Variational Bayesian Approximations Kalman Filter Based on Threshold Judgment (2309.02789v2)
Abstract: The estimation of non-Gaussian measurement noise models is a significant challenge across various fields. In practical applications, it often faces challenges due to the large number of parameters and high computational complexity. This paper proposes a threshold-based Kalman filtering approach for online estimation of noise parameters in non-Gaussian measurement noise models. This method uses a certain amount of sample data to infer the variance threshold of observation parameters and employs variational Bayesian estimation to obtain corresponding noise variance estimates, enabling subsequent iterations of the Kalman filtering algorithm. Finally, we evaluate the performance of this algorithm through simulation experiments, demonstrating its accurate and effective estimation of state and noise parameters.
- R. E. Kalman, “A new approach to linear filtering and prediction problems,” Journal of Basic Engineering, vol. 82D, pp. 35–45, 1960.
- D Middleton, “Non-gaussian noise models in signal processing for telecommunications: new methods an results for class a and class b noise models,” Information Theory IEEE Transactions on, vol. 45, no. 4, pp. 1129–1149, 1999.
- Matthew James. Beal, “Variational algorithms for approximate bayesian inference /,” Phd Thesis University of London, 2003.
- S. Sarkka and A. Nummenmaa, “Recursive noise adaptive kalman filtering by variational bayesian approximations,” IEEE Transactions on Automatic Control, vol. 54, no. 3, pp. 596–600, 2009.
- “Performance analysis of kalman filter as an equalizer in a non-gaussian environment,” in 2022 IEEE Integrated STEM Education Conference (ISEC), 2022, pp. 433–438.
- “Bridging the ensemble kalman filter and particle filters: the adaptive gaussian mixture filter,” Computational Geosciences, 2010.
- “A background-impulse kalman filter with non-gaussian measurement noises.,” IEEE Trans. Syst. Man Cybern. Syst., April 2023.
- A. P. Dempster, “Maximum likelihood from incomplete data via the em algorithm,” Journal of the Royal Statistical Society, vol. 39, 1977.
- “Maximum correntropy kalman filter,” AUTOMATICA, vol. 76, pp. 70–77, 2017.
- “Complex-valued adaptive networks based on entropy estimation,” Signal Processing, vol. 149, pp. 124–134, 2018.
- “Projected kernel recursive maximum correntropy,” Circuits and Systems II: Express Briefs, IEEE Transactions on, pp. 1–1, 2017.
- “Gaussian state estimation with non-gaussian measurement noise,” in 2018 Sensor Data Fusion: Trends, Solutions, Applications (SDF), 2018, pp. 1–5.
- “Consensus of multi-agent systems with faults and mismatches under switched topologies using a delta operator method,” Neurocomputing, vol. 315, no. NOV.13, pp. 198–209, 2018.
- “An efficient semi-blind source extraction algorithm and its applications to biomedical signal extraction,” Science in China Series F: Information Sciences, vol. 52, no. 10, pp. 1863–1874, 2009.
- Akaike and H., “A new look at the statistical model identification.,” IEEE Transactions on Automatic Control, vol. 19, no. 6, pp. 716–723, 1974.
- “Distributed minimum error entropy kalman filter,” Information Fusion, vol. 91, pp. 556–565, 2023.
- “Generalized minimum error entropy for robust learning,” Pattern Recognition, vol. 135, pp. 109188, 2023.
- “Switching criterion for sub-and super-gaussian additive noise in adaptive filtering,” Signal Processing, vol. 150, no. SEP., pp. 166–170, 2018.