On the Convergence of the Modified Riccati Equation

Abstract

The modified Riccati equation arises in the implementation of Kalman filter in target tracking under measurement uncertainty and it cannot be transformed into an equation of the form of the Riccati equation. An iterative solution algorithm of the modified Riccati equation is proposed. A method is established to decide when the proposed algorithm is faster than the classical one. Both algorithms have the same behavior: if the system is stable, then there exists a steady-state solution, while if the system is unstable, then there exists a critical value of the measurement detection probability, below which both iterative algorithms diverge. It is established that this critical value increases in a logarithmic way as the system becomes more unstable.

Online evaluation of the process noise covariance matrix for event‐based state estimators

“…Equation is similar to the modified discrete Riccati equation (MDARE) studied in the works of Boers and Driessen and Assimakis and Adam . There is no known method to solve this equation, but at least we know that if the scalar multiplying the second term of the MDARE is bounded in the interval [0,1], then converges.…”