Optimal States Estimation of an LTI System using the Unbiased FIR Filter

The unbiased linear finite impulse response (FIR) filter and the two-state Kalman filter are investigated in the optimal estimation of the two state (position and velocity) in a linear time invariant (LTI) systems in presence of additive white Gaussian noise (AWGN). In opposite to the Kalman filter, the unbiased linear FIR filter dońt need previous knowledge about noise process, this algorithm only needs two specific parameters: optimal time step and optimal number of the points in the average. We show that both algorithms produce a similar lower mean square error (MSE).