On the Convergence of the Modified Riccati Equation | Zendy

Nicholas Assimakis | Zendy; Μαρία Αδάμ | Zendy

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On the Convergence of the Modified Riccati Equation

Author(s) -

Nicholas Assimakis,

Μαρία Αδάμ

Publication year - 2012

Publication title -

isrn signal processing

Language(s) - English

Resource type - Journals

eISSN - 2090-505X

pISSN - 2090-5041

DOI - 10.5402/2012/625897

Subject(s) - riccati equation , algebraic riccati equation , mathematics , logarithm , kalman filter , convergence (economics) , linear quadratic regulator , state (computer science) , control theory (sociology) , optimal control , mathematical optimization , mathematical analysis , algorithm , partial differential equation , computer science , control (management) , statistics , artificial intelligence , economics , economic growth

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.

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