Parametric estimation of superimposed signals

The problem of parametric estimation of signals composed of a weighted sum of functions drawn from a known parametric family with unknown parameters in white Gaussian noise was studied. New closed-form expressions of the Cramer-Rao bound (CRB) for parametric estimation of superimposed signals in white Gaussian noise were derived. The effect of the amplitude correlation structure of superimposed signals on the CRB of parametric estimation of superimposed signals in white Gaussian noise was considered. Two criteria for distinguishing between best CRB and worst CRB were introduced, based on the determinant and diagonal elements of the CRB matrix, respectively. It was shown that for both criteria the best and worst correlation conditions correspond to uncorrelated and fully coherent signals, respectively. Relative phase conditions of signals that give the worst CRB were derived for the important cases of real signals, signals with special structure, and two signals with a scalar signal parameter. A Local Interaction Signal Model which limits the smallest signal parameter separations was developed based on the study of CRB. Using this model, two novel computationally efficient dynamic programming algorithms for maximum likelihood parameter estimation were developed. The computational requirements of these algorithms were studied and compared with those of other existing algorithms. Various properties of the algorithms were derived and their performance analyzed in closed form. The algorithms were used in solving a number of challenging classical problems, as well as in the restoration of noise-corrupted and blurred images. Simulation results indicate that the algorithms provide good estimation accuracy over a wide range of signal-to-noise ratio. The superior accuracy and computation efficiency of the algorithms, together with the generality of the signal model proposed, suggest that these algorithms can be used in a wide variety of signal estimation problems.U of I OnlyETDs are only available to UIUC Users without author permissio