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HW1--Satellite radiance problem :
- Solve using LU (normal equation approach by Grammian)
- Solve using QR approach
- Solve using SVD approach
- 2D interpolation using bilinear least squares
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HW2-4D-VAR/Adjoint Optimisation(ODE-Lorenz Systerm):
- Linear 4D-VAR):
- Nonlinear 4D-VAR
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HW3-Gradeint based Optimisation:
- Newton/Gradient Method.
- Conjugate Gradient.
- Broyden–Fletcher–Goldfarb–Shanno (BFGS) Algorithm.
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HW4-4D-VAR/Adjoint Optimisation(PDE)
- Linear advection equation.
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HW5-Forward Sensistivity Model
- Lagrangian forecast air temperature model.
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HW6-3DVAR
- Initialization Classical Method.
- Optimal interpolation (bicubic).
- Bayesian Formulation.
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HW7-nonlinear dynamics describing a falling body (Julier, Uhlmann, Durrant-Whyte, IEEE Transactions on Automatic Control Volume 45, 2000)
- zeroth-order filter (linearized Kalman filter)
- first-order filter (Extended Kalman Filter)
- second-order filter (Gauss filter).
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HW8-Lorenz 96 (L96) problem
- stochastic Ensemble Kalman filter (EnKF).
- Deterministic EnKF.
- Reduced-rank square root (RRSQRT) filter.
- Unscented Kalman Filter method.
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Project- Deterministic and stochastic ensemble KF approaches for 1D nonlinear Korteweg de Vries (KdV) PDE.
sayin/Optimization_Data_Assimilation_MAE_5010
Python codes for Data Assimilation course MAE-5010
Python