Non-linear filters: Adaptive filter, Kalman filter, Ensemble Kalman filter, Particle filter, Extended Kalman filter, Kernel adaptive filter, Median filter, Recursive Bayesian estimation, Invariant extended Kalman filter, Symmetry-preserving filter

Source: Wikipedia. Pages: 24. Chapters: Adaptive filter, Kalman filter, Ensemble Kalman filter, Particle filter, Extended Kalman filter, Kernel adaptive filter, Median filter, Recursive Bayesian estimation, Invariant extended Kalman filter, Symmetry-preserving filter, Total variation denoising, Ranklet, Voltage-controlled filter, Soft sensor, Covariance intersection, Auxiliary particle filter, Bilateral filter, Kushner equation. Excerpt: In statistics, the Kalman filter is a mathematical method named after Rudolf E. Kalman. Its purpose is to use measurements observed over time, containing noise (random variations) and other inaccuracies, and produce values that tend to be closer to the true values of the measurements and their associated calculated values. The Kalman filter has many applications in technology, and is an essential part of space and military technology development. A very simple example and perhaps the most commonly used type of Kalman filter is the phase-locked loop, which is now ubiquitous in FM radios and most electronic communications equipment. Extensions and generalizations to the method have also been developed. The Kalman filter produces estimates of the true values of measurements and their associated calculated values by predicting a value, estimating the uncertainty of the predicted value, and computing a weighted average of the predicted value and the measured value. The most weight is given to the value with the least uncertainty. The estimates produced by the method tend to be closer to the true values than the original measurements because the weighted average has a better estimated uncertainty than either of the values that went into the weighted average. From a theoretical standpoint, the Kalman filter is an algorithm for efficiently doing exact inference in a linear dynamical system, which is a Bayesian model similar to a hidden Markov model but where the state space of the latent variables is continuous and where all latent and observed variables have a Gaussian distribution (often a multivariate Gaussian distribution). The filter is named after Rudolf E. Kalman, though Thorvald Nicolai Thiele and Peter Swerling developed a similar algorithm earlier. Richard S. Bucy of the University of Southern California contributed to the theory, leading to it often being called the Kalman-Bucy filter. Stanley F. Schmidt is generally credited with developing the first implementat