Studying the homogeneity of the coordinate base SSC-2011 at arranging a special-purpose geodetic network

The results of studies on the SSC-2011 coordinate base homogeneity carried out in the process of linking a special-purpose geodetic network’s points to this coordinate system are presented. The research consisted of multiple determinations of the differential geodetic stations (DGS) coordinates in GSK-2011 from different types of the coordinate base of this system. In the first version, they were obtained through their binding to the nearest points of the SGN with known coordinates in the SSC-2011. In the second one, the DGS was linked to SSC-2011 by GNSS vectors to four FAGS points. In the third variant, in order to obtain these coordinates in SSC-2011 the reference were four points of the IGS network. The grid coordinates of the DGS determined in GSK-2011 from the FAGS and IGS points coincided within 1,3 cm. Those of the DGS in SSC-2011, from points of the SGN, differ from the ones obtained in the FAGS and IGS by maximum values up to 21,8 cm, 22,2 cm, 27,2 cm in the abscissa, ordinate, and position, respectively. The derived data on the degree of heterogeneity of the SGN in SSC-2011 enable concluding the impracticality of using it as the coordinate basis of this system at carrying out works, requiring positioning accuracy at the level of several centimeters.

The affine connection

The connection and the covariant derivative are treated. Connection coefficients are introduced in their role of expressing the change in the coordinate basis vectors between neighbouring points. The covariant derivative of a vector is then defined. Next we relate the connection to the metric, and obtain the Levi-Civita connection. The logic concerning what is defined and what is derived is explained carefuly. The notion of a derivative along a curve is defined. The emphasis through is on clarity and avoiding confusions arising from the plethora of concepts and symbols.

Vectors on manifolds

The vector, the dual vector (one-form), components and inner products are defined and discussed. The difference between a vector and a one-form is carefully drawn out, with examples and diagrams. Contravariant and covariant components are described, and the way in which the metric can relate them is carefully explained. The transformation of vector components under a change of coordinate basis is derived.

The Discrete Cosine Maximum Ignorance Assumption

The performance of colour correction algorithms are dependent on the reflectance sets used. Sometimes, when the testing reflectance set is changed the ranking of colour correction algorithms also changes. To remove dependence on dataset we can make assumptions about the set of all possible reflectances. In the Maximum Ignorance with Positivity (MIP) assumption we assume that all reflectances with per wavelength values between 0 and 1 are equally likely. A weakness in the MIP is that it fails to take into account the correlation of reflectance functions between wavelengths (many of the assumed reflectances are, in reality, not possible). In this paper, we take the view that the maximum ignorance assumption has merit but, hitherto it has been calculated with respect to the wrong coordinate basis. Here, we propose the Discrete Cosine Maximum Ignorance assumption (DCMI), where all reflectances that have coordinates between max and min bounds in the Discrete Cosine Basis coordinate system are equally likely. Here, the correlation between wavelengths is encoded and this results in the set of all plausible reflectances 'looking like' typical reflectances that occur in nature. This said the DCMI model is also a superset of all measured reflectance sets. Experiments show that, in colour correction, adopting the DCMI results in similar colour correction performance as using a particular reflectance set.

Monitoring of spatial data coordinate basis integrity using coordinate transformations

The modern spatial data coordinate basis (SDCB) is built taking into account the variety of existing and used today geodetic networks, models of physical fields of the Earth, cartographic models, as well as coordinate systems (СS). One of the requirements for SDCB from the standpoint of system analysis is the requirement of integrity, which presupposes the unity of the determination of coordinates, that is, the consistency of the results of determining the coordinates of the same points in different CSs. The article is devoted to the monitoring of the accuracy characteristics of the available software for coordinate transformations in terms of single-stage and multi-stage transitions between ellipsoidal coordinates of different systems.

Method of tracking of close objects with different moving characteristics by a long-range radar station

There is the necessary to design the method that will be allow to decide the existed uncertainty in using the radar for the tracking sophisticated and controlled movement targets as well as will be allow to estimate the performances to set up the measuring and extrapolated filter in terms of time and resource costs. The uncertainty lies in the fact that when tracking controlled movement targets, wide correlation strobes need to be formed, however, when tracking sophisticated targets, such strobes should be smaller. In accordance with the task of developing a methodology for calculating the trajectory of sophisticated and controlled movement targets, a method was developed by a radar. It allows for the joint detection and recognition of signals reflected from controlled movement targets, as well as linking spots to trajectories in conditions of working with sophisticated targets according to a new non-coordinate basis. This allows to resolve the uncertainty associated with the maintenance of sophisticated and controlled movement targets. Unlike existing solutions, the developed method proposes to produce parallel coherent and incoherent accumulation of the burst signal, which corresponds to taking into account the influence of fluctuations of each pulse in the burst and the entire signal. After this, the obtained values of the signal-to-noise ratios are compared with the threshold value. As a result, a decision is made on the nature of the movement of the target. The same data in conjunction with the used information is used when linking spots to trajectories to correct the parameters of the estimation and extrapolation filters, as well as when specifying the sizes of correlation gates for further tracking. We can say that to increase the effectiveness of tracking sophisticated and controlled movement targets, it is necessary to conduct joint detection and recognition of targets by their non-coordinate information, which is the difference in the signal-to-noise ratios from the outputs of the coherent and incoherent signal storage, characterizing the features of fluctuations, in the processing of information of one spot. A method has been developed that allows: constructing target tracking algorithms based on processing coordinate and noncoordinate information; to resolve the uncertainty associated with the maintenance of sophisticated and controlled movement targets; to increase the effectiveness of maintenance without attracting significant costs; the selection of sophisticated targets for the energy components of its components; to provide throughput at a given level; to reduce the errors of estimation and extrapolation of the coordinates of sophisticated targets. The practical significance of the developed technique lies in the ability of the radar to accompany sophisticated and controlled movement targets with a given value of the performance indicator. Solving the information processing problem using the joint detection and recognition method allows increasing the probability of the information of the first typical message by 15…20% while preserving the set throughput value.

Curvature Invariants for Lorentzian Traversable Wormholes

The curvature invariants of three Lorentzian wormholes are calculated and plotted in this paper. The plots may be inspected for discontinuities to analyze the traversability of a wormhole. This approach was formulated by Henry, Overduin, and Wilcomb for black holes (Henry et al., 2016). Curvature invariants are independent of coordinate basis, so the process is free of coordinate mapping distortions and the same regardless of your chosen coordinates (Christoffel, E.B., 1869; Stephani, et al., 2003). The four independent Carminati and McLenaghan (CM) invariants are calculated and the nonzero curvature invariant functions are plotted (Carminati et al., 1991; Santosuosso et al., 1998). Three traversable wormhole line elements analyzed include the (i) spherically symmetric Morris and Thorne, (ii) thin-shell Schwarzschild wormholes, and (iii) the exponential metric (Visser, M., 1995; Boonserm et al., 2018).