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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.

from Kalman Filter - Wikipedia

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How a Kalman Filter Works in Pictures

Tim Babb
20 min
Beginner
Article / Blog
Theory

This article builds up some intuition about the Kalman filter using pictures before diving into the mathematics.  A beginner will come away with an understanding of what the Kalman filter is...

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The Kalman Filter

Brian Douglas
25 min
Beginner
Article / Blog
Theory

This article introduces the Kalman filter at a high level and tries to provide some insight into how the filter is able to estimate state by combining measurements and models. 

This is an...

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Kalman Filter Design

Mathworks
30 min
Intermediate
Article / Blog
Application

This example shows how to perform Kalman filtering. Both a steady state filter and a time varying filter are designed and simulated.

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How Kalman Filters Work, Part 1

Tucker McClure
30 min
Beginner
Article / Blog
Theory

This article looks at four popular estimation filter architectures: particle filter, sigma point filter, extended Kalman filter, and the Kalman filter. It discusses how all four of these...

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An Introduction to the Kalman Filter

Greg Welch and Gary Bishop
45 min
Beginner
Article / Blog
Theory

The purpose of this paper is to provide a practical introduction to the discrete Kalman filter. This introduction includes a description and some discussion of the basic discrete Kalman...

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Kalman Filter Tutorial

Alex Becker
Beginner
Article / Blog
Theory

The Kalman Filter is an easy topic. However, many tutorials are not easy to understand. Most require extensive mathematical background which makes them difficult to understand. Also, most...

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