Frequency estimation method based on amplitude and phase combination of weight distribution

Abstract

The present invention provides a frequency estimation method based on a combination of amplitude and phase based on weighted distribution. By acquiring a spread spectrum signal and pre-processing the spread spectrum signal with zero padding, the zero-padding operation improves the spectral resolution, enriches the information of the secondary peak, and makes the calculation of the shift amount more accurate, thereby significantly improving the accuracy of the frequency estimation. The spread spectrum signal after pre-processing is subjected to interpolation processing based on the extreme point of weight adjustment, and the frequency of the spread spectrum signal is accurately estimated using the frequency estimation correction amount. The present invention uses phase and amplitude information to determine the interpolation direction, thereby improving the accuracy of the interpolation direction. It also uses a method of weighted processing of the left and right side peak peaks to calculate the interpolation numerical shift amount. Since the signal is pre-processed with zero padding, the calculation of the frequency estimation correction amount is more accurate, and ultimately effectively improves the frequency estimation accuracy of the direct spread signal. Therefore, compared with existing precise frequency capture methods, the present invention has lower computational complexity and shorter processing time.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal tracking, and in particular relates to a frequency estimation method based on amplitude and phase combination of weight distribution. Background Art

[0002] Currently, during the acquisition and tracking of direct-spread (DSS) signals, the signal frequency estimation suffers from errors due to high dynamics and strong noise environments, preventing the tracking module from quickly acquiring lock. This error is primarily due to the low signal-to-noise ratio of the received signal. To improve the signal-to-noise ratio, the correlation processing time is typically extended. However, in dynamic environments, this approach introduces frequency drift, reducing frequency estimation accuracy. Furthermore, when directly performing FFT on the signal to estimate frequency, if the carrier Doppler frequency offset is not an integer multiple of the frequency resolution, the signal's true frequency spectrum lies between the two spectral lines with the largest FFT amplitudes. This fence effect can also lead to significant measurement errors.

[0003] Current frequency estimation methods mainly fall into two categories: high-precision frequency estimation methods and frequency domain reanalysis methods. The core idea of high-precision frequency estimation methods is to improve the estimation accuracy by increasing the frequency discrimination accuracy of the Fourier transform (FFT) and amplifying the local accuracy of the spectrum. In terms of improving the FFT frequency discrimination accuracy, increasing the number of FFT points can improve the spectrum resolution, thereby improving the accuracy of frequency estimation. However, this method will increase the amount of calculation and capture time, so a trade-off needs to be made between accuracy and efficiency. Another high-precision frequency estimation method is to amplify the local accuracy of the spectrum, among which Zoom-FFT is a commonly used technology. It improves the accuracy of Doppler frequency estimation by locally amplifying the target frequency band or increasing the spectral line density. However, this type of method has high implementation complexity and low efficiency.

[0004] Frequency domain reanalysis is another common frequency estimation technique. This method analyzes the signal's frequency domain information and numerically processes the frequency information from the approximate frequency estimate. Compared to high-precision frequency estimation techniques, frequency domain reanalysis methods generally offer faster computational speeds and higher frequency resolution. Frequency domain reanalysis methods can be implemented using algorithms such as numerical fitting and frequency domain interpolation. Numerical fitting methods, such as least squares (LS), can improve frequency estimation accuracy to a certain extent, but they are computationally intensive. Frequency domain interpolation methods include the Rife algorithm, parabolic interpolation, and Quinn algorithm. These methods improve frequency estimation accuracy by processing the information related to the mainlobe and sidelobe spectral lines after the FFT. The Rife algorithm utilizes the relationship between the spectral amplitudes of the mainlobe and the next highest sidelobe for interpolation. However, in noisy environments, the sidelobe amplitude characteristics are easily affected, leading to erroneous determination of the next highest sidelobe, incorrect interpolation direction, and large frequency estimation errors. The parabolic interpolation method uses the numerical relationship between the mainlobe and sidelobes to infer the parabolic equation for interpolation fitting. However, it is susceptible to noise and is prone to underfitting, resulting in reduced accuracy. The conventional Quinn algorithm, based on the Rife algorithm, introduces phase information to determine the interpolation direction. This can address the Rife algorithm's interpolation direction errors and has low computational complexity. However, it only uses the real part of the two spectral lines within the mainlobe, resulting in limited frequency estimation accuracy.

