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FDOA
Frequency difference of arrival (FDOA) or differential Doppler (DD), is a technique analogous to TDOA for estimating the location of a radio emitter based on observations from other points. (It can also be used for estimating one's own position based on observations of multiple emitters). TDOA and FDOA are sometimes used together to improve location accuracy and the resulting estimates are somewhat independent. By combining TDOA and FDOA measurements, instantaneous geolocation can be performed in two dimensions. It differs from TDOA in that the FDOA observation points must be in relative motion with respect to each other and the emitter. This relative motion results in different doppler shifts observations of the emitter at each location in general. The relative motion can be achieved by using airborne observations in aircraft, for example. The emitter location can then be estimated with knowledge of the observation points' location and vector velocities and the observed relati ...
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TDOA
Time of arrival (TOA or ToA) is the absolute time instant when a radio signal emanating from a transmitter reaches a remote receiver. The time span elapsed since the time of transmission (TOT or ToT) is the '' time of flight'' (TOF or ToF). Time difference of arrival (TDOA) is the difference between TOAs. Usage Many radiolocation systems use TOA measurements to perform geopositioning via true-range multilateration. The true range or distance can be directly calculated from the TOA as signals travel with a known velocity. TOA from two base stations will narrow a position to a position circle; data from a third base station is required to resolve the precise position to a single point. TDOA techniques such as pseudorange multilateration use the measured time difference between TOAs. Ways of synchronization As with TDOA, synchronization of the network base station with the locating reference stations is important. This synchronization can be done in different ways: * With exa ...
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Doppler Effect
The Doppler effect or Doppler shift (or simply Doppler, when in context) is the change in frequency of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who described the phenomenon in 1842. A common example of Doppler shift is the change of pitch heard when a vehicle sounding a horn approaches and recedes from an observer. Compared to the emitted frequency, the received frequency is higher during the approach, identical at the instant of passing by, and lower during the recession. The reason for the Doppler effect is that when the source of the waves is moving towards the observer, each successive wave crest is emitted from a position closer to the observer than the crest of the previous wave. Therefore, each wave takes slightly less time to reach the observer than the previous wave. Hence, the time between the arrivals of successive wave crests at the observer is reduced, causing an increa ...
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Vector (geometric)
In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. A Euclidean vector is frequently represented by a '' directed line segment'', or graphically as an arrow connecting an ''initial point'' ''A'' with a ''terminal point'' ''B'', and denoted by \overrightarrow . A vector is what is needed to "carry" the point ''A'' to the point ''B''; the Latin word ''vector'' means "carrier". It was first used by 18th century astronomers investigating planetary revolution around the Sun. The magnitude of the vector is the distance between the two points, and the direction refers to the direction of displacement from ''A'' to ''B''. Many algebraic operations on real numbers such as addition, subtraction, multiplication, and negation have close analogues for vectors, operations whic ...
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Cross-correlation
In 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. In an autocorrelation, which is the cross-correlation of a signal with itself, there will always be a peak at a lag of zero, and its size will be the signal energy. In probability and statistics, the term ''cross-correlations'' refers to the correlations between the entries of two random vectors \mathbf and \mathbf, while the ''correlations'' of a random vector \mathbf are the correlations between the entries of \mathbf itself, those forming the correlation matrix of ...
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Bandwidth (computing)
In computing, bandwidth is the maximum rate of data transfer across a given path. Bandwidth may be characterized as network bandwidth, data bandwidth, or digital bandwidth. This definition of ''bandwidth'' is in contrast to the field of signal processing, wireless communications, modem data transmission, digital communications, and electronics, in which ''bandwidth'' is used to refer to analog signal bandwidth measured in hertz, meaning the frequency range between lowest and highest attainable frequency while meeting a well-defined impairment level in signal power. The actual bit rate that can be achieved depends not only on the signal bandwidth but also on the noise on the channel. Network capacity The term ''bandwidth'' sometimes defines the net bit rate 'peak bit rate', 'information rate,' or physical layer 'useful bit rate', channel capacity, or the maximum throughput of a logical or physical communication path in a digital communication system. For example, bandwidth test ...
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Signal-to-noise Ratio
Signal-to-noise ratio (SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to the noise power, often expressed in decibels. A ratio higher than 1:1 (greater than 0 dB) indicates more signal than noise. SNR, bandwidth, and channel capacity of a communication channel are connected by the Shannon–Hartley theorem. Definition Signal-to-noise ratio is defined as the ratio of the power of a signal (meaningful input) to the power of background noise (meaningless or unwanted input): : \mathrm = \frac, where is average power. Both signal and noise power must be measured at the same or equivalent points in a system, and within the same system bandwidth. Depending on whether the signal is a constant () or a random variable (), the signal-to-noise ratio for random noise becomes: : \mathrm = \frac where E refers to the expected value, i.e. in this case ...
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Multilateration
Trilateration is the use of distances (or "ranges") for determining the unknown position coordinates of a point of interest, often around Earth (geopositioning). When more than three distances are involved, it may be called multilateration, for emphasis. The distances or ranges might be ordinary Euclidean distances (slant ranges) or spherical distances (scaled central angles), as in '' true-range multilateration''; or biased distances (pseudo-ranges), as in ''pseudo-range multilateration''. Trilateration or multilateration should not be confused with ''triangulation'', which uses angles for positioning; and ''direction finding'', which determines the line of sight direction to a target without determining the radial distance. Terminology Multiple, sometimes overlapping and conflicting terms are employed for similar concepts – e.g., ''multilateration'' without modification has been used for aviation systems employing both true-ranges and pseudo-ranges."Multilateration (MLAT) Conc ...
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