Satellite navigationA satellite navigation or satnav system is a system that uses satellites to provide autonomous geopositioning. A satellite navigation system with global coverage is termed global navigation satellite system (GNSS). , four global systems are operational: the United States' Global Positioning System (GPS), Russia's Global Navigation Satellite System (GLONASS), China's BeiDou Navigation Satellite System, and the European Union's Galileo.
Global Positioning SystemThe Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radio navigation 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.
Fast Fourier transformA fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain (often time or space) to a representation in the frequency domain and vice versa. The DFT is obtained by decomposing a sequence of values into components of different frequencies. This operation is useful in many fields, but computing it directly from the definition is often too slow to be practical.
Galileo (satellite navigation)Galileo is a global navigation satellite system (GNSS) that went live in 2016, created by the European Union through the European Space Agency (ESA), operated by the European Union Agency for the Space Programme (EUSPA), headquartered in Prague, Czechia, with two ground operations centres in Fucino, Italy, and Oberpfaffenhofen, Germany. The €10 billion project is named after the Italian astronomer Galileo Galilei.
Satellite navigation deviceA satellite navigation device, satnav device or satellite navigation receiver is a user equipment that uses one or more of several global navigation satellite systems (GNSS) to calculate the device's geographical position and provide navigational advice. Depending on the software used, the satnav device may display the position on a map, as geographic coordinates, or may offer routing directions. four GNSS systems are operational: the original United States' Global Positioning System (GPS), the European Union's Galileo, Russia's GLONASS, and China's BeiDou Navigation Satellite System.
GLONASSGLONASS (ГЛОНАСС, ɡɫɐˈnas; Глобальная навигационная спутниковая система) is a Russian satellite navigation system operating as part of a radionavigation-satellite service. It provides an alternative to Global Positioning System (GPS) and is the second navigational system in operation with global coverage and of comparable precision. Satellite navigation devices supporting both GPS and GLONASS have more satellites available, meaning positions can be fixed more quickly and accurately, especially in built-up areas where buildings may obscure the view to some satellites.
Fourier transformIn physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made the Fourier transform is sometimes called the frequency domain representation of the original function.
GPS Block IIIGPS Block III (previously Block IIIA) consists of the first ten GPS III satellites, which will be used to keep the Navstar Global Positioning System operational. Lockheed Martin designed, developed and manufactured the GPS III Non-Flight Satellite Testbed (GNST) and all ten Block III satellites. The first satellite in the series was launched in December 2018. The United States' Global Positioning System (GPS) reached Full Operational Capability on 17 July 1995, completing its original design goals.
Indian Regional Navigation Satellite SystemThe Indian Regional Navigation Satellite System (IRNSS), with an operational name of NavIC (acronym for Navigation with Indian Constellation; also, 'sailor' or 'navigator' in Indian languages), is an autonomous regional satellite navigation system that provides accurate real-time positioning and timing services. It covers India and a region extending around it, with plans for further extension.
Discrete Fourier transformIn mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT (IDFT) is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies.
Non-uniform discrete Fourier transformIn applied mathematics, the nonuniform discrete Fourier transform (NUDFT or NDFT) of a signal is a type of Fourier transform, related to a discrete Fourier transform or discrete-time Fourier transform, but in which the input signal is not sampled at equally spaced points or frequencies (or both). It is a generalization of the shifted DFT. It has important applications in signal processing, magnetic resonance imaging, and the numerical solution of partial differential equations.
Time signalA time signal is a visible, audible, mechanical, or electronic signal used as a reference to determine the time of day. Church bells or voices announcing hours of prayer gave way to automatically operated chimes on public clocks; however, audible signals (even signal guns) have limited range. Busy seaports used a visual signal, the dropping of a ball, to allow mariners to check the chronometers used for navigation. The advent of electrical telegraphs allowed widespread and precise distribution of time signals from central observatories.
Discrete-time Fourier transformIn mathematics, the discrete-time Fourier transform (DTFT), also called the finite Fourier transform, is a form of Fourier analysis that is applicable to a sequence of values. The DTFT is often used to analyze samples of a continuous function. The term discrete-time refers to the fact that the transform operates on discrete data, often samples whose interval has units of time. From uniformly spaced samples it produces a function of frequency that is a periodic summation of the continuous Fourier transform of the original continuous function.
Cross-correlationIn signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recognition, single particle analysis, electron tomography, averaging, cryptanalysis, and neurophysiology. The cross-correlation is similar in nature to the convolution of two functions.
Fourier analysisIn mathematics, Fourier analysis (ˈfʊrieɪ,_-iər) is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. The subject of Fourier analysis encompasses a vast spectrum of mathematics.
Shor's algorithmShor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor. It is one of the few known quantum algorithms with compelling potential applications and strong evidence of superpolynomial speedup compared to best known classical (that is, non-quantum) algorithms. On the other hand, factoring numbers of practical significance requires far more qubits than available in the near future.
BeiDouThe BeiDou Navigation Satellite System (BeiDou; ) is a Chinese satellite navigation system. It consists of two separate satellite constellations. The first BeiDou system, officially called the BeiDou Satellite Navigation Experimental System and also known as BeiDou-1, consisted of three satellites which, beginning in 2000, offered limited coverage and navigation services, mainly for users in China and neighboring regions. BeiDou-1 was decommissioned at the end of 2012.
Time and frequency transferTime and frequency transfer is a scheme where multiple sites share a precise reference time or frequency. The technique is commonly used for creating and distributing standard time scales such as International Atomic Time (TAI). Time transfer solves problems such as astronomical observatories correlating observed flashes or other phenomena with each other, as well as cell phone towers coordinating handoffs as a phone moves from one cell to another.
GNSS augmentationAugmentation of a global navigation satellite system (GNSS) is a method of improving the navigation system's attributes, such as precision, reliability, and availability, through the integration of external information into the calculation process. There are many such systems in place, and they are generally named or described based on how the GNSS sensor receives the external information.
Signal processingSignal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing signals, such as sound, , potential fields, seismic signals, altimetry processing, and scientific measurements. Signal processing techniques are used to optimize transmissions, digital storage efficiency, correcting distorted signals, subjective video quality and to also detect or pinpoint components of interest in a measured signal. According to Alan V. Oppenheim and Ronald W.