[0005] Frequency estimation methods based on the improved Quinn algorithm use zero-padding and then performing an FFT to increase frequency resolution. Based on the Quinn algorithm's principles, they combine phase information to determine the interpolation direction and process the relationship between the first side peak and the main peak's amplitude to obtain the interpolated value. For example, in the literature (A Method for Improving Doppler Frequency Estimation Accuracy in a PMF-FFT System, Guilin University of Electronic Technology), the Quinn algorithm is used to determine the interpolation direction in the frequency domain. The Rife algorithm is then used to process the amplitude information of the main peak and the first side peak to obtain the interpolated value, ultimately yielding a frequency estimate. However, this method utilizes phase and amplitude information inefficiently, resulting in significant deviations in the accuracy of signal frequency estimation.

[0006] In summary, the existing frequency estimation schemes have high computational complexity, the interpolation direction judgment is easily affected by noise, the low utilization of spectrum information leads to low interpolation numerical accuracy, and the high dynamic environment and fence effect lead to large estimation errors. Summary of the Invention

[0007] In order to solve the above problems existing in the prior art, the present invention provides a frequency estimation method based on amplitude and phase combination of weight distribution. The technical problem to be solved by the present invention is achieved by the following technical solutions:

[0008] The present invention provides a frequency estimation method based on amplitude and phase combination of weight distribution, including:

[0009] S100, acquiring a spread spectrum signal and performing zero-padding preprocessing on the spread spectrum signal to obtain a spread spectrum signal after preprocessing;

[0010] S200, performing interpolation processing on the pre-processed spread spectrum signal based on the extreme value point of weight adjustment to obtain a frequency estimation correction value;

[0011] S300: accurately estimate the frequency of the spread spectrum signal using the frequency estimation correction amount.

[0012] Optionally, the S100 includes:

[0013] S110, obtaining a spread spectrum signal x(n) of length L;

[0014] S120, padding the spread spectrum signal x(n) with zeros to obtain a signal x1(n);

[0015] S130, performing Fourier transform on the signal x1(n) to obtain a frequency domain signal X(k);

[0016] S140: Use the frequency domain signal X(k) as a pre-processed spread spectrum signal.

[0017] Optionally, the S120 includes:

[0018] The tail of the spread spectrum signal x(n) is padded with 0 values of the same length L or 0 values of a length other than L to obtain a signal x1(n).

[0019] Optionally, the S200 includes:

[0020] S210, searching for a maximum point and left and right side peak points in the pre-processed spread spectrum signal;

[0021] S220, using the maximum point and the left and right side peak points, and performing stepwise calculation to obtain a modified interpolation direction parameter and a directional interpolation movement amount;

[0022] S230: Using the corrected interpolation direction parameter and the direction interpolation movement amount as a frequency estimation correction amount.

[0023] Optionally, the S220 includes:

[0024] S221, the maximum point (K0, X(K0)) and the left and right side peak points (K 0+2 , X(K 0+2 ))、(K 0-2 , X(K 0-2)) three points as input parameters, and calculate direction decision parameters α1 and α2 according to the Quinn algorithm interpolation direction; calculate the modified interpolation direction parameter r according to the direction decision parameters α1 and α2;

[0025] S222, synchronized with S221, sets the maximum point (K0, X(K0)) and the left and right side peak points (K 0+1 , X(K 0+1 ))、(K 0-1 , X(K 0-1 )) three points as input parameters, and select weight molecules Lar and Sma according to the weight judgment extreme point algorithm; calculate the directional interpolation movement amount δ according to the weight molecules Lar and Sma.

