$L_{2}-E$ FIR Smoothers for Deterministic Discrete-Time State–Space Signal Models

In this note, a new type of L
₂
- E performance criterion for a fixed-lag smoother is introduced, which is given by a gain between the energy of the external disturbances during the recent time horizon and the estimation error at the fixed-delayed time from the current one. By minimizing the maximum value of the L
₂
- E performance criterion, the L
₂
-E finite impulse response (FIR) smoother(LEFS) is obtained for a deterministic discrete-time state space signal model. The LETS is designed to meet requirements such as linearity and FIR structure with respect to measured inputs and outputs, unbiased property in the deterministic sense, and independence of any state information simultaneously. The proposed LETS is represented in a batch form for simplicity. The LETS is compared with a conventional H
_infin
Infinite Impulse Response (IIR) smoother via simulation