A method and device for accurately estimating the frequency of a Doppler signal

Abstract

The present invention discloses a method and device for accurately estimating the frequency of a Doppler signal. Aiming at the traditional iterative complex interpolation method based on DFT, the iterative and fine estimation parts in the algorithm are removed, and on this basis, a polynomial interpolation method is added. The polynomial interpolation provides higher degrees of freedom and more accurate approximation capabilities. The polynomial interpolation method can better capture the complexity and non-linear characteristics between data, thereby providing more accurate interpolation results. Based on the iterative complex interpolation method based on DFT, the present invention accurately estimates the frequency of the Doppler signal model, and further provides important scientific data for in-depth research on planets and asteroids.

Description

Technical Field

[0001] The present invention belongs to the fields of planetary exploration and Doppler signal processing, and particularly relates to a method and device for accurately estimating the frequency of Doppler signals. Technical Background

[0002] In the past few decades, humans have carried out a series of deep space exploration missions from near to far, covering a wide range from the Moon to Mars, Venus, and other planets in the solar system. In this process, space agencies in the United States, Europe, Japan and other places have successively launched more than 100 planetary probes, which have greatly enriched human understanding of the solar system and enhanced the depth and breadth of cosmic exploration.

[0003] The Doppler signal of a planetary probe is a crucial tool in the field of planetary exploration. Analyzing the Doppler frequency shift of the radio frequency signals sent to and returned by the planetary probe can obtain detailed information about the gravitational field, gravity field, rotational dynamics, and orbital parameters of the target celestial body. In addition, analyzing the Doppler signal can also help determine the speed of the spacecraft, thereby constructing an accurate orbital model and verifying the gravitational theory. Analyzing and utilizing the Doppler signal of planetary probes has significantly promoted our understanding of the dynamics and structures of planets, satellites, and asteroids, and is a crucial tool in the development of planetary science.

[0004] The overall Doppler measurement system is mainly divided into three categories according to the composition types of the uplink and downlink: one-way Doppler measurement system, two-way Doppler measurement system, and three-way Doppler measurement system.

[0005] Among them, the two-way Doppler measurement system is widely used. In the reception of the downlink signal in this system, the signal receives the signal data transmitted by the planetary probe through a VLBI antenna, and the frequency of the signal is reduced to the intermediate frequency through analog high-speed downconversion. At this time, the signal frequency is in the range of 0.5 - 2 MHz. Through an A / D sampler, the analog signal is converted into a digital signal, and digital downconversion technology is used to reduce the sampling rate of the signal again. Finally, the frequency of the signal is estimated and input into the upper computer.

[0006] In terms of Doppler signal frequency estimation, traditional algorithms are mainly divided into two categories: time-domain methods and frequency-domain methods. Time-domain methods include zero-crossing detection method, phase fitting method, phase difference weighted average method, etc. However, when dealing with low signal-to-noise ratio signals, the above methods often show low accuracy. Therefore, frequency-domain methods have become the main means of dealing with such signals. Frequency-domain methods mainly include ratio method, spectrum zooming method, energy centroid method, and phase difference method, etc. Among them, the ratio algorithm based on discrete Fourier transform is a common method. However, due to computational considerations, fast Fourier transform has also been widely used. However, when the signal frequency is close to the quantization frequency point, the above two methods will introduce large errors. Summary of the Invention

[0007] The object of the present invention is to overcome the problem of large computational complexity in the iterative process of the DFT-based iterative complex interpolation method, remove the iterative and fine estimation parts in the algorithm, and on this basis, add a polynomial interpolation method to provide a method for accurately estimating the Doppler signal frequency. By removing the iterative and fine estimation parts in the algorithm and using quadratic polynomial fitting, the position of the maximum frequency peak is accurately estimated, improving the accuracy of the algorithm.

