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    Area of Science:

    • Nuclear spectroscopy
    • Data analysis
    • Signal processing

    Background:

    • Gaussian function least square fitting is standard for nuclear spectrum analysis.
    • This method is precise but highly sensitive to noise, leading to larger residuals near spectral peaks.
    • Noise sensitivity impacts the accuracy of parameter estimation.

    Purpose of the Study:

    • To address the noise sensitivity of Gaussian function least square fitting.
    • To improve the accuracy and real-time performance of spectral peak fitting.
    • To develop a more robust fitting method for nuclear spectra.

    Main Methods:

    • Developed a Gaussian function weighted least square fitting method by introducing a weight factor.
    • Analyzed the causes of noise sensitivity in standard Gaussian fitting.
    • Replaced computationally intensive inverse matrix calculations with simple equation solving for faster parameter estimation.
    • Derived fast calculation formulas for Gaussian parameters (amplitude, center, variance).

    Main Results:

    • The weighted least square fitting method demonstrated superior performance compared to the standard method.
    • The proposed method effectively decreased noise sensitivity and reduced residual vectors near the peak.
    • Fitting precision was significantly improved.
    • Fast calculation formulas enhanced real-time performance.

    Conclusions:

    • Gaussian function weighted least square fitting offers a more satisfactory solution for nuclear spectrum analysis.
    • The method improves fitting accuracy and robustness against noise.
    • Enhanced real-time performance makes the method suitable for portable analysis equipment.