Optimum Constant-Gain Filters

The problem of estimating the state of a linear system over a finite time interval in the presence of noise is considered. The expected value of the integral of the quadratic error is taken as the performance index. A configuration of the same type as the Kaiman filter is assumed with the restriction that the gain must be constant. An integral equation is obtained as a necessary condition for the gain to be optimum, and an iterative procedure is suggested for its solution. Numerical results indicate that this filter can be significantly more accurate than one utilizing the steady-state gain of the Kalman filter.