State covariance assignment problem with measurement noise: a unified approach based on a symmetric matrix equation

AbstractWe consider a state covariance assignment problem with measurement noise. We derive a unified solution for both the continuous-time and the discrete-time case, based on a symmetric matrix equation of quadratic type. The solution includes (1) the existence condition for a feedback gain which assigns a specified covariance, (2) an explicit parametrization of the entire set of feedback gains that assign a specified covariance. We can show that the previous results for free-measurement noise can be readily derived as special cases