A Dual Approach to a Linear Smoothing Problem

In this paper, the continuous-time linear Gaussian smoothing problem is investigated by utilizing a dual approach. It is shown that the smoothing problem is a dual of an optimal regulator with a jump condition on the trajectory. By solving the dual optimal control problem, basic results established earlier on this smoothing problem are derived in a simpler way. Results are also obtained for the discrete-time linear smoothing Gaussian problem.