CN103281266B

CN103281266B - Pseudo-random Code Phase Modulation sine FM composite signal PN sequence estimation method based on linear model

Info

Publication number: CN103281266B
Application number: CN201310169308.4A
Authority: CN
Inventors: 张天骐; 白娟; 张刚; 邓灵; 李军伟; 潘毅; 杨超三
Original assignee: Chongqing University of Post and Telecommunications
Current assignee: Chongqing University of Post and Telecommunications
Priority date: 2013-05-06
Filing date: 2013-05-06
Publication date: 2016-06-15
Anticipated expiration: 2033-05-06
Also published as: CN103281266A

Abstract

The invention claims a linear model-based method for estimating a pseudo-code sequence of a pseudo-code phase-modulated sinusoidal-frequency-modulated composite signal, which belongs to the field of signal processing. The Jacobi-Anger expansion of the sinusoidal FM signal is carried out, and the nonlinear SFM signal model is transformed into a linear signal model. According to the special symmetric nature of the Bessel function, the non-negative part of the linear signal is taken, and then the pseudo-coded phase modulation signal is compounded. The time-frequency analysis of the pseudo-coded phase-modulated composite signal is carried out by using smooth pseudo-Wigner distribution, and combined with the SVD subspace decomposition method, the cross term and noise are reduced. Calculate the minimum value section of the SPWVD contour map along the frequency axis after SVD denoising enhancement processing, and complete the accurate blind estimation of the PN code sequence of the pseudo-code phase modulation composite signal by detecting the peak position and phase jump information. The method can accurately estimate the PN code under low signal-to-noise ratio, thereby more effectively improving the ability of managing and interfering with the pseudo-code phase-modulated composite signal.

Description

Pseudo-code Sequence Estimation Method Based on Linear Model

技术领域technical field

本发明涉及到信号处理技术领域，尤其是一种基于线性模型的伪码（PN码）调相正弦调频（SFM）复合信号伪码序列估计。The invention relates to the technical field of signal processing, in particular to a linear model-based pseudo code (PN code) phase modulation sinusoidal frequency modulation (SFM) composite signal pseudo code sequence estimation.

背景技术Background technique

针对伪码调相与正弦调频复合信号（PRBC-SFM）参数估计方法正处在研究阶段，由于正弦调频信号的瞬时频率是时间的非线性函数，而且其频谱包含无穷多个频率分量，即其频带宽度为很宽，再用伪码调相进行复合调制，使得这种复合信号的参数检测和估计变得更加复杂和困难。目前还没有文献对PRBC-SFM信号的PN码序列进行估计，而对于PRBC-SFM复合信号而言，伪码特征参数和波形的估计对能否有效管理或干扰该信号至关重要，因此研究PRBC-SFM复合信号伪码序列盲估计具有重要的意义。The parameter estimation method for the pseudo code phase modulation and sinusoidal frequency modulation composite signal (PRBC-SFM) is in the research stage, because the instantaneous frequency of the sinusoidal frequency modulation signal is a nonlinear function of time, and its spectrum contains infinite frequency components, that is, its The frequency bandwidth is very wide, and the pseudo-code phase modulation is used for composite modulation, which makes the parameter detection and estimation of this composite signal more complicated and difficult. At present, there is no literature to estimate the PN code sequence of the PRBC-SFM signal. For the PRBC-SFM composite signal, the estimation of the pseudo-code characteristic parameters and waveform is very important for the effective management or interference of the signal. Therefore, the study of PRBC -Blind estimation of pseudo-code sequences of SFM composite signals is of great significance.

一般地，谱相关方法和时频分析方法是典型的非平稳信号参数估计方法，谱相关方法是一种非线性运算，计算复杂，对于PRBC-SFM复合信号，该方法只适用于信噪比高的情况。时频分析对线性调频信号具有较好的时频聚集性和跟踪瞬时频率的能力，但对于非线性调频信号将失效。（参考文献：赵惠昌，熊刚，杨小牛．基于谱相关的正弦调频脉间伪码调相复合体制侦察信号识别[J]．兵工学报，2006，27（2）:258-264.）Generally, the spectral correlation method and the time-frequency analysis method are typical non-stationary signal parameter estimation methods. The spectral correlation method is a nonlinear operation with complex calculations. For PRBC-SFM composite signals, this method is only suitable for high signal-to-noise ratio Case. Time-frequency analysis has good time-frequency aggregation and the ability to track instantaneous frequency for linear frequency modulation signals, but it will fail for nonlinear frequency modulation signals. (References: Zhao Huichang, Xiong Gang, Yang Xiaoniu. Reconnaissance Signal Recognition of Sine Frequency Modulation Interpulse Pseudo-code Phase Modulation Composite System Based on Spectrum Correlation [J]. Journal of Military Engineering, 2006, 27 (2): 258-264.)

发明内容Contents of the invention

本发明所要解决的技术问题是，建立一种SFM信号的线性模型，提出基于此线性模型的PRBC-SFM复合信号PN码序列估计的方法，解决PRBC-SFM信号伪码序列估计难题，克服传统方法的非线性运算问题，同时降低噪声对PN码序列估计的影响，从而提高PRBC-SFM复合信号PN码序列估计的精度。The technical problem to be solved by the present invention is to set up a linear model of SFM signal, propose a method for PN code sequence estimation of PRBC-SFM composite signal based on this linear model, solve the difficult problem of PRBC-SFM signal pseudo-code sequence estimation, and overcome traditional methods At the same time, it reduces the impact of noise on PN code sequence estimation, thereby improving the accuracy of PN code sequence estimation for PRBC-SFM composite signals.

本发明解决上述技术问题的技术方案是，提出一种基于SFM信号线性模型的PRBC-SFM复合信号伪码序列估计方法，对SFM信号进行Jacobi-Anger展开，将非线性的SFM信号模型转化为线性信号模型，将此线性信号模型与伪码调相信号进行复合调制，即可得到PRBC-SFM复合信号的线性形式。具体包括，将复正弦调频信号s(t)=Aexp{j[ω₀t+m_fsin(ω_mt)]}，利用Jacobi-Anger进一步展为以贝塞尔函数（Bessel函数）为系数的指数级数，即根据第一类Bessel函数特殊的对称性质，取Bessel函数的非负阶数，得到SFM信号的单边线性信号形式其中K为第一类Bessel函数的最高阶数。The technical solution of the present invention to solve the above-mentioned technical problems is to propose a PRBC-SFM composite signal pseudo-code sequence estimation method based on the linear model of the SFM signal, perform Jacobi-Anger expansion on the SFM signal, and convert the nonlinear SFM signal model into a linear Signal model, the linear form of the PRBC-SFM composite signal can be obtained by compounding the linear signal model and the pseudo-code phase modulation signal. Specifically, the complex sinusoidal FM signal s(t)=Aexp{j[ω ₀ t+m _f sin(ω _m t)]} is further expanded into a Bessel function (Bessel function) as a coefficient by using Jacobi-Anger The exponential progression of , that is According to the special symmetric nature of the first kind of Bessel function, the non-negative order of Bessel function is taken to obtain the one-sided linear signal form of SFM signal where K is the highest order of the Bessel function of the first kind.

