A Method, System and Medium for Estimating Parameters of a Sinusoidal Frequency Modulation Signal

Abstract

The present invention discloses a method, system and medium for estimating parameters of a sinusoidal frequency modulation signal. The method includes the following steps: obtaining a sinusoidal frequency modulation signal, calculating the instantaneous frequency after performing differential calculation on the sinusoidal frequency modulation signal, downsampling the instantaneous frequency according to a preset maximum number of periods, and then obtaining the spectrum of the downsampled instantaneous frequency; calculating the frequency estimation value f of the sinusoidal signal in the sinusoidal frequency modulation signal according to the maximum value in the spectrum me , calculating the period of the sinusoidal signal in the sinusoidal frequency modulation signal according to the frequency estimation value f me , calculating the weighted cumulative value y of the instantaneous phase according to the period of the sinusoidal signal, the instantaneous frequency and the frequency estimation value f me , calculating the modulation index estimation value m according to the weighted cumulative value y of the instantaneous phase f and the bandwidth estimation value Bw of the sinusoidal frequency modulation signal, and calculating the carrier frequency estimation value f0 of the sinusoidal frequency modulation signal according to the modulation index estimation value m f and the frequency estimation value f me . The algorithm logic of the present invention is simple and can better estimate various parameters of the sinusoidal frequency modulation signal.

Description

Technical Field

[0001] The present invention relates to the field of signal processing, and particularly to a method, system, and medium for estimating parameters of a sinusoidal frequency modulation signal. Background Art

[0002] As a typical non-linear frequency modulation signal, the sinusoidal frequency modulation signal has characteristics such as low interception rate and high range resolution, which makes it widely used in fields such as radar, communication, and sonar.

[0003] The detection and parameter estimation of sinusoidal frequency modulation signals have become hot research issues in current radar and communication signal processing. The current main methods are to use the reassignment smoothed pseudo-Wigner-Ville distribution (RSPWVD) method or the Hough transform to estimate the parameters of sinusoidal frequency modulation signals, but they have problems such as high computational complexity and inaccurate cross-term estimation of signal parameters. Later, some scholars estimated signal parameters by fitting a high-order polynomial model for sinusoidal frequency modulation signals, but they are limited by the modulation index coefficient.

[0004] Patent CN110737868A discloses a method for estimating parameters of a sinusoidal frequency modulation signal. This method estimates the parameters of a sinusoidal signal based on a baseband signal, that is, when estimating a time signal, the carrier frequency signal of the signal needs to be accurately estimated first. And it is assumed that when the value range of the modulation index μ is the algorithm used is different from when the modulation index is greater than Finally, a method with higher accuracy is selected as the final estimation result. Therefore, this method has high algorithm complexity and large computational redundancy. It greatly limits its scope of use. Summary of the Invention

[0005] The technical problem to be solved by the present invention is: aiming at the technical problems existing in the prior art, the present invention provides a method, system, and medium for estimating parameters of a sinusoidal frequency modulation signal, whose algorithm logic is simple and can better estimate various parameters of the sinusoidal frequency modulation signal.

[0006] To solve the above technical problems, the technical solution proposed by the present invention is:

[0007] A method for estimating parameters of a sinusoidal frequency modulation signal, comprising the following steps:

[0008] Obtain a sinusoidal frequency modulation signal, perform differential calculation on the sinusoidal frequency modulation signal and then obtain the instantaneous frequency, downsample the instantaneous frequency according to a preset maximum number of periods, and then obtain the spectrum of the downsampled instantaneous frequency;

[0009] According to the position where the maximum value in the spectrum is located, calculate the frequency estimate value f of the sinusoidal signal in the sinusoidal frequency modulation signal me, and then according to the frequency estimation value f me and the signal pulse width to estimate the period of the sine signal in the sinusoidal frequency modulation signal; according to the period, instantaneous frequency of the sine signal in the sinusoidal frequency modulation signal and the frequency estimation value f me calculate the instantaneous phase weighted cumulative value y; calculate the modulation index estimation value m according to the instantaneous phase weighted cumulative value y f and the sinusoidal frequency modulation signal bandwidth estimation value Bw; according to the modulation index estimation value m f and the frequency estimation value f me calculate the carrier frequency estimation value f0 of the sinusoidal frequency modulation signal.

[0010] Further, the step of downsampling the instantaneous frequency according to a preset maximum number of periods and then finding the spectrum of the downsampled instantaneous frequency specifically includes: multiplying the system sampling rate Fs by the pulse width Pw of the sinusoidal frequency modulation signal, then dividing by the preset maximum number of periods, rounding down the calculation result to obtain the sampling multiple K, downsampling the instantaneous frequency according to the sampling multiple K, and performing a preset N-point Fourier transform on the downsampled instantaneous frequency to obtain the corresponding spectrum.