[0026] Optionally, S221 includes:

[0027] S2211, the maximum point (K0, X(K0)) and the left and right side peak points (K 0+2 , X(K 0+2 ))、(K 0-2 , X(K 0-2 The three points are used as input parameters of the Quinn algorithm, and the direction decision parameters α1 and α2 are calculated according to the Quinn algorithm interpolation direction, which are expressed as:

[0028]

[0029] Where Re represents the real part of the complex value;

[0030] S2212, determine the direction decision parameters α1 and α2 to obtain the modified interpolation direction parameter r, which is expressed as:

[0031]

[0032] Here, r=+1 indicates that the algorithm interpolation direction is to the right; r=-1 indicates that the algorithm interpolation direction is to the left.

[0033] Optionally, S222 includes:

[0034] S2221, synchronize with S221 to set the maximum point (K0, X(K0)) and the left and right side peak points (K 0+1 , X(K 0+1 ))、(K 0-1 , X(K 0-1 )) The three points are used as input parameters of the weighted extreme point algorithm, and the weight molecules Lar and Sma are selected according to the weighted extreme point algorithm, which are expressed as:

[0035]

[0036] S2222, use the weight numerator Lar, Sma to calculate the direction interpolation movement δ, expressed as:

[0037]

[0038] Among them, a, b, and c all represent weight factors.

[0039] Optionally, the S300 includes:

[0040] Calculate the corrected frequency point K using the corrected interpolation direction parameter and the direction interpolation movement amount. max and its corresponding frequency f _est , respectively expressed as:

[0041] K max =K0+r*δ(7)

[0042]

[0043] Among them, r represents the corrected interpolation direction parameter, δ represents the direction interpolation movement, and f s represents the sampling frequency, and L represents the number of signal points.

[0044] Beneficial effects:

[0045] The present invention provides a frequency estimation method based on a combination of amplitude and phase based on weighted distribution. This method obtains a spread spectrum signal and pre-processes it with zero padding. Since the zero-padding operation improves spectral resolution and enriches secondary peak information, the calculation of the shift amount is more accurate, significantly improving the accuracy of the frequency estimation. The pre-processed spread spectrum signal is then interpolated based on weighted adjustment of extreme points, and the frequency estimation correction is used to accurately estimate the frequency of the spread spectrum signal. The present invention uses phase and amplitude information to determine the interpolation direction, improving the accuracy of the interpolation direction. It also calculates the interpolation numerical shift amount by weighted processing of the left and right side peaks. Due to the signal zero-padding pre-processing, the frequency estimation correction is more accurately calculated, ultimately effectively improving the frequency estimation accuracy of the direct spread spectrum signal. Therefore, compared with existing precise frequency capture methods, the present invention has lower computational complexity and shorter processing time. The present invention will be further described in detail below with reference to the accompanying drawings and examples. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a schematic diagram of the overall flow of the frequency estimation method based on amplitude and phase combination of weight distribution provided by the present invention;

[0047] Figure 2 Schematic diagram of interpolation processing based on weight adjustment of extreme value points of the present invention;

[0048] Figure 3This is a schematic diagram of the algorithm's frequency estimation effect under zero-padding and non-zero-padding conditions;

[0049] Figure 4 This is a partial enlarged diagram showing the effect of the algorithm estimating frequency under zero-padding and non-zero-padding conditions;

[0050] Figure 5 It is a schematic diagram of the frequency estimation effect of various algorithms;

[0051] Figure 6 This is a locally enlarged schematic diagram of the frequency estimation effect of multiple algorithms;

[0052] Figure 7 This is a schematic diagram of the difference between the estimated frequency and the actual frequency by various algorithms;

[0053] Figure 8 This is a locally enlarged schematic diagram of the effect of the actual frequency difference between the frequency estimation and the actual frequency using multiple algorithms. DETAILED DESCRIPTION

[0054] The present invention will be further described in detail below with reference to specific examples, but the embodiments of the present invention are not limited thereto.

[0055] like Figure 1 The overall frequency estimation process is shown in Figure 1. It consists of three main steps: the first is signal conversion preprocessing to improve frequency estimation accuracy; the second is correction of the maximum frequency spectrum line to obtain the correction value; and the third is the precise estimation of the final frequency, using the correction value obtained in the second step to achieve a more accurate frequency estimate. These three steps are performed sequentially, and the results of the preprocessing and correction processes have a direct causal impact on the results of the third step.

