Abstract
In the state estimation by sampled data of the linear continuous-time stochastic systems, we can use the discretized Kalman Filter which is the discrete model of the continuous Kalman Filter and the discrete Kalman Filter to the discrete model of the continuous systems. These filters give us different estimated values, because the discretized Kalman Filter is not equal to the discrete Kalman Filter.
In this paper, the difference between state estimations by the discretized Kalman Filter and the discrete Kalman Filter is studied through the estimation error variance. Further, it is shown that the discrete Kalman Filter to the discrete model which has the equivalent statistical property to the continuous system at sampling points gives the unbiased estimation and makes E{x-x)T(x-x)} minimum.
