A hyperbolic frequency modulation signal parameter estimation method based on group delay iteration variable weight fitting

Abstract

The application discloses a hyperbolic frequency modulation signal parameter estimation method based on group delay iteration variable weight fitting, which comprises the following steps: first, obtaining a data sequence to be processed; second, extracting a normalized smooth amplitude spectrum; third, estimating the number of discrete frequency points and the discrete gravity frequency index of the signal bandwidth by using histogram statistics; fourth, extracting the rising edge feature and the falling edge feature of the signal; fifth, estimating the discrete upper and lower limit frequency index of the signal; sixth, extracting the group delay sequence within the discrete frequency index range; seventh, obtaining the group delay vector satisfying the normal value condition by using the continuity of the group delay sequence; eighth, performing iteration variable weight fitting on the group delay vector satisfying the normal value condition; ninth, obtaining the estimated value of the initial frequency and the period slope. The method can realize high-robust and high-precision parameter estimation of the hyperbolic frequency modulation signal without complex calculation.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of signal processing, and particularly relates to a hyperbolic frequency modulation signal parameter estimation method based on group time delay iteration variable weight fitting. BACKGROUND

[0002] The hyperbolic frequency modulation signal has Doppler invariance, and is widely applied to multiple fields such as active sonar and underwater acoustic communication. The starting frequency and the period slope are two basic parameters capable of representing the characteristics of the hyperbolic frequency modulation signal, and if they can be accurately estimated, the received hyperbolic frequency modulation signal can be recovered, which has very important significance in the fields of electronic reconnaissance and countermeasure. Therefore, the fast and accurate estimation of the starting frequency and the period slope is an important research content in the fields of active sonar and underwater acoustic communication.

[0003] The current hyperbolic frequency modulation signal parameter estimation methods mainly include: (1) maximum likelihood method, which can theoretically achieve the Cramer-Rao lower bound, but has high calculation complexity due to the absence of analytical solution; (2) methods based on time-frequency analysis and image processing, including: ① Wigner-Hough transform combining Wigner-Ville distribution and Hough transform, which needs high calculation amount for realizing high-precision parameter estimation; ② analysis using short-time Fourier transform or pseudo maximum likelihood method, the performance of which is affected by the selection of the short-time Fourier transform window length; ③ analysis using short-time fractional Fourier transform, which has high calculation complexity and mutual restriction of time-frequency resolution; (3) spectrum analysis method, which has small calculation amount, but the algorithm accuracy is limited due to the influence of noise on the spectrum. SUMMARY

[0004] The technical problem of the present application is to provide a hyperbolic frequency modulation signal parameter estimation method which can improve the parameter estimation precision without parameter search and under the premise of fast parameter estimation.

[0005] The technical scheme is that, in order to solve the above technical problem, the present application provides a hyperbolic frequency modulation signal parameter estimation method based on group time delay iteration variable weight fitting, which comprises the following steps:

[0006] (1) obtaining a hyperbolic frequency modulation signal data sequence x(n), n=0, 1, …, N-1, N being the sampling point number corresponding to the pulse width length of the detected hyperbolic frequency modulation signal;

[0007] (2) extracting the normalized smooth amplitude spectrum Y N (l) of the hyperbolic frequency modulation signal, l=0, 1, …, N / 2-1;

[0008] (3) estimating the signal bandwidth discrete frequency point number n hand a normalized smooth amplitude spectrum Y N a discrete center frequency index k of (l) g ;

[0009] (4) Extracting a normalized smooth amplitude spectrum Y of the hyperbolic frequency modulation signal according to the number of discrete frequency points and the discrete center frequency index of the signal bandwidth N a rising edge feature U(l) and a falling edge feature D(l) of (l)

[0010] (5) Estimating a discrete lower limit frequency index k of the hyperbolic frequency modulation signal according to the number of discrete frequency points and the discrete center frequency index of the signal bandwidth, and the rising edge feature and the falling edge feature lb and a discrete upper limit frequency index k hb ;

[0011] (6) Extracting a group delay sequence τ(l sp ) of the hyperbolic frequency modulation signal within a discrete frequency index range l sp =k sp ,k lb ,k lb +1,…,k hb ;

[0012] (7) Obtaining a group delay vector τ of the hyperbolic frequency modulation signal satisfying a normal value condition by using the continuity of the group delay sequence 0 ;

[0013] (8) Iterative variable weight fitting of the group delay vector τ of the hyperbolic frequency modulation signal satisfying the normal value condition 0 ;

[0014] (9) Obtaining an estimated value of the starting frequency and an estimated value of the periodic slope

[0015] Further, in step (1), the following method is used to obtain the hyperbolic frequency modulation signal data sequence x(n), n=0,1,…,N-1 to be processed, which specifically includes the following steps:

[0016] Receiving real-time collection data of N sampling points from a sensor as the hyperbolic frequency modulation signal data sequence x(n), n=0,1,…,N-1 to be processed, or extracting data of N sampling points from the time when the signal is detected as the hyperbolic frequency modulation signal data sequence x(n), n=0,1,…,N-1 to be processed from a memory, and the N is the number of sampling points corresponding to the pulse width length of the detected hyperbolic frequency modulation signal, and the value is N=2 a , and a is an integer greater than or equal to 5.

[0017] Further, in step (2), the hyperbolic frequency modulation signal normalized smooth amplitude spectrum Y is extracted by using the following method N (l),l=0,1...,N / 2-1, and specifically includes the following steps:

[0018] (2-1) performing discrete Fourier transform on the data sequence x(n), n=0,1,…,N-1 to obtain the discrete Fourier transform result X(l) of the hyperbolic frequency modulation signal;

[0019]

[0020] wherein, l is the discrete frequency index, and j is the imaginary unit, i.e.

[0021] (2-2) calculating the modulus value of the discrete Fourier transform result X(l) of the hyperbolic frequency modulation signal to obtain the amplitude spectrum X a (l) of the hyperbolic frequency modulation signal;

[0022] X a (l)=|X(l)|,l=0,1,…,N / 2-1;

[0023] (2-3) initializing each smooth parameter of the hyperbolic frequency modulation signal amplitude spectrum, specifically including the initialization of the following parameters:

[0024] ① the maximum smooth iteration number E of the hyperbolic frequency modulation signal amplitude spectrum is initialized as an integer greater than 1;

[0025] ② the smooth processing window length ξ of the hyperbolic frequency modulation signal amplitude spectrum is initialized as an odd number between 3 and 15;

[0026] ③ the smooth error decision threshold ε of the hyperbolic frequency modulation signal amplitude spectrum is initialized as a real number between 0 and 1; E E <1;

[0027] ④ the smooth iteration number e of the hyperbolic frequency modulation signal amplitude spectrum is initialized as e=1;

[0028] ⑤ the smooth amplitude spectrum S0(l) of the hyperbolic frequency modulation signal after the 0th smooth processing is initialized as S0(l)=X a (l),l=0,1,…,N / 2-1;

[0029] ⑥ the smooth error P(0) of the hyperbolic frequency modulation signal amplitude spectrum after the 0th smooth processing is initialized as P(0)=0;

[0030] (2-4) performing smooth processing on the smooth amplitude spectrum S e-1 (l) of the hyperbolic frequency modulation signal after the (e-1)th smooth processing to obtain the smooth amplitude spectrum S e ​(l) is:

[0031]

[0032] wherein, k s is the discrete frequency index within the smoothing window corresponding to the lth discrete frequency point;

[0033] (2-5) updating the hyperbolic frequency modulation signal amplitude spectrum smoothing error P(e) after the e th smoothing processing;

[0034]

[0035] (2-6) judging whether the following iterative smoothing condition is satisfied

[0036] e < E and

[0037] If the condition is satisfied, let e = e + 1, and return to step (2-4); otherwise, go to step (2-7);

[0038] (2-7) smoothing the hyperbolic frequency modulation signal amplitude spectrum S e (l) after the e th smoothing processing; N (l) to obtain the hyperbolic frequency modulation signal normalized smoothing amplitude spectrum Y e (l) :

[0039]

[0040] wherein, max[S e (l)] represents the maximum value of S e (l) within the range of 0≤l≤N / 2-1.

[0041] Further, in step (3), the signal bandwidth discrete frequency point number n h and the discrete barycentric frequency index k N of the hyperbolic frequency modulation signal normalized smoothing amplitude spectrum Y g (l) are estimated, specifically including the following steps:

[0042] (3-1) initializing the parameters for estimating the signal bandwidth discrete frequency point number n h and the discrete barycentric frequency index k g , specifically including the initialization of the following parameters:

[0043] ① the hyperbolic frequency modulation signal normalized smoothing amplitude spectrum histogram statistical starting value υ start is initialized as: 0≤υ start <1 real number;

[0044] ②Statistical endpoint value υ of the normalized smoothed amplitude spectrum histogram of hyperbolic frequency modulated signal end Initialized as: υ start <υ end Real numbers ≤ 1;

[0045] ③ The number of statistical sub-intervals C in the normalized smoothed amplitude spectrum histogram of the hyperbolic frequency modulated signal is initialized to an integer C > 5;

[0046] ④ The c-th subinterval H of the normalized smoothed amplitude spectrum histogram of the hyperbolic frequency modulated signal c Initialize to:

[0047] υ start +(c-1)(υ end -υ start ) / C≤H c <υ start +c(υ end -υ start ) / C

[0048] Where c is the discrete index of the histogram statistical sub-interval, c = 1, 2, ..., C;

[0049] ⑤ Threshold ρ for normalized smoothed amplitude spectrum pure noise discrimination of hyperbolic frequency modulated signals noi Initialize to: 0 < ρ noi Real numbers less than 0.45;

[0050] ⑥ The discrete index c of the statistical sub-interval of the normalized smoothed amplitude spectrum histogram of the hyperbolic frequency modulated signal is initialized to: c = 1;

[0051] (3-2) Normalize and smooth the amplitude spectrum Y of the hyperbolic frequency modulated signal. N The distribution of (l) is statistically analyzed using histograms. Specifically, the normalized smoothed amplitude spectrum Y of the hyperbolic frequency modulated signal is statistically analyzed. N The value of (l) falls within each subinterval H1, H2, ..., H C The number of discrete frequency points within h1, h2, ..., h C ;

[0052] (3-3) Normalize and smooth the amplitude spectrum Y of the hyperbolic frequency modulated signal. N The value of (l) falls within the c-th subinterval H. c The number of discrete frequency points h within c Determine h c >ρ noi * Check if N is true. If the condition is true, proceed to step (3-4); otherwise, proceed to step (3-5).

