Chi-square Target Models
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Chi-square Target Models
Fluctuation loss is an effect seen in radar systems as the target object moves or changes its orientation relative to the radar system. It was extensively studied during the 1950s by Peter Swerling, who introduced the Swerling models to allow the effect to be simulated. For this reason, it is sometimes known as Swerling loss or similar names. The effect occurs when the target's physical size is within a key range of values relative to the wavelength of the radar signal. As the signal reflects off various parts of the target, they may interfere as they return to the radar receiver. At any single distance from the station, this will cause the signal to be amplified or diminished compared to the baseline signal one calculates from the radar equation. As the target moves, these patterns change. This causes the signal to fluctuate in strength and may cause it to disappear entirely at certain times. The effect can be reduced or eliminated by operating on more than one frequency or using ...
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Radar
Radar is a detection system that uses radio waves to determine the distance (''ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. A radar system consists of a transmitter producing electromagnetic waves in the radio or microwaves domain, a transmitting antenna, a receiving antenna (often the same antenna is used for transmitting and receiving) and a receiver and processor to determine properties of the objects. Radio waves (pulsed or continuous) from the transmitter reflect off the objects and return to the receiver, giving information about the objects' locations and speeds. Radar was developed secretly for military use by several countries in the period before and during World War II. A key development was the cavity magnetron in the United Kingdom, which allowed the creation of relatively small systems with sub-meter resolution. Th ...
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AN/FPS-24 Radar
The AN/FPS-24 Radar was a long range early warning radar used by the United States Air Force Air Defense Command. It used a two-frequency signal in order to avoid fluctuation loss, which causes signals on single-frequency radars to fade in and out as the target moves. Reducing this effect results in a much steadier signal. General Electric was the primary contractor for the design, which operated in the very high frequency (VHF) at 214 to 236 MHz. Construction Twelve systems were built between 1958 and 1962 at various locations around the United States. Problems with the design were revealed during initial testing Eufaula AFS (Eufaula, Alabama) in 1960, resulting in modifications. Additional problems occurred in 1961 when deployment of the first production model at Point Arena Air Force Station in California. revealed bearing problems due to the antenna weight. Failures of the hydrostatic bearing often caused the early closure of some radar sites due to catastrophic damage t ...
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Radar Lock-on
Lock-on is a feature of many radar systems that allow it to automatically follow a selected target. Lock-on was first designed for the AI Mk. IX radar in the UK, where it was known as lock-follow or auto-follow. Its first operational use was in the US ground-based SCR-584 radar, which demonstrated the ability to easily track almost any airborne target, from aircraft to artillery shells. History In the post-WWII era, the term became more widely used in connection to missile guidance concepts. Many modern anti-aircraft missiles use some form of semi-active radar homing, where the missile seeker listens for reflections of the launch platform's main radar. To provide a continuous signal, the radar is locked-onto the target, following it throughout the missile's flight. Ships and surface-to-air missiles often have a dedicated illuminator radar for this purpose. In older radar systems, through the 1980s, lock-on was normally assisted by a change in the radar signal characteristics ...
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Fire-control Radar
A fire-control radar (FCR) is a radar that is designed specifically to provide information (mainly target azimuth, elevation, range and range rate) to a fire-control system in order to direct weapons such that they hit a target. They are sometimes known as targeting radars, or in the UK, gun-laying radars. If the radar is used to guide a missile, it is often known as a target illuminator or illuminator radar. A typical fire-control radar emits a narrow, intense beam of radio waves to ensure accurate tracking information and to minimize the chance of losing track of the target. This makes them less suitable for initial detection of the target, and FCRs are often partnered with a medium-range search radar to fill this role. In British terminology, these medium-range systems were known as tactical control radars. Most modern radars have a track-while-scan capability, enabling them to function simultaneously as both fire-control radar and search radar. This works either by having t ...
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Degrees Of Freedom (statistics)
In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary. Estimates of statistical parameters can be based upon different amounts of information or data. The number of independent pieces of information that go into the estimate of a parameter is called the degrees of freedom. In general, the degrees of freedom of an estimate of a parameter are equal to the number of independent scores that go into the estimate minus the number of parameters used as intermediate steps in the estimation of the parameter itself. For example, if the variance is to be estimated from a random sample of ''N'' independent scores, then the degrees of freedom is equal to the number of independent scores (''N'') minus the number of parameters estimated as intermediate steps (one, namely, the sample mean) and is therefore equal to ''N'' − 1. Mathematically, degrees of freedom is the number of dimensions of the domain o ...
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Mean
There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set. For a data set, the ''arithmetic mean'', also known as "arithmetic average", is a measure of central tendency of a finite set of numbers: specifically, the sum of the values divided by the number of values. The arithmetic mean of a set of numbers ''x''1, ''x''2, ..., x''n'' is typically denoted using an overhead bar, \bar. If the data set were based on a series of observations obtained by sampling from a statistical population, the arithmetic mean is the ''sample mean'' (\bar) to distinguish it from the mean, or expected value, of the underlying distribution, the ''population mean'' (denoted \mu or \mu_x).Underhill, L.G.; Bradfield d. (1998) ''Introstat'', Juta and Company Ltd.p. 181/ref> Outside probability and statistics, a wide range of other notions of mean are o ...
