The Kalman Filter (https://en.wikipedia.org/wiki/Kalman_filter) is a prediction-correction algorithm named after Rudolf E. Kálmán (https://en.wikipedia.org/wiki/Rudolf_E._K%C3%A1lm%C3%A1n) (1930-2016), by which we calculate recursively a dynamical system state at time t_{k} using state at previous time u_{k-1} and new information b_{k} only. This technique is presented as a generalization of the least squares model for problems with varying mean and additive noise.
The Kalman Filter was first applied in the 1960s to the problem of trajectory estimation for NASA's Apollo space program and incorporated into their space navigation computer. It is also used in the guidance and navigation systems of the NASA Space Shuttle and the attitude control and navigation systems of the International Space Station. In other words, it is mostly used for positioning and navigation systems, but it can be generalized to any time series under suitable conditions.
Rudolf Kálmán recently passed away, and I thought it was a good idea to honor his memory at Papers We Love by presenting his original paper published in 1960, "A New Approach to Linear Filtering and Prediction Problems (https://www.cs.unc.edu/~welch/kalman/media/pdf/Kalman1960.pdf)", aka Kalman Filter.
Bio
Elizabeth Ramirez (@eramirem (https://twitter.com/eramirem)) is a Senior Software Engineer at The New York Times (http://www.nytimes.com/) and M.S. candidate in Applied Mathematics at Columbia University (http://apam.columbia.edu/). She likes analytical and numerical methods for solving partial differential equations, and all things space.
