Adding test cases for analytically tractable models

[matt-graham]

To verify the correctness of the implementation of the filters we should ideally have tests checking that the estimated filtering distributions show the expected convergence as the ensemble size goes to infinity to the true filtering distributions on models for which it is tractable to exactly infer these.

One option for a class of models for which exact inference is possible is linear-Gaussian state space models for which the filtering distributions will be Gaussian and the Kalman filter can be used to efficiently compute the mean and covariance parameters for the filtering distributions at each time step. The TDAC-based model current used as the test example fits these constraints (as the deterministic dynamics are linear, we use additive Gaussian state noise, a linear observation operator and Gaussian observation noise) so would be one option. However, the overall state dimension for the default configuration with a 200×200 spatial grid (and three state variables per grid point) is 120 000 is prohibitively large for running a Kalman filter (which typically has a operation complexity per time step which scales cubically in the state dimension and memory usage which scales quadratically in the state dimension). While we could use a lower spatial resolution it is not clear how small the spatial resolution can be made without running into numerical stability issues. It may be better therefore to use a simpler linear-Gaussian model which it is possible to configure with smaller state dimensions as a test case.