Spectral moment estimation method of meteorological signals based on spectral sparse reconstruction

Abstract

The present invention discloses a method for estimating the spectral moment of a meteorological signal based on sparse signal reconstruction. The invention first adopts sparse reconstruction technology to obtain the Doppler sparse spectrum of each distance unit; in order to further suppress noise interference, the Doppler sparse spectrum is subjected to threshold detection processing to reduce the influence of noise on subsequent spectral moment estimation; finally, the Doppler velocity and spectral width of the meteorological signal are estimated by a sparse domain spectrum estimation algorithm. The effectiveness of the present invention has been verified by actual data from meteorological radar measurements, and its estimation accuracy is 9.85% and 16.96% higher than that of the radial velocity and spectral width estimated by the pulse pair method commonly used in engineering respectively. This method improves the resolution of meteorological signals in the Doppler domain by adopting sparse technology, and is suitable for low signal-to-noise ratio scenarios.

Description

Technical Field

[0001] The present invention relates to a spectral moment estimator method for meteorological signals, and in particular to a spectral moment estimator method for meteorological signals based on sparse spectrum reconstruction. Background Art

[0002] The essence of weather radar target detection lies in estimating the spectral moments of radar echoes. Spectral moment estimation can distinguish different types of weather targets, so the target type is closely related to the spectral moment parameters of the radar echo. For example, wind shear detection relies on how wind speed varies with distance, while turbulence detection relies on the severity of wind speed changes within a given area.

[0003] Meteorological targets are diffuse, composed of numerous scattering particles. The radar echo signal of a resolution unit is the superposition of the echoes from all scatterers within that unit. According to the central limit theorem, this signal is a Gaussian statistical signal, and its spectrum also follows a Gaussian distribution. Based on the Gaussian spectral characteristics of the signal, it can be deduced that the spectral moment is related to the signal's autocorrelation sequence. This leads to a spectral moment estimation method—the pulse pair method—which is computationally simple because it only uses two autocorrelation sequence values. Alternatively, direct statistical analysis of the signal's spectrum can be used for estimation, and calculations using the fast Fourier transform have also been applied. Several methods have been proposed to improve the accuracy of these methods.

[0004] However, both the traditional pulse pair method and the fast Fourier transform method have their own shortcomings. The pulse pair method is only suitable for scenarios with high signal-to-noise ratios, and its estimation performance drops sharply at low signal-to-noise ratios. The fast Fourier transform method performs well at high signal-to-noise ratios, but is severely affected by noise and its estimation performance deteriorates sharply when the spectral width is large.

[0005] In recent years, with the proposal and development of Compressive Sensing (CS) theory, compressed sensing theory has been widely used in various fields. Sparse representation is a prerequisite for compressed sensing and is one of the hottest research topics this year. The meteorological radar echo signal is a typical low-rank sparse signal that meets the conditions for sparse representation. The sparse representation theory can be applied to the data processing of meteorological radar echo signals. Therefore, the present invention applies compressed sensing theory to the spectral moment estimation of meteorological signals, constructs a redundant dictionary using the Doppler vector, and restores the sparse signal through a signal reconstruction algorithm. The reconstructed and restored sparse signal is processed, and finally, the sparse domain spectrum estimation algorithm is used to achieve accurate estimation of the spectral moment. Summary of the Invention

[0006] The purpose of the present invention is to address the defect that the signal-to-noise ratio of the measured meteorological echo signal is low and the traditional method cannot accurately and quickly realize spectral moment estimation. The compressed sensing theory is introduced into the spectral moment of the measured meteorological echo signal, a redundant dictionary is designed according to the Doppler frequency, and the meteorological signal is sparsely reconstructed. Finally, the sparse domain spectral estimation algorithm is used to realize accurate estimation of the spectral moment.

[0007] In order to achieve the above-mentioned purpose, the present invention adopts the following technical solutions:

[0008] 1. Meteorological signal preprocessing

[0009] The original meteorological signal is clutter-free, and the ground clutter is removed. If the ground clutter is not removed, the sparsely inverted meteorological signal Doppler spectrum will have a peak near the Doppler zero frequency, resulting in inaccurate spectral moment estimation of the meteorological signal.

[0010] In order to fully verify the high performance of the meteorological signal spectral moment estimation method based on spectrum sparse reconstruction, the 512-pulse meteorological signal is converted into a 64-pulse meteorological signal to reduce the number of pulses available for accumulation.

