CN110297247B - Meteorological radar wind power plant clutter suppression method based on low-rank matrix sparse recovery - Google Patents

Abstract

The invention discloses a meteorological radar wind power plant clutter suppression method based on low-rank matrix sparse recovery, which comprises the steps of utilizing the spatial correlation of meteorological signals, firstly setting distance units simultaneously containing the meteorological signals and wind turbine clutter to zero, symmetrically weighing 40 distance units on two sides of the distance units, then reconstructing distance vectors into low-rank snapshot matrixes meeting zero element random distribution pulse by pulse, and finally utilizing an inaccurate augmented Lagrange multiplier method (IALM) to minimize a nuclear norm to effectively recover the meteorological data. Simulation experiment results show that the method can effectively inhibit Wind Turbine Clutter (WTC) and noise, improve meteorological signal output signal-to-noise ratio, and is suitable for engineering application.

Description

Meteorological radar wind power plant clutter suppression method based on low-rank matrix sparse recovery

Technical Field

The invention relates to a low-rank matrix sparse recovery-based method for suppressing clutter of a meteorological radar wind power plant, and belongs to the field of meteorological radar clutter suppression.

Background

In order to cope with the potential crisis of energy and the deterioration of ecological environment such as global warming, renewable clean energy is actively developed in all countries of the world, and wind power generation has received high attention all over the world as an important form of renewable clean energy. In recent years, the scale and the number of wind power plants in the global range are exponentially increased, and the rotating speed and the length of blades of wind turbines are continuously increased, but researches show that motion noise caused by high-speed rotation of the blades of wind power plants of the wind power plants can seriously affect radar, communication navigation and other electronic equipment, so that new challenges are brought to detection of various radar targets, and the noise wave of the Wind Turbines (WTC) cannot be effectively filtered by the existing noise wave suppression technology, so that the prediction accuracy of meteorological information is seriously affected, and therefore the noise wave of the wind turbines becomes the core problem of the noise wave suppression of the current meteorological radars.

The existing clutter suppression technologies such as a time domain filtering method, a frequency domain filtering method and a filtering method based on power spectrum characteristics cause severe meteorological information loss due to frequency spectrum broadening caused by high-speed rotation of a wind turbine, so that WTC (wind turbine control) cannot be effectively suppressed, and the prediction accuracy of meteorological information is greatly influenced. After the time-frequency domain distribution characteristics of wind turbine clutter and meteorological echoes in different working modes of a meteorological radar are analyzed in detail, European and American scientists propose wind turbine clutter suppression algorithms based on multiple quadratic interpolation recovery, range-Doppler spectrum regression, recursive sparse reconstruction and the like, and the algorithms are limited by actual conditions such as wind farm scale, fan rotating speed, working modes of the meteorological radar and the like, and the algorithms cannot simultaneously give consideration to wind turbine clutter suppression and meteorological information lossless recovery. Furthermore, conventional WTC suppression methods only process data for each range cell individually, without utilizing information from other range cells. And the noise signal cannot be effectively suppressed.

Disclosure of Invention

The invention aims to solve the technical problem of providing a meteorological radar wind farm clutter suppression method based on two-dimensional combined interpolation, introducing a sparse optimization theory into meteorological radar WTC suppression, and researching a meteorological radar small wind farm clutter suppression method based on matrix completion, wherein the matrix completion theory (MC) is used as one of two important research directions of a sparse recovery theory, so that the problem of meteorological information loss caused by the methods can be avoided, meteorological signals interfered by WTC can be subjected to high-precision matrix completion, and the prediction precision of meteorological information is improved.

