Nonlinear Gaussian Filter with MultiStep Colored Noise
Abstract
:1. Introduction
2. Problem Statement
3. Main Results
3.1. Colored Noises Whitening
3.2. Design Gaussian Filter with MultiStep Colored Noise
3.2.1. OneStep Prediction
3.2.2. Measurement Update
3.3. Implementing the Gaussian Filter Using ThirdDegree SphericalRadial Rule
Algorithm 1:Cubature Kalman filter with multistep colored noise. 

4. Simulation Examples
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
${x}_{k}$  True state 
${z}_{k}$  Measurement 
${w}_{k}$  Color process noise 
${v}_{k}$  Color measurement noise 
${X}_{k}$  Whitening state 
${y}_{k}$  Whitening measurement 
${\xi}_{k}$  Whitening process noise 
${\eta}_{k}$  Whitening measurement noise 
${y}_{1:k}$  The set of measurement from moment 1 to k 
${X}_{k+1k}$  State onestep prediction of ${X}_{k+1}$ 
${P}_{k+1,k+1k}^{XX}$  Covariance onestep prediction of ${X}_{k+1}$ 
${\rho}_{k}$  Augmented state 
${\theta}_{k}$  Augmented process noise 
${a}_{ij}$  Mean of ${a}_{i}$ given ${y}_{1:j}$ 
${P}_{i,jk}^{ab}$  Crosscovariance between ${a}_{i}$ and ${b}_{j}$ given ${y}_{1:k}$ 
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Teng, Y.; Sheng, S.; Zheng, Y. Nonlinear Gaussian Filter with MultiStep Colored Noise. Actuators 2022, 11, 103. https://doi.org/10.3390/act11040103
Teng Y, Sheng S, Zheng Y. Nonlinear Gaussian Filter with MultiStep Colored Noise. Actuators. 2022; 11(4):103. https://doi.org/10.3390/act11040103
Chicago/Turabian StyleTeng, Yidi, Shouzhao Sheng, and Yubin Zheng. 2022. "Nonlinear Gaussian Filter with MultiStep Colored Noise" Actuators 11, no. 4: 103. https://doi.org/10.3390/act11040103