[0011] 2. Doppler spectrum of meteorological signals based on sparse inversion

[0012] The actual signal received by the weather radar is an M×N matrix, where M represents the number of range cells and N represents the number of pulses. In engineering practice, N is usually 64, that is, the number of pulses of the meteorological echo data of each range cell in one coherent accumulation is 64. Assume that the signal received by the mth range cell of the weather radar is y m ,y m Is an N×1 column vector. Solve y by sparse inversion technique m The meteorological signal in the redundancy dictionary X is approximately represented by the product of the complex frequency domain coefficient α. m , which can be expressed as:

[0013] y m =Xα+n (1)

[0014] In the above formula, X is the redundant dictionary constructed by the Doppler vector, which is an N×8N matrix, α is the complex amplitude estimate, which is an 8N×1 column vector, and n represents the noise vector, which is an N×1 column vector.

[0015] In the presence of noise, the complex amplitude sparse solution can be approximated by solving the following optimization problem:

[0016]

[0017] Complex amplitude estimate Represents the amplitude value corresponding to each frequency point after sparse reconstruction, and the basis pursuit denoising (BPDN) method can be used to solve the complex amplitude estimation value. λ is used to balance the relative importance between the two, and is usually taken as

[0018] 3. Redundant dictionary constructed by Doppler vector

[0019] The fact that the meteorological radar echo signal has only a limited number of peaks in the frequency domain (having sparsity) lays the foundation for the application of compressed sensing technology. Therefore, we consider using the Doppler vector to construct a redundant dictionary to achieve sparse representation of the signal. The redundant dictionary is a matrix consisting of 8N discrete frequency points and N (N = 64) pulse numbers. Let the number of pulses used for coherent accumulation to detect the spectral moment of the meteorological signal be N, and the pulse repetition frequency be f r , the Doppler frequency range (-f r / 2,f r / 2) is divided into 8N discrete frequency points f1, f2, ..., f N Frequency f i The Doppler vector can be expressed as:

[0020]

[0021] The matrix composed of the Doppler vectors at each frequency point can be written as:

[0022]

[0023] 4. Sparse Doppler spectrum preprocessing

[0024] The complex amplitude estimate obtained There are only two states in , namely zero and non-zero values. The non-zero value corresponds to the weather echo signal and the noise signal. Because of the existence of noise, the amplitude will appear at the frequency point outside the weather echo target, which will lead to inaccurate estimation. According to the relevant theory of image processing, the complex amplitude estimation value of the i-th frequency point is obtained Perform threshold detection processing:

[0025]

[0026] is the absolute value of the complex amplitude Maximum value is the detection threshold, where |·| is the absolute value operator. The complex amplitude estimate of the i-th frequency point after processing is obtained Complex amplitude estimate The noise effect on the complex amplitude estimate is reduced by threshold detection processing. and correspondingly reduces the impact of the error in spectral moment estimation.

[0027] 5. Sparse domain spectral estimation algorithm estimates spectral moments

[0028] Finally, the spectrum estimation algorithm is used in the sparse domain to realize the spectral moment estimation of the meteorological signal:

[0029] i. Doppler frequency estimation of radial velocity

[0030]

[0031] In the formula is the estimated Doppler radial velocity, f i is the frequency value of the i-th frequency point, which is an 8N equally divided point; is the i-th frequency point f i complex amplitude estimate;

[0032] ii. Estimation of spectral width;

[0033]

[0034] In the formula is the estimated Doppler spectrum width. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 :Flowchart of the spectral moment estimation method of meteorological signals based on spectral sparse reconstruction;

[0036] Figure 2 : The complex amplitude estimation value after sparse reconstruction of the 20th distance unit and threshold zeroing;

[0037] Figure 3 :Comparison of the estimated value, pulse pair method and true value in radial velocity estimation of meteorological signal spectral moment estimation method based on spectral sparse reconstruction in 1-100 distance units

[0038] Figure 4 :Comparison of the estimated value, pulse pair method and true value in spectrum width estimation of meteorological signal spectral moment estimation method based on spectral sparse reconstruction in 1-100 distance units DETAILED DESCRIPTION

[0039] The present invention will be described in further detail below with reference to the accompanying drawings.

[0040] Meteorological targets are composed of a large number of particles and are distributed targets. Considering the target echo signal in a strong ground clutter environment, each point scatterer is approximately equivalent to an ideal sphere, and the radar echo of each scattering unit is calculated. The echo signal of each range unit is generated by coherent superposition. Therefore, the superposition of all scattering point echoes within the entire beam scanning range is the radar echo, which can be expressed as

[0041]

[0042] Among them A i (t) represents the echo amplitude of the i-th scattering point; represents the echo phase of the i-th scattering point; c(t) represents the ground clutter signal, and n(t) represents the interference noise signal. The meteorological echo signal and ground clutter signal in the echo data are equivalent to the signal S(t), that is, S(t) = s(t) + c(t). The matrix form of the radar echo signal is

[0043] y m =S+n (2)

[0044] The matrix X composed of the Doppler vectors at each frequency point is the redundant dictionary (also called an overcomplete library) for signal compression processing, where each column of X is an atom in the overcomplete library. By using the atoms in the overcomplete library to replace the traditional orthogonal basis and finding the m-term atoms with the best linear combination to represent the target signal, the sparse representation of the signal under the overcomplete library can be achieved. Therefore, the received target signal S can be expressed as a linear combination of the atoms in X, that is,

[0045] y m =Xα+n (3)

[0046] in, represents the complex amplitude of the signal in the frequency domain, and There are only K non-zero components in (K<<N), that is, It is sparse, which realizes the sparse representation of the received data. The complex amplitude estimate of the signal is obtained and by estimating The frequency estimate of the signal can be obtained by finding the position of the non-zero value in the .

