TY - GEN
T1 - Minimum-energy filtering on the unit circle
AU - Zamani, Mohammad
AU - Trumpf, Jochen
AU - Mahony, Robert
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84856104429&partnerID=8YFLogxK
M3 - Conference contribution
SN - 9780858259874
T3 - Proceedings of the 2011 Australian Control Conference, AUCC 2011
SP - 236
EP - 241
BT - Proceedings of the 2011 Australian Control Conference, AUCC 2011
T2 - 1st Australian Control Conference, AUCC 2011
Y2 - 10 November 2011 through 11 November 2011
ER -