The unbiased finite impulse response (UFIR) filtering approach is developed for discrete-time state-space models with time-stamped discretely delayed and missing data. The model with $k$-step-lags in observations is transformed to have no latency and expanded on a finite horizon of $N$ most recent data points. It is shown that the optimal horizon for the UFIR filter is practically $k$-invariant, unlike the tuning factor of the $H_\infty$ filter. Higher robustness of the UFIR filter against the Kalman and $H_\infty$ filters is justified theoretically in uncertain environments with discretely delayed and missing data. Experimental verification is provided based on GPS-based tracking of a moving vehicle to demonstrate a good agreement with the theory.