Abstract This paper presents an approach of estimating a pattern or waveform from a set of noisy measurements with different amplitude levels. Smoothed reconstruction of the signals received by each sensor is also considered. The maximum likelihood procedure in the case of independent and normally distributed measurement errors is based on the singular value decomposition of a suitably arranged data matrix. Numerical bounds on the estimation error are provided. Statistical analyses of the estimators are carried out. The case of unequal noise variances among sensors is also considered. The performance of these methods is compared with that of a simple averaging method through simulations.
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