[0053] (3-4) Update the normalized smoothed amplitude spectrum Y of the hyperbolic frequency modulated signal. N The value of (l) falls within the c-th subinterval H.c The number of discrete frequency points h within c =0;

[0054] (3-5) Determine whether c < C is true. If the condition is true, let c = c + 1 and return to step (3-3); otherwise, proceed to step (3-6).

[0055] (3-6) Based on the normalized smooth amplitude spectrum Y of the hyperbolic frequency modulated signal N The value of (l) falls within the c-th subinterval H. c The number of discrete frequency points h within c Estimate the normalized smoothed amplitude spectrum of the hyperbolic frequency modulated signal and the threshold ρ for distinguishing noisy signals. sig :

[0056]

[0057] ρ sig =max[ρ sig -0.1, 0.69]

[0058] in, Represents h c The discrete frequency index c satisfies the range h within the range 1 ≤ c ≤ C. c The maximum value of c corresponds to the maximum value of the two values, and max[] means taking the largest one of the two;

[0059] (3-7) Statistical analysis of the normalized smoothed amplitude spectrum Y of hyperbolic frequency modulated signal N (l), l=0,1...,N / 2-1, satisfying ρ sig ≤Y N (l) The number of discrete frequency points ≤ 1, which gives the signal bandwidth and the number of discrete frequency points n. h And search Y N (l) satisfies ρ sig ≤Y N (l)≤1 for n h Discrete frequency index of discrete frequency points Calculate n h Discrete centroid frequency index k of discrete frequency points g :

[0060]

[0061] Where int[] represents rounding to the nearest integer, and i is the integer value within the signal bandwidth. h Discrete index of discrete frequency points.

[0062] Furthermore, in step (4), the normalized smoothed amplitude spectrum Y of the hyperbolic frequency modulated signal is extracted using the following method. Nthe rising edge feature U(l) and the falling edge feature D(l) of (l) are initialized as follows:

[0063] (4-1) calculating the normalized smooth amplitude spectrum Y of the hyperbolic frequency modulation signal N the difference sequence σ of (l) a (l):

[0064]

[0065] (4-2) calculating the normalized smooth amplitude spectrum Y of the hyperbolic frequency modulation signal N the rising edge feature U(l) and the falling edge feature D(l) of (l) are initialized as follows:

[0066] U(l) = 0, l = 0, 1,..., N / 2-1

[0067] D(l) = 0, l = 0, 1,..., N / 2-1

[0068] (4-3) initializing the parameters of the rising edge and the falling edge feature of the recalculated normalized smooth amplitude spectrum Y of the hyperbolic frequency modulation signal, including the following parameters:

[0069] ① the reference window length k of the rising edge and the falling edge feature of the recalculated normalized smooth amplitude spectrum Y of the hyperbolic frequency modulation signal rw is initialized as follows: k rw = int[max[n h *α, k g *β]], where α is a real number satisfying 0.1≤α≤0.3, β is a real number satisfying 0.01≤β≤0.1, and if k rw is less than 3, then k rw = 3; where int[] represents the rounding operation, and max[] represents the maximum of the two;

[0070] ② the discrete frequency index l of the rising edge and the falling edge feature of the recalculated normalized smooth amplitude spectrum Y of the hyperbolic frequency modulation signal EC is initialized as follows: l EC = int[k rw / 2]+1;

[0071] (4-4) respectively counting the difference sequence σ of the normalized smooth amplitude spectrum Y of the hyperbolic frequency modulation signal a (l) in the preset range of the l EC th discrete frequency index, i.e. in the range of l EC -int[k rw / 2]≤l≤l EC +int[k rw / 2], the number of discrete frequency points of all positive values and negative values of σ athe number of discrete frequency points C with (l) > 0 r the number of discrete frequency points C with (l) > 0 EC ) and σ a the number of discrete frequency points C with (l) > 0 f the number of discrete frequency points C with (l) > 0 EC );

[0072] (4-5) Recalculating the rising edge feature U(l EC ) and the falling edge feature D(l EC ) of the normalized smooth amplitude spectrum corresponding to the l EC th discrete frequency point of the hyperbolic frequency modulation signal:

[0073] U(l EC ) = σ a (l EC )C r (l EC )

[0074] D(l EC ) = σ a (l EC )C f (l EC )

[0075] (4-6) Determine whether l EC < N / 2 - int[k rw / 2] is true. If the condition is true, let l EC = l EC + 1, and return to step (4-4); otherwise, go to step (5).

[0076] Further, in step (5), the following method is used to estimate the discrete lower frequency index k lb and the discrete upper frequency index k hb of the hyperbolic frequency modulation signal, which specifically includes the following steps:

[0077] (5-1) The search window length k sw of the rising edge and the falling edge features of the hyperbolic frequency modulation signal is initialized as: k sw = int[min[n h * γ, k g * μ]], where γ is a real number satisfying 0.9 ≤ γ ≤ 1.1, μ is a real number satisfying 0.15 ≤ μ ≤ 0.25, and if k sw is less than 3, let k sw = 3; wherein int[ ] represents the rounding integer operation, min[ ] represents the minimum of the two, and n h and k g are the normalized smooth amplitude spectrum Y Nthe number of discrete frequency points and the discrete center frequency index of the signal bandwidth of (l);

[0078] (5-2) search the discrete frequency index corresponding to the maximum value of the rising edge feature U(l) and the minimum value of the falling edge feature D(l) respectively, as the discrete lower limit frequency index k lb and the discrete upper limit frequency index k hb :

[0079]

[0080]

[0081] wherein, and respectively represent the discrete frequency index l in the range of Ω1={l|max[k g -k sw ,1]≤l≤max[k g -1,1]} search the discrete frequency index corresponding to the maximum value of the rising edge feature U(l), and in the range of Ω2={l|min[k g +1,N / 2-1]≤l≤min[k g +k sw ,N / 2-1]} search the discrete frequency index corresponding to the minimum value of the falling edge feature D(l).

[0082] Further, in step (6), the following method is used to extract the group delay sequence τ(l sp ) of the hyperbolic frequency modulation signal in the range of discrete frequency index l sp , l sp =k lb , k lb +1,…,k hb , which specifically includes the following steps:

[0083] (6-1) according to the discrete Fourier transform result X(l) of the hyperbolic frequency modulation signal, obtain the spectrum phase angle Φ(l) of the hyperbolic frequency modulation signal:

[0084] Φ(l)=angle[X(l)], l=0,1,…,N / 2-1

[0085] wherein, angle[X(l)] represents the phase angle of X(l);

[0086] (6-2) calculate the difference sequence σ p (l) of the hyperbolic frequency modulation signal spectrum phase angle Φ(l):

[0087]

[0088] (6-3) Initialize the parameters of the phase angle unwrapping of the hyperbolic frequency modulated signal spectrum, specifically including the initialization of the following parameters:

[0089] ① The spectrum phase angle difference sequence after unwrapping the hyperbolic frequency modulated signal is initialized as follows: Among them, l sp =k lb ,k lb +1,…,k hb For unwrapping discrete frequency indexes of the spectral phase angle;

[0090] ② The maximum number of iterations B for unwrapping the phase angle of the hyperbolic frequency modulated signal spectrum is initialized to an integer B > 1;

[0091] ③ Hyperbolic frequency modulated signal spectrum phase angle unwrapping discrete frequency index l sp Initialized to: l sp =k lb ;

[0092] ④ The number of unwrapping iterations b for the phase angle of the hyperbolic frequency modulated signal spectrum is initialized to: b = 1;

[0093] (6-4) Determine the lth sp The spectral phase angle difference sequence after unwrapping at discrete frequency points If the condition is met, proceed to step (6-5); otherwise, proceed to step (6-6).

[0094] (6-5) Update #1 sp The spectral phase angle difference sequence after unwrapping at discrete frequency points

[0095]

[0096] (6-6) Determine whether the following spectrum phase angle unwrapping iteration conditions are met:

[0097] b < B and

[0098] If the condition is true, let b = b + 1 and return to step (6-5); otherwise, let b = 1 and proceed to step (6-7).

[0099] (6-7) Determine l sp <k hb Whether the condition is true or false, if the condition is true, then let l sp =l sp +1, and return to step (6-4); otherwise proceed to step (6-8);

[0100] (6-8) Based on the spectrum phase angle difference sequence after unwrapping the hyperbolic frequency modulated signal Extracting the group delay sequence τ(l)sp ):

[0101]

[0102] where Δf = f s / N is the frequency resolution of the discrete Fourier transform, f s is the sampling frequency.

