Bias Correction Gain for Recursive $H_\infty$-Kalman Filtering of Non-Predictive Uncertain Models
Oscar Gerardo Ibarra-Manzano, José Amparo Andrade-Lucio, Yuan Xu, Yuriy S. Shmaliy · IEEE Signal Processing Letters · 2025
The$H_\infty$problem is reformulated for the bias correction gain of the recursive$H_\infty$-Kalman filter. For uncertain processes, the gain is computed using a linear matrix inequality, a bounded real lemma modified for non-predictive state space models based on Euler's backward method, and a new theorem. It is shown numerically that the gain of the$H_\infty$-Kalman filter is between the optimal Kalman gain and the gain of the robust unbiased finite impulse response filter. The filter performances are compared in terms of root mean square error, as well as the newly introduced robustness and estimation quality factors.