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Moving Horizon Estimation
Moving horizon estimation (MHE) is an optimization approach that uses a series of measurements observed over time, containing noise (random variations) and other inaccuracies, and produces estimates of unknown variables or parameters. Unlike deterministic approaches, MHE requires an iterative approach that relies on linear programming or nonlinear programming solvers to find a solution. MHE reduces to the Kalman filter under certain simplifying conditions. A critical evaluation of the extended Kalman filter and the MHE found that the MHE improved performance at the cost of increased computational expense. Because of the computational expense, MHE has generally been applied to systems where there are greater computational resources and moderate to slow system dynamics. However, in the literature there are some methods to accelerate this method. Overview The application of MHE is generally to estimate measured or unmeasured states of dynamical systems. Initial conditions and paramet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a defin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Filtering Problem (stochastic Processes)
In the theory of stochastic processes, filtering describes the problem of determining the state of a system from an incomplete and potentially noisy set of observations. While originally motivated by problems in engineering, filtering found applications in many fields from signal processing to finance. The problem of optimal non-linear filtering (even for the non-stationary case) was solved by Ruslan L. Stratonovich (1959, 1960), see also Harold J. Kushner's work and Moshe Zakai's, who introduced a simplified dynamics for the unnormalized conditional law of the filter known as Zakai equation. The solution, however, is infinite-dimensional in the general case. Certain approximations and special cases are well understood: for example, the linear filters are optimal for Gaussian random variables, and are known as the Wiener filter and the Kalman-Bucy filter. More generally, as the solution is infinite dimensional, it requires finite dimensional approximations to be implemented in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear Filters
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function (mathematics), function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Control Theory
Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any ''delay'', ''overshoot'', or ''steady-state error'' and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required. This controller monitors the controlled process variable (PV), and compares it with the reference or set point (SP). The difference between actual and desired value of the process variable, called the ''error'' signal, or SP-PV error, is applied as feedback to generate a control action to bring the controlled process variable to the same value as the set point. Other aspects which are also studied are controllability and observability. Control theory is used in control system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nob Hill Publishing, LLC
, also known by the name NoB, is a Japanese singer. He is the former lead singer of the band Make-Up and a Project.R member. Overview With Make-Up, he recorded several songs for the anime ''Saint Seiya'', including the first opening song "Pegasus Fantasy" and the first ending song "Blue Forever". All songs were released in three albums ''Saint Seiya Hits I'' (which had the participation of Mitsuko Horie) and ''Saint Seiya '96 Song Collection''. In his solo career, he recorded the opening song for the ''Super Sentai'' series ''GoGo Sentai Boukenger'' and ''Tensou Sentai Goseiger''. He also recorded the song "Never", from the ''Saint Seiya'' anime-movie ''Heaven Chapter ~ Overture''. In 1998, he formed P.A.F. (stands for Patent Applied For, named after the PAF guitar pickups) with X Japan guitarist Pata. In about one years time they released: two albums, one mini album, one live album and two singles. In July 2007, he sang with Hironobu Kageyama, Masaaki Endoh, Yoko ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wiener Filter
In signal processing, the Wiener filter is a filter used to produce an estimate of a desired or target random process by linear time-invariant ( LTI) filtering of an observed noisy process, assuming known stationary signal and noise spectra, and additive noise. The Wiener filter minimizes the mean square error between the estimated random process and the desired process. Description The goal of the Wiener filter is to compute a statistical estimate of an unknown signal using a related signal as an input and filtering that known signal to produce the estimate as an output. For example, the known signal might consist of an unknown signal of interest that has been corrupted by additive noise. The Wiener filter can be used to filter out the noise from the corrupted signal to provide an estimate of the underlying signal of interest. The Wiener filter is based on a statistical approach, and a more statistical account of the theory is given in the minimum mean square error (MMSE) e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sliding Mode Control
