Performance of frequency estimation using sparsed sampling - Du, Liang (2018)
The frequency estimation of a complex sine wave in noise is one of the main research contents of signal processing. It is widely used in the detection of radar and sonar moving target and many effective frequency estimation algorithms have been developed. In recent years, Compressive Sensing becomes a new research hot topic in signal processing. And gradually become a new research hotspot in signal processing. It was found that if the signal is sparse or almost sparse after the decomposition under an orthonormal basis or an overcomplete atomic library, then a much smaller measurement than the original signal length obtained by the random projection ofthis signal contains most information. This dissertation first discusses two representative algorithms in the Nyquist sampling framework. One is the MLE frequency estimation method with the highest estimation accuracy. The algorithm can approach CRLB with a small number of sampling points. The other is the MUSIC algorithm, which is highly efficient in estimation efficiency and accuracy and can achieve high-resolution estimation of multiple signal frequencies. In the framework of compressive sensing, a convex optimization reconstruction algorithm is introduced, which equivalently translate the NP-hard 10 minimization problem into solvable 11 problem, such as BP and BPDN. The greedy algorithm such as OMP algorithm with high reconstruction rate is then introduced, and the algorithm for frequency estimation based on the above two algorithms is discussed. In this dissertation, several comparisons under the same framework and cross two frameworks are made from the angles of frequency estimation accuracy, sampling data storage, computational complexity and time cost. And in the CS framework, a dynamic dictionary OMP algorithm based on Bisection is proposed for compensating the inherent defects of the fixed dictionary-based algorithm, which greatly improves the estimation accuracy.