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The Bayesian detection of discontinuities in a polynomial regression and its application to the cycle-slip problem 总被引：4，自引：1，他引：3
Maria Clara de Lacy Mirko Reguzzoni Fernando Sansò Giovanna Venuti 《Journal of Geodesy》2008,82(9):527-542
This paper deals with the problem of detecting and correcting cycle-slips in Global Navigation Satellite System (GNSS) phase
data by exploiting the Bayesian theory. The method is here applied to undifferenced observations, because repairing cycle-slips
already at this stage could be a useful pre-processing tool, especially for a network of permanent GNSS stations. If a dual
frequency receiver is available, the cycle-slips can be easily detected by combining two phase observations or phase and range
observations from a single satellite to a single receiver. These combinations, expressed in a distance unit form, are completely
free from the geometry and depend only on the ionospheric effect, on the electronic biases and on the initial integer ambiguities;
since these terms are expected to be smooth in time, at least in a short period, a cycle-slip in one or both the two carriers
can be modelled as a discontinuity in a polynomial regression. The proposed method consists in applying the Bayesian theory
to compute the marginal posterior distribution of the discontinuity epoch and to detect it as a maximum a posteriori (MAP)
in a very accurate way. Concerning the cycle-slip correction, a couple of simultaneous integer slips in the two carriers is
chosen by maximazing the conditional posterior distribution of the discontinuity amplitude given the detected epoch. Numerical
experiments on simulated and real data show that the discontinuities with an amplitude 2 or 3 times larger than the noise
standard deviation are successfully identified. This means that the Bayesian approach is able to detect and correct cycle-slips
using undifferenced GNSS observations even if the slip occurs by one cycle. A comparison with the scientific software BERNESE
5.0 confirms the good performance of the proposed method, especially when data sampled at high frequency (e.g. every 1 s or
every 5 s) are available. 相似文献
2.
The Milos volcanic field includes a well-exposed volcaniclastic succession which records a long history of submarine explosive
volcanism. The Bombarda volcano, a rhyolitic monogenetic center, erupted ∼1.7 Ma at a depth <200 m below sea level. The aphyric
products are represented by a volcaniclastic apron (up to 50 m thick) and a lava dome. The apron is composed of pale gray
juvenile fragments and accessory lithic clasts ranging from ash to blocks. The juvenile clasts are highly vesicular to non-vesicular;
the vesicles are dominantly tube vesicles. The volcaniclastic apron is made up of three fades: massive to normally graded
pumice-lithic breccia, stratified pumice-lithic breccia, and laminated ash with pumice blocks. We interpret the apron beds
to be the result of water-supported, volcaniclastic mass-How emplacement, derived directly from the collapse of a small-volume,
subaqueous eruption column and from syn-eruptive, down-slope resedimentation of volcaniclastic debris. During this eruptive
phase, the activity could have involved a complex combination of phreatomagmatic explosions and minor submarine effusion.
The lava dome, emplaced later in the source area, is made up of flow-banded lava and separated from the apron by an obsidian
carapace a few meters thick. The near-vertical orientation of the carapace suggests that the dome was intruded within the
apron. Remobilization of pyroclastic debris could have been triggered by seismic activity and the lava dome emplacement.
Published online: 30 January 2003
Editorial responsibility: J. McPhie 相似文献
3.
On the explicit determination of stability constants for linearized geodetic boundary value problems
The theory of GBVPs provide the basis to the approximate methods used to compute global gravity models. A standard approximation
procedure is least squares, which implicitly assumes that data, e.g. gravity disturbance and gravity anomaly, are given functions
in L
2(S). We know that solutions in these cases exist, but uniqueness (and coerciveness which implies stability of the numerical
solutions) is the real problem. Conditions of uniqueness for the linearized fixed boundary and Molodensky problems are studied
in detail. They depend on the geometry of the boundary; however, the case of linearized fixed boundary BVP puts practically
no constraint on the surface S, while the linearized Molodensky BVP requires the previous knowledge of very low harmonics,
for instance up to degree 25, if we want the telluroid to be free to have inclinations up to 60°. 相似文献
4.
The height datum/geodetic datum problem 总被引：2，自引：0，他引：2
5.
The problem of the convergence of the collocation solution to the true gravity field was defined long ago (Tscherning in Boll
Geod Sci Affini 39:221–252, 1978) and some results were derived, in particular by Krarup (Boll Geod Sci Affini 40:225–240,
1981). The problem is taken up again in the context of the stochastic interpretation of collocation theory and some new results
are derived, showing that, when the potential T can be really continued down to a Bjerhammar sphere, we have a quite general convergence property in the noiseless case.
When noise is present in data, still reasonable convergence results hold true.
“Democrito che ’l mondo a caso pone” “Democritus who made the world stochastic” Dante Alighieri, La Divina Commedia, Inferno, IV – 136 相似文献
6.
Regional height systems do not refer to a common equipotential surface, such as the geoid. They are usually referred to the mean sea level at a reference tide gauge. As mean sea level varies (by ±1 to 2 m) from place to place and from continent to continent each tide gauge has an unknown bias with respect to a common reference surface, whose determination is what the height datum problem is concerned with. This paper deals with this problem, in connection to the availability of satellite gravity missions data. Since biased heights enter into the computation of terrestrial gravity anomalies, which in turn are used for geoid determination, the biases enter as secondary or indirect effect also in such a geoid model. In contrast to terrestrial gravity anomalies, gravity and geoid models derived from satellite gravity missions, and in particular GRACE and GOCE, do not suffer from those inconsistencies. Those models can be regarded as unbiased. After a review of the mathematical formulation of the problem, the paper examines two alternative approaches to its solution. The first one compares the gravity potential coefficients in the range of degrees from 100 to 200 of an unbiased gravity field from GOCE with those of the combined model EGM2008, that in this range is affected by the height biases. This first proposal yields a solution too inaccurate to be useful. The second approach compares height anomalies derived from GNSS ellipsoidal heights and biased normal heights, with anomalies derived from an anomalous potential which combines a satellite-only model up to degree 200 and a high-resolution global model above 200. The point is to show that in this last combination the indirect effects of the height biases are negligible. To this aim, an error budget analysis is performed. The biases of the high frequency part are proved to be irrelevant, so that an accuracy of 5 cm per individual GNSS station is found. This seems to be a promising practical method to solve the problem. 相似文献
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8.
Many problems in physical geodesy can be formulated in terms of boundary-value problems (BVPs) for the gravitational potential; many of them can be ultimately formulated as a Dirichlet problem. For this reason, there is a flourishing literature of geodetic contributions to potential theory. In this paper, the authors pick up some classical arguments from the mathematical analysis of BVPs and show, by using only Hilbert spaces of harmonic functions, how they can be systematically cast into a functional scheme clarifying the role of duality when dealing with the harmonic subspaces of classical Sobolev spaces, of any real order. The analysis is here restricted to the case of functions harmonic in spherical domains to make the results transparent and more readable by geodesists. A further step is then taken showing how to generalize the Dirichlet problem for the space of all the functions that are harmonic outside a sphere, which exploits the more general theory of Fréchet topological spaces. Basically, the result is that any functions harmonic in the exterior of a sphere can be uniquely identified by a suitably defined trace on the sphere. The paper concludes with comments and discussion of future work. 相似文献
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