. The algorithm works on gridded data. The wavelet-based segmentation proceeds in the following main steps: wavelet decomposition up to appropriately chosen level, thresholding on the chosen and adjacent levels, removal of all coefficients in the so-called influence pyramid and wavelet reconstruction. If buildings on several scaling spaces have to be segmented, the procedure should be applied iteratively. The wavelet approach makes the procedure very fast. However, the limitation of the proposed procedure is its scale-based distinction between objects to be segmented and the rest.
The DiSTFA method (Displacements and Strains using Transformation and Free Adjustment) was presented in Kamiński (2009). The method has been developed for the determination of displacements and strains of engineering objects in unstable reference systems, as well as for examining the stability of reference points. The DiSTFAG (Gross errors) method presented in the paper is the extension of the DiSTFA method making it robust to gross errors. Theoretical considerations have been supplemented with an example of a practical application on a simulated 3D surveying network.
In deformation analyses, it is important to find a stable reference frame and therefore the stability of the possible reference points must be controlled. There are several methods to test such stability. The paper’s objective is to examine one of such methods, namely the method based on application of R-estimation, for its sensitivity to gross errors. The method in question applies three robust estimators, however, it is not robust itself. The robustness of the method depends on the number of unstable points (the fewer unstable points there are, the more robust is the proposed method). Such property makes it important to know how the estimates applied and the strategy itself respond to a gross error. The empirical influence functions (EIF) can provide necessary information and help to understand the response of the strategy for a gross error. The paper presents examples of EIFs of the estimates, their application in the strategy and describes how important and useful is such knowledge in practice.