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Geometric Dilution Of Precision
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. Introduction The concept of dilution of precision (DOP) originated with users of the Loran-C navigation system. The idea of Geometric DOP is to state how errors in the measurement will affect the final state estimation. This can be defined as: :GDOP=\frac Conceptually you can geometrically imagine errors on a measurement resulting in the \Delta ( ) term changing. Ideally small changes in the measured data will not result in large changes in output location. The opposite of this ideal is the situation where the solution is very sensitive to measurement errors. The interpretation of this formula is shown in the figure to the right, showing two possible scenarios with acceptable and poor GDOP. More recently, the t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Satellite Navigation
A satellite navigation or satnav system is a system that uses satellites to provide autonomous geo-spatial positioning. It allows satellite navigation devices to determine their location (longitude, latitude, and altitude/elevation) to high precision (within a few centimetres to metres) using time signals transmitted along a line of sight by radio from satellites. The system can be used for providing position, navigation or for tracking the position of something fitted with a receiver (satellite tracking). The signals also allow the electronic receiver to calculate the current local time to a high precision, which allows time synchronisation. These uses are collectively known as Positioning, Navigation and Timing (PNT). One set of critical vulnerabilities in satellite communications are the signals that govern positioning, navigation and timing (PNT). Failure to properly secure these transmissions could not only disrupt satellite networks but wreak havoc on a host of dependent s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interferometry
Interferometry is a technique which uses the ''interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber optics, engineering metrology, optical metrology, oceanography, seismology, spectroscopy (and its applications to chemistry), quantum mechanics, nuclear and particle physics, plasma physics, remote sensing, biomolecular interactions, surface profiling, microfluidics, mechanical stress/strain measurement, velocimetry, optometry, and making holograms. Interferometers are devices that extract information from interference. They are widely used in science and industry for the measurement of microscopic displacements, refractive index changes and surface irregularities. In the case with most interferometers, light from a single source is split into two beams that travel in different optical paths, which are then combined again to produce interfer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circular Error Probable
In the military science of ballistics, circular error probable (CEP) (also circular error probability or circle of equal probability) is a measure of a weapon system's precision. It is defined as the radius of a circle, centered on the mean, whose perimeter is expected to include the landing points of 50% of the rounds; said otherwise, it is the median error radius. That is, if a given munitions design has a CEP of 100 m, when 100 munitions are targeted at the same point, 50 will fall within a circle with a radius of 100 m around their average impact point. (The distance between the target point and the average impact point is referred to as bias.) There are associated concepts, such as the DRMS (distance root mean square), which is the square root of the average squared distance error, and R95, which is the radius of the circle where 95% of the values would fall in. The concept of CEP also plays a role when measuring the accuracy of a position obtained by a navigati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Local Tangent Plane Coordinates
Local tangent plane coordinates (LTP), also known as local ellipsoidal system, local geodetic coordinate system, or local vertical, local horizontal coordinates (LVLH), are a spatial reference system based on the tangent plane defined by the local vertical direction and the Earth's axis of rotation. It consists of three coordinates: one represents the position along the northern axis, one along the local eastern axis, and one represents the vertical position. Two right-handed variants exist: east, north, up (ENU) coordinates and north, east, down (NED) coordinates. They serve for representing state vectors that are commonly used in aviation and marine cybernetics. Axes These frames are location dependent. For movements around the globe, like air or sea navigation, the frames are defined as tangent to the lines of geographical coordinates: *East-West tangent to parallels, *North-South tangent to meridians, and *Up-Down in the direction normal to the oblate spheroid used as E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix Trace
In linear algebra, the trace of a square matrix , denoted , is defined to be the sum of elements on the main diagonal (from the upper left to the lower right) of . The trace is only defined for a square matrix (). It can be proved that the trace of a matrix is the sum of its (complex) eigenvalues (counted with multiplicities). It can also be proved that for any two matrices and . This implies that similar matrices have the same trace. As a consequence one can define the trace of a linear operator mapping a finite-dimensional vector space into itself, since all matrices describing such an operator with respect to a basis are similar. The trace is related to the derivative of the determinant (see Jacobi's formula). Definition The trace of an square matrix is defined as \operatorname(\mathbf) = \sum_^n a_ = a_ + a_ + \dots + a_ where denotes the entry on the th row and th column of . The entries of can be real numbers or (more generally) complex numbers. The trace is not def ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Cospas-Sarsat Programme
