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nilsnevertree / kalman-reconstruction-partially-observed-systems

Data-driven Reconstruction of Partially Observed Dynamical Systems using Kalman Algorithms in an itterative way
GNU General Public License v3.0
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Use analogs in phase space not in time space. #26

Open nilsnevertree opened 1 year ago

nilsnevertree commented 1 year ago

With #22 the implementation of the kalman_time_independent library, the weights are performed along the time dimension. This means, the neighbours close in time are mainly used to create the LLR.

It should be better to a weights of points in the state space and not in time space. The use of Analogs in the state space would be a solution. Refer to AnDA library from Pierre Tandeo for this.

nilsnevertree commented 1 year ago

This can lead to a similar problem as in #15 but can be solved using the Eukilian distance for the weights instead of a multidimensional weight.

nilsnevertree commented 1 year ago

This problem will not be tackled up to now because using analogs might be a bit to tricky at the moment.

nilsnevertree commented 1 year ago

It can still be computed with a simple 1D value beeing the Euklidean distance $||x-x_0||$ which gives the weight. This leads to a 1D kernel which can be used by the LinearRegression function.