In this repository is included MATLAB code of the NGFs introduced in [1]. Other algorithms, which have been compared to NHFs in this paper, are also included:
- /NGF (UKF-EKF) : an implementation of the proposed NGF using an unscented Kalman filter (UKF) in the first layer of the filter (i.e., parameter estimation layer) and a bank of extended Kalman filters (EKFs) in the second layer (i.e., state estimation layer).
- /NHF (SMC-EKF) : an implementations of a nested hybrid filter (NHF) [2] using sequential Monte Carlo (SMC) in the first layer, and a bank of extended Kalman filters (EKFs) in the second layer.
- /UKF : implementation of an unscented Kalman filter (UKF) [3] using state-augmentation techniques (i.e., extending the state vector or variables with the parameters, and adding some artificial dynamics to them).
- /EnKF : implementation of an ensemble Kalman filter (EnKF) [4] using state-augmentation techniques.
The running file is main_script.m. It is necessary to add all the folders into the current MATLAB path in order to call the fuctions in them.
[1] Pérez-Vieites, S., & Míguez, J. (2021). Nested Gaussian filters for recursive Bayesian inference and nonlinear tracking in state space models. Signal Processing, 189, 108295.
[2] Pérez-Vieites, S., Mariño, I. P., & Míguez, J. (2018). Probabilistic scheme for joint parameter estimation and state prediction in cojmplex dynamical systems. Physical Review E, 98(6), 063305.
[3] Julier, S. J., Uhlmann, J. (2004). Unscented filtering and nonlinear estimation. Proceedings of the IEEE, 92 (2), 401–422.
[4] Evensen, G. (2003). The ensemble Kalman filter: Theoretical formulation and practical implementation. Ocean dynamics, 53 (4), 343–367.
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