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Article

A Novel Perspective of the Kalman Filter from the Rényi Entropy

by 1, 1,2,*, 1 and 1,2
1
Global Navigation Satellite System Research Center, Wuhan University, Wuhan 430079, China
2
Artificial Intelligence Institute, Wuhan University, Wuhan 430079, China
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(9), 982; https://doi.org/10.3390/e22090982
Received: 21 July 2020 / Revised: 31 August 2020 / Accepted: 31 August 2020 / Published: 3 September 2020
(This article belongs to the Special Issue Data Science: Measuring Uncertainties)
Rényi entropy as a generalization of the Shannon entropy allows for different averaging of probabilities of a control parameter α. This paper gives a new perspective of the Kalman filter from the Rényi entropy. Firstly, the Rényi entropy is employed to measure the uncertainty of the multivariate Gaussian probability density function. Then, we calculate the temporal derivative of the Rényi entropy of the Kalman filter’s mean square error matrix, which will be minimized to obtain the Kalman filter’s gain. Moreover, the continuous Kalman filter approaches a steady state when the temporal derivative of the Rényi entropy is equal to zero, which means that the Rényi entropy will keep stable. As the temporal derivative of the Rényi entropy is independent of parameter α and is the same as the temporal derivative of the Shannon entropy, the result is the same as for Shannon entropy. Finally, an example of an experiment of falling body tracking by radar using an unscented Kalman filter (UKF) in noisy conditions and a loosely coupled navigation experiment are performed to demonstrate the effectiveness of the conclusion. View Full-Text
Keywords: Rényi entropy; discrete Kalman filter; continuous Kalman filter; algebraic Riccati equation; nonlinear differential Riccati equation Rényi entropy; discrete Kalman filter; continuous Kalman filter; algebraic Riccati equation; nonlinear differential Riccati equation
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MDPI and ACS Style

Luo, Y.; Guo, C.; You, S.; Liu, J. A Novel Perspective of the Kalman Filter from the Rényi Entropy. Entropy 2020, 22, 982. https://doi.org/10.3390/e22090982

AMA Style

Luo Y, Guo C, You S, Liu J. A Novel Perspective of the Kalman Filter from the Rényi Entropy. Entropy. 2020; 22(9):982. https://doi.org/10.3390/e22090982

Chicago/Turabian Style

Luo, Yarong, Chi Guo, Shengyong You, and Jingnan Liu. 2020. "A Novel Perspective of the Kalman Filter from the Rényi Entropy" Entropy 22, no. 9: 982. https://doi.org/10.3390/e22090982

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