首先将SFM信号的单边线性信号s′(t)复合伪码调相信号，建立基于SFM信号线性模型的伪码调相复合信号；然后计算该信号的平滑伪维格纳-威利（Wigner-Ville）分布（SPWVD）S_x进行时频分析，为寻找伪码相位跳变点处出现的尖锐负脉冲做好准备；采用基于奇异值分解（SVD）计算S_x的奇异值分解S_x=UΛ_xV^H（其中，U、V为左右奇异矩阵，Λ_x为奇异值对角矩阵，H表示共轭转置），对Λ_x保留第一个最大奇异值，其它奇异值置零得到Λ_x′，在由S_x′=UΛ_x′V^H得到处理后的S_x′；求出S_x′沿频率轴的最小值切面图，在最小值切面图中搜索负尖峰对应的时刻，完成伪码调相复合信号PN码序列的估计。First, the unilateral linear signal s'(t) of the SFM signal is combined with the pseudo-code phase-modulated signal to establish a pseudo-code phase-modulated composite signal based on the linear model of the SFM signal; then the smooth pseudo-Wigner-Willi (Wigner -Ville) distribution (SPWVD) S _x for time-frequency analysis to prepare for looking for sharp negative pulses that appear at the phase jump point of the pseudo-code; use the singular value decomposition based on Singular Value Decomposition (SVD) to calculate S _x S _x = UΛ _x V ^H (where U and V are left and right singular matrices, Λ _x is a diagonal matrix of singular values, and H represents conjugate transpose), the first largest singular value is reserved for Λ _x , and other singular values are set to zero to obtain Λ _x′ , get the processed S _x ′ from S _x′ = UΛ _x′ V ^H ; find the minimum slice diagram of S _x′ along the frequency axis, search for the moment corresponding to the negative peak in the minimum slice diagram, and complete Estimation of the PN code sequence for pseudo-coded phase-modulated composite signals.

为了便于检测这些负脉冲的位置及相位跳变特性，准确提取PN码序列，本发明取SPWVD等高图沿其频率轴的最小值切面图，通过检测最小值切面图中的跳变脉冲的位置，就可以完成PN码（原或反）序列的准确估计。In order to facilitate the detection of the position and phase jump characteristics of these negative pulses, and accurately extract the PN code sequence, the present invention takes the minimum value section diagram of the SPWVD contour map along its frequency axis, and detects the position of the jump pulse in the minimum value section diagram. , the accurate estimation of the PN code (original or reverse) sequence can be completed.

前面所述：将非线性SFM信号模型转化为线性信号模型，具体为：将复正弦调频信号s(t)=Aexp{j[ω₀t+m_fsin(ω_mt)]}，展为以Bessel函数为系数的指数级数，取Bessel函数的非负阶数，得到SFM信号的单边线性信号其中K为第一类Bessel函数的最高阶数，A为常幅度，ω₀为载波角频率，m_f为调制指数，ω_m为调制角频率，J_k(m_f)为载波分量幅度，t为时间。基于SFM线性模型的伪码调相复合信号是将伪码的频率搬移到频率f=f₀+kf_m上，其中，f₀为载波分量，f_m为调制频率，k为第一类Bessel函数的阶数。在此基础上，计算基于SFM线性模型的伪码调相复合信号的SPWVD变换得到信号的时频分布，对信号时频分布进行SVD分解，对奇异值对角矩阵保留第一个最大奇异值，将其它奇异值置零，再恢复处理后的信号时频分布，求处理后信号时频分布的时频面沿频率轴的最小值切面，检测最小值切面的峰值，估计伪码调相复合信号PN码序列。检测最小值切面的峰值具体为：采用门限法，将门限设为切面图中最小值的一半，存在连续的SPWVD值小于门限值的三个时刻点，且满足中间点为局部极小值的位置为最小值切面的峰值。As mentioned above: the nonlinear SFM signal model is converted into a linear signal model, specifically: the complex sinusoidal frequency modulation signal s(t)=Aexp{j[ω ₀ t+m _f sin(ω _m t)]} is expanded as The exponential series with the Bessel function as the coefficient takes the non-negative order of the Bessel function to obtain the unilateral linear signal of the SFM signal where K is the highest order of the Bessel function of the first kind, A is the constant amplitude, ω ₀ is the carrier angular frequency, m _f is the modulation index, ω _m is the modulation angular frequency, J _k (m _f ) is the amplitude of the carrier component, t for time. The pseudo-code phase-modulated composite signal based on the SFM linear model is to move the frequency of the pseudo-code to the frequency f=f ₀ +kf _m , where f ₀ is the carrier component, f _m is the modulation frequency, and k is the first Bessel function of order. On this basis, calculate the SPWVD transformation of the pseudo code phase modulation composite signal based on the SFM linear model to obtain the time-frequency distribution of the signal, perform SVD decomposition on the time-frequency distribution of the signal, and retain the first largest singular value for the singular value diagonal matrix, Set the other singular values to zero, then restore the time-frequency distribution of the processed signal, find the minimum value section of the time-frequency surface of the time-frequency distribution of the processed signal along the frequency axis, detect the peak value of the minimum value section, and estimate the pseudo-code phase-modulated composite signal PN code sequence. The specific method for detecting the peak value of the minimum slice is as follows: using the threshold method, set the threshold to half of the minimum value in the slice graph, there are three consecutive time points when the SPWVD value is less than the threshold value, and the middle point is a local minimum value The location is the peak of the minimum slice.

本发明的有益效果是，采用SFM信号的线性模型，避免非线性运算带来的难题以及带宽问题，采用传统线性调频参数估计的方法就可以完成低信噪比下伪码调相复合信号PN码（原或反）序列的盲估计，从而可以提高该伪码调相复合信号的监测与管理、侦察与干扰、以及相关新体制系统设计的能力，具有广泛的应用前景。The beneficial effect of the present invention is that the linear model of the SFM signal is used to avoid the difficult problems and bandwidth problems caused by nonlinear operations, and the PN code of the pseudo-code phase-modulated composite signal under low signal-to-noise ratio can be completed by using the traditional linear frequency modulation parameter estimation method. The blind estimation of the (original or reverse) sequence can improve the monitoring and management, reconnaissance and jamming of the pseudo-code phase modulation composite signal, as well as the ability of related new system design, and has broad application prospects.

