本文選題：參數(shù)估計 + 頻率估計�。� 參考：《哈爾濱工業(yè)大學》2015年博士論文

【摘要】：長期以來,諧波信號頻率和陣列信號波達方向等特征參數(shù)估計在語音處理、振動工程、雷達、通信、生物醫(yī)學、地震勘探等領(lǐng)域得到廣泛應用。實際應用中對特征參數(shù)估計方法的精度、分辨率和計算效率的高性能要求,一直是無法回避的研究挑戰(zhàn)。但是由于觀測數(shù)據(jù)中隨機噪聲成分的存在,通常采取概率密度函數(shù)或功率譜密度等統(tǒng)計特性實現(xiàn)特征參數(shù)估計。為了獲得較高精度的特征參數(shù)估計結(jié)果,具有較高譜分辨率性能的現(xiàn)代譜估計方法成為首要選擇。其中,基于匹配濾波器組理論(Matched Filter bank theory,MAFI)的譜估計方法通過匹配濾波抑制隨機噪聲來得到較高的譜分辨率,因為無需數(shù)據(jù)建模而適用性更強。本文以MAFI理論為基礎(chǔ),著力于研究匹配濾波器迭代求解算法和特征參數(shù)估計迭代實現(xiàn)方法,以達到在提升濾波器譜分辨率性能和參數(shù)估計精度的同時,提升計算效率的目的。本文的主要研究內(nèi)容如下:(1)針對濾波器優(yōu)化設計問題開展了濾波器迭代求解方法研究。更高階次的匹配濾波器具有較高的譜分辨率性能,是獲得較高的參數(shù)估計精度的重要前提。但受到觀測數(shù)據(jù)長度的限制,存在滿秩和秩虧協(xié)方差矩陣兩種情況。傳統(tǒng)方法根據(jù)矩陣是否滿秩分別處理,現(xiàn)有的迭代求解方法迭代次數(shù)較多,所需計算消耗繁重。本文基于凸二次規(guī)劃理論對濾波器優(yōu)化設計問題進行再描述,分別采取優(yōu)化問題簡化和變量約減的方式來回避矩陣求逆和矩陣分解運算,提出濾波器迭代求解算法(Conjugate Gradient method for Convex Quadratic Problem,CG-CQP)和(New Iterative Algorithm for Rank-Deficient matrix,NIARD),為濾波器求解提供通用解決方案。實驗分析過程中,對于相同精度的濾波器解,新算法所需的迭代次數(shù)僅為現(xiàn)有迭代方法的1/25~1/8左右,所需計算消耗僅為后者的4%~18%左右,具有更高的計算效率。(2)針對多成分諧波信號頻率估計中的譜峰衰減和有偏估計問題開展研究。特征參數(shù)估計由預先劃分的均勻搜索格點上的譜峰方位得到,為了追求更高的計算效率,現(xiàn)有方法在稀疏的搜索格點上進行周期圖譜譜峰搜索,存在譜峰衰減和有偏估計問題,而且對多成分信號適用性不佳。本文首先嚴格推導了基于典型相關(guān)分析(Canonical Correlation Analysis,CCA)的功率譜,對相鄰信號成分區(qū)分能力較強且譜峰衰減較小,適用于多成分信號的譜峰粗搜索過程;然后提出一種結(jié)合譜峰粗搜索和細化搜索的兩步式頻率估計方法(Dichotomous Search for Spectral Peaks,DSSP),采取較高譜分辨率的MAFI譜在譜峰鄰域內(nèi)進行二分法細化搜索來提升估計精度。實驗分析表明,DSSP算法在有效緩解了譜峰衰減和有偏估計問題的同時,所需計算消耗僅為傳統(tǒng)實現(xiàn)方法的1/50-1/40。另外,利用幅度平方相干譜的DSSP算法可以在強噪聲背景下對微弱諧波信號頻率進行估計。(3)針對多成分諧波頻率估計所需的繁重計算消耗問題開展頻率估計迭代實現(xiàn)方法研究。因為搜索格點劃分缺乏先驗知識,傳統(tǒng)方法通過增加格點劃分密度來提升估計精度。本文基于MAFI功率譜構(gòu)造標量指標函數(shù),通過求解指標函數(shù)局部極小值點實現(xiàn)諧波頻率估計�；贛AFI功率譜和最速下降法提出的局部極小值迭代求解算法(Single local minimum ITERative search,SITER),通過回避傳統(tǒng)格點劃分和譜峰搜索過程來緩解繁重的計算消耗。而且,論文針對SITER算法對初始值敏感的弊端,分別給出單成分和多成分信號迭代初始值選擇策略。實驗分析表明,對于相同估計精度,SITER算法所需計算時間僅為傳統(tǒng)譜峰搜索方法的2.56%左右,在提高估計精度的同時實現(xiàn)計算效率的提升。(4)針對多成分信號時變頻率估計方法實時性差問題開展迭代方法研究。傳統(tǒng)時頻分析方法存在時頻分辨率差和交叉干擾項的弊端,而且二維譜峰搜索過程存在實時性差的問題。因此,本文首先推導得到MAFI時變功率譜,具有較高的時頻分辨率和時頻聚集性而且不存在交叉項干擾,適用于多成分信號時頻分析過程;然后,基于MAFI時變功率譜和SITER算法提出一種時變頻率估計迭代算法(Time-variant SITER,T-SITER),對時變頻率變化軌跡進行連續(xù)追蹤。實驗分析過程中,在較高估計精度時,T-SITER算法所需的計算消耗僅為二維譜峰搜索的0.067%,從而快速而準確地對頻率變化軌跡進行連續(xù)估計。
[Abstract]:For a long time, the parameter estimation of the frequency of harmonic signal and the direction of arrival of the array signal is widely used in the fields of speech processing, vibration engineering, radar, communication, biomedicine, seismic exploration and so on. In practical application, the precision, resolution and efficiency of the method of characteristic parameter estimation have always been an unavoidable research. However, due to the existence of random noise components in the observation data, we usually adopt the statistical properties of the probability density function or the power spectral density to estimate the characteristic parameters. In order to obtain the high precision estimation results of the characteristic parameters, the modern spectral estimation method with high spectral resolution performance is the first choice. The spectral estimation method of Matched Filter bank theory (MAFI) is used to suppress random noise by matched filtering to get high spectral resolution, because it does not need data modeling and is more applicable. Based on MAFI theory, this paper focuses on the iterative method of iterative algorithm and characteristic parameter estimation of matched filter, which is based on MAFI theory. In order to improve the resolution performance of the filter spectrum and the precision of parameter estimation, the main research contents of this paper are as follows: (1) the filter iterative solution method for filter optimization design is studied. The higher order matching filter has higher spectral resolution performance and is a higher parameter. There are two cases of full rank and rank deficiency covariance matrix under the limit of the length of the observed data. The traditional methods are processed according to the full rank of the matrix, and the number of iterations of the existing iterative methods is more, and the required calculation is heavy. Based on the convex two times programming theory, the filter optimization design is asked. The problem is re described, and the method of optimization problem simplification and variable reduction is adopted to avoid matrix inversion and matrix decomposition operation. The filter iterative solution