A Continuous-Time Recursive Fixed-Lag Smoother Converging in Finite Time

In this technical note, we propose a new fixed-lag smoother that estimates the fixed-delayed state for a stochastic continuous-time system. The estimation error variance of the proposed smoother is minimized under the constraint that the estimated state converges to the real state exactly in finite time after noises or uncertainties disappear. For numerical computing, the proposed smoother is represented in a recursive form. Unlike other approaches, any additional processes such as batch processing and sampling data through discrete-time techniques are not required to achieve the finite time convergence. A numerical example is presented to illustrate the finite time convergence of the proposed smoother in comparison with the asymptotic convergence of an optimal smoother.