$L_2$ -- $E$ FIR Filters for Deterministic Continuous-Time-State Space Signal Models

In this paper, a new $L_2$ -- $E$ performance criterion is introduced, which is represented as a gain between the disturbance during the recent time interval and the current estimation error. Based on the $L_2$ -- $E$ performance criterion, the $L_2$ -- $E$ finite impulse response (FIR) filter (LEFF) is proposed for deterministic continuous-time-state space signal models without requiring the stochastic information such as variances and means. The LEFF is designed to minimize the maximum value of the $L_2$ -- $E$ performance criterion together with prior constraints such as linearity, unbiased property in the deterministic sense, and FIR structure, simultaneously. Via simulation, the LEFF is compared with other deterministic infinite impulse response (IIR) filters such as the $H_\infty$ and $L_2$ -- $L_\infty$ filters.