[0056] Combine Figure 1 and Figure 2 The present invention provides a frequency estimation method based on amplitude and phase combination of weight distribution, including:

[0057] S100, acquiring a spread spectrum signal and performing zero-padding preprocessing on the spread spectrum signal to obtain a spread spectrum signal after preprocessing;

[0058] In an optional embodiment of the present invention, S100 includes:

[0059] S110, obtaining a spread spectrum signal x(n) of length L;

[0060] S120, performing equal-length zero padding on the spread spectrum signal x(n) to obtain a signal x1(n);

[0061] In this step, a zero value of the same length L or a zero value of a length other than L is added to the tail of the spread spectrum signal x(n) to obtain a signal x1(n).

[0062] This step can enrich the frequency domain spectrum line information by equal-length zero padding, enhance the ability to resist noise, reduce computational complexity, and improve the accuracy of frequency estimation. Figure 3 、 Figure 4 As shown, the effect of zero padding of equal length is obviously better than that of not padding zero, and the effect of zero padding of other lengths is also worse than that of zero padding of equal length. Of course, in this step, the number of zero paddings may not be equal to the length of the data.

[0063] S130, performing Fourier transform on the signal x1(n) to obtain a frequency domain signal X(k);

[0064] S140: Use the frequency domain signal X(k) as a pre-processed spread spectrum signal.

[0065] S200, performing interpolation processing on the pre-processed spread spectrum signal based on the extreme value point of weight adjustment to obtain a frequency estimation correction value;

[0066] In an optional embodiment of the present invention, S200 includes:

[0067] S210, searching for a maximum point and left and right side peak points in the pre-processed spread spectrum signal;

[0068] S220, using the maximum point and the left and right side peak points, and performing stepwise calculation to obtain a modified interpolation direction parameter and a directional interpolation movement amount;

[0069] S230: Using the corrected interpolation direction parameter and the direction interpolation movement amount as a frequency estimation correction amount.

[0070] This embodiment first finds the maximum point (K0, X(K0)) in the frequency domain signal X(k), as well as the left and right side peak points (K 0+1 ,X(K 0+1 ))、(K 0-1 ,X(K 0-1 ))、(K 0+2 ,X(K 0+2 ))、(K 0-2 ,X(K 0-2 )). It is then divided into two processes and executed simultaneously to respectively obtain the corrected interpolation direction parameter r and the directional interpolation movement amount δ. The corrected interpolation direction parameter r indicates the direction of interpolation of the present invention, wherein r = +1 indicates that the algorithm interpolation direction is to the right; r = -1 indicates that the algorithm interpolation direction is to the left. The directional interpolation movement amount δ indicates the movement value of the interpolation movement of the present invention, and the value range of δ is (0,1). This method uses a method based on the weighting of the main peak and the side peak to calculate the movement amount of the spectral line interpolation shift, making full use of the spectral line information, improving the problem of large offset error caused by the Rife algorithm's less use of spectral line information, and can effectively improve the estimation accuracy of the signal frequency.

[0071] In an optional embodiment of the present invention, S220 includes:

[0072] S221, the maximum point (K0, X(K0)) and the left and right side peak points (K 0+2 , X(K 0+2 ))、(K 0-2 , X(K 0-2 )) three points as input parameters, and calculate direction decision parameters α1 and α2 according to the Quinn algorithm interpolation direction; calculate the modified interpolation direction parameter r according to the direction decision parameters α1 and α2;

[0073] In an optional embodiment of the present invention, S221 includes:

[0074] S2211, the maximum point (K0, X(K0)) and the left and right side peak points (K 0+2 , X(K 0+2 ))、(K 0-2 , X(K 0-2 The three points are used as input parameters of the Quinn algorithm, and the direction decision parameters α1 and α2 are calculated according to the Quinn algorithm interpolation direction, which are expressed as:

[0075]

[0076] Where Re represents the real part of the complex value;

[0077] S2212, determine the direction decision parameters α1 and α2 to obtain the modified interpolation direction parameter r, which is expressed as:

[0078]

[0079] S222, synchronized with S221, sets the maximum point (K0, X(K0)) and the left and right side peak points (K 0+1 , X(K 0+1 ))、(K 0-1 , X(K 0-1 )) three points as input parameters, and select weight molecules Lar and Sma according to the weight judgment extreme point algorithm; calculate the directional interpolation movement amount δ according to the weight molecules Lar and Sma.

