时频分辨与参数估计的理论分析及算法研究
发布时间：2018-10-05 11:48
【摘要】：时频域交叠的信号分辨及参数估计问题出现在很多应用场合,例如雷达、无线通信、水声、地震波等等。早在20世纪50年代,这一问题就引起了国外学者的关注,并进行了一系列理论分析及实现方法研究,到目前为止,已有许多对多目标时频分辨及相关参数估计的研究见诸报道。随着科技进步及应用需求的提高,对多目标时频分辨及相关参数的估计也提出了更高的要求,以进行更为准确的跟踪和定位等。本文正是针对这一问题进行了理论上的分析,并提出一些解决方法。首先进行了时频分辨及参数估计的理论分析,在第二章中,对时频参数估计问题进行了比较全面的理论推导,得出了相关参数的最大似然估计及克拉美罗界,推导了多脉冲信号及多频信号相关参数的最大似然估计及克拉美罗界。从推导的结论中我们可以看到：对于脉冲信号,其脉冲时延估计精度受到信噪比SNR的影响,但是更重要的是其波形的相关特性,特别是当各脉冲信号在时域交叠时,相关特性对于估计精度的影响是决定性的；对于多频信号,在观察时间T足够长的前提下,各个频率信号之间是近似正交的,其频率估计的CRLB等于单频信号的估计。但是当时频及其他参数一起估计时,我们就很难得出其参数MLE的表达式,进而也无法得到相关参数的CRLB。在第三章中,我们对各种条件下的检测问题进行了理论分析。求得了多脉冲及多频信号的最大似然比检测器结构,并求得了相应的检测概率PD和虚警概率PFA。同样的,当时频及其他参数一起估计时,由于其各参数的MLE无法得到,进而也无法得出检测器的具体结构。在第四章中,针对多脉冲的分辨估计提出了两种解决方法,首先是使用内点法等最优化类算法来求解近距离脉冲分辨问题,获得了较好的效果,但是由于此类算法易收敛至局部最优点这一局限性,所以要结合其他传统方法来进行预处理。随后,我们又提出了一种基于泰勒级数展开的快速解法,并结合CLEAN算法的迭代处理思想,很好的完成了参数估计及近距离脉冲的分辨工作,且在处理过程中不需要提前预知目标的个数,也就是说本算法将检测和估计功能结合在了一起。此外,当脉冲非理想采样,该算法也能很好的估计出非整点的采样时延。在第五章中主要针对多频分辨及参数估计问题进行了研究。首先我们利用拟合的方法及对接收信号预处理,随后结合MUSIC及ESPRIT算法进行频率分辨估计。在选择拟合阶数的问题上,我们提出了一种改进的差分广义似然比检测(IDGLRT)的拟合阶数求解办法,相对比最优拟合而言,该IDGLRT方法在选择拟合阶数时要相对保守些,在中低信噪比区间上拟合误差要稍高一些,但在高信噪比区间上,相比未经拟合的数据有明显的性能改善。最后,我们对主要研究工作及创新进行了归纳和总结,并指出了工作的不足及发展方向。
[Abstract]:The problem of signal resolution and parameter estimation in time-frequency domain overlaps appears in many applications, such as radar, wireless communication, underwater acoustic, seismic wave and so on. As early as the 1950s, this problem has attracted the attention of foreign scholars, and a series of theoretical analysis and implementation methods have been studied. Up to now, there have been many reports on the time-frequency resolution of multi-targets and related parameter estimation. With the development of science and technology and the improvement of application demand, higher requirements are put forward for multi-target time-frequency resolution and estimation of related parameters in order to track and locate more accurately. This paper analyzes the problem in theory and puts forward some solutions. Firstly, the time-frequency resolution and parameter estimation are analyzed. In the second chapter, the theoretical derivation of time-frequency parameter estimation is made, and the maximum likelihood estimation and Clemero bound of the related parameters are obtained. The maximum likelihood estimation and Clemero bound of the correlation parameters of multi-pulse signal and multi-frequency signal are derived. From the deduced conclusion, we can see that the accuracy of pulse delay estimation is affected by signal-to-noise ratio (SNR) for pulse signal, but more important is the correlation characteristic of its waveform, especially when each pulse signal overlaps in time domain. The correlation characteristic is decisive to the estimation accuracy, and for the multi-frequency signal, the CRLB of the frequency estimation is equal to that of the single-frequency signal under the condition that the observation time T is long enough. But when the frequency and other parameters are estimated together, it is very difficult to get the expression of the parameter MLE, and then we can not get the CRLB. of the related parameter. In the third chapter, we analyze the detection problem under various conditions. The maximum likelihood ratio detector structure of multi-pulse and multi-frequency signals is obtained, and the corresponding detection probability PD and false alarm probability PFA. are obtained. Similarly, when the frequency and other parameters are estimated together, the MLE of each parameter can not be obtained and the structure of the detector can not be obtained. In the fourth chapter, two methods are proposed for the resolution estimation of multi-pulse. Firstly, the interior point method and other optimization algorithms are used to solve the short-range pulse resolution problem, and good results are obtained. However, due to the limitation that this algorithm converges to the local optimum, it is necessary to combine other traditional preprocessing methods. Then, we propose a fast solution based on Taylor series expansion, and combine with the iterative processing idea of CLEAN algorithm, we have completed the parameter estimation and the resolution of the short distance pulse. In the process of processing, there is no need to predict the number of targets in advance, that is to say, the detection and estimation functions are combined in this algorithm. In addition, when the pulse is not ideal sampling, the algorithm can also estimate the sampling time delay of non-whole point. In chapter 5, the problem of multi-frequency resolution and parameter estimation is studied. First, we preprocess the received signal by fitting method, and then we use MUSIC and ESPRIT algorithm to estimate the frequency resolution. In the problem of selecting fitting order, we propose an improved method to solve the fitting order of differential generalized likelihood ratio detection (IDGLRT). Compared with the optimal fitting, the IDGLRT method is relatively conservative in selecting the fitting order. The fitting error is slightly higher in the low signal-to-noise ratio range, but in the high signal-to-noise ratio range, the performance of the unfitted data is obviously improved. Finally, we summarized the main research work and innovation, and pointed out the shortcomings and development direction of the work.
