Bayesian recursive estimation of linear dynamic system states from measurement information

► Bayesian approach for estimating the states of linear dynamic systems. ► Kalman’s equations derived in a more accessible way to those involved with dynamic measurements. ► Evaluation of the measurement uncertainty of dynamic quantities. The evaluation of uncertainty in dynamic measurements has recently become a demanding issue. A Bayesian approach is employed here to derive the equations required to recursively generate the solution to the problem of estimating (and predicting) the states of linear dynamic systems. It is shown that this approach allows a derivation of Kalman’s filtering algorithm which is more easily accessible to those involved with dynamic measurements. The complete time-varying Kalman filter is particularly useful when the linear dynamic system and/or signal statistics are time varying and also when optimum estimates are required from the very beginning.