The accuracy of parameter estimation by curve fitting in the presence of noise

Abstract

Curve fitting of a spectrum or intensity line by chi-square minimization to obtain estimates of parameters is commonly used in fields ranging from (Raman) spectroscopy to position detection. The error or noise in the parameters such as peak position, obtained by the fitting procedure, depends on three error sources in the original data. The limited number of counts in the signal, a systematic error due to binning the data (e.g., to detector pixels), and background noise are identified as the main contributors to the inaccuracy of the estimated parameters after the fitting procedure has been completed. An analysis using analytical calculations and Monte Carlo simulations shows that the effects of limited signal counts and binning both favor a spread of the signal over as many bins as possible, while the background noise has least influence if the signal is concentrated in very few bins. These conflicting demands define a minimum attainable noise level. Hence an optimal situation can be identified where the signal is spread over a definite amount of bins to obtain minimal noise in the extracted parameters such as peak position. A good strategy is presented to obtain this optimum spread of the signal over the bins. This is very relevant to all scientific fields that make use of curve fitting, as it enables a thorough assessment and minimization of the uncertainty in the values obtained.