附图说明Description of drawings

图1本发明伪码序列估计方法示意框图；Fig. 1 schematic block diagram of pseudocode sequence estimation method of the present invention;

图2本发明伪码序列估计方法的算法流程框图；Fig. 2 algorithm flow chart of pseudo code sequence estimation method of the present invention;

图3（a）调制指数m_f=1的Bessel函数值；Figure 3(a) Bessel function value of modulation index m _f =1;

图3（b）调制指数m_f=3的Bessel函数值；Figure 3(b) Bessel function value of modulation index m _f =3;

图4本发明所使用的伪码调相SFM复合信号的SPWVD三维图；The SPWVD three-dimensional figure of the pseudo-code phase modulation SFM composite signal used by the present invention of Fig. 4;

图5本发明所使用的伪码调相SFM复合信号的SPWVD等高图；The SPWVD contour map of the pseudocode phase modulation SFM composite signal used by the present invention of Fig. 5;

图6SVD去噪增强处理后的SPWVD等高图Figure 6 SPWVD contour map after SVD denoising enhancement processing

图7SVD去噪增强处理后时频平面的最小值切面图Figure 7 The minimum value section diagram of the time-frequency plane after SVD denoising enhancement processing

图8估计到的伪码调相SFM复合信号的PN码序列Figure 8 The estimated PN code sequence of the pseudo-code phase-modulated SFM composite signal

具体实施方式detailed description

本发明提出一种基于SFM信号线性模型的伪码调相复合信号伪码序列估计方法，对SFM信号进行Jacobi-Anger（第一类贝塞尔函数级数展开）展开，将非线性SFM（正弦调频）信号模型转化为线性信号模型，将此线性信号模型与伪码调相信号复合，得到基于线性模型的复合信号。具体包括，将复正弦调频信号s(t)=Aexp{j[ω₀t+m_fsin(ω_mt)]}，利用Jacobi-Anger进一步展为以Bessel函数为系数的指数级数，即由此可知，SFM信号的频谱包含无穷多个频率分量，理论上其频带宽度为无限宽，但由第一类k阶Bessel函数的性质可知，J_k(m_f)的值随着k的增大而减小，因此只要取适当的k值使得边频分量小到可以忽略的程度，可以近似认为具有有限带宽频谱。但当调制指数m_f很大时，所需边频数也很大，即所需的带宽宽度也会增大。为了减小信号占用的频带宽度，可根据第一类Bessel函数特殊的对称性质，取Bessel函数的非负阶数，得到SFM信号的单边线性信号形式其中K为第一类Bessel函数的最高阶数。The present invention proposes a method for estimating a pseudo-code sequence of a pseudo-code phase-modulated composite signal based on the linear model of the SFM signal. The Jacobi-Anger (bessel function series expansion of the first kind) is performed on the SFM signal, and the nonlinear SFM (sine FM) signal model is transformed into a linear signal model, and the linear signal model is combined with the pseudo code phase modulation signal to obtain a composite signal based on the linear model. Specifically, the complex sinusoidal FM signal s(t)=Aexp{j[ω ₀ t+m _f sin(ω _m t)]} is further expanded into an exponential series with Bessel function as the coefficient by using Jacobi-Anger, namely It can be seen from this that the frequency _spectrum of the _SFM signal contains infinite frequency components, and its frequency bandwidth is theoretically infinite. Therefore, as long as an appropriate k value is taken so that the side frequency components are small enough to be ignored, it can be approximately considered to have a limited bandwidth spectrum. But when the modulation index m _f is very large, the number of required side frequencies is also large, that is, the required bandwidth will also increase. In order to reduce the frequency bandwidth occupied by the signal, according to the special symmetric nature of the first kind of Bessel function, the non-negative order of the Bessel function can be taken to obtain the unilateral linear signal form of the SFM signal where K is the highest order of the Bessel function of the first kind.

首先将SFM信号的单边线性信号s′(t)复合伪码调相信号，建立基于SFM信号线性模型的伪码调相复合信号。然后采用平滑伪Wigner-Ville分布（SPWVD）对该伪码调相复合信号进行时频分析，找到在伪码相位跳变点处出现尖锐的负脉冲，即可估计出所需要的伪码原序列或其反序列。First, the unilateral linear signal s'(t) of the SFM signal is combined with the pseudo-code phase-modulated signal, and the pseudo-code phase-modulated composite signal based on the linear model of the SFM signal is established. Then use the smooth pseudo-Wigner-Ville distribution (SPWVD) to analyze the time-frequency analysis of the pseudo-code phase-modulated composite signal, find the sharp negative pulse at the pseudo-code phase jump point, and then estimate the required pseudo-code original sequence or its inverse sequence.

但在较低信噪比下，该伪码调相复合信号的伪码相位信息将被噪声所淹没，严重影响伪码序列的估计。采用基于奇异值分解（SVD）的子空间方法，将受噪声污染的复合信号的时频分布分解为对应于信号的子空间和对应于噪声的子空间两部分，利用信号子空间恢复时频分布从而减小噪声的影响，实现低信噪比条件下复合信号的PN码原（或反）序列盲估计。同时，为了便于准确检测信号时频分布负脉冲的位置及相位跳变特性，本发明取SPWVD等高图沿其频率轴的最小值切面图，该最小值切面更清楚地展现了这些负脉冲的位置及相位跳变信息，通过检测最小值切面图中的跳变脉冲的位置，即可完成PN码原（或反）序列的准确估计。But at a low SNR, the pseudo-code phase information of the pseudo-code phase-modulated composite signal will be submerged by noise, which seriously affects the estimation of the pseudo-code sequence. Using the subspace method based on singular value decomposition (SVD), the time-frequency distribution of the noise-contaminated composite signal is decomposed into two parts: the subspace corresponding to the signal and the subspace corresponding to the noise, and the time-frequency distribution is restored using the signal subspace Therefore, the influence of noise is reduced, and the blind estimation of the PN code original (or reverse) sequence of the composite signal under the condition of low signal-to-noise ratio is realized. At the same time, in order to accurately detect the position and phase jump characteristics of the negative pulses in the time-frequency distribution of the signal, the present invention takes the minimum value section diagram of the SPWVD contour map along its frequency axis, and the minimum value section more clearly shows the position of these negative pulses. Position and phase jump information, by detecting the position of the jump pulse in the minimum slice diagram, the accurate estimation of the original (or reverse) sequence of the PN code can be completed.