[0011] Further, the step of calculating the frequency estimation value f of the sine signal in the sinusoidal frequency modulation signal according to the position where the maximum value in the spectrum is located me specifically includes:

[0012] finding the position idx where the maximum amplitude is located in the spectrum max , according to the position idx max calculate the initial frequency estimation value of the sine signal in the sinusoidal frequency modulation signal according to the offset relative to the spectrum center, the original signal sampling rate Fs' and the decimation factor K';

[0013] round the product of the initial frequency estimation value and the pulse width Pw of the sinusoidal frequency modulation signal to obtain the initial estimated number M of periods of the sine signal in the sinusoidal frequency modulation signal e ;

[0014] divide the initial estimated number M of periods by the pulse width Pw of the sinusoidal frequency modulation signal to obtain the frequency estimation value f of the sine signal in the sinusoidal frequency modulation signal e me .

[0015] Further, the function expression of the initial frequency estimation value of the sine signal in the sinusoidal frequency modulation signal is as follows:

[0016]

[0017] In the above formula, idx maxis the position where the maximum amplitude in the spectrum is located, N is the number of points of the Fourier transform, Fs′ is the original sampling rate of the signal, and K′ is the preset decimation factor.

[0018] Further, based on the period of the sine signal in the sinusoidal frequency modulation signal, the instantaneous frequency, and the estimated frequency f of the sine signal in the sinusoidal frequency modulation signal me Calculating the instantaneous phase weighted cumulative value y includes the following steps:

[0019] Dividing the pulse width Pw of the sinusoidal frequency modulation signal by the period of the sinusoidal frequency modulation signal, and rounding down the calculation result to obtain the number N of periods of the sine signal contained in a single pulse;

[0020] Select a target period from the N periods, and based on the instantaneous frequency and the estimated frequency f of the sine signal in the sinusoidal frequency modulation signal me Calculate the instantaneous phase weighted cumulative value within each period of the target period respectively. If there is only one period of the sine signal in the target period, the estimated modulation index m f Is estimated using the instantaneous phase weighted cumulative value y within a single period. If the target period includes at least two periods of the sine signal, the estimated modulation index m f Is estimated using the average value Y of the instantaneous phase weighted cumulative values of multiple periods.

[0021] Further, the estimated modulation index m f The functional expression of is:

[0022] When there is only one period of the sine signal in the target period:

[0023] m f = 2|y|

[0024] When the target period includes at least two periods of the sine signal:

[0025] m f = 2|Y|

[0026] In the above formula, y is the instantaneous phase weighted cumulative value within a single period, and Y is the average value of the instantaneous phase weighted cumulative values.

[0027] Further, the functional expression of the estimated bandwidth Bw of the sinusoidal frequency modulation signal is:

[0028] When there is only one period of the sine signal in the target period:

[0029]

[0030] When the target period includes at least two periods of the sine signal:

[0031]

[0032] In the above formula, y is the instantaneous phase weighted cumulative value within a single period, Y is the average value of the instantaneous phase weighted cumulative value, and T is the period of the sine signal in the sine frequency modulation signal.

[0033] Furthermore, according to the estimated modulation index m f and the estimated frequency f me The specific steps for calculating the estimated carrier frequency f0 of the sine frequency modulation signal include: selecting a target period from the N periods, integrating the instantaneous frequency of each period in the target period, and dividing the integration result by the period of the sine frequency modulation signal respectively to obtain the estimated carrier frequency of each period in the target period. If there is only one period in the target period, the estimated carrier frequency is the value of the estimated carrier frequency f0. If the target period includes at least two consecutive periods, the average value of all estimated carrier frequencies is the value of the estimated carrier frequency f0.

[0034] The present invention also proposes a sine frequency modulation signal parameter estimation system, including:

[0035] A signal processing unit, configured to obtain a sine frequency modulation signal, perform differential calculation on the sine frequency modulation signal to obtain the instantaneous frequency, downsample the instantaneous frequency according to a preset maximum number of periods, and then obtain the spectrum of the downsampled instantaneous frequency;

[0036] A parameter estimation unit, configured to calculate the estimated frequency f of the sine signal in the sine frequency modulation signal according to the position where the maximum value in the spectrum is located me , and further calculate the period of the sine signal in the sine frequency modulation signal according to the estimated frequency f me Calculate the instantaneous phase weighted cumulative value y according to the period of the sine signal in the sine frequency modulation signal, the instantaneous frequency, and the estimated frequency f of the sine signal in the sine frequency modulation signal me Calculate the estimated modulation index m according to the instantaneous phase weighted cumulative value y f and the estimated bandwidth Bw of the sine frequency modulation signal, and calculate the estimated carrier frequency f0 of the sine frequency modulation signal according to the frequency modulation index m f of the sine frequency modulation signal and the frequency f of the sine signal me

[0037] The present invention also proposes a computer-readable storage medium storing a computer program programmed or configured to execute any one of the sine frequency modulation signal parameter estimation methods.

