Uniform Analysis And Development Of Adaptive Iteration Spectrum Estimation

Frequency spectral estimation is an important means to help people understand the signal characteristics, and its essence is to estimate how the power is distributed over frequency range from a finite record of a stationary data sequence. In order to make full use of the sampled data to improve the effect of spectral estimation, we have conducted research and extension of the adaptive spectral estimation algorithm in this thesis and the main contributions are:Firstly, we propose an adaptive iterative nonparametric spectral estimation method based on generalized noise covariance. Under the framework of Weighted Least Squares (WLS), this method can simultaneously estimate the signal spectrum and observation noise. During iteration process, the method utilizes the estimation result of last time iteration to construct generalized noise covariance matrix which generally approaches the ideal one, and then takes the inverse matrix of the generalized noise covariance matrix as the weighted matrix. Due to better construction of the weighted matrix, the proposed method has characteristics of high resolution, low spectrum leakage, enhanced invertibility of signal covariance matrix and freedom of spectrum range choice.Secondly, a robust iterative adaptive spectral estimation algorithm is put forward. The algorithm makes use of iterative spectral estimation results and sampled data to build signal covariance matrix at the same time. Then, it takes advantage of robust Capon beamforming to get the optimal frequency direction vector and later solves the traditional Capon optimization problem. Analyses show that the algorithm possesses features of both Iterative Adaptive Approach (IAA) and Rank-Deficient Robust Capon Filter-bank (RD-RCF), and RD-RCF can be viewed as a special case of the algorithm. Numerical simulations validate that the robust iterative adaptive spectral estimation algorithm can get very high spectral resolution and reflect the real frequency components very well.Furthermore, the thesis presents a missing data spectral estimation approach using lq penalized matrix completion. This approach recovers the missing part of sampled signal at first and then estimates the spectral based on the overall data after recovery. The approach simultaneously exploits spectrum sparsity and the advantages of lq norm matrix completion. Numerical simulations validate that, under the simulation conditions in this paper, when the missing rate is less than10%, the proposed method acquires more accurate estimation of real frequency components than direct usage of IAA over only available data and some other methods which combines other data recovery approaches with IAA.