Optimal finite impulse response estimation of linear models in receiver channels with imbedded digital signal processing units

Two finite impulse response (FIR) estimators (optimal and unbiased) are addressed for filtering, smoothing and predicting linear time-invariant state-space signal models perturbed by white Gaussian noise in receiver channels with imbedded digital signal processing units. The FIR estimators are efficient in estimating oversampled and highly oversampled signals, respectively. Special attention is paid to the unbiased FIR (UFIR), owing to its ability of becoming optimal when the processing memory is large. An iterative UFIR algorithm is discussed in detail and compared with the Kalman filter. The optimal memory and errors are also discussed for such kind of estimators. Examples of applications are given for one-dimensional tracking of a two-state polynomial model and state estimation in a harmonic one. Based on this study, the authors show that the UFIR estimator is more efficient than the Kalman filter in blindly estimating receiver channels under the model temporary uncertainties.