[0047]

[0048] The specific signal processing steps are divided into the following five steps:

[0049] 1. Meteorological signal preprocessing

[0050] The original meteorological signal is clutter-free, and the ground clutter is removed. If the ground clutter is not removed, the sparsely inverted meteorological signal Doppler spectrum will have a peak near the Doppler zero frequency, resulting in inaccurate spectral moment estimation of the meteorological signal.

[0051] In order to fully verify the high performance of the meteorological signal spectral moment estimation method based on spectrum sparse reconstruction, the 512-pulse meteorological signal is converted into a 64-pulse meteorological signal to reduce the number of pulses available for accumulation.

[0052] 2. Doppler spectrum of meteorological signals based on sparse inversion

[0053] The actual signal received by the weather radar is an M×N matrix, where M represents the number of range cells and N represents the number of pulses. In engineering practice, N is usually 64, that is, the number of pulses of the meteorological echo data of each range cell in one coherent accumulation is 64. Assume that the signal received by the mth range cell of the weather radar is y m ,y m Is an N×1 column vector. Solve y by sparse inversion technique m The meteorological signal in the redundancy dictionary X is approximately represented by the product of the complex frequency domain coefficient α. m , which can be expressed as:

[0054] y m =Xα+n (1)

[0055] In the above formula, X is the redundant dictionary constructed by the Doppler vector, which is an N×8N matrix, α is the complex amplitude estimate, which is an 8N×1 column vector, and n represents the noise vector, which is an N×1 column vector.

[0056] In the presence of noise, the complex amplitude sparse solution can be approximated by solving the following optimization problem:

[0057]

[0058] Complex amplitude estimate Represents the amplitude value corresponding to each frequency point after sparse reconstruction, and the basis pursuit denoising (BPDN) method can be used to solve the complex amplitude estimation value. λ is used to balance the relative importance between the two, and is usually taken as

[0059] 3. Redundant dictionary constructed by Doppler vector

[0060] The fact that the meteorological radar echo signal has only a limited number of peaks in the frequency domain (having sparsity) lays the foundation for the application of compressed sensing technology. Therefore, we consider using the Doppler vector to construct a redundant dictionary to achieve sparse representation of the signal. The redundant dictionary is a matrix consisting of 8N discrete frequency points and N (N = 64) pulse numbers. Let the number of pulses used for coherent accumulation to detect the spectral moment of the meteorological signal be N, and the pulse repetition frequency be f r , the Doppler frequency range (-f r / 2,f r / 2) is divided into 8N discrete frequency points f1, f2, ..., f N Frequency f i The Doppler vector can be expressed as:

[0061]

[0062] The matrix composed of the Doppler vectors at each frequency point can be written as:

[0063]

[0064] 4. Sparse Doppler spectrum preprocessing

[0065] The complex amplitude estimate obtained There are only two states in , namely zero and non-zero values. The non-zero value corresponds to the weather echo signal and the noise signal. Because of the existence of noise, the amplitude will appear at the frequency point outside the weather echo target, which will lead to inaccurate estimation. According to the relevant theory of image processing, the complex amplitude estimation value of the i-th frequency point is obtained Perform threshold detection processing:

[0066]

[0067] is the absolute value of the complex amplitude Maximum value is the detection threshold, where |·| is the absolute value operator. The complex amplitude estimate of the i-th frequency point after processing is obtained Complex amplitude estimate The noise effect on the complex amplitude estimate is reduced by threshold detection processing. and correspondingly reduces the impact of the error in spectral moment estimation.

[0068] 5. Sparse domain spectral estimation algorithm estimates spectral moments

[0069] Finally, the spectrum estimation algorithm is used in the sparse domain to realize the spectral moment estimation of the meteorological signal:

[0070] i. Doppler frequency estimation of radial velocity

[0071]

[0072] In the formula is the estimated Doppler radial velocity, f i is the frequency value of the i-th frequency point, which is an 8N equally divided point; is the i-th frequency point f i complex amplitude estimate;

[0073] ii. Estimation of spectral width;

[0074]

[0075] In the formula is the estimated Doppler spectrum width.

