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We should implement the particle filter with the new interface functions.

This is more to make sure that LinearStateSpaceModel implements the particle filtering interface. The optimal proposal distribution should be exactly solvable for a linear, Gaussian state-space model (because it is just appropriately conditioned Gaussians), so we shouldn't need additional information in the LinearStateSpaceModel struct.

A CIR model would be good.

We should now extract the various matrices of the model using the interface functions and adapt the signature of kalman_filter and kalman_smoother to take a vector of parameter values

Add tests that ensure that the interface between models and inference engines is consistent.

This makes the process noise covariance matrix not positive definite, and MvNormal will probably fail.

Performance improvements are needed, but first we need a good set of benchmarks to evaluate performance.

Currently we have two different kinds of state-space models, the linear, Gaussian models meant for use with the Kalman filter and smoother, and general state-space models meant for use with particle filters. It would be nice to have one kind of model, and a particular interface to implement if the model is a linear, Gaussian model (and thus can be used with the Kalman filter). This way any model could be used with the particle filter while models that happen to be linear and Gaussian can be used with the Kalman filter. This could also come in handy down the line if we implement ensemble Kalman filtering methods, which use a nonlinear forward model with a Gaussian observation model.