[0080] In an optional embodiment of the present invention, S222 includes:

[0081] S2221, synchronize with S221 to set the maximum point (K0, X(K0)) and the left and right side peak points (K 0+1 , X(K 0+1 ))、(K 0-1 , X(K 0-1The three points are used as input parameters of the weighted extreme point algorithm, and the weight molecules Lar and Sma are selected according to the weighted extreme point algorithm, which are expressed as:

[0082]

[0083] S2222, use the weight numerator Lar, Sma to calculate the direction interpolation movement amount δ,

[0084] In this step, appropriate weight factors a, b, and c are selected according to the signal-to-noise ratio (a = 0.5, b = 0.3, and c = 1.2 are generally used under strong noise conditions. Fine-tuning can be performed according to the change in the intensity of the noise amplitude. When the noise is stronger, the proportion of the main peak increases, the weight of the side peaks with larger amplitudes increases, and the weight of the side peaks with smaller amplitudes decreases. When the signal-to-noise ratio is high, a = 0.4, b = 0.4, and c = 1.2 are generally used). The directional interpolation shift δ is expressed as:

[0085]

[0086] Among them, a, b, and c all represent weight factors.

[0087] The present invention can adopt other weighting methods when weighting the multi-spectral peaks during frequency interpolation shifting, such as ignoring lower peaks and only weighting the main peak and the first side peak. These adjustments can also achieve approximate accuracy and low complexity.

[0088] S300: accurately estimate the frequency of the spread spectrum signal using the frequency estimation correction amount.

[0089] This step uses the modified interpolation direction parameter and the direction interpolation movement to calculate the modified frequency point K max and its corresponding frequency f _est , respectively expressed as:

[0090] K max =K0+r*δ(7)

[0091]

[0092] Among them, r represents the corrected interpolation direction parameter, δ represents the direction interpolation movement, and f s represents the sampling frequency, and L represents the number of signal points.

[0093] The present invention can effectively enrich the frequency domain spectral line information, enhance the ability to resist noise, reduce the amount of calculation, improve the utilization of frequency domain signals, and improve the frequency estimation accuracy through the above steps. Through 100 comparisons of Monte Carlo experimental simulations, it can be shown that the algorithm has a better effect on estimating the signal frequency in the process of spread spectrum signal capture and tracking, and the estimation accuracy is more accurate. Figure 5 、 Figure 6 、 Figure 7 、 Figure 8 As shown, the frequency estimated by the frequency estimation method based on the combination of amplitude and phase based on weighted distribution is closer to the actual frequency. The frequency estimation errors obtained by the direct FFT method and the Quinn and Rife algorithms are much larger than those obtained by this method. In addition, the frequency estimation error of this method is more stable and does not suffer from occasional excessive errors, making it more suitable for practical engineering applications. In the simulation experiment, a direct-spread signal was used. After passing through a -20dB Gaussian channel, the signal Doppler was gradually reduced by 1KHz from 180KHz, and the PMF-FFT acquisition method was used.

[0094] The present invention improves on the traditional Quinn algorithm by performing equal-length zero padding of the signal during the FFT (Fast Fourier Transform) process to increase the number of spectral lines within the main peak. This allows more spectral line information to be used to more accurately estimate the frequency. Compared with existing precise frequency capture methods, the method of the present invention has lower computational complexity and shorter processing time. When performing the moving interpolation process, we can compare the relationship between the second side peak high-value frequency sampling points on both sides of the peak frequency point and the main peak amplitude, that is, K 0+2 , and K 0-2 The spectrum line X(K 0+2 )、X(K 0-2 ) and the X(K0) corresponding to point K0 to determine the interpolation direction. Furthermore, the present invention employs weighted processing of secondary peaks to calculate the amount of spectral line interpolation shift, and the weighting can be appropriately adjusted based on the influence of noise. Since the zero-padding operation improves spectral resolution, the secondary peaks provide richer information, making the calculation of the shift more accurate, thereby significantly improving the accuracy of frequency estimation.

