Explicit Solution to the Unstable Stationary Filtering Problem

An expression in closed form for the constant Kalman gain in stationary filtered estimation of linear unstable processes is obtained and bounds on the achievable accuracy of the estimate are derived. This expression is used to find lower and upper bounds for the singular values of the solution of the algebraic matrix Riccati equation and to derive the minimum-phase image of linear systems that possess zeros in the right half plane.