Frequency Estimation Methods And Simulations Under Fractional-order Non-Gaussian Noise

There are many methods for harmonic frequency estimation, such as model parameter method, non-parameter method and entropy spectral estimation method. All methods have their own advantages in different conditions. However, they can be classified to classical and modern frequency estimations. Classical frequency estimation based on the classic Fourier analysis theoretically is a linear analysis method, while modern frequency estimation is non-linear analysis method, which has a higher resolution ratio and wider adaptability. However, with the intensive study of random signals and noises, people are not satisfied with the status quo. Frequency estimation based on higher-order moments and fractional-order moments gradually becomes a new concern. Based on fractional-order moments, this dissertation studies the technologies of harmonic frequency estimation, namely the MUSIC algorithm under Gaussian noise and the FOC-MUSIC algorithm under non-Gaussian noise. The main work is as follow:(1) The essay describes the significance, status quo and research methods of harmonic frequency estimation techniques.(2) The essay describes the definition, nature and parameter model method ofαstable distribution. Moreover, it describes the probably adopted AR, MA, ARMA models in the process of analysis and the corresponding parameter estimation methods such as maximum likelihood estimation, minimum norm estimation, least-squares method and the generalized Yule-Walker.(3) The essay simulates the MUSIC algorithm and the FOC-MUSIC algorithm and does some comparative researches on the features shown by MUSCI algorithm and FOC-MUSIC algorithm based on emulated data.