[0103] Further, in step (7), the following method is used to obtain the hyperbolic frequency modulation signal group delay vector τ 0 that satisfies the normal value condition, which specifically includes the following steps:

[0104] (7-1) initialize the parameters for judging the continuity of the group delay sequence, which specifically includes the initialization of the following parameters:

[0105] ① initialize the hyperbolic frequency modulation signal group delay normal value decision threshold η as a real number satisfying 0.1≤η≤0.3;

[0106] ② initialize the hyperbolic frequency modulation signal group delay discrete frequency index l τ as l τ =k lb +1;

[0107] ③ initialize the number of hyperbolic frequency modulation signal group delay normal frequency points A as A=0;

[0108] ④ initialize the set of hyperbolic frequency modulation signal group delay normal frequency point discrete frequency indexes P as an empty set;

[0109] (7-2) judge whether the group delay τ(l τ ) of the l τ th discrete frequency point satisfies the following normal value condition:

[0110] |τ(l τ )-τ(l τ -1)|≤ητ(l τ ) and |τ(l τ )-τ(l τ +1)|≤ητ(l τ )

[0111] If the condition is satisfied, set A=A+1, the Ath normal frequency point discrete frequency index p A =l τ , and P=P∪[p A ]; wherein P∪[p A ] represents incorporating p A into the set P;

[0112] (7-3) judge whether l τ k hb-1 is true, if the condition is true, then let l τ = l τ +1, and return to step (7-2); otherwise, go to step (7-4);

[0113] (7-4) according to the hyperbolic frequency modulation signal group time delay normal frequency point discrete frequency index set P = [p1 p2 … p A ], the hyperbolic frequency modulation signal group time delay vector τ 0 satisfying the normal value condition is obtained:

[0114]

[0115] Wherein, a = 1, 2, …, A, a is the discrete index of A hyperbolic frequency modulation signal group time delay normal frequency point.

[0116] Further, in step (8), the hyperbolic frequency modulation signal group time delay vector τ 0 satisfying the normal value condition is iteratively fitted by the following method, which includes the following steps:

[0117] (8-1) the parameters of the hyperbolic frequency modulation signal group time delay iterative variable weight fitting are initialized, which includes the initialization of the following parameters:

[0118] ① the hyperbolic frequency modulation signal group time delay maximum iterative variable weight fitting times Q is initialized as: Q is an integer greater than 1;

[0119] ② the hyperbolic frequency modulation signal group time delay iterative variable weight fitting error decision threshold ε Q is initialized as: 0 < ε Q < 1 is a real number;

[0120] ③ the hyperbolic frequency modulation signal group time delay iterative variable weight fitting times q is initialized as: q = 1;

[0121] ④ the hyperbolic frequency modulation signal group time delay fitting error after the 0th iteration variable weight fitting is initialized as:

[0122] ⑤ the hyperbolic frequency modulation signal group time delay weight matrix W 0 in the 0th iteration variable weight fitting is initialized as: Wherein, represents the diagonal matrix with as the eigenvalue,

[0123] (8-2) the intermediate parameter matrix b q-1 in the q-1th iteration variable weight fitting is calculated:

[0124]

[0125] in, and These are the intermediate slope parameter and the intermediate intercept parameter in the (q-1)th iteration of the weighted fitting. It is a frequency auxiliary matrix. It is the pth a The frequency of a discrete frequency point;

[0126] (8-3) Calculate the estimated value τ of the group time delay vector obtained in the (q-1)th iteration of the variable weight fitting. q-1 ;

[0127]

[0128] in, It is the estimated value of the group delay of the a-th normal frequency point in the (q-1)-th iteration of variable weight fitting;

[0129] (8-4) Calculate the group delay estimation error of A normal frequency points in the q-th iteration of the weighted fitting.

[0130]

[0131] (8-5) Calculate the weights of the group delays of the A normal frequency points in the q-th iteration of the variable-weight fitting.

[0132]

[0133] in, represent The discrete frequency index a satisfies the range 1 ≤ a ≤ A. The maximum value, represent The discrete frequency index a satisfies the range 1 ≤ a ≤ A. The minimum value;

[0134] (8-6) Obtain the hyperbolic frequency modulated signal group delay weight matrix W in the q-th iteration of the variable weight fitting. q :

[0135]

[0136] (8-7) Update the hyperbolic frequency modulated signal group delay fitting error after the qth iteration of weighted fitting.

[0137]

[0138] (8-8) Determine whether the following group delay iterative weighted fitting conditions are met:

[0139] q < Q and

[0140] If the condition is true, let q = q + 1, and return to step (8-2); otherwise, go to step (9).

[0141] Further, in step (9), the intermediate slope parameter and the intermediate intercept parameter The estimation value of the starting frequency of the hyperbolic frequency modulation signal and the estimation value of the period slope

[0142]

[0143] Beneficial effects, compared with the prior art, the technical scheme of the present application has the following beneficial technical effects:

[0144] 1、The present application makes full use of the energy distribution characteristics of the hyperbolic frequency modulation signal amplitude spectrum and the noise amplitude spectrum, preliminarily estimates the bandwidth of the hyperbolic frequency modulation signal based on histogram statistics, as shown in step 3, and uses the center of gravity frequency of the observed signal amplitude spectrum instead of the commonly used peak frequency, thereby improving the robustness of the subsequent fine bandwidth estimation.

[0145] 2、The present application makes full use of the transient characteristics of the hyperbolic frequency modulation signal spectrum, finely estimates the bandwidth of the hyperbolic frequency modulation signal, as shown in steps 4 and 5, and the extracted transient characteristic parameters can still better reflect the frequency domain distribution characteristics of the hyperbolic frequency modulation signal at low signal-to-noise ratio, thereby improving the robustness and accuracy of the bandwidth estimation.

[0146] 3、The present application makes full use of the continuity characteristics of the group delay, retains the normal values in the extracted group delay of the hyperbolic frequency modulation signal, as shown in step 7, thereby improving the robustness and accuracy of the hyperbolic frequency modulation signal parameter estimation.

[0147] 4、The present application uses the iterative variable weight least square fitting method to adaptively adjust the weights corresponding to the group delay at each frequency point, as shown in step 8, thereby improving the fitting effect of the group delay and further improving the robustness and accuracy of the hyperbolic frequency modulation signal parameter estimation. BRIEF DESCRIPTION OF DRAWINGS

[0148] Figure 1 is a flowchart of the method of the present application;

[0149] Figure 2 is a hyperbolic frequency modulation signal normalized amplitude spectrum and normalized smoothed amplitude spectrum graph of example 1;

[0150] Figure 3 is a hyperbolic frequency modulation signal normalized smoothed amplitude spectrum histogram of example 1;

[0151] Figure 4 Transient feature and bandwidth estimation result figure of hyperbolic frequency modulation signal of embodiment 1;

[0152] Figure 5 Group delay sequence extraction result figure of hyperbolic frequency modulation signal of embodiment 1;

[0153] Figure 6 Normalized amplitude spectrum and normalized smooth amplitude spectrum figure of hyperbolic frequency modulation signal of embodiment 2;

[0154] Figure 7 Histogram of normalized smooth amplitude spectrum of hyperbolic frequency modulation signal of embodiment 2;

[0155] Figure 8 Transient feature and bandwidth estimation result figure of hyperbolic frequency modulation signal of embodiment 2;

[0156] Figure 9 Group delay sequence extraction result figure of hyperbolic frequency modulation signal of embodiment 2. DETAILED DESCRIPTION

[0157] In order to better understand the purpose, structure and function of the present application, the present application will be further described below in combination with the drawings.

[0158] As shown in Figure 1 , the present application proposes a hyperbolic frequency modulation signal parameter estimation method based on group delay iterative variable weight fitting, which comprises the following steps:

[0159] (1) obtaining a hyperbolic frequency modulation signal data sequence x(n), n=0, 1, …, N-1, N being the sampling point number corresponding to the pulse width length of the detected hyperbolic frequency modulation signal;

[0160] (2) extracting the normalized smooth amplitude spectrum Y N (l) of the hyperbolic frequency modulation signal, l=0, 1, …, N / 2-1;

[0161] (3) using histogram statistics to estimate the signal bandwidth discrete frequency point number n h of the hyperbolic frequency modulation signal and the discrete barycenter frequency index k g of the normalized smooth amplitude spectrum Y N (l);

[0162] (4) according to the signal bandwidth discrete frequency point number and the discrete barycenter frequency index, extracting the rising edge feature U(l) and the falling edge feature D(l) of the normalized smooth amplitude spectrum Y N (l) of the hyperbolic frequency modulation signal;

[0163] (5) According to the number of discrete frequency points and the discrete center frequency index of the signal bandwidth, and the rising edge feature and the falling edge feature, estimate the discrete lower limit frequency index k of the hyperbolic frequency modulation signal lb and the discrete upper limit frequency index k hb ;

[0164] (6) Extract the group delay sequence τ(l sp ) of the hyperbolic frequency modulation signal in the discrete frequency index l sp range, l sp =k lb , k lb +1,…,k hb ;

[0165] (7) Obtain the group delay vector τ 0 of the hyperbolic frequency modulation signal that satisfies the normal value condition by using the continuity of the group delay sequence;

[0166] (8) Perform iterative variable weight fitting on the group delay vector τ 0 of the hyperbolic frequency modulation signal that satisfies the normal value condition;

[0167] (9) Obtain the estimated value of the starting frequency f0 and the estimated value of the period slope a

[0168] Further, in step (1), the following method is used to obtain the hyperbolic frequency modulation signal data sequence x(n), n=0,1,…,N-1 to be processed, which specifically includes the following steps:

[0169] Real-time acquisition data of N sampling points received from the sensor are taken as the hyperbolic frequency modulation signal data sequence x(n), n=0,1,…,N-1 to be processed, or data of N sampling points from the time when the signal is detected are extracted from the memory as the hyperbolic frequency modulation signal data sequence x(n), n=0,1,…,N-1 to be processed, and the N is the sampling point number corresponding to the pulse width length of the detected hyperbolic frequency modulation signal, and the value is N=2 a , and a is an integer greater than or equal to 5.

