Positioning systems in Minkowski space-time: Bifurcation problem and observational data

In the framework of relativistic positioning systems in Minkowski space-time, the determination of the inertial coordinates of a user involves the {\em bifurcation problem} (which is the indeterminate location of a pair of different events receiving the same emission coordinates). To solve it, in addition to the user emission coordinates and the emitter positions in inertial coordinates, it may happen that the user needs to know {\em independently} the orientation of its emission coordinates. Assuming that the user may observe the relative positions of the four emitters on its celestial sphere, an observational rule to determine this orientation is presented. The bifurcation problem is thus solved by applying this observational rule, and consequently, {\em all} of the parameters in the general expression of the coordinate transformation from emission coordinates to inertial ones may be computed from the data received by the user of the relativistic positioning system.Comment: 10 pages, 7 figures. The version published in PRD contains a misprint in the caption of Figure 3, which is here amende

Second Order Design of Geodetic Networks by the Simulated Annealing Method

The problem of determining the required precision in observations in order to obtain a desired precision in final parameters, classically known as the second order design problem, is revisited in this paper and proposed to be solved by the simulated annealing method. An example and a flexible implementation in MATLAB are given. © 2011 American Society of Civil Engineers.Baselga Moreno, S. (2011). Second Order Design of Geodetic Networks by the Simulated Annealing Method. Journal of Surveying Engineering. 137(4):167-173. doi:10.1061/(ASCE)SU.1943-5428.0000053167173137

Strain Rate Distribution in South‐Central Tibet From Two Decades of InSAR and GPS

The degree to which deformation and seismicity is focused on major mapped structures remains a key unknown in assessing seismic hazards and testing continental deformation models. Here we combine 208 Global Positioning System (GPS) velocities with 12‐track Interferometric Synthetic Aperture Radar (InSAR) rate maps to form high‐resolution velocity and strain rate fields for south‐central Tibet. Our results show that deformation is not evenly distributed across the region. We find a few zones with high strain rates, most notably the Yutian‐Zhongba strain rate zone. However, the average of the strain rates is similar within and outside the mapped fault zones. In addition, the slip rates are low on all the conjugate strike‐slip faults widespread in central Tibet. The observations are difficult to reconcile with time‐invariant block models or with continuum models that lack mechanisms for strain localization. Our results support arguments that the most robust estimates of seismic hazard should integrate seismicity catalogues, active fault maps, and geodetic strain rate models

Closed-Form transformation between geodetic and ellipsoidal coordinates

We present formulas for direct closed-form transformation between geodetic coordinates(Φ, λ, h) and ellipsoidal coordinates (β, λ, u) for any oblate ellipsoid of revolution.These will be useful for those dealing with ellipsoidal representations of the Earth's gravityfield or other oblate ellipsoidal figures. The numerical stability of the transformations for nearpolarand near-equatorial regions is also considered

DESIGN OF GEODETIC NETWORKS BASED ON OUTLIER IDENTIFICATION CRITERIA: AN EXAMPLE APPLIED TO THE LEVELING NETWORK

We present a numerical simulation method for designing geodetic networks. The quality criterion considered is based on the power of the test of data snooping testing procedure. This criterion expresses the probability of the data snooping to identify correctly an outlier. In general, the power of the test is defined theoretically. However, with the advent of the fast computers and large data storage systems, it can be estimated using numerical simulation. Here, the number of experiments in which the data snooping procedure identifies the outlier correctly is counted using Monte Carlos simulations. If the network configuration does not meet the reliability criterion at some part, then it can be improved by adding required observation to the surveying plan. The method does not use real observations. Thus, it depends on the geometrical configuration of the network; the uncertainty of the observations; and the size of outlier. The proposed method is demonstrated by practical application of one simulated leveling network. Results showed the needs of five additional observations between adjacent stations. The addition of these new observations improved the internal reliability of approximately 18%. Therefore, the final designed network must be able to identify and resist against the undetectable outliers – according to the probability levels