Bayesian interpretation of Kalman filtering

Abstract

In this paper, the formula for the Bayesian estimation of the state values under a linear trend vector time series model is drived and the effect of the initial prior on the Bayesian estimation for the different values of the covariance matrix of prior is investigated. We first introduced the state space model and the Kalman filtering on it. Next, we examined the Kalman filter method as well as the Maximum A Posteriori (MAP) method. Then we considered the effect of initialization by the prior on the Bayesian estimation of state values and derived the formula for the state estimation for some initial condition. We also demonstrated through simulation experiments the estimation results by the Kalman filter and MAP methods and the effects of the initial conditions of the prior.