[0008] To achieve the above object of the invention, the technical solution of the present invention is a method for accurately estimating the Doppler signal frequency. Through in-depth research on the traditional DFT-based iterative complex interpolation method, it is found that the influence of iteration and fine estimation on signal frequency estimation is relatively small. Therefore, the algorithm iteration and fine estimation are removed to reduce the computational complexity and speed up the solution speed. And in order to further improve the estimation accuracy of the algorithm under low signal-to-noise ratio, on this basis, a polynomial interpolation method is added. By means of quadratic polynomial fitting, the position of the maximum frequency peak is accurately estimated, further improving the accuracy of the algorithm. The specific steps are as follows:

[0009] S1, Pad zeros to the Doppler complex signal and perform Fourier transform;

[0010] S2, Using the result obtained in step S1, take the maximum value point after Fourier transform and the Fourier transform values of the four points around it for quadratic polynomial fitting interpolation to obtain the interpolated maximum value point;

[0011] S3, With the interpolated maximum value point obtained in step S2 as the center, take a certain range interval within the neighborhood for three-line interpolation iterative calculation to obtain the frequency residual value;

[0012] S4, Using the frequency calculation formula, obtain the final frequency value according to the maximum value point obtained in step S2, the frequency residual value obtained in step S3, and the sequence length.

[0013] Further, in step S1, the specific formula of the Doppler complex signal x(n) is:

[0014] x(n) = A(n)e j2πfn + w(n)

[0015] In the formula, n is the discrete time index, j is the imaginary unit, f is the frequency, A(n) is the amplitude of the signal, and w(n) is the phase of the signal.

[0016] Further, in step S2, the specific steps for performing quadratic polynomial fitting interpolation are:

[0017] S21, Take the maximum value point m k after transformation and m around itk ±2, m k ±1.5, m k ±1, m k The fast Fourier transform values corresponding to ±0.5;

[0018] S22, Obtain the quadratic polynomial fitting interpolation formula by solving the fitting polynomial coefficients a, b, c using the least squares method;

[0019] S23, Use the quadratic polynomial to find the function values of the boundary points and compare them with the function values when its first derivative is zero. The larger value is the maximum / minimum value point m obtained by interpolating using the quadratic polynomial fitting interpolation formula r .

[0020] Furthermore, in step S21, the maximum value point m after transformation k The corresponding fast Fourier transform value X 0 The calculation formula is:

[0021]

[0022] In the formula, x 2N (n) is the Doppler complex signal, j is the imaginary unit, n is the time index, and 2N is the sequence length;

[0023] The maximum value point m after transformation k The m around k The fast Fourier transform values X corresponding to ±i′ ±i′ The calculation formula is:

[0024]

[0025] In the formula, i′ is the distance from the maximum value point, and the values are 0.5, 1, 1.5, 2.

[0026] Furthermore, in step S22, the formulas for solving the fitting polynomial coefficients a, b, c using the least squares method are:

[0027]

[0028] In the formula, z 1 to is the maximum value point m after transformation k and its surrounding n 1 observations, such as m k ±2, m k ±1.5, m k ±1, m k ±0.5, y 1 to is the initial residual of the corresponding observation value, that is, the observation value minus 0, which can be understood as z 1to at m k and the fast Fourier transform values of the observed values around it, n 1 is the number of observed values.

[0029] Furthermore, in step S23, the quadratic polynomial extreme value method is used to obtain its extreme value in the boundary point interval, and then it is compared with the boundary point value. The maximum value is the interpolation result m calculated by the fitted polynomial r , and the specific steps are as follows:

[0030] Step1. Take the first derivative of the polynomial function value with respect to the independent parameter t to obtain the first derivative expression;

[0031] f(t) = at 2 + bt + c

[0032] In the formula, f(t) is the polynomial function value, t is the independent parameter, and a, b, c are the estimated polynomial coefficients;

[0033]

[0034] In the formula, represents taking the first derivative of f(t) at t;

[0035] Step2. Let the derivative value of the first derivative expression be 0 and solve for the independent parameter t 0 numerical value;

[0036]

[0037] In the formula, t 0 represents the value of the parameter when the first derivative function value is 0;

[0038] Step3. Substitute t 0 into f(t) to obtain the extreme value f(t 0 );

[0039] Step4. Substitute t 1 = m k + 2, t 2 = m k - 2 into the first derivative expression to obtain f(m k + 2), f(m k - 2). The t value corresponding to the maximum value among the obtained f(t 0 ), f(m k + 2), f(m k - 2) is m r , and the maximum value point m r after interpolation is obtained.

