|
Estimation Of Signal Parameters Via Rotational Invariance Techniques
In estimation theory, estimation of signal parameters via rotational invariant techniques (ESPRIT) is a technique to determine parameters of a mixture of sinusoids in a background noise. This technique is first proposed for frequency estimation, however, with the introduction of phased-array systems in daily use technology, it is also used for Angle of arrival estimationsVolodymyr Vasylyshyn. Direction of arrival estimation using ESPRIT with sparse arrays.// Proc. 2009 European Radar Conference (EuRAD). – 30 Sept.-2 Oct. 2009. - Pp. 246 - 249. /ref> as well. General description Dividing into virtual sub-arrays Defining a signal vector as, a(w_k)= \quad e^ \quad e^ \quad ... \quad e^T where w_k represents the radial frequency of k-th sinusoid, a Vandermonde matrix for K number of sinusoids can be constructed, as in A = (w_1) \quad a(w_2) \quad ... \quad a(w_K)/math> The matrix A may be divided into two sets, A_1 = _ \quad 0A and A_2 = \quad I_A where I_ i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ESPRIT 2D
Esprit or L'Esprit may refer to: * the French for Spirit (animating force), Spirit; as a loanword: ** Enthusiasm, intense interest or motivation ** Morale, motivation and readiness ** Geist "mind/spirit; intellect" * Esprit (name), a given name and surname * Esprit (magazine), ''Esprit'' (magazine), a periodical * L'esprit (In the Nursery album) * Lotus Esprit, a car * Esprit Holdings, a clothing manufacturer * Esprit D'Air, a Japanese metal band * European Strategic Program on Research in Information Technology, a cooperative government program * Estimation of signal parameters via rotational invariance techniques, a signal processing method * European System Providing Refueling, Infrastructure and Telecommunications, a planned module of the Lunar Gateway See also * {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Estimation Theory
Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An ''estimator'' attempts to approximate the unknown parameters using the measurements. In estimation theory, two approaches are generally considered: * The probabilistic approach (described in this article) assumes that the measured data is random with probability distribution dependent on the parameters of interest * The set-membership approach assumes that the measured data vector belongs to a set which depends on the parameter vector. Examples For example, it is desired to estimate the proportion of a population of voters who will vote for a particular candidate. That proportion is the parameter sought; the estimate is based on a small random sample of voters. Alternatively, it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sine Wave
A sine wave, sinusoidal wave, or just sinusoid is a curve, mathematical curve defined in terms of the ''sine'' trigonometric function, of which it is the graph of a function, graph. It is a type of continuous wave and also a Smoothness, smooth periodic function. It occurs often in mathematics, as well as in physics, engineering, signal processing and many other fields. Formulation Its most basic form as a function of time (''t'') is: y(t) = A\sin(2 \pi f t + \varphi) = A\sin(\omega t + \varphi) where: * ''A'', ''amplitude'', the peak deviation of the function from zero. * ''f'', ''frequency, ordinary frequency'', the ''Real number, number'' of oscillations (cycles) that occur each second of time. * ''ω'' = 2''f'', ''angular frequency'', the rate of change of the function argument in units of radians per second. * \varphi, ''phase (waves), phase'', specifies (in radians) where in its cycle the oscillation is at ''t'' = 0. When \varphi is non-zero, the entire waveform appears to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phased-array
In antenna theory, a phased array usually means an electronically scanned array, a computer-controlled array of antennas which creates a beam of radio waves that can be electronically steered to point in different directions without moving the antennas. In a simple array antenna, the radio frequency current from the transmitter is fed to multiple individual antenna elements with the proper phase relationship so that the radio waves from the separate elements combine ( superpose) to form beams, to increase power radiated in desired directions and suppress radiation in undesired directions. In a phased array, the power from the transmitter is fed to the radiating elements through devices called ''phase shifters'', controlled by a computer system, which can alter the phase or signal delay electronically, thus steering the beam of radio waves to a different direction. Since the size of an antenna array must extend many wavelengths to achieve the high gain needed for narrow bea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angle Of Arrival
The angle of arrival (AoA) of a signal is the direction from which the signal (e.g. radio, optical or acoustic) is received. Measurement Measurement of AoA can be done by determining the direction of propagation of a radio-frequency wave incident on an antenna array or determined from maximum signal strength during antenna rotation. The AoA can be calculated by measuring the time difference of arrival (TDOA) between individual elements of the array. Generally this TDOA measurement is made by measuring the difference in received phase at each element in the antenna array. This can be thought of as beamforming in reverse. In beamforming, the signal from each element is weighed to "steer" the gain of the antenna array. In AoA, the delay of arrival at each element is measured directly and converted to an AoA measurement. Consider, for example, a two element array spaced apart by one-half the wavelength of an incoming RF wave. If a wave is incident upon the array at boresight, it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Max Overlapping Subarrays
