Since then, thanks to advances in digital computing, Kalman filters have become the subject of extensive research and application, especially in the field of autonomous or assisted navigation. Kalman filters are described by a series of recursive mathematical formulas. They provide an efficient and computable method to estimate the state of a process and minimize the mean square error of the estimate. Kalman filters are widely used and powerful: they can estimate the past and current states of a signal and even the future state, even if the exact nature of the model is not known. This article introduces discrete Kalman theory and practical methods, including a description and discussion of the Kalman filter and its derivatives: the extended Kalman filter, and gives a relatively simple example with a diagram.
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