The optimal finite impulse response (FIR) filter is applied to systems with both unknown inputs and noise, in order to obtain noise-suppressed estimates of the unknown inputs. The unknown inputs are modeled as random-walk processes and estimated together with the state. Using the optimal FIR filtering algorithm, the estimate for each unknown input is shown to be independent of the window initial state and also of other unknown inputs. A detection scheme for an unknown input is developed utilizing a test variable independently of other unknown inputs. Finally, numerical examples are given to show the performance of the proposed estimation and detection method.