[0038] Compared with the prior art, the advantages of the present invention are:

[0039] ​The present invention calculates the instantaneous frequency after performing differential calculation on the sinusoidal frequency modulation signal. The instantaneous frequency is a single-carrier signal. The sinusoidal frequency modulation signal is modulated on a frequency band, which is convenient for frequency-domain analysis. The instantaneous frequency is downsampled to improve the frequency resolution and reduce the influence of the frequency of the sinusoidal frequency modulation signal on the normalized error of parameter estimation. Fourier analysis is performed on the down-converted instantaneous frequency, and the frequency spectrum diagram can be obtained. The frequency estimation value of the sinusoidal frequency modulation signal can be conveniently obtained on the frequency spectrum diagram, which provides convenience for the estimation of other parameters such as the bandwidth and carrier frequency of the sinusoidal frequency modulation signal. In addition, the present invention obtains the bandwidth estimation value and carrier frequency estimation value of the sinusoidal frequency modulation signal by averaging the estimation values within multiple periods, reduces the influence of noise on the estimation, and improves the estimation accuracy. Description of the Drawings

[0040] Figure 1 It is a flowchart of an embodiment of the present invention.

[0041] Figure 2 It is a curve diagram of the bandwidth estimation error of the sinusoidal frequency modulation signal in an embodiment of the present invention.

[0042] Figure 3 It is a curve diagram of the carrier frequency estimation error of the sinusoidal frequency modulation signal in an embodiment of the present invention. Detailed Embodiment

[0043] The present invention will be further described below in conjunction with the accompanying drawings of the specification and specific preferred embodiments, but the protection scope of the present invention is not limited thereby.

[0044] The expression of the sinusoidal frequency modulation signal is:

[0045]

[0046] where s(t) is the received sinusoidal frequency modulation signal, f0 is the carrier frequency to be estimated, m f is the modulation index to be estimated, f m is the frequency of the sinusoidal signal in the sinusoidal frequency modulation signal to be estimated, θ is the initial phase of the sinusoidal signal in the sinusoidal frequency modulation signal, j is the imaginary unit in the complex number field, and A is the signal amplitude of the sinusoidal frequency modulation signal.

[0047] Differentiate the sinusoidal frequency modulation signal, that is, take the conjugate product of the sinusoidal frequency modulation signals at two different times, and we can get:

[0048]

[0049] where s(t) and s(t - 1) are the received sinusoidal frequency modulation signals at two different times, f0 is the carrier frequency to be estimated, m f is the modulation index to be estimated, f mLet \(f\) be the frequency of the sine signal in the sinusoidal frequency modulation signal to be estimated, \(\theta\) be the initial phase of the sine signal in the sinusoidal frequency modulation signal, \(j\) be the imaginary unit in the complex number field, and \(A\) be the signal amplitude of the sinusoidal frequency modulation signal;

[0050] Then, find the instantaneous phase of the signal \(s(t)s^*(t - 1)\) after taking the difference, and its instantaneous frequency calculation can be expressed as:

[0051]

[0052] That is, we can obtain:

[0053]

[0054] where \(m\) f ' = \(m\) f \(f\) m , \(f_0\) is the carrier frequency to be estimated, \(m\) f is the modulation index to be estimated, \(f\) m is the frequency of the sine signal in the sinusoidal frequency modulation signal to be estimated, \(\theta\) is the initial phase of the sine signal in the sinusoidal frequency modulation signal, and \(j\) is the imaginary unit in the complex number field.

[0055] As can be seen from Equation (4), the instantaneous frequency is the time-domain waveform of the sine signal in the sinusoidal frequency modulation signal. It is a single-carrier signal and has a single spectral line in the frequency spectrum. That is, perform a Fourier transform on the instantaneous frequency to obtain the corresponding frequency spectrum diagram, and find the position corresponding to the maximum amplitude in the frequency spectrum, so as to obtain the estimated value of the frequency \(f\) m of the sine signal in the sinusoidal frequency modulation signal, denoted as \(\hat{f}\) me .

