Optimal estimation of hybrid models in state-space with FIR structures

An optimal finite impulse response (FIR) estimator is adapted for discrete filtering, smoothing, and prediction of hybrid (continuous/discrete) models over N nearest past measurement points. Its unbiased FIR (UFIR) version ignoring noise and initial errors is also discussed for near optimal estimation when N >;>; 1. The UFIR estimator is represented with an iterative Kalman-like algorithm efficient for highly oversampled data. An example of applications is given for the Global Positioning System-based measurement of time errors in a crystal clock.