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1. Autodifferentiable Ensemble Kalman Filters

   https://doi.org/10.1137/21M1434477  

   Chen, Yuming; Sanz-Alonso, Daniel; Willett, Rebecca (June 2022, SIAM Journal on Mathematics of Data Science)
2. Ensemble Kalman Filters with Resampling

   https://doi.org/10.1137/23M1594935  

   Al-Ghattas, Omar; Bao, Jiajun; Sanz-Alonso, Daniel (June 2024, SIAM/ASA Journal on Uncertainty Quantification)
3. Spectral diagonal ensemble Kalman filters

   https://doi.org/10.5194/npg-22-485-2015  

   Kasanický, I.; Mandel, J.; Vejmelka, M. (January 2015, Nonlinear Processes in Geophysics)

   A new type of ensemble Kalman filter is developed, which is based on replacing the sample covariance in the analysis step by its diagonal in a spectral basis. It is proved that this technique improves the approximation of the covariance when the covariance itself is diagonal in the spectral basis, as is the case, e.g., for a second-order stationary random field and the Fourier basis. The method is extended by wavelets to the case when the state variables are random fields which are not spatially homogeneous. Efficient implementations by the fast Fourier transform (FFT) and discrete wavelet transform (DWT) are presented for several types of observations, including high-dimensional data given on a part of the domain, such as radar and satellite images. Computational experiments confirm that the method performs well on the Lorenz 96 problem and the shallow water equations with very small ensembles and over multiple analysis cycles. 

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4. Risk-Sensitive Extended Kalman Filter

   Jordana, Armand; Meduri, Avadesh; Arlaud, Etienne; Carpentier, Justin; Righetti, Ludovic (May 2024, IEEE)
5. Risk-Sensitive Extended Kalman Filter

   https://doi.org/10.1109/ICRA57147.2024.10611266  

   Jordana, Armand; Meduri, Avadesh; Arlaud, Etienne; Carpentier, Justin; Righetti, Ludovic (May 2024, IEEE)

   Designing robust algorithms in the face of estimation uncertainty is a challenging task. Indeed, controllers seldom consider estimation uncertainty and only rely on the most likely estimated state. Consequently, sudden changes in the environment or the robot’s dynamics can lead to catastrophic behaviors. Leveraging recent results in risk-sensitive optimal control, this paper presents a risk-sensitive Extended Kalman Filter that can adapt its estimation to the control objective, hence allowing safe output-feedback Model Predictive Control (MPC). By taking a pessimistic estimate of the value function resulting from the MPC controller, the filter provides increased robustness to the controller in phases of uncertainty as compared to a standard Extended Kalman Filter (EKF). The filter has the same computational complexity as an EKF and can be used for real-time control. The paper evaluates the risk-sensitive behavior of the proposed filter when used in a nonlinear MPC loop on a planar drone and industrial manipulator in simulation, as well as on an external force estimation task on a real quadruped robot. These experiments demonstrate the ability of the approach to significantly improve performance in face of uncertainties. 

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