[0056] However, when the sinusoidal frequency modulation signal is unknown, the change range of the frequency \(f\) m of the sine signal in the sinusoidal frequency modulation signal is very large. Since the system sampling rate is fixed at \(F_s\), the number of points for the Fourier transform is also fixed, so the frequency spectrum resolution is also fixed. Due to different frequencies \(f\) m , the normalized error of the estimated value \(\hat{f}\) me varies greatly.

[0057] For example, when \(F_s = 4800\ MHz\) and the number of points for the Fourier transform \(N = 16384\), the corresponding frequency spectrum resolution is When \(f\) m = 100\ MHz\), the estimation error caused by the frequency spectrum resolution is \(df = 0.00146484375\ MHz\), while when \(f\) m = 1\ MHz\), the corresponding normalized error is \(df = 0.146484375\ MHz\), which has a great impact on subsequent estimations.

[0058] Therefore, based on this, we further improve and propose a method for estimating the parameters of a sinusoidal frequency-modulated signal, for the instantaneous frequency to perform downsampling to reduce the sampling rate and improve the frequency resolution, as Figure 1 shown, including the following steps:

[0059] S1) Obtain a sinusoidal frequency-modulated signal, perform differential calculation on the sinusoidal frequency-modulated signal and then obtain the instantaneous frequency, which is the time-domain waveform of the sinusoidal signal in the sinusoidal frequency-modulated signal. Then, downsample the instantaneous frequency according to the preset maximum number of periods M_max, and perform Fourier transform on the downsampled instantaneous frequency to obtain the corresponding spectrum;

[0060] S2) According to the position of the maximum value in the spectrum, the frequency estimation value f me of the sinusoidal signal in the sinusoidal frequency-modulated signal can be calculated. Furthermore, according to the frequency estimation value f me estimate the period of the sinusoidal signal in the sinusoidal frequency-modulated signal; According to the period, instantaneous frequency of the sinusoidal signal in the sinusoidal frequency-modulated signal and the frequency estimation value f me calculate the instantaneous phase weighted cumulative value y; Calculate the modulation index estimation value m f and the sinusoidal frequency-modulated signal bandwidth estimation value Bw according to the instantaneous phase weighted cumulative value y; According to the modulation index estimation value m f and the frequency estimation value f me calculate the carrier frequency estimation value f0 of the sinusoidal frequency-modulated signal.

[0061] In this embodiment, the step of downsampling the instantaneous frequency according to the preset maximum number of periods and then obtaining the corresponding spectrum by performing a transform on the downsampled instantaneous frequency specifically includes:

[0062] S1.1) Multiply the system sampling rate Fs by the pulse width Pw of the sinusoidal frequency-modulated signal to obtain the total number of sampling points of the pulse signal, and then divide it by twice the preset maximum number of periods M_max, that is, the downsampling multiple K is obtained. It can be seen from formula (5) that as long as the number of signal periods is less than or equal to the preset number of periods, the extracted signal still complies with the Nyquist sampling theorem; The calculation expression of the sampling multiple K is as follows:

[0063]

[0064] In the above formula, represents rounding down, Fs is the system sampling rate, Pw is the pulse width of the sinusoidal frequency-modulated signal, and M_max is the preset maximum number of periods;

[0065] S1.2) Downsample the instantaneous frequency according to the sampling multiple K;

[0066] S1.3) Perform an N-point Fourier transform on the downsampled instantaneous frequency to obtain the corresponding spectrum.

[0067] In this embodiment, in step S2), according to the position of the maximum value in the spectrum, calculate the frequency estimation value f of the sine signal in the sinusoidal frequency modulation signal me The steps specifically include:

[0068] S2.1a) Find the position idx of the maximum amplitude in the spectrum max , and according to the position idx max Calculate the initial frequency estimation value f' of the sine signal in the sinusoidal frequency modulation signal based on the offset relative to the spectrum center, the original signal sampling rate Fs', and the decimation factor K' me , and the calculation formula is as follows:

[0069]

[0070] In the above formula, idx max is the position of the maximum amplitude in the spectrum, N is the number of points of the Fourier transform, Fs' is the original signal sampling rate, and K' is the preset decimation factor;

[0071] S2.1b) Round the product of the initial frequency estimation value f' me and the pulse width Pw of the sinusoidal frequency modulation signal to obtain the initial estimated number M of cycles of the sine signal in the sinusoidal frequency modulation signal e , and the calculation formula is as follows:

[0072] M e = round(f' me ·Pw) (7)