[0170] Further, in step (2), the following method is used to extract the hyperbolic frequency modulation signal normalized smooth amplitude spectrum Y N (l), l=0,1...,N / 2-1, which specifically includes the following steps:

[0171] (2-1) Perform discrete Fourier transform on the data sequence x(n), n=0,1,…,N-1 to obtain the discrete Fourier transform result X(l) of the hyperbolic frequency modulation signal;

[0172]

[0173] Where l is the discrete frequency index, and j is the imaginary unit, i.e.

[0174] (2-2) Calculate the magnitude of the discrete Fourier transform result X(l) of the hyperbolic frequency modulated signal to obtain the amplitude spectrum X of the hyperbolic frequency modulated signal. a (l);

[0175] X a (l)=|X(l)|,l=0,1,…,N / 2-1;

[0176] (2-3) Initialize the smoothing parameters of the hyperbolic frequency modulated signal amplitude spectrum, specifically including the initialization of the following parameters:

[0177] ① The maximum number of smoothing iterations E of the hyperbolic frequency modulated signal amplitude spectrum is initialized to an integer E > 1;

[0178] ② The window length ξ for smoothing the amplitude spectrum of hyperbolic frequency modulation signals is initialized to an odd number of 3 ≤ ξ ≤ 15;

[0179] ③ Decision threshold ε for amplitude spectrum smoothing error of hyperbolic frequency modulated signal E Initialize to: 0 < ε E Real numbers less than 1;

[0180] ④ The number of iterations e for smoothing the amplitude spectrum of the hyperbolic frequency modulated signal is initialized to: e = 1;

[0181] ⑤ The smoothed amplitude spectrum S0(l) of the hyperbolic frequency modulated signal after the 0th smoothing process is initialized as: S0(l) = X a (l), l=0,1,…,N / 2-1;

[0182] ⑥ The amplitude spectrum smoothing error P(0) of the hyperbolic frequency modulated signal after the 0th smoothing process is initialized as: P(0)=0;

[0183] (2-4) Smoothing amplitude spectrum S of hyperbolic frequency modulated signal after e-1th smoothing process e-1 (l) Perform smoothing processing to obtain the smoothed amplitude spectrum S of the hyperbolic frequency modulated signal after the e-th smoothing processing. e (l) is:

[0184]

[0185] Where, k s This is the index of the discrete frequency within the smoothing window corresponding to the l-th discrete frequency point;

[0186] (2-5) Update the amplitude spectrum smoothing error P(e) of the hyperbolic frequency modulated signal after the e-th smoothing process;

[0187]

[0188] (2-6) judging whether the following iterative smoothing condition is satisfied

[0189] e < E and

[0190] If the condition is satisfied, let e = e + 1, and return to step (2-4); otherwise, go to step (2-7);

[0191] (2-7) smoothing the hyperbolic frequency modulation signal after the e-th smoothing processing e (l) to obtain a hyperbolic frequency modulation signal normalized smoothed amplitude spectrum Y N (l):

[0192]

[0193] where max[S e (l)] represents the maximum value of S e (l) within the range of 0≤l≤N / 2-1. e

[0194] Further, in step (3), the number n h of signal bandwidth discrete frequency points of the hyperbolic frequency modulation signal and the discrete barycentric frequency index k N of the normalized smoothed amplitude spectrum Y g are estimated, specifically including the following steps:

[0195] (3-1) initializing each parameter for estimating the number n h of signal bandwidth discrete frequency points and the discrete barycentric frequency index k g , specifically including the initialization of the following parameters:

[0196] ① the hyperbolic frequency modulation signal normalized smoothed amplitude spectrum histogram statistical starting value υ start is initialized as: 0≤υ start <1, which is a real number;

[0197] ② the hyperbolic frequency modulation signal normalized smoothed amplitude spectrum histogram statistical ending value υ end is initialized as: υ start <υ end ≤1, which is a real number;

[0198] ③ the hyperbolic frequency modulation signal normalized smoothed amplitude spectrum histogram statistical sub-interval number C is initialized as: C>5, which is an integer;

[0199] ④ the c-th sub-interval H c of the hyperbolic frequency modulation signal normalized smoothed amplitude spectrum histogram is initialized as:​

[0200] υ start +(c-1)(υ end -υ start ) / C≤H c <υ start +c(υ end -υ start ) / C

[0201] Where c is the discrete index of the histogram statistical sub-interval, c = 1, 2, ..., C;

[0202] ⑤ Threshold ρ for normalized smoothed amplitude spectrum pure noise discrimination of hyperbolic frequency modulated signals noi Initialize to: 0 < ρ noi Real numbers less than 0.45;

[0203] ⑥ The discrete index c of the statistical sub-interval of the normalized smoothed amplitude spectrum histogram of the hyperbolic frequency modulated signal is initialized to: c = 1;

[0204] (3-2) Normalize and smooth the amplitude spectrum Y of the hyperbolic frequency modulated signal. N The distribution of (l) is statistically analyzed using histograms. Specifically, the normalized smoothed amplitude spectrum Y of the hyperbolic frequency modulated signal is statistically analyzed. N The value of (l) falls within each subinterval H1, H2, ..., H C The number of discrete frequency points within h1, h2, ..., h C ;

[0205] (3-3) Normalize and smooth the amplitude spectrum Y of the hyperbolic frequency modulated signal. N The value of (l) falls within the c-th subinterval H. c The number of discrete frequency points h within c Determine h c >ρ noi If the condition is true, proceed to step (3-4); otherwise, proceed to step (3-5).

[0206] (3-4) Update the normalized smoothed amplitude spectrum Y of the hyperbolic frequency modulated signal. N The value of (l) falls within the c-th subinterval H. c The number of discrete frequency points h within c =0;

[0207] (3-5) Determine whether c < C is true. If the condition is true, let c = c + 1 and return to step (3-3); otherwise, proceed to step (3-6).

[0208] (3-6) Based on the normalized smooth amplitude spectrum Y of the hyperbolic frequency modulated signal N The value of (l) falls within the c-th subinterval H. c The number of discrete frequency points h withinc , estimate the hyperbolic frequency modulation signal normalized smooth amplitude spectrum noise signal discrimination threshold p sig :

[0209]

[0210] p sig = max[p sig -0.1, 0.69]

[0211] wherein, represents the maximum value of h c in the range of discrete frequency index c satisfying 1≤c≤C, and max[] represents taking the maximum of the two; c , and max[] represents taking the maximum of the two;

[0212] (3-7) count the number of discrete frequency points in the hyperbolic frequency modulation signal normalized smooth amplitude spectrum Y N (l), l=0,1..., N / 2-1 that satisfy p sig ≤Y N (l)≤1, that is, obtain the number of signal bandwidth discrete frequency points n h , and search for the discrete frequency index of the n N discrete frequency points Y sig (l) that satisfy p N ≤Y h (l)≤1 Calculate the discrete center frequency index k h of the n g discrete frequency points:

[0213]

[0214] wherein, int[] represents rounding operation, and i is the discrete index of the n h discrete frequency points in the signal bandwidth range.

[0215] Further, in step (4), the rising edge feature U(l) and the falling edge feature D(l) of the hyperbolic frequency modulation signal normalized smooth amplitude spectrum Y N (l) are extracted by the following method, which specifically includes the following steps:

[0216] (4-1) calculate the difference sequence s a (l) of the hyperbolic frequency modulation signal normalized smooth amplitude spectrum Y N (l):

[0217]

[0218] (4-2) extract the rising edge feature U(l) and the falling edge feature D(l) of the hyperbolic frequency modulation signal normalized smooth amplitude spectrum Y NThe rising edge feature U(l) and the falling edge feature D(l) of (l) are initialized:

[0219] U(l) = 0, l = 0, 1,..., N / 2-1

[0220] D(l) = 0, l = 0, 1,..., N / 2-1

[0221] (4-3) The parameters of the rising edge and the falling edge features of the re-computed normalized smooth amplitude spectrum of the hyperbolic frequency modulation signal are initialized, which specifically includes the initialization of the following parameters:

[0222] ① The reference window length k of the re-computed normalized smooth amplitude spectrum of the hyperbolic frequency modulation signal is initialized. rw The initialization is: k rw = int[max[n h *α, k g *β]], α is a real number satisfying 0.1≤α≤0.3, β is a real number satisfying 0.01≤β≤0.1, if k rw is less than 3, then k rw = 3; wherein, int[ ] represents the rounding operation, and max[ ] represents the maximum of the two;

[0223] ② The discrete frequency index l of the re-computed normalized smooth amplitude spectrum of the hyperbolic frequency modulation signal is initialized. EC The initialization is: l EC = int[k rw / 2]+1;

[0224] (4-4) The number of discrete frequency points of the difference sequence σ a (l) of the normalized smooth amplitude spectrum of the hyperbolic frequency modulation signal in the preset range of the l EC th discrete frequency index, that is, in the range of l EC -int[k rw / 2]≤l≤l EC +int[k rw / 2], the number of discrete frequency points C a (l r ) satisfying σ EC (l) > 0 and the number of discrete frequency points C a (l f ) satisfying σ EC (l) < 0 are counted respectively.

