Robust Recursive Least-Squares Finite Impulse Response Filter in Linear Continuous-Time Stochastic Systems with Uncertainties

The current research designs an original robust recursive least-squares (RLS) finite impulse response (FIR) filter for linear continuous-time systems with uncertainties in both the system and observation matrices. These uncertainties in the state-space model generate the degraded signal and observed value. The robust RLS FIR filter does not account for the norm-bounded uncertainties in the system and observation matrices. This study uses an observable companion form to represent the degraded signal state-space model. The system and observation matrices are estimated based on the author's previous computational methods. The robust RLS FIR filtering problem aims to minimize the mean-square errors in FIR filtering for the system state. The robust FIR filtering estimate is formulated as an integral transformation of the degraded observations using an impulse response function. Section 3 obtains the integral equation satisfied by the optimal impulse response function. Theorem 1 presents the robust RLS FIR filtering algorithms for the signal and the system state. This integral equation derives the robust RLS-FIR filtering algorithms. Numerical simulation examples show the validity of the proposed robust RLS FIR filter.