【学位授予单位】：东南大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TN911.23
[Abstract]:The problem of signal resolution and parameter estimation in time-frequency domain overlaps appears in many applications, such as radar, wireless communication, underwater acoustic, seismic wave and so on. As early as the 1950s, this problem has attracted the attention of foreign scholars, and a series of theoretical analysis and implementation methods have been studied. Up to now, there have been many reports on the time-frequency resolution of multi-targets and related parameter estimation. With the development of science and technology and the improvement of application demand, higher requirements are put forward for multi-target time-frequency resolution and estimation of related parameters in order to track and locate more accurately. This paper analyzes the problem in theory and puts forward some solutions. Firstly, the time-frequency resolution and parameter estimation are analyzed. In the second chapter, the theoretical derivation of time-frequency parameter estimation is made, and the maximum likelihood estimation and Clemero bound of the related parameters are obtained. The maximum likelihood estimation and Clemero bound of the correlation parameters of multi-pulse signal and multi-frequency signal are derived. From the deduced conclusion, we can see that the accuracy of pulse delay estimation is affected by signal-to-noise ratio (SNR) for pulse signal, but more important is the correlation characteristic of its waveform, especially when each pulse signal overlaps in time domain. The correlation characteristic is decisive to the estimation accuracy, and for the multi-frequency signal, the CRLB of the frequency estimation is equal to that of the single-frequency signal under the condition that the observation time T is long enough. But when the frequency and other parameters are estimated together, it is very difficult to get the expression of the parameter MLE, and then we can not get the CRLB. of the related parameter. In the third chapter, we analyze the detection problem under various conditions. The maximum likelihood ratio detector structure of multi-pulse and multi-frequency signals is obtained, and the corresponding detection probability PD and false alarm probability PFA. are obtained. Similarly, when the frequency and other parameters are estimated together, the MLE of each parameter can not be obtained and the structure of the detector can not be obtained. In the fourth chapter, two methods are proposed for the resolution estimation of multi-pulse. Firstly, the interior point method and other optimization algorithms are used to solve the short-range pulse resolution problem, and good results are obtained. However, due to the limitation that this algorithm converges to the local optimum, it is necessary to combine other traditional preprocessing methods. Then, we propose a fast solution based on Taylor series expansion, and combine with the iterative processing idea of CLEAN algorithm, we have completed the parameter estimation and the resolution of the short distance pulse. In the process of processing, there is no need to predict the number of targets in advance, that is to say, the detection and estimation functions are combined in this algorithm. In addition, when the pulse is not ideal sampling, the algorithm can also estimate the sampling time delay of non-whole point. In chapter 5, the problem of multi-frequency resolution and parameter estimation is studied. First, we preprocess the received signal by fitting method, and then we use MUSIC and ESPRIT algorithm to estimate the frequency resolution. In the problem of selecting fitting order, we propose an improved method to solve the fitting order of differential generalized likelihood ratio detection (IDGLRT). Compared with the optimal fitting, the IDGLRT method is relatively conservative in selecting the fitting order. The fitting error is slightly higher in the low signal-to-noise ratio range, but in the high signal-to-noise ratio range, the performance of the unfitted data is obviously improved. Finally, we summarized the main research work and innovation, and pointed out the shortcomings and development direction of the work.
【学位授予单位】：东南大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TN911.23
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