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Kalman Filter

In 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, containing 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, one of the primary developers of its theory.

The algorithm works in a two-step process. In the prediction step, the Kalman filter produces estimates of the current state variables, along with their uncertainties. Once the outcome of the next measurement (necessarily corrupted with some amount of error, including random noise) is observed, these estimates are updated using a weighted average, with more weight being given to estimates with higher certainty. The algorithm is recursive. It can run in real time, using only the present input measurements and the previously calculated state and its uncertainty matrix; no additional past information is required.

Extensions and generalizations to the method have also been developed, such as the extended Kalman filter and the unscented Kalman filter which work on nonlinear systems. The underlying model is a hidden Markov model where the state space of the latent variables is continuous and all latent and observed variables have Gaussian distributions. Also, the Kalman filter has been successfully used in multi-sensor fusion, and distributed sensor networks to develop distributed or consensus Kalman filter.

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Introduction to the Kalman Filter

Submitted by Brian Douglas on Fri, 11/06/2020
Explanation 13 resources

If you've heard of the Kalman filter before but haven't had a chance to understand what it is, how it helps us solve state estimation problems, or how to implement one yourself, then this is...

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Kalman Filter Basics

Submitted by Melda Ulusoy on Mon, 04/04/2022
Explanation 7 resources

This journey consists of several educational videos to introduce the basics of Kalman filtering and a virtual lab to let you practice the design and implementation of linear and extended...

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