The invention adopts the following technical scheme for solving the technical problems:

the invention provides a low-rank matrix sparse recovery-based method for suppressing clutter of a meteorological radar wind power plant, which comprises the following specific steps of:

step 1, inputting a meteorological radar echo signal, wherein an input signal under the mth pulse of the ith distance unit is as follows:

x_i(m)＝s_i(m)+c_i(m)+w_i(m)+n_i(m)

where, i is 1, L is the number of distance units, M is 1, M is the number of coherent accumulation pulses, s is the number of coherent accumulation pulses_i(m)、c_i(m)、w_i(m) and n_i(m) meteorological, ground clutter, wind turbine clutter WTC, and noise signals at the mth pulse for the ith range unit, respectively;

step 2, constructing a low-rank snapshot matrix of random sampling, specifically:

40 distance units are respectively taken from two sides of the ith distance unit, and echo signals [ x ] in the ith distance unit are processed_i(1),x_i(2),..,x_i(M)]Setting zero to obtain an observation matrix X_L×M：

From X_L×MConstructing a randomly sampled low-rank snapshot matrix, wherein the construction criterion is as follows: successive approximation observation matrix X_L×MVector [ x ] under mth pulse₁(m),x₂(m),...,x_L(m)]^TBuild up of a snap matrix

Wherein m is₁And m₂Respectively representing the number of rows and columns, m, of the snap matrix₁×m₂＝L，m₁＝m₂Elements of the p-th row and q-th column of the snapshot matrix

Echo signal x_i(m) constructing a low-rank snapshot matrix X as follows:

defining meteorological signals s by X_i(m) the low-rank snapshot matrix S constructed after zeroing the ith distance unit is as follows:

definition of ground clutter signal c by X_i(m) the low-rank snapshot matrix C constructed after zeroing the ith distance unit is as follows:

defining the noise signal n by X_i(m) the low-rank snapshot matrix N constructed after zeroing the ith distance unit is as follows:

WTC signal w_i(m) the constructed low-rank snapshot matrix W is a zero matrix;

and 3, recovering the meteorological signals after the WTC is inhibited through a matrix completion model:

wherein min (·) represents the minimization process, | | · | | | purple_*Denotes the nuclear norm, P_ΩRepresents a mapping projected onto a sparse matrix subspace that is non-zero only in the index set omega, which leaves the elements of the matrix in omega unchanged, the elements outside omega zeroed out,

and 4, solving a matrix completion model by using an inaccurate augmented Lagrange multiplier method IALM, and outputting a signal after the WTC is inhibited.

As a further technical scheme of the present invention, the lagrangian function in step 4 is:

wherein Y is Y₀+ μ (X-S-N-W) is a Lagrangian multiplier matrix; y is₀The initial value of the Lagrange multiplier matrix is 0; mu is a penalty factor, | ·| non-woven phosphor powder_FRepresents F norm, | ·| non-conducting phosphor_FThe number of the F-norm is shown,

tr (-) denotes taking the trace of the matrix,

the representation takes the real part of the complex number,<·,·>representing the inner product of the matrix.

As a further technical scheme of the invention, the step of solving by using the non-precise augmented Lagrange multiplier method IALM comprises the following steps:

the method for solving the problem by using the non-precise augmented Lagrange multiplier method IALM comprises the following steps:

1) let Y₀＝0、W₀＝0，N＝0，μ₀＞0，ρ＞1，k＝0，η＝10^-3Wherein W is₀0 denotes the initial value of the wind turbine clutter to be suppressed;

2) using the formula (U, sigma, V)^H)＝svd(X-N_k-W_k+μ_k ^-1Y_k) And

and (4) updating S:

wherein S_k+1And S_kRespectively representing the k +1 and k updates, W, of the meteorological signal S_kRepresents the kth update, N, of the WTC signal W_kIndicating the kth update of noise N, Y_kRepresents the kth update, μ, of the Lagrangian multiplier matrix Y_kA kth update representing a penalty factor μ;

3) updating W:

wherein

Indicating index sets except omega;

4)