如前所述，对于复正弦调频信号As mentioned earlier, for a complex sinusoidal FM signal

s(t)=Aexp{j[ω₀t+m_fsin(ω_mt)]}（1）s(t)=Aexp{j[ω ₀ t+m _f sin(ω _m t)]} (1)

式中，A为常幅度，ω₀为载波角频率，m_f为调制指数，ω_m为调制角频率，t为时间变量，j为虚单位。利用Jacobi-Anger展开恒等式where A is the constant amplitude, ω ₀ is the carrier angular frequency, m _f is the modulation index, ω _m is the modulation angular frequency, t is the time variable, and j is the imaginary unit. Expansion of Identities Using Jacobi-Anger

$exp exp ((jz jz sin sin θ θ)) = = {Σ Σ}_{k k = = - - \infty \infty}^{\infty \infty} {J J}_{k k} ((z z)) exp exp ((jkθ jkθ)) - - - - - - ((22))$

式（2）中J_k(z)为第一类k阶Bessel函数，k为Bessel函数的阶数。将式（2）代入式（1），式（1）可以重新表示为In formula (2), J _k (z) is the first kind of k-order Bessel function, and k is the order of Bessel function. Substituting formula (2) into formula (1), formula (1) can be re-expressed as

$s the s ((t t)) {Σ Σ}_{k k = = - - \infty \infty}^{\infty \infty} {AJ AJ}_{k k} (({m m}_{f f})) exp exp {{j j [[(({ω ω}_{00} + + {kω kω}_{m m})) t t]]}} - - - - - - ((33))$

上式中，J_k(m_f)是以调制指数m_f为变量的第一类k阶Bessel函数。In the above formula, J _k (m _f ) is the first kind of k-order Bessel function whose modulation index m _f is a variable.

由式（3）可知，SFM信号可以表示成一系列谐波的线性组合，谐波幅度由第一类Bessel函数确定。式（3）的WVD变换为It can be seen from formula (3) that the SFM signal can be expressed as a linear combination of a series of harmonics, and the amplitude of the harmonics is determined by the Bessel function of the first kind. The WVD transformation of formula (3) is

${W W}_{s the s} ((t t,, ω ω)) = = {&Integral; &Integral;}_{- - \infty \infty}^{\infty \infty} s the s ((t t + + \frac{τ τ}{22})) {s the s}^{* *} ((t t - - \frac{τ τ}{22})) {e e}^{- - jωτ jωτ} d d τ τ = = 22 πA πA {Σ Σ}_{- - \infty \infty}^{\infty \infty} {J J}_{k k} (({m m}_{f f})) δ δ ((ω ω - - {ω ω}_{00} - - {kω kω}_{m m})) - - - - - - ((44))$

上式中，δ(·)是狄拉克冲激函数。由式（4）可知，正弦调频信号的W_s(t,ω)是一组离散的冲激函数，当k=0时就是载波分量f₀，其幅度为J₀(m_f)；当k≠0时，在载波两侧对称地分布上下边频分量f₀±kf_m，以调制频率f_m为间隔，载波分量幅度为J_k(m_f)；由第一类Bessel函数性质J_-k(m_f)=(-1)^kJ_k(m_f)可知，当k为奇数时，上下边频幅度的极性相反；当k为偶数时，上下边频幅度的极性相同。In the above formula, δ(·) is the Dirac impulse function. It can be seen from formula (4) that W _s (t,ω) of the sinusoidal FM signal is a set of discrete impulse functions, when k=0 is the carrier component f ₀ , and its amplitude is J ₀ (m _f ); when k When ≠0, the upper and lower frequency components f ₀ ±kf _m are symmetrically distributed on both sides of the carrier, with the modulation frequency f _m as the interval, and the amplitude of the carrier component is J _k (m _f ); from the property of the Bessel function of the first kind J _-k (m _f )=(-1) ^k J _k (m _f ) It can be seen that when k is an odd number, the polarities of the upper and lower side frequency amplitudes are opposite; when k is an even number, the polarities of the upper and lower side frequency amplitudes are the same.

而且，W_s(t,ω)包含无穷多个频率分量，理论上频带宽度为无限宽。然而实际上边频幅度J₀(m_f)随着k的增大而逐渐减小，因此只要取适当的k值使边频分量小到可以忽略的程度，可以近似认为具有有限频谱。Furthermore, W _s (t,ω) includes an infinite number of frequency components, and theoretically, the frequency bandwidth is infinite. However, in fact, the side frequency amplitude J ₀ (m _f ) gradually decreases with the increase of k, so as long as an appropriate value of k is taken to make the side frequency component small enough to be ignored, it can be approximately considered to have a limited frequency spectrum.

${W W}_{s the s} ((t t,, ω ω)) = = 22 πA πA {Σ Σ}_{k k = = - - K K}^{K K} {J J}_{k k} (({m m}_{f f})) δ δ ((ω ω - - {ω ω}_{00} - - {kω kω}_{m m})) - - - - - - ((55))$

上式中，K为第一类Bessel函数的最高阶数。In the above formula, K is the highest order number of the Bessel function of the first kind.

通常采用频带宽度应包括幅度大于未调载波的10%以上的边频分量，即|J₀(m_f)|≥0.1。当m_f≥1，取边频数K=m_f+1即可。但当调制指数m_f很大时，所需边频数也很大，即所需的带宽宽度也会增大。由第一类Bessel函数特殊的对称性质，本发明仅取Bessel函数的非负阶数，则SFM信号的单边线性信号为：Generally, the frequency bandwidth should include side frequency components whose amplitude is greater than 10% of the unmodulated carrier, that is, |J ₀ (m _f )|≥0.1. When m _f ≥ 1, just take the edge frequency K=m _f +1. But when the modulation index m _f is very large, the number of required side frequencies is also large, that is, the required bandwidth will also increase. By the special symmetry property of the first kind of Bessel function, the present invention only takes the non-negative order of Bessel function, then the one-sided linear signal of SFM signal is:

${s the s}^{' '} ((t t)) = = {Σ Σ}_{k k = = 00}^{K K} {AJ AJ}_{k k} (({m m}_{f f})) exp exp {{j j [[(({ω ω}_{00} + + {kω kω}_{m m})) t t]]}} - - - - - - ((66))$

由此，得到基于该线性模型的一个伪码周期内的伪码调相复合信号为Thus, the pseudo-code phase-modulated composite signal in a pseudo-code period based on the linear model is obtained as