[0076] The following analysis analyzes the performance of a spectral moment estimation method for meteorological signals based on spectral sparse reconstruction. The relevant meteorological data comes from the IDRA polarimetric X-band (9.475 GHz, horizontal / vertical polarization) FMCW radar, developed at Delft University of Technology. Table 1 lists the specific system parameters of the IDRA radar.

[0077] Table 1 Weather radar system parameters

[0078]

[0079] Let k represent the current number of range units, and K represent the maximum number of range units of the weather radar echo. The algorithm is implemented by judging whether the spectral moment estimation is completed based on the number of range units. Figure 1 shown.

[0080] The true value of the meteorological signal spectral moment estimation is the spectral moment obtained by the FFT algorithm of 512 pulses. Table 2 shows the spectral moment estimation errors of different data processing methods, with the error being measured in terms of root mean square error.

[0081] Table 2 Spectral moment estimation errors of different data processing methods

[0082] Treatment Radial velocity estimation error Spectral width estimation error No threshold set to zero 8.0562dB 12.7976dB Threshold zero -11.1592dB -7.7609dB Pulse pair method -10.0826dB -4.3999dB

[0083] The present invention studies a method for estimating the spectral moment of meteorological signals based on sparse signal reconstruction, applies the algorithm to measured data with low signal-to-noise ratio, and uses the 512-pulse FFT method as the true value. The experimental results of the algorithm verify the effectiveness of the scheme of the present invention. The present invention only requires estimated prediction samples and does not require a covariance matrix, and has high real-time performance. After using this algorithm, the estimated error of the radial velocity is -11.1592dB, and the estimated error of the spectral width is -7.7609dB, which meet the expected indicators. During the rapid change of the spectral moment of the meteorological signal, its estimation accuracy is 9.85% and 16.96% higher than that of the radial velocity and spectral width estimated by the pulse pair method commonly used in engineering respectively.

[0084] Compared to the pulse pair method, this algorithm has less stringent requirements on the number of pulses and is less sensitive to the signal-to-noise ratio, making it suitable for situations with low signal-to-noise ratios and a small number of pulses. Therefore, the proposed solution has high real-time performance and is suitable for real-time parallel processing in engineering projects. It requires less pulse data and has high accuracy.

Claims

1. A spectral moment estimation method for meteorological signals based on sparse spectrum reconstruction, characterized by The steps include: Step 1: Doppler spectrum of meteorological signal based on sparse inversion What the weather radar actually receives is an M×N signal matrix, where M represents the number of range units and N represents the number of pulses. In engineering practice, N is usually 64, that is, the number of pulses of the meteorological echo data of each range unit coherently accumulated at one time is 64. Assuming that the signal received by the mth range unit of the weather radar is y m ,y m is an N×1 column vector; solve y by sparse inversion technique m The meteorological signal in the redundancy dictionary X is approximately represented by the product of the complex frequency domain coefficient α. m , which can be expressed as: y m =Xα+n (1) In the above formula, x is the redundant dictionary constructed by the Doppler vector, which is an N×8N matrix, α is the complex amplitude estimate, which is an 8N×1 column vector, and n represents the noise vector, which is an N×1 column vector; In the presence of noise, the complex amplitude sparse solution can be approximated by solving the following optimization problem: Complex amplitude estimate Represents the amplitude value corresponding to each frequency point after sparse reconstruction, and the basis pursuit denoising (BPDN) method can be used to solve the complex amplitude estimation value; and λ is used to balance the relative importance between the two, which can usually be taken as Step 2: Sparse Doppler spectrum preprocessing The complex amplitude estimate obtained There are only two states in the image processing, zero and non-zero. The non-zero position corresponds to the weather echo signal and the noise signal. Due to the existence of noise, the amplitude will appear at the frequency point outside the weather echo target, which will lead to inaccurate estimation. According to the relevant theory of image processing, the complex amplitude estimation value of the i-th frequency point is obtained. Perform threshold detection processing: is the absolute value of the complex amplitude Maximum value is the detection threshold, where |·| is the absolute value operator; the complex amplitude estimate of the i-th frequency point after processing is obtained Complex amplitude estimate The noise effect on the complex amplitude estimate is reduced by threshold detection processing. The influence of spectral moment estimation error is reduced accordingly. Step 3: Spectral moment estimation algorithm based on sparse domain Finally, the spectrum estimation algorithm is used in the sparse domain to realize the spectral moment estimation of the meteorological signal: i. Doppler frequency estimation of radial velocity In the formula is the estimated Doppler radial velocity, f i is the frequency value of the i-th frequency point, which is an 8N equally divided point; is the i-th frequency point f i complex amplitude estimate; ii. Estimation of spectral width; In the formula is the estimated Doppler spectrum width.

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