[0040] Furthermore, the specific implementation method of step S3 is:

[0041] S31, taking the amplitude at the highest point and the amplitude near the highest point to calculate the residual;

[0042] S32, using the residual to obtain the precise value of the frequency estimation and calculate the expected value;

[0043] S33, using the expected value to improve the new Doppler complex signal expression, and jointly solving it to obtain the frequency residual value after three-line interpolation.

[0044] Further, in step S33, the residual calculation formula in S31 is changed to:

[0045]

[0046] In the formula, A 1 is the amplitude of the signal, i represents the number of iterations, X 0 is the fast Fourier transform value corresponding to the maximum point after transformation, X ±0.5 is the m around the maximum point after transformation k ±0.5 corresponds to the fast Fourier transform value, j is the imaginary unit, n is the time index, and 2N is the sequence length;

[0047] Further derivation of the above two formulas yields:

[0048]

[0049] Then we get the frequency residual value after trilinear interpolation:

[0050]

[0051] In the formula, h 1 (i+1) represents the frequency residual value of the i+1th iteration, h 1 (i) Represents the frequency residual value of the i-th iteration.

[0052] Furthermore, in step S4, the formula of the frequency value f is:

[0053]

[0054] In the formula, m r is the maximum point after interpolation, is the frequency residual value representing the i-th iteration, and 2N is the sequence length.

[0055] The present invention also provides a Doppler signal frequency accurate estimation device, comprising:

[0056] one or more processors;

[0057] A storage device for storing one or more programs, which when executed by the one or more processors, cause the one or more processors to implement a method for accurately estimating the Doppler signal frequency as described in the above technical solution.

[0058] Advantages of the present invention: Based on the iterative complex interpolation method of DFT, in the asteroid exploration mission, a method for accurately estimating the Doppler signal frequency is used to analyze the Doppler signal. The difference from the original algorithm lies in the use of the polynomial interpolation method. Compared with the trilinear interpolation method, a main advantage of the polynomial interpolation method is its higher mathematical fitting performance. The polynomial interpolation method approximates the curve of the data by fitting a polynomial function between the data points. Compared with the linear fitting of the trilinear interpolation method, the polynomial interpolation provides higher degrees of freedom and more accurate approximation ability. The polynomial interpolation method can better capture the complexity and non-linear characteristics between the data, thus providing more accurate interpolation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a flowchart of the improved complex interpolation method in the embodiment of the present invention.

[0060] Figure 2 It is a variance comparison diagram of the complex iterative interpolation method based on DFT and the improved complex interpolation method in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0061] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments; based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the scope of protection of the present invention.

[0062] To better understand the technical solutions of the present invention, the present invention will be further described in detail below in conjunction with the embodiments.

[0063] The present invention proposes to apply the polynomial interpolation method to the accurate estimation of the Doppler signal frequency. Specifically, this method removes the iterative and fine estimation parts in the algorithm, and by means of quadratic polynomial fitting, accurately estimates the position where the maximum frequency peak is located, improves the accuracy of the algorithm, and accurately estimates the Doppler signal frequency.

[0064] Therefore, the key improvement proposed by the present invention is: the use of the polynomial interpolation method. Compared with the trilinear interpolation method, a main advantage of the polynomial interpolation method is its higher mathematical fitting performance. Using this method for Doppler signal calculation effectively reduces the computational amount of data processing and improves the operation speed.