[0095] It is worth noting that the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of the technical features indicated. Therefore, features specified as "first" or "second" may explicitly or implicitly include one or more of such features. In the description of the present invention, "plurality" means two or more, unless otherwise specifically defined.

[0096] Although the present application is described herein with reference to various embodiments, those skilled in the art will be able to understand and implement other variations of the disclosed embodiments in practicing the claimed application by reviewing the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality.

[0097] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should be considered to fall within the scope of protection of the present invention.

Claims

1. A frequency estimation method based on amplitude and phase combination of weight distribution, characterized in that: include: S100, acquiring a spread spectrum signal and performing zero-padding preprocessing on the spread spectrum signal to obtain a spread spectrum signal after preprocessing; S200, performing interpolation processing on the pre-processed spread spectrum signal based on the extreme value point of weight adjustment to obtain a frequency estimation correction; S200 includes: S210, searching for a maximum point and left and right side peak points in the pre-processed spread spectrum signal; S220, using the maximum point and the left and right side peak points, and performing the step of obtaining the corrected interpolation direction parameter and the direction interpolation movement amount; S220 includes: S221, the maximum point ( , ) and left and right side peaks ( )、( ) three points as input parameters, and calculate the direction decision parameter according to the Quinn algorithm interpolation direction and ; Determine the parameters according to the direction and Calculate the corrected interpolation direction parameters ; S221 includes: S2211, the maximum point ( , ) and left and right side peaks ( )、( ) three points as the input parameters of the Quinn algorithm, and the direction decision parameter is calculated according to the Quinn algorithm interpolation direction and , respectively expressed as: in, It means taking the real part of the complex value; S2212, direction decision parameters and Make a judgment to obtain the corrected interpolation direction parameter , expressed as: in, Indicates that the algorithm interpolation direction is to the right; Indicates that the algorithm interpolation direction is to the left; S222, synchronized with S221, sets the maximum point ( , ) and left and right side peaks ( , )、( , ) three points as input parameters, and select the weight molecules Lar and Sma according to the weight judgment extreme point algorithm; calculate the direction interpolation movement amount according to the weight molecules Lar and Sma ; S222 includes: S2221, synchronize with S221 to set the maximum point ( , ) and left and right side peaks ( , )、( , ) three points as the input parameters of the weighted extreme point algorithm, and the weight numerator is selected according to the weighted extreme point algorithm 、 , respectively expressed as: S2222, using weight numerator 、 Input calculation direction interpolation movement , expressed as: in, 、 、 Both represent weight factors; S230, using the corrected interpolation direction parameter and the direction interpolation movement amount as a frequency estimation correction amount; S300: accurately estimate the frequency of the spread spectrum signal using the frequency estimation correction amount.

2. The frequency estimation method based on amplitude and phase combination of weight distribution according to claim 1, characterized in that: S100 includes: S110, obtaining a spread spectrum signal x(n) of length L; S120, padding the spread spectrum signal x(n) with zeros to obtain a signal x1(n); S130, performing Fourier transform on the signal x1(n) to obtain a frequency domain signal X(k); S140: Use the frequency domain signal X(k) as a pre-processed spread spectrum signal.

3. The frequency estimation method based on amplitude and phase combination of weight distribution according to claim 2, characterized in that: The S120 includes: The tail of the spread spectrum signal x(n) is padded with 0 values of the same length L or 0 values of a length other than L to obtain a signal x1(n).

4. The frequency estimation method based on amplitude and phase combination of weight distribution according to claim 1, characterized in that: S300 includes: Calculate the corrected frequency point using the corrected interpolation direction parameter and the direction interpolation movement and its corresponding frequency , respectively expressed as: in, represents the corrected interpolation direction parameter, Indicates the direction interpolation movement, represents the sampling frequency, Indicates the number of signal points.

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