A Continuous-time Fixed-lag Smoother Converging in Finite Time

In this paper, we propose a new fixed-lag smoother that estimates the fixed-delayed state for a continuous-time stochastic 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 differential form. In order to achieve the convergence in finite time, any additional processes such as batch processing and sampling data through discrete-time techniques are not required. A numerical example is presented to illustrate the finite time convergence of the proposed smoother in comparison with the asymptotic convergence of the conventional Kalman smoothers.