[0065] An embodiment provides a method for accurately estimating the frequency of a Doppler signal. The specific steps are as follows:

[0066] S1. Perform zero-padding on the Doppler complex signal and perform Fourier transform.

[0067] S2. Using the result obtained in step S1, take the Fourier transform values corresponding to the maximum point after transformation and the four points around it for quadratic polynomial fitting interpolation to obtain the interpolated maximum and minimum points.

[0068] S3. Taking the interpolated maximum and minimum points obtained in step S2 as the center, take a certain range interval within the neighborhood for three-line interpolation to calculate the frequency residual.

[0069] S4. Using the frequency calculation formula, obtain the final frequency value based on the maximum and minimum points obtained in step S2, the frequency residual obtained in step S3, and the sequence length.

[0070] Further, in step S1, the specific formula of the Doppler complex signal x(n) is:

[0071] x(n) = A(n)e j2πfn + w(n)

[0072] In the formula, n is the discrete time index, j is the imaginary unit, f is the frequency, A(n) is the amplitude of the signal, and w(n) is the phase of the signal. The complex signal can be understood as a vector varying with time on the complex plane. The real part corresponds to the actual value of the signal, and the imaginary part corresponds to the phase of the signal. The complex signal can more comprehensively describe the frequency components and phase information of the signal.

[0073] Further, in step S1, perform a 2N-point fast Fourier transform on the Doppler complex signal x(n) to obtain the transformed signal X(m), where m is the transformed time index.

[0074] Further, in step S2, the specific steps for performing quadratic polynomial fitting interpolation are as follows:

[0075] S21. Take the maximum point m k after transformation and m k ±2, m k ±1.5, m k ±1, m k ±0.5 corresponding fast Fourier transform values.

[0076] S22. Solve the fitting polynomial coefficients a, b, c by the least squares method to obtain the quadratic polynomial fitting interpolation formula.

[0077] S23. Use a quadratic polynomial to find the function value at the boundary point and compare it with the function value when its first derivative is zero. The larger value is the maximum / minimum point m after interpolation obtained by fitting the quadratic polynomial interpolation formula. r 。

[0078] Further, in step S21, the transformed maximum point m k The corresponding fast Fourier transform value X 0 The calculation formula is:

[0079]

[0080] In the formula, x is the Doppler complex signal, j is the imaginary unit, n is the time index, and 2N is the sequence length.

[0081] Further, in step S21, the transformed maximum point m k Around m k The corresponding fast Fourier transform values X for ±i' ±i′ The calculation formula is:

[0082]

[0083] In the formula, x is the Doppler complex signal, j is the imaginary unit, n is the time index, 2N is the sequence length, and i' is the distance from the maximum point, with values of 0.5, 1, 1.5, 2.

[0084] Since x 2N (n) is obtained by padding zeros to the original signal, and the subsequent N samples are all 0. Only the sum of the first N values needs to be calculated, and x(n) can be used to replace x 2N (n) in the formula.

[0085]

[0086] Further, in step S22, the quadratic polynomial fitting interpolation formula is:

[0087] f(t) = at 2 + bt + c

[0088] In the formula, f(t) is the polynomial function value, t is the independent parameter, and a, b, c are the polynomial coefficients.

[0089] Further, in step S22, the formulas for solving the fitting polynomial coefficients a, b, c by the least squares method are:

[0090]

[0091] In the formula, z 1 To Is the transformed maximum point mk and n observations around it 1 such as m k ±2, m k ±1.5, m k ±1, m k ±0.5, y 1 to is the initial residual of the corresponding observation value, that is, the observation value minus 0, which can be simply understood as z 1 to the fast Fourier transform value on m k and its surrounding observation values, n 1 is the number of observation values.

[0092] Furthermore, in step S23, the quadratic polynomial extreme value method is used to obtain m k the extreme value in this point interval, and then compare it with the boundary point value. The maximum value is the interpolation result m of the fitted polynomial calculation r .