[0225] (4-5) The rising edge feature U(l EC ) and the falling edge feature D(l EC ) of the normalized smooth amplitude spectrum corresponding to the l EC):

[0226] U(l EC )=σ a (l EC C r (l EC )

[0227] D(l EC )=σ a (l EC C f (l EC )

[0228] (4-6) Determine l EC <N / 2-int[k rw If the condition is true, then let l [2] be true. EC =l EC +1 and return to step (4-4); otherwise, proceed to step (5).

[0229] Furthermore, in step (5), the discrete lower limit frequency index k of the hyperbolic frequency modulated signal is estimated using the following method. lb and discrete upper frequency index k hb Specifically, it includes the following steps:

[0230] (5-1) Search window length k for the rising and falling edge characteristics of hyperbolic frequency modulation signal sw Initialized to: k sw =int[min[n h *γ,k g *μ]], γ is a real number of 0.9≤γ≤1.1, μ is a real number of 0.15≤μ≤0.25, if k sw If it is less than 3, then let k sw =3; where int[] represents rounding to the nearest integer, min[] represents taking the smaller of the two, and n h and k g These are the normalized smoothed amplitude spectra Y of the hyperbolic frequency modulated signal obtained in step (3). N (l) Signal bandwidth, number of discrete frequency points, and index of discrete centroid frequency;

[0231] (5-2) Search for the discrete frequency indices corresponding to the maximum value of the rising edge feature U(l) and the minimum value of the falling edge feature D(l) respectively, and use them as the discrete lower limit frequency index k. lb and discrete upper frequency index k hb :

[0232]

[0233]

[0234] wherein, and respectively represent the discrete frequency index l searching for the maximum value of the rising edge feature U(l) in the range of Ω1={l|max[k g -k sw ,1]≤l≤max[k g -1,1]} and the discrete frequency index l searching for the minimum value of the falling edge feature D(l) in the range of Ω2={l|min[k g +1,N / 2-1]≤l≤min[k g +k sw ,N / 2-1]}.

[0235] Further, in step (6), the following method is used to extract the group delay sequence τ(l sp ) of the hyperbolic frequency modulation signal in the range of discrete frequency index l sp , l sp =k lb ,k lb +1,…,k hb , which specifically includes the following steps:

[0236] (6-1) According to the discrete Fourier transform result X(l) of the hyperbolic frequency modulation signal, the spectral phase angle Φ(l) of the hyperbolic frequency modulation signal is obtained:

[0237] Φ(l)=angle[X(l)], l=0,1,…,N / 2-1

[0238] wherein, angle[X(l)] represents the phase angle of X(l);

[0239] (6-2) The difference sequence σ p (l) of the spectral phase angle Φ(l) of the hyperbolic frequency modulation signal is calculated:

[0240]

[0241] (6-3) The parameters for the spectral phase angle unwrapping of the hyperbolic frequency modulation signal are initialized, which specifically includes the initialization of the following parameters:

[0242] ① The spectral phase angle difference sequence after the unwrapping of the hyperbolic frequency modulation signal is initialized as: wherein, l sp =k lb ,k lb +1,Ω,k hb is the spectral phase angle unwrapping discrete frequency index;

[0243] ② The maximum iteration number B of the spectral phase angle unwrapping of the hyperbolic frequency modulation signal is initialized as: an integer greater than 1.

[0244] ③ Hyperbolic frequency modulated signal spectrum phase angle unwrapping discrete frequency index l sp Initialized to: l sp =k lb ;

[0245] ④ The number of unwrapping iterations b for the hyperbolic frequency modulated signal spectrum phase angle is initialized to: b = 1;

[0246] (6-4) Determine the lth sp The spectral phase angle difference sequence after unwrapping at discrete frequency points If the condition is met, proceed to step (6-5); otherwise, proceed to step (6-6).

[0247] (6-5) Update #1 sp The spectral phase angle difference sequence after unwrapping at discrete frequency points

[0248]

[0249] (6-6) Determine whether the following spectrum phase angle unwrapping iteration conditions are met:

[0250] b < B and

[0251] If the condition is true, let b = b + 1 and return to step (6-5); otherwise, let b = 1 and proceed to step (6-7).

[0252] (6-7) Determine l sp <k hb Whether the condition is true or false, if the condition is true, then let l sp =l sp +1, and return to step (6-4); otherwise proceed to step (6-8);

[0253] (6-8) Based on the spectrum phase angle difference sequence after unwrapping the hyperbolic frequency modulated signal Extracting the group delay sequence τ(l) sp ):

[0254]

[0255] Where, Δf=f s / N is the frequency resolution of the Discrete Fourier Transform, f s The sampling frequency.

[0256] Furthermore, in step (7), the hyperbolic frequency modulated signal group delay vector τ that satisfies the normal value condition is obtained using the following method. 0 Specifically, it includes the following steps:

[0257] (7-1) Initialize each parameter for judging the continuity of the group delay sequence, including the following parameters:

[0258] ① The hyperbolic frequency modulation signal group delay normal value decision threshold η is initialized as a real number: 0.1≤η≤0.3;

[0259] ② The hyperbolic frequency modulation signal group delay discrete frequency index l τ is initialized as: l τ =k lb +1;

[0260] ③ The hyperbolic frequency modulation signal group delay normal frequency point number A is initialized as: A=0;

[0261] ④ The hyperbolic frequency modulation signal group delay normal frequency point discrete frequency index set P is initialized as an empty set;

[0262] (7-2) Judge whether the group delay τ(l τ ) of the l τ th discrete frequency point satisfies the following normal value condition:

[0263] |τ(l τ )-τ(l τ -1)|ητ(l τ ) and |τ(l τ )-τ(l τ +1)|≤ητ(l τ )

[0264] If the condition is satisfied, A=A+1, the Ath normal frequency point discrete frequency index p A =l τ , and P=P∪[p A ] are obtained, wherein P∪[p A ] represents that p A is incorporated into the set P;

[0265] (7-3) Judge whether l τ <k hb -1 is satisfied, if the condition is satisfied, l τ =l τ +1, and step (7-2) is returned; otherwise, step (7-4) is entered;

[0266] (7-4) Obtain the hyperbolic frequency modulation signal group delay vector τ A satisfying the normal value condition according to the hyperbolic frequency modulation signal group delay normal frequency point discrete frequency index set P=[p1 p2 … p 0 ]:

[0267]

[0268] wherein, a = 1, 2, …, A, a is the discrete index of the normal frequency point of the hyperbolic frequency modulation signal group delay.

[0269] Further, in step (8), the hyperbolic frequency modulation signal group delay vector τ 0 is iteratively fitted with the following method, which includes the following steps:

[0270] (8-1) Initialize the parameters of the hyperbolic frequency modulation signal group delay iterative variable weight fitting, which includes the following parameter initialization:

[0271] ① The maximum number of hyperbolic frequency modulation signal group delay iterative variable weight fitting Q is initialized as: an integer Q > 1;

[0272] ② The hyperbolic frequency modulation signal group delay iterative variable weight fitting error decision threshold ε Q is initialized as: a real number 0 < ε Q < 1;

[0273] ③ The number of hyperbolic frequency modulation signal group delay iterative variable weight fitting q is initialized as: q = 1;

[0274] ④ The hyperbolic frequency modulation signal group delay fitting error after the 0th iteration variable weight fitting is initialized as:

[0275] ⑤ The hyperbolic frequency modulation signal group delay weight matrix W 0 in the 0th iteration variable weight fitting is initialized as: wherein, is a diagonal matrix with as the eigenvalue,

[0276] (8-2) Calculate the intermediate parameter matrix b q-1 in the q-1th iteration variable weight fitting:

[0277]

[0278] wherein, and are the intermediate slope parameter and the intermediate intercept parameter in the q-1th iteration variable weight fitting, is the frequency auxiliary matrix, is the frequency of the p a th discrete frequency point;

[0279] (8-3) Calculate the estimation value τ q-1 of the group delay vector obtained in the q-1th iteration variable weight fitting;

[0280]

[0281] wherein, is the estimated value of the group delay of the a-th normal frequency in the q-th iteration variable weight fitting;

[0282] (8-4) calculating the group delay estimation error of the A normal frequencies in the q-th iteration variable weight fitting

[0283]

[0284] (8-5) calculating the weight of the group delay of the A normal frequencies in the q-th iteration variable weight fitting

[0285]

[0286] wherein, represents the maximum value of a within the range of 1≤a≤A represents the minimum value of a within the range of 1≤a≤A

[0287] (8-6) obtaining the hyperbolic frequency modulation signal group delay weight matrix W in the q-th iteration variable weight fitting q :

[0288]

[0289] (8-7) updating the hyperbolic frequency modulation signal group delay fitting error after the q-th iteration variable weight fitting

[0290]

[0291] (8-8) judging whether the following group delay iteration variable weight fitting condition is met:

[0292] q

[0293] If the condition is met, let q=q+1, and return to step (8-2); otherwise, go to step (9).

[0294] Further, in step (9), according to the intermediate slope parameter and the intermediate intercept parameter in the q-th iteration variable weight fitting, the following method is used to obtain the estimated value of the hyperbolic frequency modulation signal starting frequency and the estimated value of the period slope

[0295] ​​​​

[0296] In the embodiment of the application, the model of the received hyperbolic frequency modulation signal x(t) is:

[0297]

[0298] wherein A is the amplitude of the hyperbolic frequency modulation signal, τ0 is the starting time of the hyperbolic frequency modulation signal, τ is the pulse width of the hyperbolic frequency modulation signal, f1 is the starting frequency of the hyperbolic frequency modulation signal, f2 is the terminal frequency of the hyperbolic frequency modulation signal, and k0 is the period slope of the hyperbolic frequency modulation signal, and is defined as: ω(t) is a Gaussian white noise with a mean of zero and a variance of σ 2 The size of the variance σ 2 depends on the signal-to-noise ratio SNR: SNR = 10log 10 [A 2 / 2σ 2 ].