$x x ((t t)) = = p p ((t t)) \cdot &Center Dot; {s the s}^{' '} ((t t)) = = {Σ Σ}_{i i = = 00}^{P P - - 11} {C C}_{i i} ψ ψ ((t t - - {iT iT}_{p p})) \cdot \cdot {Σ Σ}_{k k = = 00}^{K K} {AJ AJ}_{k k} (({m m}_{f f})) exp exp {{j j [[(({ω ω}_{00} + + {kω kω}_{m m})) t t]]}} - - - - - - ((77))$

式中，C_i∈{+1,-1}为PN码序列， $ψ (t) = \{\begin{matrix} 1, & 0 \leq t \leq T_{p} \\ 0, & others \end{matrix}$ 为宽度为T_p的单位子脉冲，P为伪码位数。令In the formula, C _i ∈ {+1,-1} is the PN code sequence, $ψ (t) = \{\begin{matrix} 1, & 0 \leq t \leq T_{p} \\ 0, & others \end{matrix}$ is a unit sub-pulse with a width T _p , and P is the number of pseudocode bits. make

$p p ((t t)) = = {Σ Σ}_{i i = = 00}^{P P - - 11} {C C}_{i i} ψ ψ ((t t - - {iT iT}_{p p})) - - - - - - ((88))$

可以将式（8）看成是P个方波之和，即Equation (8) can be regarded as the sum of P square waves, namely

p(t)=p₀(t)+p₁(t)+…p_P-1(t)（9）p(t)=p ₀ (t)+p ₁ (t)+...p _P-1 (t) (9)

每个方波在不同的时间段，即iT_p<t<(i+1)T_p，0≤i<P-1。则一个周期的PN码p(t)的WVD分布：Each square wave is in a different time period, that is, iT _p <t<(i+1)T _p , 0≤i<P-1. Then the WVD distribution of a period of PN code p(t):

${W W}_{p p} ((t t,, ω ω)) = = {&Integral; &Integral;}_{- - \infty \infty}^{\infty \infty} p p ((t t + + \frac{τ τ}{22})) {p p}^{* *} ((t t - - \frac{τ τ}{22})) {e e}^{- - jωτ jωτ} dτ dτ = = {Σ Σ}_{i i = = 00}^{P P - - 11} {W W}_{{p p}_{i i}} ((t t,, ω ω)) + + 22 Re Re {Σ Σ}_{i i = = 00}^{P P - - 22} {Σ Σ}_{k k = = i i + + 11}^{P P - - 11} {W W}_{{p p}_{i i} {p p}_{k k}} ((t t,, ω ω)) - - - - - - ((1010))$

由式（10）中，和分别为自WVD、互WVD分布。由此可知，该时频平面上将出现交叉项，将会严重影响参数估计。为了减小各个方波间交叉项的影响，可以选用SPWVD对伪码调相信号进行时频分析，SPWVD定义为：From formula (10), and are self-WVD and mutual-WVD distributions, respectively. It can be seen that there will be cross terms on the time-frequency plane, which will seriously affect the parameter estimation. In order to reduce the influence of the cross term between each square wave, SPWVD can be selected to perform time-frequency analysis on the pseudo code phase modulation signal. SPWVD is defined as:

${SPWD SPWD}_{s the s} ((t t,, ω ω)) = = {&Integral; &Integral;}_{- - \infty \infty}^{\infty \infty} {&Integral; &Integral;}_{- - \infty \infty}^{\infty \infty} Φ Φ ((u u,, τ τ)) s the s ((t t - - u u + + \frac{τ τ}{22})) {s the s}^{* *} ((t t - - u u - - \frac{τ τ}{22})) {e e}^{- - jωτ jωτ} dudτ dudτ - - - - - - ((1111))$

上式中，核函数Φ(u,τ)=g(u)h(τ)分别采用时间域g(u)和频率域h(τ)独立的平滑函数，即通过适当调节平滑函数g(u)和h(τ)得到抑制交叉项的SPWVD，使得In the above formula, the kernel function Φ(u,τ)=g(u)h(τ) adopts independent smoothing functions in the time domain g(u) and frequency domain h(τ) respectively, that is, by properly adjusting the smoothing function g(u ) and h(τ) get the SPWVD that suppresses the cross term such that

${SPWVD SPWVD}_{p p} ((t t,, ω ω)) \approx \approx {Σ Σ}_{i i = = 00}^{P P - - 11} {WVD WVD}_{{p p}_{i i}} ((t t,, ω ω)) - - - - - - ((1212))$

则SFM信号的单边线性信号的SPWVD根据式（6）为：Then the SPWVD of the unilateral linear signal of the SFM signal is according to formula (6):

${SPWVD SPWVD}_{{s the s}^{' '}} ((t t,, ω ω)) = = 22 πA πA {Σ Σ}_{k k = = 00}^{K K} {J J}_{k k} (({m m}_{f f})) δ δ ((ω ω - - {ω ω}_{00} - - {kω kω}_{m m})) - - - - - - ((1313))$

由于x(t)=p(t)·s′(t)，则基于SFM线性模型的伪码调相复合信号的SPWVD为p(t)和s′(t)两信号时频分布在频率轴的卷积，即Since x(t)=p(t) s′(t), the SPWVD of the pseudo-code phase-modulated composite signal based on the SFM linear model is that the time-frequency distribution of the two signals p(t) and s′(t) is on the frequency axis the convolution of

${SPWVD SPWVD}_{x x} ((t t,, ω ω)) = = {SPWVD SPWVD}_{p p} ((t t,, ω ω)) &CircleTimes; &CircleTimes; 22 πA πA {Σ Σ}_{k k = = 00}^{K K} {J J}_{k k} (({m m}_{f f})) δ δ ((ω ω - - {ω ω}_{00} - - {kω kω}_{m m}))$

$= = 22 πA πA {Σ Σ}_{k k = = 00}^{K K} {J J}_{k k} (({m m}_{f f})) {SPWVD SPWVD}_{p p} ((t t,, ω ω - - {ω ω}_{00} - - {kω kω}_{m m}))$

$= = 22 πA πA {Σ Σ}_{k k = = 00}^{K K} {J J}_{k k} (({m m}_{f f})) {Σ Σ}_{i i = = 00}^{P P = = 11} {SPWVD SPWVD}_{{p p}_{i i}} ((t t,, ω ω - - {ω ω}_{00} - - {kω kω}_{m m})) - - - - - - ((1414))$

由式（14）可知，基于SFM线性模型的伪码调相复合信号的SPWVD_x(t,ω)是将伪码SPWVD_p(t,ω)的频率搬移到频率f=f₀+kf_m上。From formula (14), it can be seen that the SPWVD _x (t, ω) of the pseudo-code phase-modulated composite signal based on the SFM linear model is to move the frequency of the pseudo-code SPWVD _p (t, ω) to the frequency f=f ₀ +kf _m .