[0093] The specific steps are as follows:

[0094] Step1: Take the first derivative of the polynomial function value with respect to the independent parameter t to obtain the first derivative expression.

[0095] f(t) = at 2 + bt + c

[0096] In the formula, f(t) is the polynomial function value, t is the independent parameter, and a, b, c are the estimated polynomial coefficients.

[0097]

[0098] In the formula, represents taking the first derivative of f(t) at t.

[0099] Step2: Let the derivative value of the first derivative expression be 0 and solve for the independent parameter t 0 numerical value.

[0100]

[0101] In the formula, t 0 represents the value of the parameter when the first derivative function value is 0.

[0102] Step3: Substitute t 0 into f(t) to obtain the extreme value f(t 0 ).

[0103] Step4: Substitute t 1 = m k + 2, t 2 = mk Substitute -2 into the first - order derivative expression to obtain f(m K + 2), f(m k - 2). The obtained f(t 0 ), f(m k + 2), f(m k - 2). The t value corresponding to the maximum value among them is m r , and the maximum - value point m r after interpolation is obtained.

[0104] Furthermore, in step S3, taking the interpolated maximum - value point obtained in step S2 as the center, a certain - range interval within the neighborhood is taken to perform three - line interpolation to calculate the frequency residual. The specific steps are as follows:

[0105] S31. Take the amplitude highest point and the amplitudes near the highest point to calculate the residual;

[0106] S32. Use the residual to obtain the accurate value of the frequency estimate and calculate the expected value;

[0107] S33. Use the expected value to improve and obtain a new Doppler complex - signal expression, and solve simultaneously to obtain the frequency residual value after three - line interpolation;

[0108] Furthermore, in step S31, take the amplitude highest point m r and the amplitudes at the highest point ±0.5, and calculate the residual h 1 through the iterative interpolation method to obtain:

[0109]

[0110] In the formula, X is the corresponding fast Fourier transform value, m r is the interpolated maximum - value point, x is the Doppler complex signal, j is the imaginary unit, n is the time index, 2N is the sequence length. Since x 2N (n) is obtained by padding zeros to the original signal, the subsequent N samples are all 0, and only the sum of the first N values needs to be calculated. x(n) can be used to replace x 2N (n) in the formula.

[0111] Furthermore, in step S32,

[0112] E(X 0 )≈X 0 , E(X ±0.5 )≈X ±0.5

[0113] E represents the expected value. X 0 , X ±0.5 are the corresponding fast Fourier transform values.

[0114] Further, in step S33, the formula for calculating the residual in S31 is changed to:

[0115]

[0116] In the formula, A 1 is the amplitude of the signal, i represents the number of iterations, h 1 (i) represents the residual value of the i-th iteration, h 1 (i+1) represents the residual value of the (i + 1)-th iteration, X is the corresponding fast Fourier transform value, m r is the maximum or minimum value point after interpolation, and 2N is the sequence length.

[0117] Further derivation of the above two formulas gives:

[0118]

[0119] In the formula, i represents the number of iterations, h 1 (i) represents the residual value of the i-th iteration, h 1 (i+1) represents the residual value of the (i + 1)-th iteration, X is the corresponding fast Fourier transform value, and 2N is the sequence length.

[0120] Furthermore, the iterative calculation formula for the residual calculation after three-line interpolation can be obtained:

[0121]

[0122] In the formula, i represents the number of iterations, h 1 (i+1) represents the residual value of the (i + 1)-th iteration, h 1 (i) represents the residual value of the i-th iteration, X is the corresponding fast Fourier transform value, and 2N is the sequence length.

[0123] Further, in step S4, using the frequency residual obtained in S3, the formula for the frequency value f is:

[0124]

[0125] In the formula, m r is the maximum or minimum point after interpolation, is the result of the iterative calculation of the frequency residual, and 2N is the sequence length.

