An unbiased p-step predictive FIR filter for a class of noise-free discrete-time models with independently observed states

The paper addresses a new unbiased p-step toward predictive finite impulse response (FIR) filter for a class of discrete-time deterministic state space models, which states are represented on a horizon of N past points with degree polynomials and observed independently. It is implied that measurements are not available at a current time point n. The problem arises in synchronization and tracking when a signal is lost. Generic coefficients are derived via the Bernoulli polynomials for a two-parameter family of the polynomial filter gains. A generalization is provided for the linear (ramp) and quadratic filter gains. We show that the solution proposed is efficient in applications to predictive filtering of the states of local clocks of digital communication network nodes when a synchronizing signal is temporarily not available.