在高信噪比下，观察基于SFM线性模型的伪码调相复合信号的SPWVD三维图，在伪码调相复合信号PN码相位跳变点处均存在一负尖峰，在SPWVD等高图上，在伪码相位跳变点均存在峰值，求出SPWVD值在每一时刻沿频率轴的最小值，得到最小值切面。通过检测最小切面中峰值位置及相位跳变特性，就可以估计伪码调相复合信号PN码原（或反）序列。但随着信噪比的降低，伪码相位跳变信息将被噪声严重影响。为此，采用基于SVD的子空间分解法，将受噪声严重影响的伪码调相复合信号的时频分布分解为对应的信号子空间和对应的噪声子空间，仅利用信号子空间来恢复时频分布从而减小噪声的影响。Under high signal-to-noise ratio, observe the SPWVD three-dimensional map of the pseudo code phase modulation composite signal based on the SFM linear model. There is a negative peak at the PN code phase jump point of the pseudo code phase modulation composite signal. On the SPWVD contour map , there are peaks at the phase jump points of the pseudo-code, and the minimum value of the SPWVD value along the frequency axis at each moment is obtained to obtain the minimum value section. By detecting the peak position and phase jump characteristics in the minimum cut plane, the original (or reverse) sequence of the PN code of the pseudo-code phase-modulated composite signal can be estimated. However, with the reduction of SNR, the phase jump information of the pseudo-code will be seriously affected by the noise. To this end, the subspace decomposition method based on SVD is used to decompose the time-frequency distribution of the pseudo-code phase-modulated composite signal seriously affected by noise into the corresponding signal subspace and the corresponding noise subspace, and only the signal subspace is used to restore the time-frequency distribution. frequency distribution to reduce the influence of noise.

图1示出了基于SFM线性模型的伪码调相复合信号PN码序列估计的基本流程，将含噪的基于SFM线性模型的伪码调相复合信号经过SPWVD，得到减小交叉项的时频分布，再经SVD变换去噪增强处理，进一步抑制交叉项和噪声，进而准确地估计伪码调相复合信号PN码原（或反）序列。Figure 1 shows the basic process of PN code sequence estimation of the pseudo-code phase-modulated composite signal based on the SFM linear model. After the noisy pseudo-code phase-modulated composite signal based on the SFM linear model is subjected to SPWVD, the time-frequency with reduced cross term is obtained. distribution, and then denoised and enhanced by SVD transform to further suppress the cross term and noise, and then accurately estimate the original (or inverse) sequence of the PN code of the pseudo-code phase-modulated composite signal.

图2为本发明算法流程图，计算基于SFM线性模型的伪码调相复合信号的SPWVD变换得到信号的时频分布，该时频分布不仅体现了与伪码有关的参数和载波调制信息，而且对交叉项和噪声也有很好的抑制作用，然后对时频分布进行SVD变换去噪增强处理，消除噪声影响。保留奇异值对角矩阵的第一个最大奇异值，将其他奇异值置零，再恢复出时频分布。求出经SVD去噪增强处理后时频面沿频率轴的最小值切面，通过检测最小值切面的峰值，完成伪码调相复合信号PN码原（或反）序列的估计。Fig. 2 is algorithm flowchart of the present invention, calculates the time-frequency distribution that obtains the time-frequency distribution of signal based on the SPWVD transformation of the pseudo-code phase modulation composite signal of SFM linear model, this time-frequency distribution not only embodies the parameter and carrier modulation information relevant with pseudo-code, and It also has a good suppression effect on cross-terms and noise, and then performs SVD transformation denoising enhancement processing on the time-frequency distribution to eliminate the influence of noise. Retain the first largest singular value of the singular value diagonal matrix, set the other singular values to zero, and restore the time-frequency distribution. Find the minimum value section of the time-frequency surface along the frequency axis after SVD denoising enhancement processing, and complete the estimation of the original (or reverse) sequence of the PN code of the pseudo-code phase modulation composite signal by detecting the peak value of the minimum value section.

图3分别给出了m_f=1和m_f=3的Bessel函数。从图中可以看出，k>m_f+1以上的边频幅度J_k(m_f)均小于0.1，可以忽略不计。Figure 3 shows the Bessel functions of m _f =1 and m _f =3 respectively. It can be seen from the figure that the edge frequency amplitude J _k (m _f ) above k>m _f +1 is less than 0.1 and can be ignored.

假设接收信号是信噪比为SNR=10dB的伪码调相复合信号，从基于SFM线性模型的伪码调相复合信号的WVD、SPWVD等高图可清楚地体现SPWWD对于信号特征的展示以及对交叉项的抑制。图4为基于SFM线性模型的伪码调相复合信号的三维图。在伪码相位跳变点处出现负尖峰，通过检测这些负尖峰，即可得到PN码原（或反）序列的估计。Assuming that the received signal is a pseudo-code phase-modulated composite signal with a signal-to-noise ratio of SNR=10dB, the WVD and SPWVD contour maps of the pseudo-code phase-modulated composite signal based on the SFM linear model can clearly reflect the display of signal characteristics by SPWWD and the Suppression of cross terms. Fig. 4 is a three-dimensional diagram of a pseudo-code phase-modulated composite signal based on the SFM linear model. Negative peaks appear at the jump point of the phase of the pseudo code, and by detecting these negative peaks, the estimation of the original (or reverse) sequence of the PN code can be obtained.

为了进一步详细说明PN码序列估计的具体方法。先对基于SFM线性模型的PN码调相复合信号进行离散化，然后对该离散信号求取其SPWVD，加入归一化零均值复高斯白噪声，信噪比SNR=10dB；In order to further specify the specific method of PN code sequence estimation. First discretize the PN code phase-modulated composite signal based on the SFM linear model, then calculate the SPWVD of the discrete signal, add normalized zero-mean complex Gaussian white noise, and the signal-to-noise ratio SNR=10dB;

伪码调相复合信号的PN码序列，伪码周期均取P=15位。采样率Sa=100位/chip。调频信号载波频率为f₀=0.35，调制指数m_f=3，调制频率f_m=0.03。SFM线性模型的最高阶数K=4，图6为伪码复合信号SPWVD的等高图。图6体现了伪码相位跳变信息以及调频信号的参数特征。For the PN code sequence of the pseudo-code phase-modulated composite signal, the period of the pseudo-code is P=15 bits. Sampling rate Sa=100 bits/chip. The carrier frequency of the FM signal is f ₀ =0.35, the modulation index m _f =3, and the modulation frequency f _m =0.03. The highest order of the SFM linear model is K=4, and Figure 6 is the contour map of the pseudo-code composite signal SPWVD. Figure 6 shows the phase jump information of the pseudocode and the parameter characteristics of the FM signal.

