Alternative smoothing algorithms for on-line estimation problems

In recent years, much emphasis has been placed on the Kalman filter to solve on-line estimation problems. Smoothers, which determine state estimates at a certain time t using measurements between 0 and T, have been used primarily in off-line estimation schemes. This paper presents alternative forms of smoothers that can be used for on-line estimation problems. The alternative smoothing algorithms provide state estimates which are more refined than Kalman filtered state estimates. The alternative smoothing algorithms are illustrated in two examples. The first example considers a linear discrete-time system while the second example considers a nonlinear continuous-time system with discrete-time measurements.