[0126] Through the above process, the present invention realizes the key improvement:

[0127] (1) Steps S2 to S4 effectively reduce the interference factors in the Doppler signal estimation and solve the problem of signal processing accuracy.

[0128] (2) Innovated the estimation method of Doppler signals. Compared with the traditional method, it reduces the computational complexity of frequency estimation of Doppler signals.

[0129] The simulation method was used to compare the accuracy of the improved algorithm and the original algorithm, and analyze the performance of the algorithm under different signal-to-noise ratios. Frequency estimation was performed on a complex signal with a frequency f = 364.3413135 Hz. The sampling frequency of the signal was 2048 Hz. Under the condition of a signal-to-noise ratio of -15 to 15 dB, the accuracy was compared between the complex iterative interpolation method based on DFT and the improved complex interpolation method. The results obtained are as Figure 2 shown.

[0130] From Figure 2 it can be seen that in the range where the signal-to-noise ratio is between -15 dB and 5 dB, the results of the improved algorithm are better than those of the complex iterative interpolation method based on DFT. Considering that the signal-to-noise ratio of actual deep space signals is relatively low, the improved complex interpolation method is more suitable for processing Doppler signals.

[0131] In specific implementation, the method proposed by the technical solution of the present invention can be automatically run by those skilled in the art using computer software technology. The system device for implementing the method, such as a computer-readable storage medium storing the corresponding computer program of the technical solution of the present invention and a computer device including running the corresponding computer program, should also be within the protection scope of the present invention.

[0132] In some possible embodiments, a device for accurately estimating the frequency of Doppler signals is provided, including a processor and a memory. The memory is used to store program instructions, and the processor is used to call the stored instructions in the memory to execute a method for accurately estimating the frequency of Doppler signals as described above.

[0133] In some possible embodiments, a storage medium for accurately estimating the frequency of Doppler signals is provided, including a readable storage medium. A computer program is stored on the readable storage medium. When the computer program is executed, it implements a method for accurately estimating the frequency of Doppler signals as described above.

[0134] It should be understood that the above description of the preferred embodiments is relatively detailed, and it should not be considered as a limitation to the protection scope of the patent of the present invention. Under the inspiration of the present invention, those of ordinary skill in the art can also make substitutions and deformations without departing from the protection scope defined by the claims of the present invention, and all fall within the protection scope of the present invention. The scope of protection requested by the present invention shall be subject to the appended claims.

Claims

1. A method for accurately estimating Doppler signal frequency, characterized in that: The steps include: S1, perform zero padding operation on the Doppler complex signal and perform Fourier transform; S2, using the result obtained in step S1, taking the Fourier transform values ​​corresponding to the maximum value point after Fourier transform and the four points around it, and performing quadratic polynomial fitting interpolation to obtain the maximum value point after interpolation; In step S2, the specific steps of performing quadratic polynomial fitting interpolation are: S21, take the maximum value point m after transformation k and the surrounding m k ±2, m k ±1.5, m k ±1, m k ±0.5 corresponds to the fast Fourier transform value; S22, solving the fitted polynomial coefficients a, b, c by the least square method to obtain a quadratic polynomial fitting interpolation formula; S23, using the quadratic polynomial to find the boundary point function value, and compare it with the function value when the first-order derivative is zero, where the larger value is the maximum value point m after interpolation obtained by using the quadratic polynomial fitting interpolation formula r ; S3, taking the interpolated maximum point obtained in step S2 as the center, taking a certain range of intervals in the neighborhood to perform three-line interpolation iterative calculation to obtain the frequency residual value; S4, using a frequency calculation formula, obtain a final frequency value according to the maximum value point obtained in step S2, the frequency residual value obtained in step S3, and the sequence length.

2. The method for accurately estimating Doppler signal frequency according to claim 1, characterized in that: In step S1, the specific formula of the Doppler complex signal x(n) is: x(n)=A(n)e j2πfn +w(n) Where n is the discrete time index, j is the imaginary unit, f is the frequency, A(n) is the amplitude of the signal, and w(n) is the phase of the signal.