algorithm (Conjugate Gradient method for Convex Quadratic Problem, CG-CQP) and (New Iterative Algorithm for) are provided for the filter solution. General solution. In the process of experimental analysis, the number of iterations needed for the new algorithm for the same precision is only about 1/25~1/8 of the existing iterative method. The required calculation consumption is only about 4%~18% of the latter, and has higher computational efficiency. (2) the spectral peak attenuation and biased estimation in the frequency estimation of multicomponent harmonic signals are used. The characteristic parameters are estimated by the azimuth of the spectral peaks on the pre divided uniform search lattice. In order to pursue higher computing efficiency, the existing methods carry out the periodic spectrum peak search on the sparse search lattice, have the problem of spectral peak attenuation and biased estimation, and are not suitable for the multicomponent signal. The power spectrum based on Canonical Correlation Analysis (CCA) is derived, which has a strong ability to distinguish the adjacent signal components and less peak attenuation. It is suitable for the spectrum peak search process of multicomponent signals, and then a two step frequency estimation method (Dichotomous Search for, which combines spectral peak rough search and thinning search) is proposed. Spectral Peaks, DSSP), using a MAFI spectrum with high spectral resolution to improve the estimation precision in the spectral peak neighborhood, the experimental analysis shows that the DSSP algorithm is effective in alleviating the spectral peak attenuation and biased estimation, while the required computation cost is only 1/50-1/40. of the traditional method, and the amplitude squared coherence is used. The spectral DSSP algorithm can estimate the frequency of weak harmonic signal in strong noise background. (3) to study the iterative realization method of frequency estimation for the heavy computing consumption problem required by the multicomponent harmonic frequency estimation. Because the search lattice division lacks prior knowledge, the traditional square method improves the estimation precision by increasing the density of the lattice point division. In this paper, based on the MAFI power spectrum construction scalar index function, the harmonic frequency estimation is realized by solving the local minimum point of the index function. The local minimum iterative solution algorithm based on the MAFI power spectrum and the fastest descent method (Single local minimum ITERative search, SITER) is avoided by avoiding the traditional lattice division and the spectrum peak search process. To alleviate the heavy computing consumption, the paper gives the initial value selection strategy of the single component and multi component signal for the SITER algorithm, which is sensitive to the initial value. The experimental analysis shows that for the same estimation accuracy, the calculation time of the SITER algorithm is only about 2.56% of the traditional spectral peak search method, and the estimation accuracy is improved. At the same time, the calculation efficiency is promoted. (4) the iterative method is used to study the problem of real time difference of the time-frequency estimation method of multicomponent signals. The traditional time-frequency analysis method has the disadvantages of the time frequency resolution and the cross interference, and the two dimensional peak search process has the problem of poor real-time performance. Therefore, this paper first derives the MAFI time. The variable power spectrum, with high time-frequency resolution and time frequency aggregation and no cross term interference, is suitable for the time-frequency analysis of multicomponent signals; then, a time-varying frequency estimation iterative algorithm (Time-variant SITER, T-SITER) is proposed based on the MAFI time-varying power spectrum and SITER algorithm, and the time-varying frequency change trajectory is continuously traced. In the process of experimental analysis, the calculation consumption required by the T-SITER algorithm is only 0.067% of the two-dimensional spectral peak search in the high estimation accuracy, thus the continuous estimation of the frequency change trajectory is fast and accurate.
【學位授予單位】：哈爾濱工業(yè)大學
【學位級別】：博士
【學位授予年份】：2015
【分類號】：TN911.23;TN713

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