Linear Models Estimation in Receiver Channels with Imbedded DSP Units Using Optimal FIR Structures

摘要

The optimal and unbiased finite impulse response (FIR) estimators are addressed for filtering, smoothing, and prediction of linear time-invariant state-space signal models perturbed by white Gaussian noise in receiver channels with imbedded digital signal processing units. The estimators are efficient for oversampled and highly oversampled signals, respectively. Special attention is paid to the unbiased FIR (UFIR) one due to its ability of becoming optimal when the processing memory is large. An iterative UFIR algorithm is discussed in detain and compared to 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. It is shown that the UFIR estimator is more efficient than the Kalman filter for blind estimation in receiver channels.