Unified Maximum Likelihood Form for Bias Constrained FIR Filters

In this letter, the maximum likelihood (ML) finite-impulse response (FIR) filter is proposed for discrete time-variant state-space models with nonsingular system matrix. The ML FIR filter has the deadbeat property and its form is universal for all known bias constrained FIR filters. By the identity weighting matrix, the ML FIR filter becomes the unbiased FIR filter, which ignores the noise statistics and the initial error statistics. Otherwise, the ML FIR filter is equivalent to the optimal FIR filter with embedded unbiasedness and to the minimum variance unbiased FIR filter. An example of a stochastic resonator demonstrates higher immunity of the ML FIR filter against errors in the imprecisely defined noise statistics than in the Kalman filter.