[0073] In the above formula, round represents rounding, f' me is the initial frequency estimation value of the sine signal in the sinusoidal frequency modulation signal, and Pw is the pulse width of the sinusoidal frequency modulation signal;

[0074] S2.1c) Divide the initial estimated number M of cycles e by the pulse width Pw of the sinusoidal frequency modulation signal to obtain the frequency estimation value f of the sine signal in the sinusoidal frequency modulation signal me , and the functional expression of the frequency estimation value f of the sine signal in the sinusoidal frequency modulation signal me is as follows:

[0075]

[0076] In the above formula, M e is the initial estimated number of cycles of the sine signal in the sinusoidal frequency modulation signal, and Pw is the pulse width of the sinusoidal frequency modulation signal.

[0077] Obtain the frequency estimation value \(f\) of the sine signal in the sinusoidal frequency modulation signal me After that, the period of the sine signal in the sinusoidal frequency modulation signal can be estimated, that is

[0078] In this embodiment, according to the period, instantaneous frequency of the sine signal in the sinusoidal frequency modulation signal and the frequency estimation value \(f\) of the sine signal in the sinusoidal frequency modulation signal me Calculating the instantaneous phase weighted cumulative value \(y\) includes the following steps:

[0079] S2.2a) Divide the pulse width \(Pw\) of the sinusoidal frequency modulation signal by the period of the sine signal in the sinusoidal frequency modulation signal, and round down the calculation result to obtain the number \(N\) of sine signal periods contained in a single pulse. The calculation formula is as follows:

[0080]

[0081] In the above formula, represents rounding down, \(T\) is the period of the sine signal in the sinusoidal frequency modulation signal, \(f\) me is the frequency estimation value of the sine signal in the sinusoidal frequency modulation signal, and \(Pw\) is the pulse width of the sinusoidal frequency modulation signal;

[0082] S2.2b) Select the target period from the \(N\) periods, and calculate the instantaneous phase weighted cumulative value within each period of the target period according to the instantaneous frequency and the frequency estimation value \(f\) of the sine signal in the sinusoidal frequency modulation signal me If there is only one sine signal period in the target period, the modulation index estimation value \(m\) f is estimated using the instantaneous phase weighted cumulative value \(y\) within a single period. If there are at least two sine signal periods in the target period, the modulation index estimation value \(m\) f is estimated using the average value \(Y\) of the instantaneous phase weighted cumulative values of multiple periods.

[0083] In this embodiment, the functional expression of the instantaneous phase weighted cumulative value \(y\) is:

[0084]

[0085] In the above formula is the instantaneous frequency, \(f\) me is the frequency estimation value of the sine signal in the sinusoidal frequency modulation signal.

[0086] In this embodiment, the functional expression of the average value \(Y\) of the instantaneous phase weighted cumulative values is:

[0087]

[0088] In the above formula, k ranges from 1 to M, where M is the number of accumulation periods, and y(kT) is the instantaneous phase weighted cumulative value within the k-th period.

[0089] For the relationship between the instantaneous phase weighted cumulative value y and the estimated value m of the modulation index f and the estimated value Bw of the bandwidth of the sinusoidal frequency modulation signal, the derivation is as follows:

[0090]

[0091] In the above formula, m f ' = m f f m , m f is the modulation index to be estimated, f m is the frequency of the sine signal to be estimated in the sinusoidal frequency modulation signal, θ is the initial phase of the sine signal in the sinusoidal frequency modulation signal, j is the imaginary unit in the complex number field, and T is the period of the sine signal in the sinusoidal frequency modulation signal;

[0092] According to the properties of the sine function,

[0093]

[0094] In the above formula, T is the period of the sine signal in the sinusoidal frequency modulation signal, and ω is the angular frequency of the sine signal in the sinusoidal frequency modulation signal.

[0095] Then, according to equations (12) and (13), we can obtain:

[0096]

[0097] In the above formula, m f ' = m f f m , m f is the modulation index to be estimated, f m is the frequency of the sine signal to be estimated in the sinusoidal frequency modulation signal, θ is the initial phase of the sine signal in the sinusoidal frequency modulation signal, T is the period of the sine signal in the sinusoidal frequency modulation signal, and y(kT) is the instantaneous phase weighted cumulative value within each period.

