時(shí)頻分辨與參數(shù)估計(jì)的理論分析及算法研究
發(fā)布時(shí)間：2018-10-05 11:48
【摘要】：時(shí)頻域交疊的信號(hào)分辨及參數(shù)估計(jì)問(wèn)題出現(xiàn)在很多應(yīng)用場(chǎng)合,例如雷達(dá)、無(wú)線通信、水聲、地震波等等。早在20世紀(jì)50年代,這一問(wèn)題就引起了國(guó)外學(xué)者的關(guān)注,并進(jìn)行了一系列理論分析及實(shí)現(xiàn)方法研究,到目前為止,已有許多對(duì)多目標(biāo)時(shí)頻分辨及相關(guān)參數(shù)估計(jì)的研究見(jiàn)諸報(bào)道。隨著科技進(jìn)步及應(yīng)用需求的提高,對(duì)多目標(biāo)時(shí)頻分辨及相關(guān)參數(shù)的估計(jì)也提出了更高的要求,以進(jìn)行更為準(zhǔn)確的跟蹤和定位等。本文正是針對(duì)這一問(wèn)題進(jìn)行了理論上的分析,并提出一些解決方法。首先進(jìn)行了時(shí)頻分辨及參數(shù)估計(jì)的理論分析,在第二章中,對(duì)時(shí)頻參數(shù)估計(jì)問(wèn)題進(jìn)行了比較全面的理論推導(dǎo),得出了相關(guān)參數(shù)的最大似然估計(jì)及克拉美羅界,推導(dǎo)了多脈沖信號(hào)及多頻信號(hào)相關(guān)參數(shù)的最大似然估計(jì)及克拉美羅界。從推導(dǎo)的結(jié)論中我們可以看到：對(duì)于脈沖信號(hào),其脈沖時(shí)延估計(jì)精度受到信噪比SNR的影響,但是更重要的是其波形的相關(guān)特性,特別是當(dāng)各脈沖信號(hào)在時(shí)域交疊時(shí),相關(guān)特性對(duì)于估計(jì)精度的影響是決定性的；對(duì)于多頻信號(hào),在觀察時(shí)間T足夠長(zhǎng)的前提下,各個(gè)頻率信號(hào)之間是近似正交的,其頻率估計(jì)的CRLB等于單頻信號(hào)的估計(jì)。但是當(dāng)時(shí)頻及其他參數(shù)一起估計(jì)時(shí),我們就很難得出其參數(shù)MLE的表達(dá)式,進(jìn)而也無(wú)法得到相關(guān)參數(shù)的CRLB。在第三章中,我們對(duì)各種條件下的檢測(cè)問(wèn)題進(jìn)行了理論分析。求得了多脈沖及多頻信號(hào)的最大似然比檢測(cè)器結(jié)構(gòu),并求得了相應(yīng)的檢測(cè)概率PD和虛警概率PFA。同樣的,當(dāng)時(shí)頻及其他參數(shù)一起估計(jì)時(shí),由于其各參數(shù)的MLE無(wú)法得到,進(jìn)而也無(wú)法得出檢測(cè)器的具體結(jié)構(gòu)。在第四章中,針對(duì)多脈沖的分辨估計(jì)提出了兩種解決方法,首先是使用內(nèi)點(diǎn)法等最優(yōu)化類算法來(lái)求解近距離脈沖分辨問(wèn)題,獲得了較好的效果,但是由于此類算法易收斂至局部最優(yōu)點(diǎn)這一局限性,所以要結(jié)合其他傳統(tǒng)方法來(lái)進(jìn)行預(yù)處理。隨后,我們又提出了一種基于泰勒級(jí)數(shù)展開(kāi)的快速解法,并結(jié)合CLEAN算法的迭代處理思想,很好的完成了參數(shù)估計(jì)及近距離脈沖的分辨工作,且在處理過(guò)程中不需要提前預(yù)知目標(biāo)的個(gè)數(shù),也就是說(shuō)本算法將檢測(cè)和估計(jì)功能結(jié)合在了一起。此外,當(dāng)脈沖非理想采樣,該算法也能很好的估計(jì)出非整點(diǎn)的采樣時(shí)延。在第五章中主要針對(duì)多頻分辨及參數(shù)估計(jì)問(wèn)題進(jìn)行了研究。首先我們利用擬合的方法及對(duì)接收信號(hào)預(yù)處理,隨后結(jié)合MUSIC及ESPRIT算法進(jìn)行頻率分辨估計(jì)。在選擇擬合階數(shù)的問(wèn)題上,我們提出了一種改進(jìn)的差分廣義似然比檢測(cè)(IDGLRT)的擬合階數(shù)求解辦法,相對(duì)比最優(yōu)擬合而言,該IDGLRT方法在選擇擬合階數(shù)時(shí)要相對(duì)保守些,在中低信噪比區(qū)間上擬合誤差要稍高一些,但在高信噪比區(qū)間上,相比未經(jīng)擬合的數(shù)據(jù)有明顯的性能改善。最后,我們對(duì)主要研究工作及創(chuàng)新進(jìn)行了歸納和總結(jié),并指出了工作的不足及發(fā)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.
【學(xué)位授予單位】：東南大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2015
【分類號(hào)】：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.
【學(xué)位授予單位】：東南大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2015
【分類號(hào)】：TN911.23
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5 何姣s，
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