多项式相位信号的检测和参数估计

发布时间：2018-11-22 10:14

【摘要】：多项式相位信号广泛应用于雷达、声呐、无线通信和地震学等领域,对此,对多项式相位信号的检测和参数估计是一个具有重要理论意义和重要应用价值的研究方向。另一方面,噪声在物质世界无处不在,多项式相位信号往往淹没在噪声中,因此,减少多项式相位信号的检测和参数估计的信噪比门限成为许多研究者努力的一个目标。对多项式相位信号的检测和参数估计算法,大致可分为两类,一类是多线性变换,比如高阶模糊函数和它的乘积版本--乘积高阶模糊函数;另一类是相位展开的方式,比如Kitchen’s的相位展开估计算法和Djuric的估计算法。这两类算法都有它们的优点和缺点。在过去二十年里,对于单分量多项式相位信号的检测和参数估计,提出了许多理论和方法,然而这些理论和方法对于处理多分量多项式相位信号有着限制和缺陷,主要是多分量多项式相位信号的处理比单分量复杂得多,因此,结合已有的对多项式相位信号的处理方法,本文展开了如下方面的创新性研究:1、采用稀疏分解对加性高斯白噪声中多项式相位信号进行检测和参数估计。系统研究了在加性高斯白噪声条件下,采用稀疏分解实现对多项式相位信号的最优检测,并结合快速傅里叶变换,提出一种针对多项式相位信号的快速稀疏分解算法,该算法大大降低了参数估计的信噪比门限2、结合字典学习算法和稀疏表示实现对加性高斯白噪声中多项式相位信号的去噪。提出一种能去除多项式相位信号噪声的字典学习算法,用这种算法得到的字典,采用稀疏表示,能有效地提高信噪比。3、分析并解决了乘积三次相位函数与高阶模糊函数(Product Cubic Phase Function and High-order Ambiguity Function,PCPF-HAF)算法在多分量多项式相位信号参数估计中存在的不确定性问题。分析了PCPF-HAF算法在估计多分量多项式相位信号参数的存在的不确定性问题,对于这个问题,提出了两种有效的解决方法,一种采用设定三个时间点的方式,这种方法主要根据分量在三个时间点上所求的频率在同一条直线上;第二种方法采用两个时间点的方式,对于各种可能的最高两阶的相位参数组成的多项式相位信号,把它们与变换后的信号相乘并求和,则求和最大值所对应的参数估计就是正确的参数估计。4、提出了基于PCPF-HAF的优化多分量多项式相位信号参数估计算法为了PCPF-HAF算法能用快速傅里叶变换,提出利用非一致间隔采样方法,并针对多分量的三阶多项式相位信号不能使用多个滞后时间达到相乘的目的,提出采用多个比例因子来达到相乘的目的。在提出的优化算法中,针对滤波/相位展开的改进参数估计算法没有实现对幅值参数的改进,提出采用奇异值分解的方法改进幅值参数的估计。
[Abstract]:Polynomial phase signals are widely used in radar, sonar, wireless communication and seismology. Therefore, the detection and parameter estimation of polynomial phase signals have important theoretical significance and important application value. On the other hand, noise is ubiquitous in the material world and polynomial phase signals are often submerged in noise. Therefore, reducing the signal-to-noise ratio (SNR) threshold of polynomial phase signal detection and parameter estimation has become a goal of many researchers. The detection and parameter estimation algorithms of polynomial phase signal can be divided into two categories: one is multi-linear transformation, such as high-order fuzzy function and its product version-product high-order fuzzy function; The other is phase unwrapping, such as Kitchen's 's phase unwrapping estimation algorithm and Djuric's estimation algorithm. Both algorithms have their advantages and disadvantages. In the past two decades, many theories and methods have been proposed for the detection and parameter estimation of single-component polynomial phase signals. However, these theories and methods have limitations and defects in the processing of multi-component polynomial phase signals. The processing of multi-component polynomial phase signal is much more complicated than that of single component. Therefore, combining with the existing processing methods of polynomial phase signal, the following innovative researches are carried out in this paper: 1. Sparse decomposition is used to detect and estimate polynomial phase signals in additive Gao Si white noise. Under the condition of additive Gao Si white noise, the optimal detection of polynomial phase signal is realized by sparse decomposition, and a fast sparse decomposition algorithm for polynomial phase signal is proposed in combination with fast Fourier transform (FFT). This algorithm greatly reduces the SNR threshold of parameter estimation by 2, and combines dictionary learning algorithm and sparse representation to realize the denoising of polynomial phase signals in additive Gao Si white noise. This paper presents a dictionary learning algorithm which can remove the noise of polynomial phase signal. The dictionary obtained by this algorithm can effectively improve the signal-to-noise ratio (SNR) by using sparse representation. The uncertainty of product cubic phase function and high-order ambiguity function (Product Cubic Phase Function and High-order Ambiguity Function,PCPF-HAF algorithm in multi-component polynomial phase signal estimation is analyzed and solved. This paper analyzes the uncertainty of PCPF-HAF algorithm in estimating the parameters of multi-component polynomial phase signal. For this problem, two effective solutions are proposed, one is to set three time points, and the other is to solve the problem. This method is mainly based on the frequency of the component at three time points in the same line. In the second method, the polynomial phase signals composed of the highest two order phase parameters are multiplied and summed by the transformed signals in two time points. Then the parameter estimation corresponding to the summation maximum value is the correct parameter estimation. 4. An optimized multi-component polynomial phase signal parameter estimation algorithm based on PCPF-HAF is proposed so that the PCPF-HAF algorithm can use fast Fourier transform. A non-uniform interval sampling method is proposed. In view of the fact that multi-component third-order polynomial phase signals can not be multiplied by multiple delay time, multiple scale factors are proposed to multiply each other. In the proposed optimization algorithm, the improved filtering / phase unwrapping parameter estimation algorithm has not realized the improvement of the amplitude parameter, so the singular value decomposition method is proposed to improve the amplitude parameter estimation.
【学位授予单位】：重庆大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TN911.23

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