[0098] Therefore, after step S2.2b) of this embodiment, according to the average value Y of the instantaneous phase weighted cumulative value, the estimated value m of the modulation index f and the estimated value Bw of the bandwidth of the sinusoidal frequency modulation signal, the specific steps include: step S2.2c) obtaining the estimated value m of the modulation index f and the estimated value Bw of the bandwidth of the sinusoidal frequency modulation signal. The function expressions of the estimated value m of the modulation index f and the estimated value Bw of the bandwidth of the sinusoidal frequency modulation signal are:

[0099] When there is only one period of the sine signal in the target period:

[0100] m f = 2|y| (15)

[0101]

[0102] When there are at least two periods of the sine signal in the target period:

[0103]

[0104]

[0105] In formulas (15) to (18), y is the instantaneous phase weighted cumulative value within a single period, Y is the average value of the instantaneous phase weighted cumulative values over multiple periods, and T is the period of the sine signal in the sine frequency modulation signal.

[0106] In this embodiment, according to the modulation index estimated value m f and the frequency estimated value f me The specific steps for calculating the carrier frequency estimated value f0 of the sine frequency modulation signal include:

[0107] S2.3) Select a target period from the N periods, integrate the instantaneous frequency of each period in the target period and divide the integration result by the period of the sine frequency modulation signal respectively to obtain the carrier frequency estimated value f(kT) of each period in the target period. If there is only one period in the target period, the carrier frequency estimated value f(kT) is the value of the carrier frequency estimated value f0. If there are at least two consecutive periods in the target period, the average value of all carrier frequency estimated values f(kT) is the value of the carrier frequency estimated value f0.

[0108] For the instantaneous frequency The relationship between the period T of the sine frequency modulation signal and the carrier frequency estimated value f0 is deduced as follows:

[0109] Within one period T, there is:

[0110]

[0111] In the above formula, is the instantaneous frequency, and T is the period of the sine signal in the sine frequency modulation signal;

[0112] Substitute formula (4) into formula (19) to obtain:

[0113]

[0114] In the above formula, m f ' = mf f m , where \(f_0\) is the carrier frequency to be estimated, and \(m\) f is the modulation index, \(f\) m is the frequency of the sine signal in the sinusoidal frequency modulation signal, \(T\) is the period of the sine signal in the sinusoidal frequency modulation signal, and \(m\) f 、\(f\) m and \(T\) have been estimated by the foregoing steps;

[0115] Therefore, the estimated value of the carrier frequency \(f_0\) is:

[0116]

[0117] In the above formula, \(A\) is the integration result of the instantaneous frequency in one period, and \(T\) is the period of the sine frequency modulation signal;

[0118] Based on Equation (21), the functional expression of the estimated carrier frequency \(f(kT)\) can be obtained as:

[0119]

[0120] In the above formula, \(k\) ranges from 1 to \(M\), where \(M\) is the number of accumulation periods, is the instantaneous frequency, and \(T\) is the period of the sine signal in the sinusoidal frequency modulation signal.

[0121] In step S2) of this embodiment, the target period may only include the period of one sine signal, which is applicable to the case where the estimation accuracy requirement is not high. While meeting the system estimation performance, it reduces the system overhead and achieves a balance between speed and accuracy. When the target period includes at least two sine signal periods, it is applicable to the case where the accuracy requirement is relatively high. By calculating the estimated values within multiple periods and taking their average as the final estimated result, the influence of noise on the estimation is reduced and the estimation accuracy is improved.

[0122] The results obtained by simulating the method in this embodiment under the signal-to-noise ratio of 5 - 15 dB are as shown in Figure 2 and Figure 3 . It can be seen that when the signal-to-noise ratio is lower than 8 dB, the normalized errors of the carrier frequency and bandwidth estimation of the sinusoidal frequency modulation signal are both less than 10 -3 . And the signal-to-noise ratio of about 8 dB is the detection threshold for the non-cooperative detection system for pulse signals. Under this signal-to-noise ratio, the method of this embodiment can better estimate the signal parameters, with low complexity and strong practical value.

[0123] For the sine wave frequency of the sinusoidal frequency modulation signal in this embodiment, its initial estimation accuracy is related to the number of Fourier transform points. The error brought by the Fourier transform is very small. By downsampling the instantaneous frequency, the resulting normalized error is less than 0.1. And an error of 0.1 is not sufficient to affect the number of periods \(M\) eThe estimate of M e The estimate of is independent of the first estimate value of f me and is only related to the pulse width Pw. At the same time, it can be seen from Equation (6) that in this embodiment, the frequency estimate value f me is only related to the pulse width Pw, and its estimation accuracy is linearly related to the pulse width Pw. Therefore, the influence of other parameters is eliminated, and the estimation accuracy is improved.

