Parameter Estimation Of Chirp Signals Based On MCMC And Its Applications To Synthetic Aperture Radar Imaging

Chirp signals are widely used in radar, sonar, communications, seismology, medical imaging and other applications. Hence the research of parameter estimation of chirp signals has its great theoretical significance and practical value. In the framework of maximum likelihood estimation (MLE), this thesis studies new algorithms of parameter estimation of mono-component and multi-component chirp signals in additive Gaussian white noise. And the new algorithms are also applied to synthetic aperture radar (SAR) imaging. The main contributions and innovations of this thesis are shown as follows:By applying Markov Chain Monte Carlo (MCMC) algorithms to parameter estimation of mono-component chirp signals and making improvements to enhance the algorithm efficiency, three novel methods based on MCMC approaches are proposed, which can attain the maximum likelihood estimates of mono-component chirp parameters. The computational burdens of the methods are modest. The proposed methods jointly estimate the chirp parameters, so there is no error propagation effect. They are also applicable to the estimation problem of short data records. Moreover, they can estimate over a wide range of parameter values. Simulations show that the Cramer-Rao bound (CRB) can be attained by the proposed methods even at low signal-to-noise ratio (SNR).Average first-order efficiency is defined in order to measure the efficiencies of MCMC algorithms. Through this measure, numerical simulations verify that the Metropolis-Adjusted-Langevin's (MAL) algorithm is more efficient than the random walk Metropolis-Hastings algorithm, i.e. the MAL algorithm is faster to converge than the random walk Metropolis-Hastings algorithm.A new method based on MCMC approaches to achieve the MLE of multi-component chirp signals is proposed, which uses the simulated annealing based single element random walk Metropolis-Hastings algorithm. The proposed method solves the cross-term problem in the multi-component estimation. It jointly estimates the chirp parameters, so there is no error propagation effect. It can estimate over a wide range of parameter values. The proposed method can also deal with the estimation problem of short data records and the computational burden is modest. Simulations show that its estimation performance can attain the CRB even at low SNR and the threshold SNR of the proposed method is 2dB lower than that of the multi-component chirp estimation algorithm based on importance sampling.The proposed parameter estimation algorithms of chirp signals based on MCMC approaches are applied to the SAR imaging of stationary point targets and moving targets respectively. In the imaging process, they estimate the Doppler parameters of the targets in order to form the autofocus function and perform the azimuth autofocus. Imaging experiments on the raw data of stationary point targets and moving targets are performed by using the proposed estimation methods and good imaging results are acquired.