State and Parameter Estimation from Observed Signal Increments
Abstract
:1. Introduction
2. Mathematical Problem Formulation
3. Parameter Estimation from Noiseless Data
3.1. Feedback Particle Filter
3.2. Ensemble Kalman–Bucy Filter
4. State Estimation for Noisy Data
4.1. Generalised Feedback Particle Filter Formulation
4.2. Generalised Kalman–Bucy Filter
4.3. Ensemble Kalman–Bucy Filter
5. Combined State and Parameter Estimation
5.1. Feedback Particle Filter Formulation
5.2. Ensemble Kalman–Bucy Filter
6. Numerical Results
6.1. Parameter Estimation for the Ornstein–Uhlenbeck Process
6.2. Averaging
6.3. Homogenisation
6.4. Nonparametric Drift and State Estimation
6.5. Spde Parameter Estimation
6.6. Discussion
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A. The Filtering Equations for Correlated Noise
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Nüsken, N.; Reich, S.; Rozdeba, P.J. State and Parameter Estimation from Observed Signal Increments. Entropy 2019, 21, 505. https://doi.org/10.3390/e21050505
Nüsken N, Reich S, Rozdeba PJ. State and Parameter Estimation from Observed Signal Increments. Entropy. 2019; 21(5):505. https://doi.org/10.3390/e21050505
Chicago/Turabian StyleNüsken, Nikolas, Sebastian Reich, and Paul J. Rozdeba. 2019. "State and Parameter Estimation from Observed Signal Increments" Entropy 21, no. 5: 505. https://doi.org/10.3390/e21050505