Robust Recursive Least-Squares Wiener Fixed-Interval Smoother Based on Innovation Approach in Linear Continuous-Time Stochastic Systems with Uncertainties

This study develops a robust recursive least-squares (RLS) Wiener fixed-interval (FI) smoother by exploiting covariance information for linear continuous-time systems that face uncertainties in both their system and observation matrices. Uncertainties in the state-space model cause degradations in the signal and observed values. The robust FI smoothing and filtering methods introduced do not assume that the system and the observation matrix have norm-bounded uncertainties. An observable companion form represents the state space model of the degraded signal. Robust RLS FI smoothing is to minimize the mean-square value of the smoothing errors of the system state over a fixed interval. Section 3 introduces an integral equation satisfied by the impulse response function that is optimal for robust FI smoothing estimation of the system state. An integral equation for the impulse response function, which provides a filtering estimate of the state of the degraded system, is also shown. Theorem 1 presents the robust RLS FI smoothing and filtering algorithm for the signal and the system state using covariance information. Theorem 2 presents the robust RLS Wiener (RLSW) FI smoothing and filtering algorithm for the signal and the system state. Robust RLS FI smoother outperforms robust RLS filter in estimation accuracy, as shown by the FI smoothing error covariance function in Section 5. Numerical simulation examples demonstrate that the robust RLSW FI smoother achieves superior signal estimation accuracy compared to the robust RLSW filter.