Mathematical test criteria for filtering complex systems: Plentiful observations
Journal of Computational Physics
Mathematical strategies for filtering complex systems: Regularly spaced sparse observations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Numerical strategies for filtering partially observed stiff stochastic differential equations
Journal of Computational Physics
Journal of Computational Physics
Interpolating Irregularly Spaced Observations for Filtering Turbulent Complex Systems
SIAM Journal on Scientific Computing
Filtering skill for turbulent signals for a suite of nonlinear and linear extended Kalman filters
Journal of Computational Physics
Dynamic Stochastic Superresolution of sparsely observed turbulent systems
Journal of Computational Physics
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The filtering skill for turbulent signals from nature is often limited by model errors created by utilizing an imperfect model for filtering. Updating the parameters in the imperfect model through stochastic parameter estimation is one way to increase filtering skill and model performance. Here a suite of stringent test models for filtering with stochastic parameter estimation is developed based on the Stochastic Parameterization Extended Kalman Filter (SPEKF). These new SPEKF-algorithms systematically correct both multiplicative and additive biases and involve exact formulas for propagating the mean and covariance including the parameters in the test model. A comprehensive study is presented of robust parameter regimes for increasing filtering skill through stochastic parameter estimation for turbulent signals as the observation time and observation noise are varied and even when the forcing is incorrectly specified. The results here provide useful guidelines for filtering turbulent signals in more complex systems with significant model errors.