Minimum-energy filtering on the unit circle

摘要

Abstract— We apply Mortensen’s deterministic filtering approachudto derive a third order minimum-energy filter for audsystem defined on the unit circle. This yields the exact formudof a minimum-energy filter (namely an observer plus a Riccatiudequation that updates the observer gain). The proposed Riccatiudequation is perturbed by a term depending on the third orderudderivative of the value function of the associated optimal controludproblem. The proposed filter is third order in the sense thatudit approximates the dynamics of the third order derivate ofudthe value function by neglecting the fourth order derivativeudof the value function. Additionally, we show that the nearoptimaludfilter proposed by Coote et al. in prior work can indeedudbe derived from a second order application of Mortensen’sudapproach to minimum-energy filtering on the unit circle.