Title :
Minimum-energy filtering on the unit circle
Author :
Zamani, Mohammad ; Trumpf, Jochen ; Mahony, Robert
Author_Institution :
Sch. of Eng., Australian Nat. Univ., Canberra, ACT, Australia
Abstract :
We apply Mortensen´s deterministic filtering approach to derive a third order minimum-energy filter for a system defined on the unit circle. This yields the exact form of a minimum-energy filter (namely an observer plus a Riccati equation that updates the observer gain). The proposed Riccati equation is perturbed by a term depending on the third order derivative of the value function of the associated optimal control problem. The proposed filter is third order in the sense that it approximates the dynamics of the third order derivate of the value function by neglecting the fourth order derivative of the value function. Additionally, we show that the near-optimal filter proposed by Coote et al. in prior work can indeed be derived from a second order application of Mortensen´s approach to minimum-energy filtering on the unit circle.
Keywords :
Riccati equations; filtering theory; optimal control; Riccati equation; deterministic filtering approach; fourth order derivative; near-optimal filter; optimal control problem; third order minimum-energy filter; unit circle; value function; Approximation methods; Current measurement; Mathematical model; Observers; Optimization; Riccati equations;
Conference_Titel :
Australian Control Conference (AUCC), 2011
Conference_Location :
Melbourne, VIC
Print_ISBN :
978-1-4244-9245-9