[0299] The above received hyperbolic frequency modulation signal x(t) is discretely sampled at a sampling frequency f s , and the hyperbolic frequency modulation signal sampling data sequence x(n) is obtained as:

[0300]

[0301] wherein n0 = int(τ0f s ), and N = int(τf s ).

[0302] Embodiment 1:

[0303] The simulation hyperbolic frequency modulation signal parameters are set as: signal amplitude A = 1, signal starting time τ0 = 0.01 s, signal pulse width τ = 1 s, signal starting frequency f1 = 400 Hz, signal terminal frequency f2 = 450 Hz, and signal period slope k0 = 2.7778 × 10 -4 Hz -1 s -1 , that is, the simulation signal is an up-frequency modulation signal, the sampling frequency f s = 2 kHz, and the signal-to-noise ratio SNR = -3 dB.

[0304] The simulation hyperbolic frequency modulation signal is parameter-estimated as follows:

[0305] According to step (1), 2000 sampling points of data containing the entire pulse signal are extracted from the memory as the data sequence x(n) to be processed;

[0306] Based on step (2), the maximum number of smoothing iterations for the hyperbolic frequency modulated (HFM) signal amplitude spectrum is set to E = 10, the smoothing window length for the HFM signal amplitude spectrum is set to ξ = 5, and the smoothing error decision threshold for the HFM signal amplitude spectrum is set to ε. E =0.01; For the hyperbolic frequency modulated signal sampling data sequence x(n), the normalized smoothed amplitude spectrum Y of the hyperbolic frequency modulated signal is obtained. N (l), such as Figure 2 As shown;

[0307] Based on step (3), set the initial value υ for the normalized smoothed amplitude spectrum histogram statistics of the hyperbolic frequency modulated signal. start =0, the statistical endpoint of the normalized smoothed amplitude spectrum histogram of the hyperbolic frequency modulated signal υ end =0.9, the number of statistical sub-intervals in the normalized smoothed amplitude spectrum histogram of the hyperbolic FM signal C=9, the pure noise discrimination threshold ρ of the normalized smoothed amplitude spectrum of the hyperbolic FM signal noi =0.4; for the normalized smoothed amplitude spectrum Y of the hyperbolic frequency modulated signal N (l) Perform histogram statistics, such as Figure 3 As shown;

[0308] Based on step (4), set parameters α = 0.2 and β = 0.05 to obtain the reference window length k for recalculating the rising and falling edge characteristics of the normalized smoothed amplitude spectrum of the hyperbolic frequency modulated signal. rw According to the Y N (l), to obtain the rising edge feature U(l) and falling edge feature D(l) of the normalized smoothed amplitude spectrum of the hyperbolic frequency modulated signal;

[0309] Based on step (5), set parameters γ = 1.1 and μ = 0.22, and calculate the search window length k of the rising and falling edge characteristics of the hyperbolic frequency modulated signal. sw Based on U(l) and D(l), search for the discrete lower limit frequency index k. lb and discrete upper frequency index k hb ,like Figure 4 As shown;

[0310] According to step (6), the maximum number of iterations for unwrapping the phase angle of the hyperbolic frequency modulated signal spectrum is set to B = 10; based on the discrete Fourier transform result X(l) of the hyperbolic frequency modulated signal, the group delay sequence τ(l) is extracted. sp ),like Figure 5 As shown;

[0311] According to step (7), the decision threshold η for the normal value of hyperbolic FM signal group delay is set to 0.2, based on the τ(l sp This yields the hyperbolic frequency modulated signal group delay vector τ that satisfies the normal value condition. 0 ;

[0312] According to step (8), the maximum number of iterations for the hyperbolic FM signal group delay is set to Q=10, and the decision threshold ε for the iterations for the hyperbolic FM signal group delay is set to... Q =0.01, for the τ 0 Perform iterative variable weight fitting to obtain the intermediate slope parameter in the q-th iteration of the variable weight fitting. and the intermediate intercept parameter

[0313] According to step (9), based on the intermediate slope parameter and the intermediate intercept parameter Obtain the starting frequency of the hyperbolic frequency modulated signal. and periodic slope They are respectively:

[0314]

[0315] The starting frequency of a hyperbolic frequency modulated signal and periodic slope The relative errors are as follows:

[0316]

[0317] Example 2:

[0318] The simulated hyperbolic frequency modulated signal parameters are set as follows: signal amplitude A = 1, signal start time τ0 = 0.01s, signal pulse width τ = 2s, signal start frequency f1 = 660Hz, signal end frequency f2 = 500Hz, and signal period slope k0 = -2.4242 × 10⁻⁶. -4 Hz -1 s -1 That is, the simulated signal is a down-modulated signal with a sampling frequency f. s =2kHz, signal-to-noise ratio (SNR) = 0dB.

[0319] The following section estimates the parameters of the simulated hyperbolic frequency modulated signal:

[0320] According to step (1), extract the data of 4000 sampling points containing the entire pulse signal from the memory as the data sequence x(n) to be processed;

[0321] Based on step (2), the maximum number of smoothing iterations for the hyperbolic frequency modulated (HFM) signal amplitude spectrum is set to E = 10, the smoothing window length for the HFM signal amplitude spectrum is set to ξ = 5, and the smoothing error decision threshold for the HFM signal amplitude spectrum is set to ε. E =0.01; For the hyperbolic frequency modulated signal sampling data sequence x(n), the normalized smoothed amplitude spectrum Y of the hyperbolic frequency modulated signal is obtained. N (l), such as Figure 6 As shown;

[0322] Based on step (3), set the initial value υ for the normalized smoothed amplitude spectrum histogram statistics of the hyperbolic frequency modulated signal. start =0, the statistical endpoint of the normalized smoothed amplitude spectrum histogram of the hyperbolic frequency modulated signal υ end =0.9, the number of statistical sub-intervals in the normalized smoothed amplitude spectrum histogram of the hyperbolic FM signal C=9, the pure noise discrimination threshold ρ of the normalized smoothed amplitude spectrum of the hyperbolic FM signal noi =0.4; for the normalized smoothed amplitude spectrum Y of the hyperbolic frequency modulated signal N (l) Perform histogram statistics, such as Figure 7 As shown;

[0323] Based on step (4), set parameters α = 0.2 and β = 0.05 to obtain the reference window length k for recalculating the rising and falling edge characteristics of the normalized smoothed amplitude spectrum of the hyperbolic frequency modulated signal. rw According to the Y N (l), to obtain the rising edge feature U(l) and falling edge feature D(l) of the normalized smoothed amplitude spectrum of the hyperbolic frequency modulated signal;

[0324] Based on step (5), set parameters γ = 1.1 and μ = 0.22, and calculate the search window length k of the rising and falling edge characteristics of the hyperbolic frequency modulated signal. sw Based on U(l) and D(l), search for the discrete lower limit frequency index k. lb and discrete upper frequency index k hb ,like Figure 8 As shown;

[0325] According to step (6), the maximum number of iterations for unwrapping the phase angle of the hyperbolic frequency modulated signal spectrum is set to B = 10; based on the discrete Fourier transform result X(l) of the hyperbolic frequency modulated signal, the group delay sequence τ(l) is extracted. sp ),like Figure 9 As shown;

[0326] According to step (7), the decision threshold for the normal value of the hyperbolic FM signal group delay is set to η = 0.2, based on the τ(l sp This yields the hyperbolic frequency modulated signal group delay vector τ that satisfies the normal value condition. 0 ;

[0327] According to step (8), the maximum number of iterations for the hyperbolic FM signal group delay is set to Q = 10, and the decision threshold ε for the iteration and weighted fitting error of the hyperbolic FM signal group delay is set. Q =0.01, for the τ 0 Perform iterative weighted fitting to obtain the intermediate slope parameter after the q-th iteration of weighted fitting. and the intermediate intercept parameter

[0328] According to step (9), the initial frequency and the period slope of the hyperbolic frequency modulation signal are obtained according to the intermediate slope parameter and the intermediate intercept parameter respectively.

[0329]

[0330] The relative errors of the initial frequency and the period slope of the hyperbolic frequency modulation signal are respectively:

[0331]

[0332] It is to be understood that the present application is described by way of example only, and that modifications and alterations can be made to the features and embodiments described herein without departing from the spirit and scope of the application. In addition, modifications and alterations can be made to the features and embodiments described herein to adapt them to specific circumstances and materials without departing from the spirit and scope of the application. Accordingly, the present application is not limited to the specific embodiments disclosed herein, but rather encompasses all embodiments falling within the scope of the claims appended hereto.​​​​

