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