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Ensemble Kalman filter

The ensemble Kalman filter (EnKF) is a recursive filter suitable for problems with a large number of variables, such as discretizations of partial differential equations in geophysical models. The EnK

Window function

In signal processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen interval, norm

Multitaper

In signal processing, multitaper is a spectral density estimation technique developed by David J. Thomson. It can estimate the power spectrum SX of a stationary ergodic finite-variance random process

Smoothing problem (stochastic processes)

The smoothing problem (not to be confused with smoothing in statistics, image processing and other contexts) is the problem of estimating an unknown probability density function recursively over time

Maximum likelihood sequence estimation

Maximum likelihood sequence estimation (MLSE) is a mathematical algorithm to extract useful data out of a noisy data stream.

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 o

Zakai equation

In filtering theory the Zakai equation is a linear stochastic partial differential equation for the un-normalized density of a hidden state. In contrast, the Kushner equation gives a non-linear stocha

Spectral density estimation

In statistical signal processing, the goal of spectral density estimation (SDE) or simply spectral estimation is to estimate the spectral density (also known as the power spectral density) of a signal

Whittle likelihood

In statistics, Whittle likelihood is an approximation to the likelihood function of a stationary Gaussian time series. It is named after the mathematician and statistician Peter Whittle, who introduce

Compressed sensing

Compressed sensing (also known as compressive sensing, compressive sampling, or sparse sampling) is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solu

Generalized pencil-of-function method

Generalized pencil-of-function method (GPOF), also known as matrix pencil method, is a signal processing technique for estimating a signal or extracting information with complex exponentials. Being si

Recursive Bayesian estimation

In probability theory, statistics, and machine learning, recursive Bayesian estimation, also known as a Bayes filter, is a general probabilistic approach for estimating an unknown probability density

Time–frequency representation

A time–frequency representation (TFR) is a view of a signal (taken to be a function of time) represented over both time and frequency. Time–frequency analysis means analysis into the time–frequency do

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 techniqu

Matched filter

In signal processing, a matched filter is obtained by correlating a known delayed signal, or template, with an unknown signal to detect the presence of the template in the unknown signal. This is equi

SAMV (algorithm)

SAMV (iterative sparse asymptotic minimum variance) is a parameter-free superresolution algorithm for the linear inverse problem in spectral estimation, direction-of-arrival (DOA) estimation and tomog

Multi-fractional order estimator

The multi-fractional order estimator (MFOE) is a straightforward, practical, and flexible alternative to the Kalman filter (KF) for tracking targets. The MFOE is focused strictly on simple and pragmat

Invariant extended Kalman filter

The invariant extended Kalman filter (IEKF) (not to be confused with the iterated extended Kalman filter) was first introduced as a version of the extended Kalman filter (EKF) for nonlinear systems po

Covariance intersection

Covariance intersection is an algorithm for combining two or more estimates of state variables in a Kalman filter when the correlation between them is unknown.

Minimum mean square error

In statistics and signal processing, a minimum mean square error (MMSE) estimator is an estimation method which minimizes the mean square error (MSE), which is a common measure of estimator quality, o

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

Fast Kalman filter

The fast Kalman filter (FKF), devised by Antti Lange (born 1941), is an extension of the Helmert–Wolf blocking (HWB) method from geodesy to safety-critical real-time applications of Kalman filtering (

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

Independent component analysis

In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate signal into additive subcomponents. This is done by assuming that at most one subcomp

Savitzky–Golay filter

A Savitzky–Golay filter is a digital filter that can be applied to a set of digital data points for the purpose of smoothing the data, that is, to increase the precision of the data without distorting

List of window functions

In discrete-time signal processing, windowing is a preliminary signal shaping technique, usually applied to improve the appearance and usefulness of a subsequent Discrete Fourier Transform. Several wi

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 kn

Symmetry-preserving filter

In mathematics, Symmetry-preserving observers, also known as invariant filters, are estimation techniques whose structure and design take advantage of the natural symmetries (or invariances) of the co

Unscented transform

The unscented transform (UT) is a mathematical function used to estimate the result of applying a given nonlinear transformation to a probability distribution that is characterized only in terms of a

Switching Kalman filter

The switching Kalman filtering (SKF) method is a variant of the Kalman filter. In its generalised form, it is often attributed to Kevin P. Murphy, but related switching state-space models have been in

Kosambi–Karhunen–Loève theorem

In the theory of stochastic processes, the Karhunen–Loève theorem (named after Kari Karhunen and Michel Loève), also known as the Kosambi–Karhunen–Loève theorem is a representation of a stochastic pro

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

Kushner equation

In filtering theory the Kushner equation (after Harold Kushner) is an equation for the conditional probability density of the state of a stochastic non-linear dynamical system, given noisy measurement

Linear prediction

Linear prediction is a mathematical operation where future values of a discrete-time signal are estimated as a linear function of previous samples. In digital signal processing, linear prediction is o

Generalized filtering

Generalized filtering is a generic Bayesian filtering scheme for nonlinear state-space models. It is based on a variational principle of least action, formulated in generalized coordinates of motion.

Wiener deconvolution

In mathematics, Wiener deconvolution is an application of the Wiener filter to the noise problems inherent in deconvolution. It works in the frequency domain, attempting to minimize the impact of deco

Amari distance

The Amari distance is a measure between two invertible matrices, useful for checking for convergence in independent component analysis algorithms and for comparing solutions. For two invertible matric

Bellman filter

The Bellman filter is an algorithm that estimates the value sequence of hidden states in a state-space model. It is a generalization of the Kalman filter, allowing for nonlinearity in both the state a

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