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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] |
Kalman Filter
For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. Kálmán, who was one of the primary developers of its theory. This digital filter is sometimes termed the ''Stratonovich–Kalman–Bucy filter'' because it is a special case of a more general, nonlinear filter developed somewhat earlier by the Soviet mathematician Ruslan Stratonovich. In fact, some of the special case linear filter's equations appeared in papers by Stratonovich that were published before summer 1960, when Kalman met with Stratonovich during a conference in Moscow. Kalman filtering has numerous te ... [...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 unsub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nuisance Parameter
Nuisance (from archaic ''nocence'', through Fr. ''noisance'', ''nuisance'', from Lat. ''nocere'', "to hurt") is a common law tort. It means that which causes offence, annoyance, trouble or injury. A nuisance can be either public (also "common") or private. A public nuisance was defined by English scholar Sir James Fitzjames Stephen as, "an act not warranted by law, or an omission to discharge a legal duty, which act or omission obstructs or causes inconvenience or damage to the public in the exercise of rights common to all Her Majesty's subjects". ''Private nuisance'' is the interference with the right of specific people. Nuisance is one of the oldest causes of action known to the common law, with cases framed in nuisance going back almost to the beginning of recorded case law. Nuisance signifies that the "right of quiet enjoyment" is being disrupted to such a degree that a tort is being committed. Definition Under the common law, persons in possession of real property ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extended Kalman Filter
In estimation theory, the extended Kalman filter (EKF) is the nonlinear version of the Kalman filter which linearizes about an estimate of the current mean and covariance. In the case of well defined transition models, the EKF has been considered the ''de facto'' standard in the theory of nonlinear state estimation, navigation systems and GPS. History The papers establishing the mathematical foundations of Kalman type filters were published between 1959 and 1961. The Kalman filter is the optimal linear estimator for ''linear'' system models with additive independent white noise in both the transition and the measurement systems. Unfortunately, in engineering, most systems are ''nonlinear'', so attempts were made to apply this filtering method to nonlinear systems; most of this work was done at NASA Ames. The EKF adapted techniques from calculus, namely multivariate Taylor series expansions, to linearize a model about a working point. If the system model (as described below) is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stanley F
Stanley may refer to: Arts and entertainment Film and television * ''Stanley'' (1972 film), an American horror film * ''Stanley'' (1984 film), an Australian comedy * ''Stanley'' (1999 film), an animated short * ''Stanley'' (1956 TV series), an American situation comedy * ''Stanley'' (2001 TV series), an American animated series Other uses in arts and entertainment * ''Stanley'' (play), by Pam Gems, 1996 * Stanley Award, an Australian Cartoonists' Association award * '' Stanley: The Search for Dr. Livingston'', a video game * Stanley (Cars), a character in ''Cars Toons: Mater's Tall Tales'' * '' The Stanley Parable'', a 2011 video game developed by Galactic Cafe, and its titular character, Stanley Businesses and organisations * Stanley, Inc., American information technology company * Stanley Aviation, American aerospace company * Stanley Black & Decker, formerly The Stanley Works, American hardware manufacturer ** Stanley knife, a utility knife * Stanley bottle, a brand ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extended Kalman Filter
In estimation theory, the extended Kalman filter (EKF) is the nonlinear version of the Kalman filter which linearizes about an estimate of the current mean and covariance. In the case of well defined transition models, the EKF has been considered the ''de facto'' standard in the theory of nonlinear state estimation, navigation systems and GPS. History The papers establishing the mathematical foundations of Kalman type filters were published between 1959 and 1961. The Kalman filter is the optimal linear estimator for ''linear'' system models with additive independent white noise in both the transition and the measurement systems. Unfortunately, in engineering, most systems are ''nonlinear'', so attempts were made to apply this filtering method to nonlinear systems; most of this work was done at NASA Ames. The EKF adapted techniques from calculus, namely multivariate Taylor series expansions, to linearize a model about a working point. If the system model (as described below) is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