3. The method for accurately estimating Doppler signal frequency according to claim 1, characterized in that: In step S21, the transformed maximum point m k The corresponding fast Fourier transform value X0 calculation formula is: In the formula, x 2N (n) is the Doppler complex signal, j is the imaginary unit, n is the time index, and 2N is the sequence length; The maximum point m after transformation k Around m k ±i' corresponds to the fast Fourier transform value X ±i' The calculation formula is: In the formula, i' is the distance from the maximum value point, and its values ​​are 0.5, 1, 1.5, and 2.

4. The method for accurately estimating Doppler signal frequency according to claim 1, characterized in that: In step S22, the formula for solving the fitted polynomial coefficients a, b, c by the least squares method is: In the formula, z1 to is the maximum value point m after transformation k And the n1 observations around it, y1 to is the initial residual corresponding to the observed value, that is, the observed value minus 0, which can be understood as z1 to In m k and the fast Fourier transform values ​​on its surrounding observations, n1 is the number of observations.

5. The method for accurately estimating Doppler signal frequency according to claim 3, characterized in that: In step S23, the quadratic polynomial extreme value method is used to obtain the extreme value in the boundary point interval, and then compared with the boundary point value, where the maximum value is the interpolation result m calculated by the fitted polynomial r , the specific steps are: Step 1. Take the first-order derivative of the polynomial function value with respect to the independent parameter t and obtain the first-order derivative expression; f(t)=at 2 +bt+c Where f(t) is the value of the polynomial function, t is the independent parameter, and a, b, c are the estimated polynomial coefficients; In the formula, It means that f(t) takes the first derivative at t; Step 2, let the derivative value of the first-order derivative expression be 0, and solve the value of the independent parameter t0; In the formula, t0 represents the value of the parameter when the first-order derivative function value is 0; Step 3, Substitute t0 into f(t) to obtain the extreme value f(t0); Step 4: Set t1 = m k +2,t2=m k Substituting -2 into the first-order derivative expression, we get f(m k +2), f(m k -2), the obtained f(t0), f(m k +2), f(m k -2) The value of t corresponding to the maximum value is m r , get the maximum point m after interpolation r .

6. The method for accurately estimating Doppler signal frequency according to claim 1, characterized in that: The specific implementation of step S3 is: S31, taking the amplitude at the highest point and the amplitude near the highest point to calculate the residual; S32, using the residual to obtain the precise value of the frequency estimation and calculate the expected value; S33, using the expected value to improve the new Doppler complex signal expression, and jointly solving it to obtain the frequency residual value after three-line interpolation.

7. The method for accurately estimating Doppler signal frequency according to claim 6, characterized in that: In step S33, the residual calculation formula in S31 is changed to: Where A1 is the amplitude of the signal, i represents the number of iterations, X0 is the fast Fourier transform value corresponding to the maximum value after transformation, and X ±0.5 is the m around the maximum point after transformation k ±0.5 corresponds to the fast Fourier transform value, j is the imaginary unit, n is the time index, and 2N is the sequence length; Further derivation of the above two formulas yields: Then we get the frequency residual value after trilinear interpolation: In the formula, h1 (i+1) represents the frequency residual value of the i+1th iteration, h1 (i) Represents the frequency residual value of the i-th iteration.

8. The method for accurately estimating Doppler signal frequency according to claim 1, characterized in that: In step S4, the formula for the frequency value f is: In the formula, m r is the maximum value point after interpolation, is the frequency residual value representing the i-th iteration, and 2N is the sequence length.

9. A device for accurately estimating Doppler signal frequency, characterized in that: include: one or more processors; A storage device for storing one or more programs, which, when executed by the one or more processors, enables the one or more processors to implement a Doppler signal frequency accurate estimation method as claimed in any one of claims 1 to 8.

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