基于线性正则变换的QFM信号参数估计理论与方法研究

发布时间：2018-05-22 15:14

本文选题：线性正则变换 + 二次调频信号　；参考：《北京理工大学》2014年博士论文

【摘要】：二次调频信号是在自然界和工程技术领域中都有着广泛存在的一种非平稳信号，噪声背景中二次调频信号的时频分析及参数估计是它在实际应用中需要解决的共性问题。因此对二次调频信号的检测和参数估计问题进行研究具有重要理论意义和实际应用价值。传统的二次调频信号参数估计算法主要通过高阶次的非线性变换进行降阶，进而使用已有的或构造新的时频分布估计参数。但这类算法的高阶次非线性变换会带来较高的信噪比门限和较低的输出信噪比，或者运算量较大。线性正则变换作为Fourier变换、分数阶Fourier变换的推广形式，具有三个自由参数，因而灵活性更强，并且具有快速算法，故变换的运算量较低。为丰富和发展线性正则变换的基础理论和探讨高性能的二次调频信号参数估计算法，，本文结合线性正则变换在信号处理方面的优势和特点，构造基于线性正则变换的新的时频分布，研究它们的相关理论，并探讨相关理论成果在二次调频信号参数估计中的应用。主要的贡献及创新性成果如下： 1、为深入研究二次调频信号参数估计问题，本文首先研究了线性正则变换的相关基础理论。首先提出了基于线性正则变换的模糊函数，对它的相关特征性质作了深入的分析和研究；进一步考察了基于线性正则变换的模糊函数与其它时频分析工具之间的关系，发现一些常用的时频分布可以由基于线性正则变换的模糊函数来表示；给出了常见信号的基于线性正则变换的模糊函数。对于信号线性正则变换后的模糊函数，研究了它的卷积性、乘积性及相关性等特性。再次，提出基于线性正则变换的Wigner-Ville分布这一新的时频分布，推导了它的一些新的重要性质，研究了与其它时频分析方法之间的关系，并对常见信号的基于线性正则变换的Wigner-Ville分布进行了分析等。最后，针对二维线性正则变换，在给出它的一些常用性质的基础上，提出了二维线性正则域的卷积、乘积理论，并通过实例验证了二维线性正则变换的数值计算，分析了二维线性正则变换的运算量。上述线性正则变换的基本理论的建立，一方面进一步丰富了线性正则变换的理论体系，另一方面也为研究二次调频信号的参数估计算法奠定了相关理论基础。 2、提出了基于广义线性正则变换的二次调频信号参数估计算法。在线性正则变换的定义中用信号的四阶非线性变换来代替信号本身，提出了广义线性正则变换，并用其来估计二次调频信号的三阶相位系数；从均方误差、输出信噪比及运算量等角度研究了本算法的性能，并从这三个方面与现有的四阶非线性变换算法相比较。结果显示，与其它算法相比，本算法的均方误差具有更低的信噪比门限；当输入信噪比满足一定条件时，本算法的输出信噪比要高于其它常见四阶非线性变换算法，并且要达到同样大小的输出信噪比，本算法所需的采样点比其它算法少很多。由于本算法只需一维搜索且线性正则变换具有快速算法，本算法的运算量较低，具有较高运算效率。 3、提出了基于线性正则变换的模糊函数的二次调频信号参数估计算法。基于线性正则变换的模糊函数对二次调频信号具有良好的聚焦特性，利用这种聚焦性估计信号的二阶相位系数和三阶相位系数，进而利用Dechirp技术和Fourier变换估计一阶相位系数和幅值。理论分析和仿真结果表明，由于本算法为二阶非线性变换，本算法具有非常低的信噪比门限(-3dB)，相对于具有四阶和六阶非线性变换的算法而言，低信噪比时的估计精度大大提高；通过分析输入信噪比和输出信噪比的关系发现，在输入信噪比大于-10dB时，本算法的输出信噪比高于基于广义线性正则变换算法、积分广义模糊函数算法和多项式相位变换等算法；当输入信噪比大于7dB时，要达到同样大小的输出信噪比，本算法所需采样点数分别是广义线性正则变换算法、积分广义模糊函数算法和多项式相位算法的采样点的1/2左右、1/4左右和1/9左右。这说明，在达到相同大小的输出信噪比时，本算法所需的采样点数更少。由于本算法能一次估计出三个参数，高阶相位系数对低阶相位系数误差传递小，使得低阶系数的估计值更为准确。
[Abstract]:The two frequency modulation signal is a non-stationary signal which exists widely in the field of nature and engineering technology. The time frequency analysis and parameter estimation of the two frequency modulation signal in the noise background are the common problems which it needs to be solved in the practical application. Therefore, it is important to study the detection and parameter estimation of the two frequency modulation signals. Theoretical significance and practical application value.
The traditional two frequency modulation signal parameter estimation algorithm mainly uses the higher order nonlinear transformation to reduce the order, and then uses the existing or constructs the new time-frequency distribution estimation parameters. However, the high order nonlinear transformation of this kind of algorithm will bring high signal to noise ratio threshold and lower output signal to noise ratio, or a large amount of operation. As Fourier transform, the generalized form of fractional order Fourier transform has three free parameters, so it is more flexible and has a fast algorithm, so the computation of the transformation is low. The basic theory of the linear regular transformation and the two frequency modulation parameter estimation algorithm for high performance are discussed. In the light of the advantages and characteristics of signal processing, a new time-frequency distribution based on linear regular transformation is constructed, their related theories are studied, and the application of relevant theoretical results to the estimation of the parameters of the two frequency modulation signal is discussed. The main contributions and innovative results are as follows:
1, in order to study the parameter estimation of two frequency modulation signals, the basic theory of linear regular transformation is first studied. First, a fuzzy function based on linear regular transformation is proposed, and the characteristic properties of the linear regular transform are deeply analyzed and studied; and the fuzzy function and other time based on linear regular transformation are further investigated. The relationship between frequency analysis tools shows that some commonly used time frequency distributions can be expressed by fuzzy functions based on linear regular transformation, and a fuzzy function based on linear regular transformation of common signals is given. The convolution, product property and correlation properties of the fuzzy functions after the linear regular transformation of signals are studied. In this paper, the new time frequency distribution of Wigner-Ville distribution based on linear