[0124] This embodiment also proposes a system for estimating the parameters of a sinusoidal frequency modulation signal, including:

[0125] A signal processing unit, configured to obtain a sinusoidal frequency modulation signal, perform differential calculation on the sinusoidal frequency modulation signal to obtain an instantaneous frequency, perform downsampling on the instantaneous frequency according to a preset maximum number of periods, and then obtain the spectrum of the downsampled instantaneous frequency;

[0126] A parameter estimation unit, configured to calculate the frequency estimate value f of the sinusoidal signal in the sinusoidal frequency modulation signal according to the position where the maximum value in the spectrum is located me , and further calculate the period of the sinusoidal signal in the sinusoidal frequency modulation signal according to the frequency estimate value f me and the signal pulse width, calculate the instantaneous phase weighted cumulative value y according to the period, instantaneous frequency and the frequency estimate value f of the sinusoidal signal in the sinusoidal frequency modulation signal me calculate the modulation index estimate value m according to the instantaneous phase weighted cumulative value y f and the sinusoidal frequency modulation signal bandwidth estimate value Bw, and calculate the carrier frequency estimate value f0 of the sinusoidal frequency modulation signal according to the frequency estimate value f me , modulation index estimate value m f Calculate the carrier frequency estimate value f0 of the sinusoidal frequency modulation signal.

[0127] This embodiment also proposes a computer-readable storage medium, which stores a computer program programmed or configured to execute the method for estimating the parameters of a sinusoidal frequency modulation signal according to this embodiment.

[0128] The above is only a preferred embodiment of the present invention, and does not impose any form of limitation on the present invention. Although the present invention has been disclosed above with a preferred embodiment, it is not intended to limit the present invention. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention without departing from the technical solution of the present invention shall fall within the scope of the technical solution of the present invention.

Claims

1. A method for estimating the parameters of a sinusoidal frequency modulation signal, characterized in that Including the following steps: Obtain a sinusoidal frequency modulation signal, perform differential calculation on the sinusoidal frequency modulation signal to obtain the instantaneous frequency, downsample the instantaneous frequency according to a preset maximum number of periods, and then obtain the spectrum of the downsampled instantaneous frequency. The steps of downsampling the instantaneous frequency according to a preset maximum number of periods and then obtaining the spectrum of the downsampled instantaneous frequency specifically include: multiplying the system sampling rate Fs by the pulse width Pw of the sinusoidal frequency modulation signal, then dividing by the preset maximum number of periods, rounding down the calculation result to obtain the sampling multiple K, downsampling the instantaneous frequency according to the sampling multiple K, and performing a preset N-point Fourier transform on the downsampled instantaneous frequency to obtain the corresponding spectrum; Calculate the frequency estimation value \(f\) of the sine signal in the sine frequency modulation signal according to the position of the maximum value in the said frequency spectrum me , and then according to the frequency estimation value \(f\) me estimate the period of the sine signal in the sine frequency modulation signal; according to the period, instantaneous frequency of the sine signal in the sine frequency modulation signal and the frequency estimation value \(f\) me calculate the instantaneous phase weighted cumulative value \(y\); calculate the modulation index estimation value \(m\) according to the instantaneous phase weighted cumulative value \(y\) f and the sine frequency modulation signal bandwidth estimation value \(B_w\); according to the modulation index estimation value \(m\) f and the frequency estimation value \(f\) me calculate the carrier frequency estimation value \(f_0\) of the sine frequency modulation signal.

2. The method for estimating parameters of a sinusoidal frequency modulation signal according to claim 1, wherein Calculate the frequency estimation value f of the sine signal in the sinusoidal frequency modulation signal according to the position of the maximum value in the said frequency spectrum me The steps specifically include: Locate the position idx where the maximum amplitude in the spectrum lies max , based on the position idx max calculate the initial estimated value of the frequency of the sine signal in the chirp signal according to the offset relative to the spectrum center, the original sampling rate Fs' of the signal, and the decimation factor K' Round the product of the initial frequency estimate and the pulse width Pw of the sinusoidal frequency modulation signal to obtain an initial estimated number M of periods of the sinusoidal signal in the sinusoidal frequency modulation signal e ; Divide the initial cycle estimation number M e by the pulse width Pw of the sinusoidal frequency modulation signal to obtain the frequency estimation value f of the sinusoidal signal in the sinusoidal frequency modulation signal me .

3. The method for estimating the parameters of a sinusoidal frequency modulation signal according to claim 2, wherein The function expression of the initial estimated value of the frequency of the sinusoidal signal in the sinusoidal frequency modulation signal is as follows: In the above formula, idx max is the position where the maximum amplitude in the spectrum is located, N is the number of points of the Fourier transform, Fs′ is the original sampling rate of the signal, and K′ is the preset decimation factor.

