In this chapter we consider sequential Bayesian inference in which we consider the Bayesian estimation of a dynamic system which is changing in time. We start by considering tracking a single target observed from a single sensor. For most applications the sequential Bayesian filter is analytically intractable. In this case we consider the Kalman filter. This is a special case of linear Gaussian systems in which the equations are tractable and a closed form recursive solution available. We consider several data fusion applications of the Kalman filter including digital image stabilizer and small fast moving object (golf ball) detection and tracking. We consider several important variants of the Kalman filter including robust, augmented, extended, unscented, switching and ensemble Kalman filters. We then consider the generalization of the Kalman filter to track multiple targets. Finally we consider multi-sensor multi-temporal fusion.