Max or MAX may refer to: Animals * Max (dog) (1983–2013), at one time purported to be the world's oldest living dog * Max (English Springer Spaniel), the first pet dog to win the PDSA Order of Merit (animal equivalent of OBE) * Max (gorilla) (1971–2004), a western lowland gorilla at the Johannesburg Zoo who was shot by a criminal in 1997 Brands and enterprises * Australian Max Beer * Max Hamburgers, a fast-food corporation * MAX Index, a Hungarian domestic government bond index * Max Fashion, an Indian clothing brand Computing * MAX (operating system), a Spanish-language Linux version * Max (software), a music programming language * Commodore MAX Machine * Multimedia Acceleration eXtensions, extensions for HP PA-RISC Films * ''Max'' (1994 film), a Canadian film by Charles Wilkinson * ''Max'' (2002 film), a film about Adolf Hitler * ''Max'' (2015 film), an American war drama film Games * '' Dancing Stage Max'', a 2005 game in the ''Dance Dance Revolution'' series * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vandermonde Matrix
In linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row: an matrix :V=\begin 1 & x_1 & x_1^2 & \dots & x_1^\\ 1 & x_2 & x_2^2 & \dots & x_2^\\ 1 & x_3 & x_3^2 & \dots & x_3^\\ \vdots & \vdots & \vdots & \ddots &\vdots \\ 1 & x_m & x_m^2 & \dots & x_m^ \end, or :V_ = x_i^ \, for all indices and . Some authors define the Vandermonde matrix as the transpose of the above matrix. The determinant of a square Vandermonde matrix is called a ''Vandermonde polynomial'' or ''Vandermonde determinant''. Its value is the polynomial :\det(V) = \prod_ (x_j - x_i) which is non-zero if and only if all x_i are distinct. The Vandermonde determinant was sometimes called the ''discriminant'', although, presently, the discriminant of a polynomial is the square of the Vandermonde determinant of the roots of the polynomial. The Vandermonde determinant is an alternating form in the x_i, meaning that exchang ... [...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] |
Singular Value Decomposition
In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any \ m \times n\ matrix. It is related to the polar decomposition. Specifically, the singular value decomposition of an \ m \times n\ complex matrix is a factorization of the form \ \mathbf = \mathbf\ , where is an \ m \times m\ complex unitary matrix, \ \mathbf\ is an \ m \times n\ rectangular diagonal matrix with non-negative real numbers on the diagonal, is an n \times n complex unitary matrix, and \ \mathbf\ is the conjugate transpose of . Such decomposition always exists for any complex matrix. If is real, then and can be guaranteed to be real orthogonal matrices; in such contexts, the SVD is often denoted \ \mathbf^\mathsf\ . The diagonal entries \ \sigma_i = \Sigma_\ of \ \mathbf\ are uniquely determined by and are known as the singular values of . The n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudo Inverse
In mathematics, and in particular, algebra, a generalized inverse (or, g-inverse) of an element ''x'' is an element ''y'' that has some properties of an inverse element but not necessarily all of them. The purpose of constructing a generalized inverse of a matrix is to obtain a matrix that can serve as an inverse in some sense for a wider class of matrices than invertible matrices. Generalized inverses can be defined in any mathematical structure that involves associative multiplication, that is, in a semigroup. This article describes generalized inverses of a matrix A. A matrix A^\mathrm \in \mathbb^ is a generalized inverse of a matrix A \in \mathbb^ if AA^\mathrmA = A. A generalized inverse exists for an arbitrary matrix, and when a matrix has a regular inverse, this inverse is its unique generalized inverse. Motivation Consider the linear system :Ax = y where A is an n \times m matrix and y \in \mathcal R(A), the column space of A. If A is nonsingular (which implies n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Least Squares
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each individual equation. The most important application is in data fitting. When the problem has substantial uncertainties in the independent variable (the ''x'' variable), then simple regression and least-squares methods have problems; in such cases, the methodology required for fitting errors-in-variables models may be considered instead of that for least squares. Least squares problems fall into two categories: linear or ordinary least squares and nonlinear least squares, depending on whether or not the residuals are linear in all unknowns. The linear least-squares problem occurs in statistical regressio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems. As of 2020, MATLAB has more than 4 million users worldwide. They come from various backgrounds of engineering, science, and economics. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was based on his 1960s PhD thesis. Moler became a math professor at the University of New Mexico and starte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