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Chi-squared Distribution
In probability theory and statistics, the chi-squared distribution (also chi-square or \chi^2-distribution) with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables. The chi-squared distribution is a special case of the gamma distribution and is one of the most widely used probability distributions in inferential statistics, notably in hypothesis testing and in construction of confidence intervals. This distribution is sometimes called the central chi-squared distribution, a special case of the more general noncentral chi-squared distribution. The chi-squared distribution is used in the common chi-squared tests for goodness of fit of an observed distribution to a theoretical one, the independence of two criteria of classification of qualitative data, and in confidence interval estimation for a population standard deviation of a normal distribution from a sample standard deviation. Many other statistical tests a ...
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Carcinotron
A backward wave oscillator (BWO), also called carcinotron or backward wave tube, is a vacuum tube that is used to generate microwaves up to the terahertz range. Belonging to the traveling-wave tube family, it is an oscillator with a wide electronic tuning range. An electron gun generates an electron beam that interacts with a slow-wave structure. It sustains the oscillations by propagating a traveling wave backwards against the beam. The generated electromagnetic wave power has its group velocity directed oppositely to the direction of motion of the electrons. The output power is coupled out near the electron gun. It has two main subtypes, the M-type (M-BWO), the most powerful, and the O-type (O-BWO). The output power of the O-type is typically in the range of 1 mW at 1000 GHz to 50 mW at 200 GHz. Carcinotrons are used as powerful and stable microwave sources. Due to the good quality wavefront they produce (see below), they find use as illuminators in terahertz ...
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Frequency Agility
Frequency agility is the ability of a radar system to quickly shift its operating frequency to account for atmospheric effects, jamming, mutual interference with friendly sources, or to make it more difficult to locate the radar broadcaster through radio direction finding. The term can also be applied to other fields, including lasers or traditional radio transceivers using frequency-division multiplexing, but it remains most closely associated with the radar field and these other roles generally use the more generic term "frequency hopping". Description Jamming Radar systems generally operate by sending out short pulses of radio energy and then turning off the broadcaster and listening for the returning echoes from various objects. Because efficient signal reception requires careful tuning throughout the electronics in the transceiver, each operating frequency required a dedicated transceiver. Due to the size of the tube-based electronics used to construct the transceivers, early ...
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Multipath Propagation
In radio communication, multipath is the propagation phenomenon that results in radio signals reaching the receiving antenna by two or more paths. Causes of multipath include atmospheric ducting, ionospheric reflection and refraction, and reflection from water bodies and terrestrial objects such as mountains and buildings. When the same signal is received over more than one path, it can create interference and phase shifting of the signal. Destructive interference causes fading; this may cause a radio signal to become too weak in certain areas to be received adequately. For this reason, this effect is also known as multipath interference or multipath distortion. Where the magnitudes of the signals arriving by the various paths have a distribution known as the Rayleigh distribution, this is known as Rayleigh fading. Where one component (often, but not necessarily, a line of sight component) dominates, a Rician distribution provides a more accurate model, and this is known as Ri ...
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Peter Swerling
Peter Swerling (4 March 1929 – 25 August 2000) was one of the most influential radar theoreticians in the second half of the 20th century. He is best known for the class of statistically "fluctuating target" scattering models he developed at the RAND Corporation in the early 1950s to characterize the performance of pulsed radar systems, referred to as Swerling Targets I, II, III, and IV in the literature of radar. Swerling also contributed to the optimal estimation of orbits of satellites and trajectories of missiles, anticipating the development of the Kalman filter. He also founded two companies, one of which continues his engineering work today. Biography Early life and family Peter Swerling was born in New York City on 4 March 1929 to Jo Swerling and Florence (née Manson) Swerling. He grew up in Beverly Hills, California, where his father was a successful screenwriter. Peter had a younger brother, Jo, Jr. Swerling’s father recognized his young son’s intellectual gift ...
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Radar Display
A radar display is an electronic device to present radar data to the operator. The radar system transmits pulses or continuous waves of electromagnetic radiation, a small portion of which backscatter off targets (intended or otherwise) and return to the radar system. The receiver converts all received electromagnetic radiation into a continuous electronic analog signal of varying (or oscillating) voltage that can be converted then to a screen display. Modern systems typically use some sort of raster scan display to produce a map-like image. Early in radar development, however, numerous circumstances made such displays difficult to produce. People ultimately developed several different display types. Oscilloscopes Early radar displays used adapted oscilloscopes with various inputs. An oscilloscope generally receives three ''channels'' of varying (or oscillating) voltage as input and displays this information on a cathode ray tube. The oscilloscope amplifies the input voltages a ...
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