Related papers: An Autonomous Reference Frame for Relativistic GNS…
The basic elements of the relativistic positioning systems in a two-dimensional space-time have been introduced in a previous work [Phys. Rev. D {\bf 73}, 084017 (2006)] where geodesic positioning systems, constituted by two geodesic…
Estimating the absolute orientation of a local system relative to a global navigation satellite system (GNSS) reference often suffers from local minima and high dependency on satellite availability. Existing methods for this alignment task…
We present a theoretical foundation for relativistic astronomical measurements in curved space-time. In particular, we discuss a new iterative approach for describing the dynamics of an astronomical N-body system. To do this, we generalize…
The relativity of Global Positioning System (GPS) pseudorange measurements is explored within the geometrical optics approximation in the curved space-time near Earth. A space-time grid for navigation is created by the discontinuities…
The surge of deep-space probes makes it unsustainable to navigate them with standard radiometric tracking. Self-driving interplanetary satellites represent a solution to this problem. In this work, a full vision-based navigation algorithm…
A generalized definition of a frame of reference in spaces with affine connections and metrics is proposed based on the set of the following differential-geometric objects: (a) a non-null (non-isotropic) vector field, (b) the orthogonal to…
Conventional autonomous Unmanned Air Vehicle (abbr. UAV) autopilot systems use Global Navigation Satellite System (abbr. GNSS) signal for navigation. However, autopilot systems fail to navigate due to lost or jammed GNSS signal. To solve…
One of the fundamental postulates of the special relativity theory is existence of a single system of universal coordinate transforms for inertial reference frames, that is coordinate transforms, which are uniquely determined by space-time…
With the rapid expansion of low Earth orbit (LEO) constellations, thousands of satellites are now in operation, many equipped with onboard GNSS receivers capable of continuous orbit determination and time synchronization. This development…
In hostile environments, GNSS is a potentially unreliable solution for self-localization and navigation. Many systems only use an IMU as a backup system, resulting in integration errors which can dramatically increase during mission…
This paper considers the localization problem in a 5G-aided global navigation satellite system (GNSS) based on real-time kinematic (RTK) technique. Specifically, the user's position is estimated based on the hybrid measurements, including…
Currently, digital maps are indispensable for automated driving. However, due to the low precision and reliability of GNSS particularly in urban areas, fusing trajectories of independent recording sessions and different regions is a…
A local positional system (LPS) is proposed, in which particles are launched at given velocities, and a sensor system measures the trajectory of particles in the platform frame. These measurements allow us to restore the position and…
Spaceborne gravity gradients are proposed in this paper to provide autonomous orbit determination capabilities for near Earth satellites. The gravity gradients contain useful position information which can be extracted by matching the…
We consider imaging of fast moving small objects in space, such as low earth orbit satellites, which are also rotating around a fixed axis. The imaging system consists of ground based, asynchronous sources of radiation and several passive…
Modelling interactions is critical in learning complex dynamical systems, namely systems of interacting objects with highly non-linear and time-dependent behaviour. A large class of such systems can be formalized as $\textit{geometric…
To help future mobile agents plan their movement in harsh environments,a predictive model has been designed to determine what areas would be favorable for Global Navigation Satellite System (GNSS) positioning. The model is able to predict…
Nowadays, the Global Navigation Satellite Systems (GNSS), working like global positioning systems, are the GPS (NAVSTAR) and the GLONASS, which only are operative when several relativistic effects are corrected. In the next years the…
We calculate the special and general relativistic effects of the Global Positioning System (GPS), especially the effects depending on the small deviation of the orbit from the circular one. This effect is well known but, to our knowledge,…
Autonomous orbit determination via integration of epoch-differenced gravity gradients and starlight refraction is proposed in this paper for low-Earth-orbiting satellites operating in GPS-denied environments. The starlight refrac-tion can…