Blending prior from Prior engine

[jgomezdans]

Prior engine provides temporally and spatially resolved prior information. this needs integrating. This means that we need to blend whatever is coming from the past time step output with the prior information by the Prior Engine. Given the latter is just a a diagonal matrix, this is quite simple once the prior data have been put into vector/matrix format.

[jgomezdans]

See Eqns. 9 and 10 in here

[jgomezdans]

For matrices, the equations in here work OK. The definition Sigma_3^{-1} is just a sum of inverse matrices, but the definition mu_3 requires Sigma_3 (no inverse), but in order to approximate it, we can take Sigma_1 and Sigma_2 to be diagonal as it's just a scaling here.