基于匹配滤波器组理论的参数估计迭代方法研究

发布时间：2018-06-12 06:29

本文选题：参数估计 + 频率估计　；参考：《哈尔滨工业大学》2015年博士论文

【摘要】：长期以来,谐波信号频率和阵列信号波达方向等特征参数估计在语音处理、振动工程、雷达、通信、生物医学、地震勘探等领域得到广泛应用。实际应用中对特征参数估计方法的精度、分辨率和计算效率的高性能要求,一直是无法回避的研究挑战。但是由于观测数据中随机噪声成分的存在,通常采取概率密度函数或功率谱密度等统计特性实现特征参数估计。为了获得较高精度的特征参数估计结果,具有较高谱分辨率性能的现代谱估计方法成为首要选择。其中,基于匹配滤波器组理论(Matched Filter bank theory,MAFI)的谱估计方法通过匹配滤波抑制随机噪声来得到较高的谱分辨率,因为无需数据建模而适用性更强。本文以MAFI理论为基础,着力于研究匹配滤波器迭代求解算法和特征参数估计迭代实现方法,以达到在提升滤波器谱分辨率性能和参数估计精度的同时,提升计算效率的目的。本文的主要研究内容如下:(1)针对滤波器优化设计问题开展了滤波器迭代求解方法研究。更高阶次的匹配滤波器具有较高的谱分辨率性能,是获得较高的参数估计精度的重要前提。但受到观测数据长度的限制,存在满秩和秩亏协方差矩阵两种情况。传统方法根据矩阵是否满秩分别处理,现有的迭代求解方法迭代次数较多,所需计算消耗繁重。本文基于凸二次规划理论对滤波器优化设计问题进行再描述,分别采取优化问题简化和变量约减的方式来回避矩阵求逆和矩阵分解运算,提出滤波器迭代求解算法(Conjugate Gradient method for Convex Quadratic Problem,CG-CQP)和(New Iterative Algorithm for Rank-Deficient matrix,NIARD),为滤波器求解提供通用解决方案。实验分析过程中,对于相同精度的滤波器解,新算法所需的迭代次数仅为现有迭代方法的1/25~1/8左右,所需计算消耗仅为后者的4%~18%左右,具有更高的计算效率。(2)针对多成分谐波信号频率估计中的谱峰衰减和有偏估计问题开展研究。特征参数估计由预先划分的均匀搜索格点上的谱峰方位得到,为了追求更高的计算效率,现有方法在稀疏的搜索格点上进行周期图谱谱峰搜索,存在谱峰衰减和有偏估计问题,而且对多成分信号适用性不佳。本文首先严格推导了基于典型相关分析(Canonical Correlation Analysis,CCA)的功率谱,对相邻信号成分区分能力较强且谱峰衰减较小,适用于多成分信号的谱峰粗搜索过程;然后提出一种结合谱峰粗搜索和细化搜索的两步式频率估计方法(Dichotomous Search for Spectral Peaks,DSSP),采取较高谱分辨率的MAFI谱在谱峰邻域内进行二分法细化搜索来提升估计精度。实验分析表明,DSSP算法在有效缓解了谱峰衰减和有偏估计问题的同时,所需计算消耗仅为传统实现方法的1/50-1/40。另外,利用幅度平方相干谱的DSSP算法可以在强噪声背景下对微弱谐波信号频率进行估计。(3)针对多成分谐波频率估计所需的繁重计算消耗问题开展频率估计迭代实现方法研究。因为搜索格点划分缺乏先验知识,传统方法通过增加格点划分密度来提升估计精度。本文基于MAFI功率谱构造标量指标函数,通过求解指标函数局部极小值点实现谐波频率估计。基于MAFI功率谱和最速下降法提出的局部极小值迭代求解算法(Single local minimum ITERative search,SITER),通过回避传统格点划分和谱峰搜索过程来缓解繁重的计算消耗。而且,论文针对SITER算法对初始值敏感的弊端,分别给出单成分和多成分信号迭代初始值选择策略。实验分析表明,对于相同估计精度,SITER算法所需计算时间仅为传统谱峰搜索方法的2.56%左右,在提高估计精度的同时实现计算效率的提升。(4)针对多成分信号时变频率估计方法实时性差问题开展迭代方法研究。传统时频分析方法存在时频分辨率差和交叉干扰项的弊端,而且二维谱峰搜索过程存在实时性差的问题。因此,本文首先推导得到MAFI时变功率谱,具有较高的时频分辨率和时频聚集性而且不存在交叉项干扰,适用于多成分信号时频分析过程;然后,基于MAFI时变功率谱和SITER算法提出一种时变频率估计迭代算法(Time-variant SITER,T-SITER),对时变频率变化轨迹进行连续追踪。实验分析过程中,在较高估计精度时,T-SITER算法所需的计算消耗仅为二维谱峰搜索的0.067%,从而快速而准确地对频率变化轨迹进行连续估计。
[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.
【学位授予单位】：哈尔滨工业大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TN911.23;TN713

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