Kalman filtering with inequality constraints for turbofan engine health estimation

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Kalman filtering with state constraints: a survey of linear and nonlinear algorithms (2010, background): “If the process noise covariance Q does not satisfy (52) then it can be projected onto a modified covariance Q̃ that does satisfy the constraint to make the system consistent.”
State and parameter estimation of hydrologic models using the constrained ensemble Kalman filter (2009, background): “The solution of equation (23) would also be a solution by setting the inequality constraint to equality constraint [Simon and Simon, 2006; Thacker, 2007].”
On unscented Kalman filtering with state interval constraints (2010, methodology): “On the other hand, the interval-constrained unscented transform (ICUT) [35] generates sigma points satisfying dk 6 Xj;k 6 ek; j ¼ 0; . . . ;2n: ð5:1Þ To do so, unlike in (3.3), Xk is chosen as Xk ¼ x̂k11 ð2nþ1Þ þ 0n 1 h1;kcol1 ðPxxk Þ 1=2 h i . . . hn;kcoln ðPxxk Þ 1=2 h ih hnþ1;k colnþ1 ðPxxk Þ…”
Ltd Registered in England and Wales Registered Number : 1072954 Registered office : (2004, unknown): “2005), parameter estimation (Chia, Chow, and Chizeck 1991; Aguirre, Barroso, Saldanha, and Mendes 2004; Nepomuceno, Takahashi, Aguirre, Neto, and Mendes 2004; Walker 2006; Aguirre, Alves, and Corrêa 2007), tracking and navigation (Wen and Durrant-Whyte 1992; Alouani and Blair 1993; Dissanayake, Sukk”