5) updating Y_k：Y_k+1＝Y_k+μ_k(X-S_k+1-N_k+1-W_k+1)；

6) Updating mu_kTo mu_k+1：μ_k+1＝ρμ_k；

7) If the following formula is not satisfied, the algorithm is not converged, let k ← k +1, go to step 2, otherwise go to step 8:

||S_k-S_k-1||_F/||S_k||_F≤η；

8) and (4) ending the circulation and outputting:

as a further technical scheme of the invention, the IALM is utilized to successively output the snapshot matrix of the recovered echo signals under each pulse after completion

Sequentially extracting the first column and the last row in each matrix, and forming M L multiplied by 1-dimensional vectors by the first column and the last row

Then, the M L multiplied by 1 dimensional vectors form an M multiplied by L dimensional echo signal recovery matrix

Get

The ith row vector in the space is used as the meteorological signal of the ith distance unit which is recovered sparsely

Advantageous effects

The method can effectively recover meteorological data by utilizing an IALM algorithm, inhibits clutter of the wind turbine, improves the signal-to-noise ratio of echo signals, and has strong practicability, small calculation amount and good engineering application prospect.

Drawings

FIG. 1 is a signal processing flow diagram of the present invention;

FIG. 2 is a histogram of characteristic values of a snapshot matrix;

FIG. 3 is a power spectrum of a meteorological signal before and after matrix completion under noise interference and no noise interference meteorological signals;

FIG. 4 is the meteorological signal amplitude before and after matrix completion under noise interference and noise interference;

FIG. 5 is a graph of signal recovery error for different signal-to-noise ratios;

FIG. 6 is the meteorological signal speed value before and after the IALM algorithm recovers.

Detailed Description

The technical scheme of the invention is further explained in detail by combining the attached drawings:

the invention mainly researches a weather radar wind power plant clutter matrix completion inhibition algorithm based on a snapshot matrix, and FIG. 1 is a method processing flow. The method mainly comprises the following steps:

step one, modeling of meteorological radar echo signals, specifically:

the meteorological radar receiving signal mainly comprises a meteorological signal, a ground clutter signal and a noise signal. Assuming that the ith range bin contains the WTC signal at the same time, the input signal at the mth pulse is noted as:

x_i(m)＝s_i(m)+c_i(m)+w_i(m)+n_i(m),m＝1,...,M (1)

wherein s is_i(m) is a meteorological signal, c_i(m) is a ground clutter signal, w_i(m) is WTC signal, n_i(M) is a noise signal, M is a coherent accumulation pulse number, and M is 64;

step two, constructing a low-rank snapshot matrix of random sampling, specifically:

40 distance units are respectively taken from two sides of the ith distance unit, and echo signals [ x ] in the ith distance unit are processed_i(1),x_i(2),..,x_i(M)]Set to zero, the observation matrix X can be obtained_L×M

Wherein X_L×MDimension of (1) is L multiplied by M, L is the distance unit number, L is 81, and M is the pulse number;

from X_L×MConstructing a low-rank random sampling snapshot matrix, wherein the construction criterion is as follows:

successive approximation observation matrix X_L×MVector [ x ] under mth pulse₁(m),x₂(m),...,x_L(m)]^TBuild up of a snap matrix

m₁,m₂Satisfy m₁×m₂＝L，m₁＝m₂The numbers of rows and columns of the snapshot matrix are denoted by 9, respectively. K is used as element of p-th row and q-th column of snapshot matrix_p,qIs shown, i.e.

Satisfy the requirement of

Echo signal x_i(m) constructing a low-rank snapshot matrix X as follows:

defining meteorological signals s by X_i(m) the low-rank snapshot matrix S constructed after zeroing the ith distance unit is as follows:

definition of ground clutter c by X_i(m) the low-rank snapshot matrix C constructed after zeroing the ith distance unit is as follows:

definition of noise n by X_i(m) the low-rank snapshot matrix N constructed after zeroing the ith distance unit is as follows:

WTC is known to exist only in the ith range cell, i.e., WTC signals are W in the observation matrix_L×M：

In pair W_L×MAfter the signal in the ith distance unit is set to zero, WTC signal w_i(m) constructing a low-rank snapshot matrix W which is a zero matrix, namely W is equal to 0.