4. The sine frequency modulation signal parameter estimation method according to claim 1, wherein Estimate the period, instantaneous frequency of the sine signal in the sine frequency modulation signal and the estimated value f of the frequency of the sine signal in the sine frequency modulation signal me Calculating the weighted cumulative value y of the instantaneous phase includes the following steps: Dividing the pulse width Pw of the sinusoidal frequency modulation signal by the period of the sinusoidal frequency modulation signal, and rounding down the calculation result to obtain the number of periods N of the sinusoidal signal contained in a single pulse; Select a target period from the N periods, and estimate the frequency f of the sine signal in the instantaneous frequency and the sinusoidal frequency modulation signal me Calculate the weighted cumulative value of the instantaneous phase in each period of the target period respectively. If there is only one period of the sine signal in the target period, the estimated value m of the modulation index f Use the weighted cumulative value y of the instantaneous phase within a single period for estimation. If the target period includes at least two periods of the sine signal, the estimated value m of the modulation index f Use the average value Y of the weighted cumulative values of the instantaneous phase in multiple periods for estimation.

5. The method for estimating the parameters of a sinusoidal frequency modulation signal according to claim 4, characterized in that, The estimated modulation index value m f has the following functional expression: When there is only one period of the sinusoidal signal in the target period: m f = 2|y|; When the target period includes at least two periods of the sinusoidal signal: m f = 2|Y| In the above formula, y is the weighted cumulative value of the instantaneous phase within a single period, and Y is the average value of the weighted cumulative values of the instantaneous phase.

6. The sine frequency modulation signal parameter estimation method according to claim 4, wherein The function expression of the estimated value Bw of the bandwidth of the sinusoidal frequency modulation signal is: When there is only one period of the sinusoidal signal in the target period: When the target period includes at least two periods of the sinusoidal signal: In the above formula, y is the weighted cumulative value of the instantaneous phase within a single period, Y is the average value of the weighted cumulative values of the instantaneous phase, and T is the period of the sinusoidal signal in the sinusoidal frequency modulation signal.

7. The method for estimating the parameters of a sinusoidal frequency modulation signal according to claim 4, wherein According to the modulation index estimation value m f and the frequency estimation value f me The specific steps for calculating the carrier frequency estimation value f0 of the sinusoidal frequency modulation signal are as follows: Select a target period from the N periods, integrate the instantaneous frequency of each period in the target period, and divide the integration results by the period of the sinusoidal frequency modulation signal respectively to obtain the carrier frequency estimation value of each period in the target period. If there is only one period in the target period, the carrier frequency estimation value is the value of the carrier frequency estimation value f0. If the target period includes at least two consecutive periods, the average value of all carrier frequency estimation values is the value of the carrier frequency estimation value f0.

8. A system for estimating the parameters of a sinusoidal frequency modulation signal, characterized in that Including: A signal processing unit, configured to obtain a sinusoidal frequency modulation signal, perform differential calculation on the sinusoidal frequency modulation signal to obtain the instantaneous frequency, downsample the instantaneous frequency according to a preset maximum number of periods, and then obtain the spectrum of the downsampled instantaneous frequency. The steps of downsampling the instantaneous frequency according to a preset maximum number of periods and then obtaining the spectrum of the downsampled instantaneous frequency specifically include: multiplying the system sampling rate Fs by the pulse width Pw of the sinusoidal frequency modulation signal, then dividing by the preset maximum number of periods, rounding down the calculation result to obtain the sampling multiple K, downsampling the instantaneous frequency according to the sampling multiple K, and performing a preset N-point Fourier transform on the downsampled instantaneous frequency to obtain the corresponding spectrum; A parameter estimation unit for calculating a frequency estimation value f of a sine signal in the sine frequency modulation signal according to a position where a maximum value in the spectrum is located me , and then calculating a period of the sine signal in the sine frequency modulation signal according to the frequency estimation value f me , calculating an instantaneous phase weighted cumulative value y according to the period, the instantaneous frequency of the sine signal in the sine frequency modulation signal, and the frequency estimation value f of the sine signal in the sine frequency modulation signal me , calculating a modulation index estimation value m according to the instantaneous phase weighted cumulative value y f , and estimating a bandwidth Bw of the sine frequency modulation signal, and calculating a carrier frequency estimation value f0 of the sine frequency modulation signal according to the frequency modulation index m f of the sine frequency modulation signal and the frequency f of the sine signal me .

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that is programmed or configured to execute the sinusoidal frequency modulation signal parameter estimation method according to any one of claims 1 to 7.

Images