Fully Probabilistic Design for Knowledge Transfer in a Pair of Kalman Filters

The problem of Bayesian knowledge transfer from a secondary to a primary Kalman filter is addressed. The secondary filter makes available its probabilistic data predictor, but an explicit Bayesian conditioning mechanism between the filters is assumed to be unavailable. Thus, fully probabilistic design is adopted. This leads to a novel and fully tractable three-step recursive extension of the traditional Kalman filter flow, involving an extra data-like step for merging the secondary data predictor. An adapted form of the algorithm yields performance in simulation equal to that of measurement vector fusion, with the advantage that the Bayesian design allows full distributional knowledge to be transferred. There is flexibility in the way probabilistic knowledge transfer between interacting Kalman filters can be specified using this optimal Bayesian design strategy, and these options are discussed in the letter.