Step three, sparsely recovering meteorological signals by using a low-rank matrix, which specifically comprises the following steps:

the matrix completion model can realize completion of unknown elements by constraining rank minimization according to partial matrix elements, and after the WTC is removed, meteorological data can be recovered through the following matrix completion model to inhibit the WTC:

where min (-) represents the minimization process, | | | suspension_FRepresents the F norm:

tr (-) denotes taking the trace of the matrix, P_ΩRepresenting a mapping projected onto a sparse matrix subspace of only the index set Ω non-zeroIt makes the elements of the matrix in Ω unchanged, and the elements outside Ω are set to zero, which is formulated as follows:

solving the optimization problem in the formula (2) by using an Inaccurate Augmented Lagrange Multiplier (IALM), wherein the classical matrix completion algorithm is only applicable to a real matrix, the matrix constructed herein is a complex matrix, the classical matrix completion algorithm is expanded to a complex field, and a corresponding lagrange function L (S, W, N, Y, μ) can be expressed as:

wherein Y ═ Y₀+ μ (X-S-N-W) is the Lagrangian multiplier matrix, Y₀Is an initial value, the value is 0, mu > 0 represents a penalty factor, | | · | | luminance_*Representing the kernel norm, which is the sum of all singular values of the matrix,

representing the real part of the complex, < X, Y > - [ tr (X)^HY) represents the inner product of the matrix.

First, a shrink operator is defined as:

the IALM algorithm steps are as follows:

inputting: x_ijObserving the sample, wherein (i, j) belongs to omega, and the matrix X belongs to R_m×n

1) Let Y₀＝0、W₀＝0，N＝0，μ₀＞0，ρ＞1，k＝0，η＝10-³Wherein W is₀0 represents the initial value of the wind turbine noise which needs to be suppressed, and the value is 0;

2) when the convergence formula in 9) is not satisfied, the solution is solved by using 3) and 4)

Wherein S_kIndicating the kth update, W, of the meteorological signal S_kRepresents the kth update, N, of the WTC signal W_kIndicating the kth update of noise N, Y_kRepresents the kth update, μ, of the Lagrangian multiplier matrix Y_kA kth update representing a penalty factor μ;

3)(U,Σ,V^H)＝svd(X-N_k-W_k+μ_k ^-1Y_k)；

4)

5) updating W:

wherein

Indicating index sets except omega;

6)

7) updating Y_k：Y_k+1＝Y_k+μ_k(X-S_k+1-N_k+1-W_k+1)；

8) Updating mu_kTo mu_k+1：μ_k+1＝ρμ_k；

9) If the following formula is not true, the algorithm is not converged, let k ← k +1, go to step 2, otherwise go to step 10:

||S_k-S_k-1||_F/||S_k||_F≤η；

10) and (4) ending the circulation and outputting:

utilizing IALM iterative algorithm to successively output snapshot matrix of echo signals under each pulse recovered after completion

k is iteration times, a first column and a last row in each matrix are sequentially extracted, and the first column and the last row form M L multiplied by 1-dimensional vectors

Then, the M L multiplied by 1 dimensional vectors form an M multiplied by L dimensional echo signal recovery matrix

Get matrix

The ith row vector in (1) is:

wherein

And recovering the meteorological signal of the ith distance unit for sparseness.

Next, testing the algorithm through MATLAB, verifying the effectiveness of the matrix completion algorithm in recovering meteorological signals, wherein simulation parameters of the radar system are shown in Table 1; assuming that echo signals exist in 1 st to 100 th range units and 64 pulses are total, WTC exists in 25 th range unit of the sampling matrix, zero setting processing is carried out on the WTC, and vectors under each pulse are sequentially constructed into a snapshot matrix.