In control systems, sliding mode control (SMC) is a nonlinear control method that alters the dynamics of a nonlinear system by applying a discontinuous control signal (or more rigorously, a set-valued control signal) that forces the system to "slide" along a cross-section of the system's normal behavior. The state- feedback control law is not a continuous function of time. Instead, it can switch from one continuous structure to another based on the current position in the state space. Hence, sliding mode control is a variable structure control method. The multiple control structures are designed so that trajectories always move toward an adjacent region with a different control structure, and so the ultimate trajectory will not exist entirely within one control structure. Instead, it will ''slide'' along the boundaries of the control structures. The motion of the system as it slides along these boundaries is called a ''sliding mode'' and the geometrical locus consisting of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schmidt–Kalman Filter
The Schmidt–Kalman Filter is a modification of the Kalman filter for reducing the dimensionality of the state estimate, while still considering the effects of the additional state in the calculation of the covariance matrix and the Kalman gains. A common application is to account for the effects of nuisance parameters such as sensor biases without increasing the dimensionality of the state estimate. This ensures that the covariance matrix will accurately represent the distribution of the errors. The primary advantage of utilizing the Schmidt–Kalman filter instead of increasing the dimensionality of the state space is the reduction in computational complexity. This can enable the use of filtering in real-time systems. Another usage of Schmidt–Kalman is when residual biases are unobservable; that is, the effect of the bias cannot be separated out from the measurement. In this case, Schmidt–Kalman is a robust way to not try and estimate the value of the bias, but only keep tra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recursive Least Squares
Recursive least squares (RLS) is an adaptive filter algorithm that recursively finds the coefficients that minimize a weighted linear least squares cost function relating to the input signals. This approach is in contrast to other algorithms such as the least mean squares (LMS) that aim to reduce the mean square error. In the derivation of the RLS, the input signals are considered deterministic, while for the LMS and similar algorithms they are considered stochastic. Compared to most of its competitors, the RLS exhibits extremely fast convergence. However, this benefit comes at the cost of high computational complexity. Motivation RLS was discovered by Gauss but lay unused or ignored until 1950 when Plackett rediscovered the original work of Gauss from 1821. In general, the RLS can be used to solve any problem that can be solved by adaptive filters. For example, suppose that a signal d(n) is transmitted over an echoey, noisy channel that causes it to be received as :x(n)=\sum_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Predictor Corrector
Predictor may refer to: * Branch predictor, a part of many modern processors * Kerrison Predictor, a military fire-control computer * Predictor variable, also known as an independent variable * A type of railway level crossing, circuit that tries to achieve a constant warning time by predicting the speed of the approaching train * Something which makes a prediction See also * * * Prediction (other) A prediction is a statement or claim that a particular event will occur in the future. Prediction may also refer to: * ''Prediction'' (film), a 1993 Russian film *"Prediction", a song by Steel Pulse from their 1978 album ''Handsworth Revolution'' ... * Predict (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Particle Filter
Particle filters, or sequential Monte Carlo methods, are a set of Monte Carlo algorithms used to solve filtering problems arising in signal processing and Bayesian statistical inference. The filtering problem consists of estimating the internal states in dynamical systems when partial observations are made and random perturbations are present in the sensors as well as in the dynamical system. The objective is to compute the posterior distributions of the states of a Markov process, given the noisy and partial observations. The term "particle filters" was first coined in 1996 by Del Moral about mean-field interacting particle methods used in fluid mechanics since the beginning of the 1960s. The term "Sequential Monte Carlo" was coined by Liu and Chen in 1998. Particle filtering uses a set of particles (also called samples) to represent the posterior distribution of a stochastic process given the noisy and/or partial observations. The state-space model can be nonlinear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-linear Filter
In signal processing, a nonlinear (or non-linear) filter is a filter whose output is not a linear function of its input. That is, if the filter outputs signals ''R'' and ''S'' for two input signals ''r'' and ''s'' separately, but does not always output ''αR'' + ''βS'' when the input is a linear combination ''αr'' + ''βs''. Both continuous-domain and discrete-domain filters may be nonlinear. A simple example of the former would be an electrical device whose output voltage ''R''(''t'') at any moment is the square of the input voltage ''r''(''t''); or which is the input clipped to a fixed range 'a'',''b'' namely ''R''(''t'') = max(''a'', min(''b'', ''r''(''t''))). An important example of the latter is the running-median filter, such that every output sample ''R''''i'' is the median of the last three input samples ''r''''i'', ''r''''i''−1, ''r''''i''−2. Like linear filters, nonlinear filters may be shift invariant or not. Non-linear filters ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