regular transformation is proposed, and some new important properties are derived. The relationship between the time frequency analysis method and the other time-frequency analysis methods is studied. The Wigner-Ville distribution based on the linear regular transformation of the common signals is analyzed. Finally, the two dimensional linear regular transformation is given. On the basis of some of its common properties, the convolution and product theory of two-dimensional linear regular domain is proposed, and the numerical calculation of the two-dimensional linear regular transformation is verified by an example. The computation of the two-dimensional linear regular transformation is analyzed. The basic theory of the above linear regular transformation is established. On the one hand, it enriches the linear regular transformation further. The theoretical system, on the other hand, has laid a theoretical foundation for studying the parameter estimation algorithm of the two frequency modulation signal.
2, a parameter estimation algorithm for two frequency modulation signals based on generalized linear regular transformation is proposed. In the definition of linear regular transformation, the four order nonlinear transformation of signal is used to replace the signal itself. A generalized linear regular transformation is proposed, which is used to estimate the three phase coefficient of the two frequency modulation signal, and the signal to noise ratio is output from the mean square error and the signal to noise ratio. The performance of this algorithm is studied and compared with the existing four order nonlinear transformation algorithms. The results show that the mean square error of this algorithm has a lower SNR threshold compared with other algorithms. When the input signal to noise ratio satisfies certain conditions, the output signal to noise ratio of this algorithm is higher than that of the other four other four common algorithms. In order to achieve the same size of the output signal to noise ratio of the same size, the algorithm needs less sampling points than other algorithms. Because this algorithm only needs one dimension search and the linear regular transformation has a fast algorithm, the algorithm has low computation and high operation efficiency.
3, a parameter estimation algorithm for the two frequency modulation signal of fuzzy function based on linear regular transformation is proposed. The fuzzy function based on linear regular transform has good focusing characteristic on the two frequency modulation signal. The two order phase coefficient and the three order phase number of the signal are estimated by this focus, and then the Dechirp technology and the Fourier transform are used to estimate the signal. The theoretical analysis and simulation results show that this algorithm has a very low signal to noise ratio threshold (-3dB) because this algorithm is a two order nonlinear transformation. Compared with the four order and six order nonlinear transformation algorithms, the estimated precision of the low signal to noise ratio is greatly improved, and the input signal to noise ratio and the output signal are analyzed. When the input signal-to-noise ratio is greater than -10dB, the output signal-to-noise ratio of this algorithm is higher than that based on the generalized linear regular transform algorithm, the integral generalized fuzzy function algorithm and the polynomial phase transformation algorithm. When the input signal to noise ratio is greater than 7dB, the output signal to noise ratio of the same size should be reached, the number of sampling points required in this algorithm is respectively The sampling points of the generalized linear regular transformation algorithm, the integral generalized fuzzy function algorithm and the polynomial phase algorithm are about 1/2, about 1/4 and 1/9. This shows that the number of sampling points in this algorithm is less when the output signal to noise ratio of the same size is reached. Because this algorithm can estimate three parameters at a time, the high order phase coefficient is to the lower order phase. The transmission error of bit coefficient is small, which makes the estimation value of low order coefficient more accurate.
【学位授予单位】：北京理工大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN911.23

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