Ensemble-Kalman-Filter

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Ensemble-Kalman-Filter

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EnKF in Matlab for a system of two PDEs modeling burglar behavior (model of Short et al.)

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# Ensemble-Kalman-Filter
EnKF in Matlab for a system of two PDEs modeling burglar behavior (model of Short et al.)

## Note:
I have experienced several bugs in Matlab's solvepde() function on Matlab R2016a. 
- For instance, the stated restart from the last time point does not work for systems of PDEs.
My workaround consists in defining an anonymous function that takes the value of the last (point of time of the) solution. This function is taken as the new initial value in the solution process.
- Saving the workspace after a successful simulation, clearing all variables and loading the workspace will result in an error ("initial conditions either do not exist or are empty") trying to delete the initial condition model.deleteInitialCondition and setting a new one using SetInitialConditions via anonymous function on the loaded model. I guess some internal variable is missing. Workaround: Run the MAIN function for a couple of seconds and abort. This will apparently load the missing data.
- When doing simulations, clearing all variables results in a small chance some internal variable still persists.

Since I don't own the Matlab license for the university version, my bugreport won't be even looked at.

# Files
```
Short.m: Solves Short's et al. PDE system with the following coefficients and initial value:
acoeffunction.m: Coefficient a function for our PDE system
ccoeffunction.m: Coefficient c function for our PDE system
fcoeffunction.m: Coefficient f function for our PDE system
u0fun.m: Initial value u0 function for our PDE system

EnKF.m: Ensemble Kalman-Filter performing the aggregation between last aggregated solution simulated 
        to the next time point with the observational data for that point.
EnKF_ens_create.m: creates the ensemble
EnKF_main.m: MAIN

save_fig.m: saves all open plot windows as portable network graphics
subplot4.m: Arranges the solutions as four subplots: artificial solution, 
            noisy observation, solution prior to EnKF and aggregated solution (EnKF).
short_bsp.m: Example script for the unfiltered solution of Short's model.
```

Ensemble-Kalman-Filter

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