2019 Volume 2019 Pages 7-12
For discrete-time linear stochastic systems with unknown disturbances, we consider the optimal filter with disturbance decoupling property and the equation (i.e., Riccati equation) which the covariance matrices of the estimation errors of the filter satisfy. Assuming that the stochastic processes have constant coefficients, we prove convergence of the Riccati equation and derive a simple equation (called the algebraic Riccati equation (ARE)) which is the limit of the Riccati equation under some conditions similar to those for the Kalman filter. We also prove asymptotic stability of the systems whose optimal gains are determined by the ARE.