如图7所示为最小值切面图，搜索最小值切面图的尖峰，记录各峰值对应的时刻，假定伪码序列的起始时刻位置t₁和终点时刻位置t_end，同时将t₁和t_end也记为尖峰位置，得到尖峰时刻向量t=[t₁,t₂,t₃,t₄,…,t_end]，其中t₁=0，t_end为一重复周期伪码序列的长度。As shown in Figure 7, it is the minimum slice graph, search for the peaks of the minimum slice graph, and record the time corresponding to each peak, assuming the start time position t ₁ and the end point time position t _end of the pseudocode sequence, and simultaneously set t ₁ and t _end is also recorded as the peak position, and the peak moment vector t=[t ₁ ,t ₂ ,t ₃ ,t ₄ ,…,t _end ] is obtained, where t ₁ =0, and t _end is the length of a repetition period pseudocode sequence.

由于尖峰具有sinc函数形式，检测尖峰个数，只需检测主尖峰，为了有效地检测出主尖峰位置，抑制旁瓣带来的误判，可采用门限法，本发明最优可将门限设为切面图中最小值的一半。判断尖峰可采用以下方法：存在连续的SPWVD值小于门限值的三个时刻点，且满足中间点为局部极小值。Because the peak has a sinc function form, the number of detection peaks only needs to detect the main peak. In order to effectively detect the position of the main peak and suppress the misjudgment caused by the side lobe, the threshold method can be used. The present invention can optimally set the threshold as Half of the minimum value in the slice graph. The following method can be used to judge the peak: there are three consecutive time points when the SPWVD value is less than the threshold value, and the middle point is satisfied as a local minimum value.

下面举例说明PN码序列估计的具体步骤：The following example illustrates the specific steps of PN code sequence estimation:

1)搜索尖峰时刻向量t=[t₁,t₂,t₃,t₄,…,t_end]，计算相邻尖峰的时间间隔，得到时间间隔向量Δt=[Δt₁,Δt₂,△t₃,…](Δt_i=t_i+1-_ti,i=1,2,…,end-1)；1) Search the peak time vector t=[t ₁ ,t ₂ ,t ₃ ,t ₄ ,…,t _end ], calculate the time interval between adjacent peaks, and obtain the time interval vector Δt=[Δt ₁ ,Δt ₂ ,Δt ₃ ,…](Δt _i =t _i+1 - _t i,i=1,2,…,end-1);

2)计算向量Δt的最小值，记为Δt_min，也即伪码码元宽度的估计值 2) Calculate the minimum value of the vector Δt, which is denoted as Δt _min , that is, the estimated value of the pseudocode symbol width

3)根据公式：计算各时间间隔包含的码元数，其中，round(·)表示下取整，得到码元数向量count=[num₁,num₂,…num_end-1]。由于存在0或π的初始相位模糊问题，所以一个伪码周期的伪码原序列估计为：3) According to the formula: Calculate the number of symbols included in each time interval, where round( ) means rounding down to obtain the number of symbols vector count=[num ₁ , num ₂ ,…num _end-1 ]. Due to the initial phase ambiguity problem of 0 or π, the pseudo code original sequence of a pseudo code period is estimated as:

或反序列估计为： or inverse sequence estimated as:

对基于SFM线性模型的伪码复合信号在SNR=0dB下的原PN码序列，获得伪码信号在低信噪比下的SPWVD的最小切面图。在低信噪比下，信号时频分布中伪码相位跳变信息被噪声严重影响，不能准确提取伪码复合信号的伪码信息。为了减小噪声的影响，准确提取伪码相位跳变信息，采用基于SVD的子空间分解法，将计算出的SPWVD时频分布分解为对应的有用信号子空间和噪声的子空间。令S_x=SPWVD_x(t,ω)，表示含有噪声的时频分布，对其进行奇异值分解得到：For the original PN code sequence of the pseudo-code composite signal based on the SFM linear model at SNR=0dB, the minimum section diagram of SPWVD of the pseudo-code signal at low SNR is obtained. Under low signal-to-noise ratio, the pseudo-code phase jump information in the time-frequency distribution of the signal is seriously affected by noise, and the pseudo-code information of the pseudo-code composite signal cannot be accurately extracted. In order to reduce the influence of noise and accurately extract the phase jump information of the pseudo code, the calculated SPWVD time-frequency distribution is decomposed into the corresponding useful signal subspace and noise subspace by using the subspace decomposition method based on SVD. Let S _x =SPWVD _x (t,ω) represent the time-frequency distribution containing noise, and perform singular value decomposition on it to obtain:

S_x=UΛ_xV^H（15）S _x = UΛ _x V ^H (15)

式（15）中，H表示共轭转置，U、V表示左、右奇异矩阵，Λ_x为奇异值对角矩阵，若r=rank(S_x)，则Λ_x可以表示为In formula (15), H represents the conjugate transpose, U and V represent the left and right singular matrices, Λ _x is the diagonal matrix of singular values, if r=rank(S _x ), then Λ _x can be expressed as

${Λ Λ}_{x x} = = diag diag (({σ σ}_{{x x}_{11}} + + {σ σ}_{ω ω}^{22},, {σ σ}_{{x x}_{22}} + + {σ σ}_{ω ω}^{22},, \cdot &Center Dot; \cdot \cdot \cdot &Center Dot;,, {σ σ}_{{x x}_{r r}} + + {σ σ}_{ω ω}^{22},, {σ σ}_{ω ω}^{22},, \cdot \cdot \cdot \cdot \cdot &Center Dot;,, {σ σ}_{ω ω}^{22})) - - - - - - ((1616))$

式（16）中， $σ_{x_{1}} &GreaterEqual; σ_{x_{1}} &GreaterEqual; \cdot \cdot {\cdot σ}_{x_{r}} &GreaterEqual; 0 .$ In formula (16), $σ_{x_{1}} &Greater Equal; σ_{x_{1}} &Greater Equal; &Center Dot; &Center Dot; {\cdot σ}_{x_{r}} &Greater Equal; 0 .$