The International Cospas-Sarsat Programme is a satellite-aided search and rescue (SAR) initiative. It is organized as a treaty-based, nonprofit, intergovernmental, humanitarian cooperative of 45 nations and agencies (see infobox). It is dedicated to detecting and locating emergency locator radio beacons activated by persons, aircraft or vessels in distress, and forwarding this alert information to authorities that can take action for rescue. Distress alerts are detected, located and forwarded to over 200 countries and territories at no cost to beacon owners or the receiving government agencies. Cospas-Sarsat was conceived and initiated by Canada, France, the United States, and the former Soviet Union in 1979. The first rescue using the technology of Cospas-Sarsat occurred on . The definitive agreement of the organization was signed by those four States as the "Parties" to the agreement on 1 July 1988. The term Cospas-Sarsat derives from COSPAS (КОСПАС), an acronym f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Distress Frequency
An international distress frequency is a radio frequency that is designated for emergency communication by international agreement. History For much of the 20th century, 500 kHz was the primary international distress frequency. Its use has been phased out in favor of the Global Maritime Distress Safety System. Use of some distress frequencies is permitted for calling other stations to establish contact, whereupon the stations move to another frequency. Such channels are known as ''distress, safety and calling frequencies''. Satellite processing from all 121.5 or 243 MHz locators has been discontinued. Since February 1, 2009, the U.S. Coast Guard only monitors distress signals from emergency position indicating radio beacons (EPIRBs) that broadcast using digital 406 MHz signals. Digital 406 MHz models became the only ones approved for use in both commercial and recreational watercraft worldwide on January 1, 2007. Maritime Mobile Service frequencies Internatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Least-squares Normal Matrix
In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values of the variable being observed) in the input dataset and the output of the (linear) function of the independent variable. Geometrically, this is seen as the sum of the squared distances, parallel to the axis of the dependent variable, between each data point in the set and the corresponding point on the regression surface—the smaller the differences, the better the model fits the data. The resulting estimator can be expressed by a simple formula, especially in the case of a simple linear regression, in which there is a single regressor on the right side of the regression equation. The OLS estimator is consistent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Derivative
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry. The partial derivative of a function f(x, y, \dots) with respect to the variable x is variously denoted by It can be thought of as the rate of change of the function in the x-direction. Sometimes, for z=f(x, y, \ldots), the partial derivative of z with respect to x is denoted as \tfrac. Since a partial derivative generally has the same arguments as the original function, its functional dependence is sometimes explicitly signified by the notation, such as in: :f'_x(x, y, \ldots), \frac (x, y, \ldots). The symbol used to denote partial derivatives is ∂. One of the first known uses of this symbol in mathematics is by Marquis de Condorcet from 1770, who used it for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Covariance Matrix
In probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between each pair of elements of a given random vector. Any covariance matrix is symmetric and positive semi-definite and its main diagonal contains variances (i.e., the covariance of each element with itself). Intuitively, the covariance matrix generalizes the notion of variance to multiple dimensions. As an example, the variation in a collection of random points in two-dimensional space cannot be characterized fully by a single number, nor would the variances in the x and y directions contain all of the necessary information; a 2 \times 2 matrix would be necessary to fully characterize the two-dimensional variation. The covariance matrix of a random vector \mathbf is typically denoted by \operatorname_ or \Sigma. Definition Throughout this article, boldfaced unsubsc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Pyramid
In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it is a right square pyramid, and has symmetry. If all edge lengths are equal, it is an equilateral square pyramid, the Johnson solid General square pyramid A possibly oblique square pyramid with base length ''l'' and perpendicular height ''h'' has volume: :V=\frac l^2 h. Right square pyramid In a right square pyramid, all the lateral edges have the same length, and the sides other than the base are congruent isosceles triangles. A right square pyramid with base length ''l'' and height ''h'' has surface area and volume: :A=l^2+l\sqrt, :V=\frac l^2 h. The lateral edge length is: :\sqrt; the slant height is: :\sqrt. The dihedral angles are: :*between the base and a side: :::\arctan \left(\right); :*between two sides: :::\arccos \left(\right). Equilateral square pyramid, Johnson solid J1 If all edges have the same length, then the sides are e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radar Jammer
Radar jamming and deception is a form of electronic countermeasures that intentionally sends out radio frequency signals to interfere with the operation of radar by saturating its receiver with noise or false information. Concepts that blanket the radar with signals so its display cannot be read are normally known as jamming, while systems that produce confusing or contradictory signals are known as deception, but it is also common for all such systems to be referred to as jamming. There are two general classes of radar jamming, mechanical and electronic. Mechanical jamming entails reflecting enemy radio signals in various ways to provide false or misleading target signals to the radar operator. Electronic jamming works by transmitting additional radio signals towards enemy receivers, making it difficult to detect real target signals, or take advantage of known behaviors of automated systems like radar lock-on to confuse the system. Various counter-countermeasures can sometimes he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
