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Adaptive Hierarchical Bayesian Kalman Filtering

We also have a model used to construct any given Kalman filter, called the design model, which is given by

Using this notation, the Kalman equations for any filter then become

p®^- = ®^Dv°;<s>^,D +Qf_,

Notę the dependence now of the eąuation for the posterior estimate of the system State on the truth model.

To answer the questions mentioned above, we must develop expressions for the various error terms. We can derive the error committed by using a design model prior estimate as an estimate of the truth model State x,^r+1, which we will signify as e“₊,, where

-    _ T _ ~D-

^e»+l ^{_ X}<+1 ^x»+l

where V<D =

We can similarly derive the posterior error as

where VH = H^r-H°