只保留对角矩阵Λ_x第一个最大奇异值，其它奇异值全部置为0，即有Only keep the first largest singular value of the diagonal matrix Λ _x , and set all other singular values to 0, that is,

${Λ Λ}_{{x x}^{' '}} = = diag diag (({σ σ}_{{x x}_{11}} + + {σ σ}_{ω ω}^{22},, 00,, \cdot \cdot \cdot \cdot \cdot &Center Dot;,, 0,0 0,0,, \cdot &Center Dot; \cdot \cdot \cdot &Center Dot;,, 00)) - - - - - - ((1717))$

对处理后的Λ_x′再利用SVD恢复，即有Use SVD to restore the processed Λ _x′ , that is,

S_x′=UΛ_x′V^H（18）S _x′ = UΛ _x′ V ^H (18)

式（18）中，S_x′为去噪增强后时频平面。取该平面沿频率轴的最小值切面，可以明显看出伪码相位跳变点的位置。In formula (18), S _x′ is the time-frequency plane after denoising enhancement. Taking the minimum value section of the plane along the frequency axis, the position of the phase jump point of the pseudo-code can be clearly seen.

取该平面沿频率轴的最小值切面，根据伪码相位跳变点的位置，搜索负尖峰位置对应的时刻，就可得到时刻向量t=[0,200,300,400,600,700,1100,1400,1500]；时间间隔向量Δt=[200,100,100,200,100,400,300,100]；Δt_min=100，则时间间隔向量所含的码元数向量count={2,1,1,2,1,4,3,1}，估计的伪码序列为原码序列：{+1,+1,-1,+1,-1,-1,+1,-1,-1,-1,-1,+1,+1,+1,-1}或反码序列：{-1,-1,+1,-1,+1,+1,-1,+1,+1,+1,+1,-1,-1,-1,+1}。Take the minimum value section of the plane along the frequency axis, and search for the time corresponding to the negative peak position according to the position of the pseudocode phase jump point, and then you can get the time vector t=[0,200,300,400,600,700,1100,1400,1500]; the time interval vector Δt =[200,100,100,200,100,400,300,100]; Δt _min =100, then the number of code elements contained in the time interval vector count={2,1,1,2,1,4,3,1}, the estimated pseudo-code sequence is the original code sequence : {+1,+1,-1,+1,-1,-1,+1,-1,-1,-1,-1,+1,+1,+1,-1} or inverse Sequence: {-1,-1,+1,-1,+1,+1,-1,+1,+1,+1,+1,-1,-1,-1,+1}.

如图8所示为估计到的伪码调相SFM复合信号的PN码序列。在与原PN码序列进行比较后表明，本发明提出的方法能较好地抑制噪声的影响，准确地估计伪码复合信号的PN码（原或反）序列。利用本发明提出的方法，可以抑制伪码复合信号时频分布中的交叉项和噪声，从而可以提高伪码复合信号PN码原（或反）序列估计精度。Figure 8 shows the estimated PN code sequence of the pseudo-code phase-modulated SFM composite signal. After comparing with the original PN code sequence, it is shown that the method proposed by the invention can better suppress the influence of noise and accurately estimate the PN code (original or reverse) sequence of the pseudo-code composite signal. By using the method proposed by the invention, the cross term and noise in the time-frequency distribution of the pseudo-code composite signal can be suppressed, thereby improving the estimation accuracy of the PN code original (or reverse) sequence of the pseudo-code composite signal.

Claims

1. a kind of pseudo-code phase modulation sinusoidal frequency modulation composite signal pseudo-code sequence estimation method based on sinusoidal frequency modulation SFM signal linear model, is characterized in that, comprises the following steps: SFM signal is carried out the first kind of Bessel function series expansion, will The complex sinusoidal FM signal s(t)=Aexp{j[ω ₀ t+m _f sin(ω _m t)]} is expanded into an exponential series with the Bessel function as the coefficient, and the non-negative order of the Bessel function is taken to obtain the SFM single-sided linear signal The unilateral linear signal s'(t) of the SFM signal is combined with the pseudo-code phase-modulated signal to establish a pseudo-code phase-modulated composite signal based on the linear model of the SFM signal; the pseudo-code phase-modulated composite signal is established using smooth pseudo-Wigner-Ville distribution SPWVD Carry out time-frequency analysis to find the sharp negative pulse that appears at the phase jump point of the pseudo-code; use SVD to calculate the singular value S _x = UΛ _x V ^H , retain the first largest singular value of the diagonal matrix Λ _x , and other Set the singular value to zero to get Λ _x′ , and then restore the calculation S _x′ = UΛ _x′ V ^H to get the singular value S _x′ ; find the minimum slice diagram of S _x′ along the frequency axis, and search for the negative value in the minimum slice diagram. At the moment corresponding to the peak, the estimation of the PN code sequence of the pseudo-code phase-modulated composite signal is completed, where K is the highest order of the first Bessel function, A is the constant amplitude, and J _k (m _f ) is the amplitude of the kth carrier component , m _f is the modulation index, j is the imaginary unit, ω ₀ is the angular frequency of the carrier, ω _m is the angular frequency of the modulation, t is the time variable, S _x is the time-frequency distribution of the pseudo-code composite signal containing noise, and S _x′ is the SVD The time-frequency distribution of the pseudo-code composite signal after denoising and enhancement processing, H represents the conjugate transpose, U, V are the left and right singular matrices, and Λ _x is the singular value diagonal matrix.

2. estimation method according to claim 1, it is characterized in that, based on the pseudo-code phase-modulated composite signal of SFM linear model, the frequency of pseudo-code is moved to frequency f=f ₀ +kf _m , wherein, f ₀ is The carrier component, k is the order number of the Bessel function of the first kind, and f _m is the modulation frequency.

3. estimation method according to claim 1, is characterized in that, calculates the time-frequency distribution that obtains the time-frequency distribution of signal based on the SPWVD transformation of the pseudo-code phase-modulated composite signal of SFM linear model, after carrying out SVD decomposition to signal time-frequency distribution, retain singularity The first largest singular value of the value diagonal matrix, set the other singular values to zero, and then recover and calculate the time-frequency distribution after denoising and enhancement by SVD, obtain the minimum value section of the time-frequency plane along the frequency axis, and detect the minimum value The peak value of the cut plane is used to estimate the PN code sequence of the pseudo-code phase-modulated composite signal.

4. The estimation method according to claim 3, wherein the detection of the peak value of the minimum value slice is specifically, adopting the threshold method, setting the threshold as half of the minimum value in the slice figure, and there are continuous SPWVD values less than the threshold value The three time points of , and the position where the middle point is a local minimum is the peak value of the minimum cut surface.