INFORMATION-BASED PREDICTION OF THE PRECISION AND EVALUATION OF THE ACCURACY OF THE RESULTS FROM AN ADAPTIVE FILTER

This paper demonstrates the prediction of the relative standard deviations of the amplitude estimates for overlapped target and interferant Gaussian peaks that simulate overlapped spectral responses. The estimates for the target (known) peak amplitude are obtained by using an adaptive Kalman filter; the estimates for the interferant (unknown) peak amplitude are obtained by subtraction of the estimated contribution of the target peak from the overlapped spectrum. Repeated computer simulations show that the behavior of the averages and relative standard deviations of the amplitude estimates for both peaks and for the position of the interferant peak show some similarities as a function of the peak overlap and the amplitude ratio of the peaks. Given a model for the target peak, the relative standard deviations for the areas of both peaks can be predicted based on the function of mutual information using a single spectrum, without resorting to repeated simulations.