Compressed Sensing Theory In The Application Of The Lfm Signal Parameter Estimation

Compressed Sensing theory combines the traditional signal sampling with signal compression, which can break through the Nyquist sampling constraint when sampling the sparse signal. This new theory leads to a thought revolution of signal processing and becomes the frontier research field in the international academic community in recent years. The compressed sensing theory is studied and applied in the parameter estimation of the LFM signal in this paper. The OMP algorithm is used to estimate the signal parameter through searching for the position of the optimal matching atom. Because the performance of the OMP algorithm is affected by the correlation between the atoms of redundant dictionary, this paper adopts the modified OMP algorithm based on sensing dictionary to improve the performance. However, the amount of calculation of OMP algorithm will increase sharply for high accuracy of parameter estimation, this paper introduces two fast optimization algorithms to increase the calculation speed. The main content of this article is as follows:1. Compressed sensing theory is studied from the serial aspects such as the sparse representation of signals, incoherent measurement of signal and sparse reconstruction algorithm.2. An algorithm based on compressed sensing is proposed to estimate the parameters of LFM signal. First, construct the observation matrix, build the model of LFM signal and over-completed dictionary, and then estimate the parameters using OMP algorithm to search for the optimal matching atoms.3. Modified OMP algorithm based on sensing dictionary is used to estimate the parameters of LFM signal. It can solve the problem of the strong coherence between the atoms and improve the performance of estimation. Two methods, alternating projection and linear constraints Fresenius norm least method, are proposed to design the sensing dictionary. What’s more, a regularized method is proposed to design sensing dictionary in the noisy case.4. The genetic algorithm and the particle swarm optimization algorithm are used to estimate the parameters of LFM signal which can solve the problem of large computation and increase the calculation speed of the OPM algorithm.