• Corpus ID: 230438787

Kalman Filter from the Mutual Information Perspective

@article{Luo2021KalmanFF,
  title={Kalman Filter from the Mutual Information Perspective},
  author={Yarong Luo and Jianlang Hu and Chi Guo},
  journal={ArXiv},
  year={2021},
  volume={abs/2101.00757}
}
Kalman filter is a best linear unbiased state estimator. It is also comprehensible from the point view of the Bayesian estimation. However, this note gives a detailed derivation of Kalman filter from the mutual information perspective for the first time. Then we extend this result to the Rényi mutual information. Finally we draw the conclusion that the measurement update of the Kalman filter is the key step to minimize the uncertainty of the state of the dynamical system. 

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A derivation of the general Bayesian filter is presented, then adapted to adapt it for Markov systems, and it is shown that the variable relationship can be any function, and thus, approximations, such as the extended Kalman Filter, the unscented Kalman filter and other Kalman variants are special cases as well.
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Lectures on Strapdown Inertial Navigation Algorithm and Integrated Navigation Principles
  • 2019