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Adaptiye Hierarchical Bayesian Kalman Filtering

section, into a Kalman filter based on the parameter values specified in the first example. It is clearly seen that estimates of current State are ąuite poor due the inability of the Kalman filter, as specified, to track the autocorrelation.

Rather than pre-specifying all the parameters associated with the system state-space model, we need to employ a methodology that allows for estimating any unknown parameters from the observed data. Those estimates can then be used in the Kalman filter State estimation process. The method used here is a hierarchical Bayes approach first introduced in Magill (1963 and 1965). The goal is to rewrite the Kalman State estimation equations in terms of a density that expresses our lack of knowledge about the unknown parameters and then to develop a set of recursive eąuations for calculating that density as data samples are taken. A brief derivation is given to further establish notation.

First of all, we want our estimator to have the generał form

Figurę 5. Process Data and Kalman Estimate with Mis-Specified

Parameters.