Claims

1. A method for estimating parameters of hyperbolic frequency modulated signals based on group delay iterative weighted fitting, characterized in that, Includes the following steps: (1) Obtain the hyperbolic frequency modulation signal data sequence x(n), n=0,1,…,N-1, where N is the number of sampling points corresponding to the pulse width length of the detected hyperbolic frequency modulation signal; (2) Extract the normalized and smoothed amplitude spectrum Y of the hyperbolic frequency modulated signal. N (l), l=0,1...,N / 2-1; (3) Using histogram statistics, estimate the signal bandwidth and the number of discrete frequency points n of the hyperbolic frequency modulated signal. h and normalized smoothed amplitude spectrum Y N Discrete centroid frequency index k of (l) g ; (4) Extract the normalized smoothed amplitude spectrum Y of the hyperbolic frequency modulated signal based on the signal bandwidth, the number of discrete frequency points, and the discrete centroid frequency index. N The rising edge feature U(l) and falling edge feature D(l) of (l); (5) Based on the number of discrete frequency points and the discrete centroid frequency index of the signal bandwidth, as well as the rising edge and falling edge characteristics, estimate the discrete lower limit frequency index k of the hyperbolic frequency modulated signal. lb and discrete upper frequency index k hb ; (6) Extract the hyperbolic frequency modulated signal at the discrete frequency index l sp Group delay sequence τ(l) within the range sp ),l sp =k lb ,k lb +1,…,k hb ; (7) Utilizing the continuity of the group delay sequence, the hyperbolic frequency modulated signal group delay vector τ that satisfies the normal value condition is obtained. 0 ; (8) The time delay vector τ of the hyperbolic frequency modulated signal group that meets the normal value condition. 0 Perform iterative weighted fitting; (9) Based on the results of the last iteration of weighted fitting, the estimated value of the starting frequency of the hyperbolic frequency modulated signal is obtained. and the estimated value of the periodic slope In step (3), the signal bandwidth and the number of discrete frequency points n of the hyperbolic frequency modulated signal are estimated. h and normalized smoothed amplitude spectrum Y N Discrete centroid frequency index k of (l) g Specifically, it includes the following steps: (3-1) For the estimated signal bandwidth and the number of discrete frequency points n h and discrete centroid frequency index k g The parameters are initialized, specifically including the initialization of the following parameters: ①Statistical starting value υ of normalized smoothed amplitude spectrum histogram of hyperbolic frequency modulated signal start Initialize to: 0≤υ start Real numbers less than 1; ②Statistical endpoint value υ of the normalized smoothed amplitude spectrum histogram of hyperbolic frequency modulated signal end Initialized as: υ start <υ end Real numbers ≤ 1; ③ The number of statistical sub-intervals C in the normalized smoothed amplitude spectrum histogram of the hyperbolic frequency modulated signal is initialized to an integer C > 5; ④ The c-th subinterval H of the normalized smoothed amplitude spectrum histogram of the hyperbolic frequency modulated signal c Initialize to: u start +(c-1)(υ end -u start ) / C≤H c <y start +c(u end -u start ) / C Where c is the discrete index of the histogram statistical sub-interval, c = 1, 2, ..., C; ⑤ Threshold ρ for normalized smoothed amplitude spectrum pure noise discrimination of hyperbolic frequency modulated signals noi Initialize to: 0 < ρ noi Real numbers < 0.45; ⑥ The discrete index c of the statistical sub-interval of the normalized smoothed amplitude spectrum histogram of the hyperbolic frequency modulated signal is initialized to: c = 1; (3-2) Normalize and smooth the amplitude spectrum Y of the hyperbolic frequency modulated signal. N The distribution of (l) is statistically analyzed using histograms. Specifically, the normalized smoothed amplitude spectrum Y of the hyperbolic frequency modulated signal is statistically analyzed. N The value of (l) falls within each subinterval H1, H2, ..., H C The number of discrete frequency points within h1, h2, ..., h C ; (3-3) Normalize and smooth the amplitude spectrum Y of the hyperbolic frequency modulated signal. N The value of (l) falls within the c-th subinterval H. c The number of discrete frequency points h within c Determine h c >ρ noi * Check if N is true. If the condition is true, proceed to step (3-4); otherwise, proceed to step (3-5). (3-4) Update the normalized smoothed amplitude spectrum Y of the hyperbolic frequency modulated signal. N (The value of l0 falls within the c-th subinterval H) c The number of discrete frequency points h within c =0; (3-5) Determine whether c < C is true. If the condition is true, let c = c + 1 and return to step (3-3); otherwise, proceed to step (3-6). (3-6) Based on the normalized smooth amplitude spectrum Y of the hyperbolic frequency modulated signal N The value of (l) falls within the c-th subinterval H. c The number of discrete frequency points h within c Estimate the normalized smoothed amplitude spectrum of hyperbolic frequency modulated signal and the threshold ρ for distinguishing noisy signals. sig : r sig =max[ρ sig -0.1, 0.69] in, Represents h c The discrete frequency index c satisfies the range h within the range 1 ≤ c ≤ C. c The maximum value of c corresponds to the maximum value of the two values, and max[] means taking the largest one of the two; (3-7) Statistical analysis of the normalized smoothed amplitude spectrum Y of hyperbolic frequency modulated signal N (l), l=0,1...,N / 2-1, satisfying ρ sig ≤Y N (l) The number of discrete frequency points ≤ 1, which gives the signal bandwidth and the number of discrete frequency points n. h And search Y N (l) satisfies ρ sig ≤Y N (l)≤1 for n h Discrete frequency index of discrete frequency points Calculate n h Discrete centroid frequency index k of discrete frequency points g : Where int[] represents rounding to the nearest integer, and i is the integer value within the signal bandwidth. h Discrete index of discrete frequency points; In step (4), the normalized smoothed amplitude spectrum Y of the hyperbolic frequency modulated signal is extracted using the following method. N The rising edge feature U(l0) and falling edge feature D(l) of (l) specifically include the following steps: (4-1) Calculate the normalized smoothed amplitude spectrum Y of the hyperbolic frequency modulated signal. N (l) difference sequence σ a (l): (4-2) Normalize and smooth the amplitude spectrum Y of the hyperbolic frequency modulated signal. N The rising edge feature U(l) and falling edge feature D(l) are initialized: U(l)=0,l=0,1,...,N / 2-1 D(l)=0,l=0,1,...,N / 2-1 (4-3) Initialize the parameters for the rising and falling edge characteristics of the normalized smoothed amplitude spectrum of the hyperbolic frequency modulated signal, specifically including the initialization of the following parameters: ① The reference window length k for recalculating the rising and falling edge characteristics of the normalized smoothed amplitude spectrum of the hyperbolic frequency modulated signal. rw Initialized to: k rw =int[max[n h *α,k g *β]], α is a real number 0.1≤α≤0.3, β is a real number 0.01≤β≤0.1, if k rw If it is less than 3, then let k rw =3; where int[] represents rounding to the nearest integer, and max[] represents taking the larger of the two; ②Recalculate the discrete frequency index l of the rising and falling edge characteristics of the normalized smoothed amplitude spectrum of the hyperbolic frequency modulated signal. EC Initialized to: l EC =int[k rw / 2]+1; (4-4) Calculate the difference sequence σ of the normalized smoothed amplitude spectrum of the hyperbolic frequency modulated signal. a (l) in the l EC The number of discrete frequency points with positive and negative values ​​within a preset range of discrete frequency indexes, i.e., in l EC -int[k rw / 2]≤l≤l EC +int[k rw Within the range of [ / 2], all satisfying σ a The number of discrete frequency points C (l) > 0 r (l EC and satisfying σ a The number of discrete frequency points C (l) < 0 f (l EC ); (4-5) Recalculate the hyperbolic frequency modulated signal l EC Rising edge characteristics U(l) of the normalized smoothed amplitude spectrum corresponding to each discrete frequency point EC ) and falling edge characteristics D(l EC ): The(l EC )=σ a (the EC )C r (the EC ) D(l EC )=σ a (L EC )C f (L EC ) (4-6) Determine l EC <N2-int[k rw If the condition is true, then let l [2] be true. EC =l EC +1, and return to step (4-4); otherwise, proceed to step (5); In step (5), the discrete lower limit frequency index k of the hyperbolic frequency modulated signal is estimated using the following method. lb and discrete upper frequency index k hb Specifically, it includes the following steps: (5-1) Search window length k for the rising and falling edge characteristics of hyperbolic frequency modulation signal sw Initialized to: k sw =int[min[n h *γ,k g *μ]], γ is a real number of 0.9≤γ≤1.1, μ is a real number of 0.15≤μ≤0.25, if k sw If it is less than 3, then let k sw =3; where int[] represents rounding to the nearest integer, min[] represents taking the smallest of the two, and n h and k g These are the normalized smoothed amplitude spectra Y of the hyperbolic frequency modulated signal obtained in step (3). N (l) Signal bandwidth, number of discrete frequency points, and discrete centroid frequency index; (5-2) Search for the discrete frequency indices corresponding to the maximum value of the rising edge feature U(l) and the minimum value of the falling edge feature D(l) respectively, and use them as the discrete lower limit frequency index k. lb and discrete upper frequency index k hb : in, and These represent the discrete frequency index l at Ω1={l|max[k g -k sw ,1]≤l≤max[k g Search for the discrete frequency index corresponding to the maximum value of the rising edge feature U(l) within the range of -1,1]}, and in Ω2={l|min[k g +1,N / 2-1]≤l≤min[k g +k sw Search for the discrete frequency index corresponding to the minimum value of the falling edge feature D(l) within the range of [N / 2-1]; In step (6), the hyperbolic frequency modulated signal at discrete frequency index l is extracted using the following method. sp Group delay sequence τ(l) within the range sp ),l sp =k lb ,k lb +1,…,k hb Specifically, it includes the following steps: (6-1) Based on the discrete Fourier transform result X(l) of the hyperbolic frequency modulated signal, the spectral phase angle Φ(l) of the hyperbolic frequency modulated signal is obtained: Φ(l)=angle[X)l)],l=0,1,…,N / 2-1 Where angle[X(l)] represents the phase angle of X(l); (6-2) Calculate the difference sequence σ of the phase angle Φ(l) of the hyperbolic frequency modulated signal spectrum. p (l): (6-3) Initialize the parameters of the phase angle unwrapping of the hyperbolic frequency modulated signal spectrum, specifically including the initialization of the following parameters: ① The spectrum phase angle difference sequence after unwrapping the hyperbolic frequency modulated signal is initialized as follows: Among them, l sp =k lb ,k lb +1,…,k hb For unwrapping discrete frequency indexes of the spectral phase angle; ② The maximum number of iterations B for unwrapping the phase angle of the hyperbolic frequency modulated signal spectrum is initialized to an integer B > 1; ③ Hyperbolic frequency modulated signal spectrum phase angle unwrapping discrete frequency index l sp Initialized to: l sp =k lb ; ④ The number of unwrapping iterations b for the phase angle of the hyperbolic frequency modulated signal spectrum is initialized to: b = 1; (6-4) Determine the lth sp The spectral phase angle difference sequence after unwrapping at discrete frequency points If the condition is met, proceed to step (6-5); otherwise, proceed to step (6-6). (6-5) Update #1 sp The spectral phase angle difference sequence after unwrapping at discrete frequency points (6-6) Determine whether the following spectrum phase angle unwrapping iteration conditions are met: b < B and If the condition is true, let b = b + 1 and return to step (6-5); otherwise, let b = 1 and proceed to step (6-7). (6-7) Determine l sp <k hb Whether the condition is true or false, if the condition is true, then let l sp =l sp +1, and return to step (6-4); otherwise proceed to step (6-8); (6-8) Based on the spectrum phase angle difference sequence after unwrapping the hyperbolic frequency modulated signal Extracting the group delay sequence τ(l) sp ): Where, Δf=f s / N is the frequency resolution of the Discrete Fourier Transform, f s The sampling frequency; In step (7), the hyperbolic frequency modulated signal group delay vector τ that satisfies the normal value condition is obtained using the following method. 0 Specifically, it includes the following steps: (7-1) Initialize the parameters for determining the continuity of the group delay sequence, specifically including the initialization of the following parameters: ① The decision threshold η for the normal value of the hyperbolic frequency modulated signal group delay is initialized to a real number of 0.1 ≤ η ≤ 0.3; ② Hyperbolic frequency modulated signal group time delay discrete frequency index l τ Initialized to: l τ =k lb +1; ③ The number A of normal frequency points with time delay of hyperbolic FM signal group is initialized to: A = 0; ④ The set of discrete frequency indices P of the normal frequency point of the hyperbolic frequency modulation signal group delay is initialized to an empty set; (7-2) Determine the lth τ The group delay τ(l) at discrete frequency points τ Does it meet the following normal value conditions: |τ(l τ ) - τ(l τ -1)| ≤ ητ(l τ ) and |τ(l τ ) - τ(l τ +1)| ≤ τη(l τ ) If the condition is true, then let A = A + 1, and let p be the discrete frequency index of the A-th normal frequency point. A =l τ P = P∪[p A ]; where P∪[p A ] indicates that p A Merge into set P; (7-3) Determine l τ <k hb If the condition is true, then let l be true. τ =l τ +1, and return to step (7-2); otherwise proceed to step (7-4); (7-4) Based on the discrete frequency index set P = [p1 p2 … p] of the normal frequency point of the hyperbolic frequency modulation signal group delay, P = [p1 p2 … p] A The hyperbolic frequency modulated signal group delay vector τ that satisfies the normal value condition is obtained. 0 : in, a is a discrete index of the normal frequency points of the time delay of A hyperbolic frequency modulated signal groups; In step (8), the hyperbolic frequency modulated signal group delay vector τ that meets the normal value condition is processed using the following method. 0 The iterative weighted fitting process includes the following steps: (8-1) Initialize the parameters of the hyperbolic frequency modulated signal group time delay iterative weighted fitting, specifically including the initialization of the following parameters: ① The maximum number of iterative weighted fitting iterations Q for the hyperbolic frequency modulated signal group delay is initialized to an integer Q > 1; ②Decision threshold ε for hyperbolic frequency modulated signal group delay iterative weighted fitting error Q Initialize to: 0 < ε Q Real numbers less than 1; ③ The number of iterations for the hyperbolic frequency modulated signal group time delay iterative weighted fitting, q, is initialized to: q = 1; ④ Group delay fitting error of hyperbolic frequency modulated signal after the 0th iteration of variable weight fitting Initialize to: ⑤ The hyperbolic frequency modulated signal group delay weight matrix W in the 0th iteration of variable weight fitting 0 Initialize to: in, Indicates A diagonal matrix of eigenvalues. (8-2) Calculate the intermediate parameter matrix b in the (q-1)th iteration of the weighted fitting. q - 1 : in, and These are the intermediate slope parameter and the intermediate intercept parameter in the (q-1)th iteration of the weighted fitting. It is a frequency auxiliary matrix. It is the pth a The frequency of a discrete frequency point; (8-3) Calculate the estimated value τ of the group time delay vector obtained in the (q-1)th iteration of the variable weight fitting. q-1 ; in, It is the estimated value of the group delay of the a-th normal frequency point in the (q-1)-th iteration of variable weight fitting; (8-4) Calculate the group delay estimation error of A normal frequency points in the q-th iteration of the weighted fitting. (8-5) Calculate the weights of the group delays of the A normal frequency points in the q-th iteration of the variable-weight fitting. in, represent The discrete frequency index a satisfies the range 1 ≤ a ≤ A. The maximum value, represent The discrete frequency index a satisfies the range 1 ≤ a ≤ A. The minimum value; (8-6) Obtain the hyperbolic frequency modulated signal group delay weight matrix W in the q-th iteration of the variable weight fitting. q : (8-7) Update the hyperbolic frequency modulated signal group delay fitting error after the qth iteration of weighted fitting. (8-8) Determine whether the following group delay iterative weighted fitting conditions are met: q < Q and If the condition is met, let q = q + 1 and return to step (8-2); otherwise, proceed to step (9).

