Unbiased FIR Filtering for Time-Stamped Discretely Delayed and Missing Data

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
_∞
filter. Higher robustness of the UFIR filter against the Kalman and H
_∞
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.