Observability of discretized partial differential equations
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Mathematical test criteria for filtering complex systems: Plentiful observations
Journal of Computational Physics
Mathematical test criteria for filtering complex systems: Plentiful observations
Journal of Computational Physics
Test models for improving filtering with model errors through stochastic parameter estimation
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
Journal of Computational Physics
Optimal filtering of complex turbulent systems with memory depth through consistency constraints
Journal of Computational Physics
Dynamic Stochastic Superresolution of sparsely observed turbulent systems
Journal of Computational Physics
Hi-index | 31.49 |
Real time filtering of noisy turbulent signals through sparse observations on a regularly spaced mesh is a notoriously difficult and important prototype filtering problem. Simpler off-line test criteria are proposed here as guidelines for filter performance for these stiff multi-scale filtering problems in the context of linear stochastic partial differential equations with turbulent solutions. Filtering turbulent solutions of the stochastically forced dissipative advection equation through sparse observations is developed as a stringent test bed for filter performance with sparse regular observations. The standard ensemble transform Kalman filter (ETKF) has poor skill on the test bed and even suffers from filter divergence, surprisingly, at observable times with resonant mean forcing and a decaying energy spectrum in the partially observed signal. Systematic alternative filtering strategies are developed here including the Fourier Domain Kalman Filter (FDKF) and various reduced filters called Strongly Damped Approximate Filter (SDAF), Variance Strongly Damped Approximate Filter (VSDAF), and Reduced Fourier Domain Kalman Filter (RFDKF) which operate only on the primary Fourier modes associated with the sparse observation mesh while nevertheless, incorporating into the approximate filter various features of the interaction with the remaining modes. It is shown below that these much cheaper alternative filters have significant skill on the test bed of turbulent solutions which exceeds ETKF and in various regimes often exceeds FDKF, provided that the approximate filters are guided by the off-line test criteria. The skill of the various approximate filters depends on the energy spectrum of the turbulent signal and the observation time relative to the decorrelation time of the turbulence at a given spatial scale in a precise fashion elucidated here.