2. The method for estimating hyperbolic frequency modulated signal parameters based on group delay iterative weighted fitting according to claim 1, characterized in that, In step (1), the hyperbolic frequency modulated signal data sequence x(n), n=0,1,…,N-1, is obtained using the following method, specifically including the following steps: The hyperbolic frequency modulated (HFM) signal data sequence x(n), n = 0, 1, ..., N-1, is obtained from the sensor by receiving real-time data from N sampling points, or by retrieving data from the memory starting from the moment the signal is detected, as the hyperbolic frequency modulated (HFM) signal data sequence x(n), n = 0, 1, ..., N-1, where N is the number of sampling points corresponding to the pulse width of the detected hyperbolic frequency modulated (HFM) signal, and is set to N = 2. a , where a is an integer greater than or equal to 5.

3. The method for estimating hyperbolic frequency modulated signal parameters based on group delay iterative weighted fitting according to claim 1, characterized in that, In step (2), the normalized smoothed amplitude spectrum Y of the hyperbolic frequency modulated signal is extracted using the following method. N (l), l=0,1...,N / 2-1, specifically including the following steps: (2-1) Perform a discrete Fourier transform on the data sequence x(n), n=0,1,…,N-1 to obtain the discrete Fourier transform result X(l) of the hyperbolic frequency modulated signal; Where l is the discrete frequency index, and j is the imaginary unit, i.e. (2-2) Calculate the magnitude of the discrete Fourier transform result X(l) of the hyperbolic frequency modulated signal to obtain the amplitude spectrum X of the hyperbolic frequency modulated signal. a (l); X a (l)=|X(l)|,l=0,1,…,N / 2-1; (2-3) Initialize the smoothing parameters of the hyperbolic frequency modulated signal amplitude spectrum, specifically including the initialization of the following parameters: ① The maximum number of smoothing iterations E of the hyperbolic frequency modulated signal amplitude spectrum is initialized to an integer E>1; ② The window length ξ for smoothing the amplitude spectrum of hyperbolic frequency modulation signals is initialized to an odd number of 3 ≤ ξ ≤ 15; ③ Decision threshold ε for amplitude spectrum smoothing error of hyperbolic frequency modulated signal E Initialize to: 0 < ε E Real numbers less than 1; ④ The number of iterations e for smoothing the amplitude spectrum of the hyperbolic frequency modulated signal is initialized to: e = 1; ⑤ The smoothed amplitude spectrum S0(l) of the hyperbolic frequency modulated signal after the 0th smoothing process is initialized as: S0(l) = X a (l), l=0,1,…,N / 2-1; ⑥ The amplitude spectrum smoothing error P(0) of the hyperbolic frequency modulated signal after the 0th smoothing process is initialized as: P(0)=0; (2-4) Smoothing amplitude spectrum S of hyperbolic frequency modulated signal after e-1th smoothing process e-1 (l) Perform smoothing processing to obtain the smoothed amplitude spectrum S of the hyperbolic frequency modulated signal after the e-th smoothing processing. e (l) is: Where, k s This is the index of the discrete frequency within the smoothing window corresponding to the l-th discrete frequency point; (2-5) Update the amplitude spectrum smoothing error P(e) of the hyperbolic frequency modulated signal after the e-th smoothing process; (2-6) Determine whether the following iterative smoothing conditions are met. e<E and If the condition is true, let e = e + 1 and return to step (2-4); otherwise, proceed to step (2-7). (2-7) Smooth amplitude spectrum S of hyperbolic frequency modulated signal after the e-th smoothing process e (l) Normalization is performed to obtain the normalized smoothed amplitude spectrum Y of the hyperbolic frequency modulated signal. N (l): Where max[S e (l)] represents S e The discrete frequency index l of (l) satisfies the range S within the range of 0 ≤ l ≤ N / 2-1. e The maximum value of (l).

4. The method for estimating hyperbolic frequency modulated signal parameters based on group delay iterative weighted fitting according to claim 1, characterized in that, In step (9), the intermediate slope parameter in the q-th iteration of the variable weight fitting is used. and the intermediate intercept parameter The estimated starting frequency of the hyperbolic frequency modulated signal is obtained using the following method. and the estimated value of the periodic slope

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