基于MCMC的Chirp信号参数估计及其在SAR成像中的应用
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摘要
线性调频(chirp)信号广泛地应用于雷达、声纳、通信、地震学、医学成像等领域,因而研究chirp信号参数估计具有重要的理论意义和实用价值。本论文在最大似然估计的框架下研究高斯白噪声中单分量和多分量chirp信号参数估计新算法,并将新算法应用到合成孔径雷达(Synthetic Aperture Radar, SAR)成像当中。论文工作的主要成果和创新点如下:
将马尔可夫链蒙特卡洛(Markov Chain Monte Carlo, MCMC)方法应用到单分量chirp信号参数估计,并逐渐加以改进,提高算法效率,提出三种基于MCMC的实现单分量chirp信号最大似然参数估计的新方法。这些方法计算量适中,联合估计各参数,无误差传递效应,可适用于小样本数量的参数估计,具有较宽的参数估计范围。仿真实验表明三种方法的估计性能在较低信噪比时达到Cramer-Rao界(CRB)。
定义平均第一阶效率来衡量MCMC算法的效率,并利用平均第一阶效率通过仿真实验验证了Metropolis-Adjusted-Langevin’s (MAL)算法比随机移动Metropolis-Hastings算法效率更高,即收敛速度更快。
提出一种基于MCMC的实现多分量chirp信号最大似然参数估计的新方法,该方法采用基于模拟退火的单元素随机移动Metropolis-Hastings算法。它解决了多分量估计中的交叉量问题,联合估计各参数,无误差传递效应,具有较宽的参数估计范围,可适用于小样本数量的参数估计,并且计算量适中。仿真实验表明其估计性能可在较低信噪比下达到CRB,信噪比门限比基于重要采样的多分量chirp信号参数估计算法低2dB。
将基于MCMC的chirp信号参数估计新算法分别应用到SAR对静止点目标和动目标成像上,在成像过程中用来估计目标的多普勒参数,以
形成聚焦函数,进行方位向聚焦。利用参数估计新算法,对静止点目标和动目标的实际数据分别进行成像实验,获得一定的成像效果。
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.
将马尔可夫链蒙特卡洛(Markov Chain Monte Carlo, MCMC)方法应用到单分量chirp信号参数估计,并逐渐加以改进,提高算法效率,提出三种基于MCMC的实现单分量chirp信号最大似然参数估计的新方法。这些方法计算量适中,联合估计各参数,无误差传递效应,可适用于小样本数量的参数估计,具有较宽的参数估计范围。仿真实验表明三种方法的估计性能在较低信噪比时达到Cramer-Rao界(CRB)。
定义平均第一阶效率来衡量MCMC算法的效率,并利用平均第一阶效率通过仿真实验验证了Metropolis-Adjusted-Langevin’s (MAL)算法比随机移动Metropolis-Hastings算法效率更高,即收敛速度更快。
提出一种基于MCMC的实现多分量chirp信号最大似然参数估计的新方法,该方法采用基于模拟退火的单元素随机移动Metropolis-Hastings算法。它解决了多分量估计中的交叉量问题,联合估计各参数,无误差传递效应,具有较宽的参数估计范围,可适用于小样本数量的参数估计,并且计算量适中。仿真实验表明其估计性能可在较低信噪比下达到CRB,信噪比门限比基于重要采样的多分量chirp信号参数估计算法低2dB。
将基于MCMC的chirp信号参数估计新算法分别应用到SAR对静止点目标和动目标成像上,在成像过程中用来估计目标的多普勒参数,以
形成聚焦函数,进行方位向聚焦。利用参数估计新算法,对静止点目标和动目标的实际数据分别进行成像实验,获得一定的成像效果。
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.
引文
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Xia X.G. System identification using chirp signals and time-variant filters in the joint time-frequency domain. IEEE Transactions on Signal Processing, 1997, 45(8): 2072~2084
Boushash B., Whitehouse H.J. Seismic applications of the Wigner-Ville distribution. In Proceedings of IEEE International Symposium on Circiuts and Systems, San Jose, CA, USA, 1986: 34~37
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Raney R.K. Synthetic aperture imaging radar and moving targets. IEEE Transactions on Aerospace and Electronic System, 1971, 7(3): 490~505
Tretter S. Estimating the frequency of a noisy sinusoid by linear regression. IEEE Transactions on Information Theory, 1985: 832~835
Djuric P.M., Kay S.M. Parameter estimation of chirp signals. IEEE Transactions on Acoustics, Speech, & Signal Processing, 1990, 38(12): 2118~2126
Djuric P.M., Kay S.M. A simple frequency rate estimator. In Proceedings of 1989 International Conference on Acoustics, Speech, and Signal Processing, (ICASSP’89), 1989: 2254~2257
Slocumb B.J., Kitchen J. A polynomial phase parameter estimation-phase unwrapping algorithm. In Proceedings of 1994 International Conference on Acoustics, Speech, and Signal Processing, (ICASSP’94), 1994: 129~132
Jones H.E. Weighting coefficients for chirp rate estimation. IEEE Transactions on Signal Processing, 1995, 43(1): 366~367
Fiore P.D., Lang S.W. Efficient phase-only frequency estimation. In Proceedings of 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing, (ICASSP’96), 1996: 2809~2812
Lang S.W., Musicus B.R. Frequency estimation from phase differences. In Proceedings of 1989 International Conference on Acoustics, Speech, and Signal Processing, (ICASSP’89), 1989: 2140~2143
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