The global navigation satellite system (GNSS) positioning for receiver's position is derived through the calculation steps, or algorithm, given below. In essence, a GNSS receiver measures the transmitting time of GNSS signals emitted from four or more GNSS satellites (giving the pseudorange) and these measurements are used to obtain its position (i.e., spatial coordinates) and reception time.
in which is the orbital eccentric anomaly of satellite , is the mean anomaly, is the eccentricity, and .
The Global Positioning System (GPS), originally NAVSTAR GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite systems (GNSS) that provides geolocation and time information to a GPS receiver anywhere on or near the Earth where there is an unobstructed line of sight to four or more GPS satellites. Obstacles such as mountains and buildings block the relatively weak GPS signals.
In physics, an orbit is the gravitationally curved trajectory of an object, such as the trajectory of a planet around a star or a natural satellite around a planet. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion.
In physics, spacetime is any mathematical model which fuses the three dimensions of space and the one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why different observers perceive where and when events occur differently.
In geometry, a simplex is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.
The moment of inertia, otherwise known as the mass moment of inertia, angular mass or rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis; similar to how mass determines the force needed for a desired acceleration. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rate of rotation.
The Zeeman effect, named after the Dutch physicist Pieter Zeeman, is the effect of splitting of a spectral line into several components in the presence of a static magnetic field. It is analogous to the Stark effect, the splitting of a spectral line into several components in the presence of an electric field. Also similar to the Stark effect, transitions between different components have, in general, different intensities, with some being entirely forbidden, as governed by the selection rules.
In atomic physics, hyperfine structure is defined by small shifts and splittings in the energy levels of atoms, molecules, and ions, due to interaction between the state of the nucleus and the state of the electron clouds.
Dilution of precision (DOP), or geometric dilution of precision (GDOP), is a term used in satellite navigation and geomatics engineering to specify the Error propagation as a mathematical effect of navigation satellite geometry on positional measurement precision.
The pseudorange is the pseudo distance between a satellite and a navigation satellite receiver —for instance Global Positioning System (GPS) receivers.
In quantum mechanics, a two-state system is a quantum system that can exist in any quantum superposition of two independent quantum states. The Hilbert space describing such a system is two-dimensional. Therefore, a complete basis spanning the space will consist of two independent states. Any two-state system can also be seen as a qubit.
In geometry and linear algebra, a Cartesian tensor uses an orthonormal basis to represent a tensor in a Euclidean space in the form of components. Converting a tensor's components from one such basis to another is through an orthogonal transformation.
In quantum physics, the spin–orbit interaction is a relativistic interaction of a particle's spin with its motion inside a potential. A key example of this phenomenon is the spin–orbit interaction leading to shifts in an electron's atomic energy levels, due to electromagnetic interaction between the electron's magnetic dipole, its orbital motion, and the electrostatic field of the positively charged nucleus. This phenomenon is detectable as a splitting of spectral lines, which can be thought of as a Zeeman effect product of two relativistic effects: the apparent magnetic field seen from the electron perspective and the magnetic moment of the electron associated with its intrinsic spin. A similar effect, due to the relationship between angular momentum and the strong nuclear force, occurs for protons and neutrons moving inside the nucleus, leading to a shift in their energy levels in the nucleus shell model. In the field of spintronics, spin–orbit effects for electrons in semiconductors and other materials are explored for technological applications. The spin–orbit interaction is one cause of magnetocrystalline anisotropy and the spin Hall effect.
In signal processing, a polyphase matrix is a matrix whose elements are filter masks. It represents a filter bank as it is used in sub-band coders alias discrete wavelet transforms.
Pulse compression is a signal processing technique commonly used by radar, sonar and echography to increase the range resolution as well as the signal to noise ratio. This is achieved by modulating the transmitted pulse and then correlating the received signal with the transmitted pulse.
Reaction–diffusion systems are mathematical models which correspond to several physical phenomena. The most common is the change in space and time of the concentration of one or more chemical substances: local chemical reactions in which the substances are transformed into each other, and diffusion which causes the substances to spread out over a surface in space.
In fluid dynamics, Airy wave theory gives a linearised description of the propagation of gravity waves on the surface of a homogeneous fluid layer. The theory assumes that the fluid layer has a uniform mean depth, and that the fluid flow is inviscid, incompressible and irrotational. This theory was first published, in correct form, by George Biddell Airy in the 19th century.
In probability theory and statistics, the generalized chi-squared distribution is the distribution of a linear sum of independent non-central chi-squared variables, or of a quadratic form of a multivariate normal distribution. It is a generalization of the chi-squared distribution. There are several other such generalizations for which the same term is sometimes used. Some of them are special cases of the family discussed here, for example the noncentral chi-squared distribution and the gamma distribution.
GNSS enhancement refers to techniques used to improve the accuracy of positioning information provided by the Global Positioning System or other global navigation satellite systems in general, a network of satellites used for navigation. Enhancement methods of improving accuracy rely on external information being integrated into the calculation process. There are many such systems in place and they are generally named or described based on how the GPS sensor receives the information. Some systems transmit additional information about sources of error, others provide direct measurements of how much the signal was off in the past, while a third group provide additional navigational or vehicle information to be integrated in the calculation process.
Orbit modeling is the process of creating mathematical models to simulate motion of a massive body as it moves in orbit around another massive body due to gravity. Other forces such as gravitational attraction from tertiary bodies, air resistance, solar pressure, or thrust from a propulsion system are typically modeled as secondary effects. Directly modeling an orbit can push the limits of machine precision due to the need to model small perturbations to very large orbits. Because of this, perturbation methods are often used to model the orbit in order to achieve better accuracy.
Electric dipole spin resonance (EDSR) is a method to control the magnetic moments inside a material using quantum mechanical effects like the spin–orbit interaction. Mainly, EDSR allows to flip the orientation of the magnetic moments through the use of electromagnetic radiation at resonant frequencies. EDSR was first proposed by Emmanuel Rashba.