TABLE 1 Snapshot matrix simulation parameters

Pulse repetition frequency	1000Hz
		Carrier frequency	5.5GHz
Height of radar	1000m
		Signal to noise ratio	30dB
Number of pulses	64
		Number of distance units	100
Number of matrix lines	10
		Number of columns of matrix	10

The known snapshot matrix is a matrix with 10 rows and 10 columns, the supplemented matrix is rearranged into an L multiplied by 1 dimensional matrix, the rest 63 pulse signals are simulated in sequence, and the 25 th vector element under each pulse extracted forms an echo signal after WTC suppression. In order to clearly understand the effect of the algorithm of the present invention on WTC and noise suppression, fig. 3 shows that the doppler spectrum of the meteorological signals with different power noise added, the substrate noise caused by the noise and the reconstruction error of the defect signal fluctuates greatly before WTC is suppressed by matrix completion. The simulation results in FIG. 3 show that the meteorological signal center frequency is about before and after the matrix completion under the condition that the SNR is 30dB360Hz, when the frequency is close to the central frequency, the influence of noise interference is very weak, and the meteorological signal recovery precision is higher. The peak side lobe has a certain inhibiting effect on high interference noise, and the noise power is reduced by about 5-10 dB. Doppler frequency f_dWhen the frequency is 300Hz or 400Hz, the noise is reduced by 15-20 dB, and the suppression effect is optimal.

The meteorological signal amplitude is as shown in fig. 4, and the change of the signal amplitude before and after the matrix completion can be clearly displayed. The magnitude recovered by the matrix completion is 1.2412 e-002% error compared to the original value. To quantitatively analyze the recovery performance of the MC algorithm, the following root mean square error is defined as a performance index:

according to the simulation data of FIG. 4, the root mean square error RMSE of the meteorological signal amplitude which is completed based on the snapshot matrix construction can be 1.71e-2, and the variance Var is defined to measure the dispersion degree of the signals before and after the suppression

The variance Var1 of the meteorological signal amplitude in the time domain before matrix completion suppression is 7.1107e-005, and the variance Var2 of the meteorological signal amplitude in the time domain after the suppression is 1.3303e-005, so that the discrete degree is greatly reduced, the deviation degree from the true value is reduced, the fluctuation caused by noise interference is reduced, and the signal-to-noise ratio is improved. Simulation results and data analysis show that the algorithm greatly improves the performance of matrix completion, and accurate recovery of meteorological signals is realized while WTC is inhibited.

In order to analyze the influence of the signal-to-noise ratio of the input signal on the performance of the algorithm, signal recovery errors under different signal-to-noise ratios are drawn into a curve chart shown in fig. 5, wherein the variation range of the signal-to-noise ratio is 0dB to 30dB, and it can be seen from the graph that the root mean square error for performing matrix completion on missing data is reduced along with the increase of the signal-to-noise ratio of the input signal, the higher the signal-to-noise ratio of the input signal is, the smaller the influence of noise factors on singular value decomposition is when singular value decomposition is performed, and the higher the matrix completion recovery precision is.

Fig. 6 is values of meteorological signal speed before and after the IALM algorithm is restored, and the meteorological signal speed after restoration is:

wherein < is a phase taking position,

a first order autocorrelation parameter representing a sequence of echo samples, wherein

Is the conjugate transpose of the recovered meteorological signal. The radial velocity estimate fluctuates significantly at low signal-to-noise ratios, with large deviations from the true value. But as the signal-to-noise ratio increases, the error of the radial velocity estimate gradually decreases, eventually converging to a true value.

According to the method, interference data are removed by using a WTC detection algorithm, a low-rank completion matrix meeting the random distribution of missing elements is constructed according to the spatial correlation of meteorological signals, and the problem of minimizing the constrained rank is solved by an IALM iterative algorithm to effectively recover the meteorological data. Simulation experiment results show that the algorithm can effectively inhibit WTC and noise interference, improve the signal-to-noise ratio of echo signals and has good engineering application prospect.

Claims (1)

1. The method for suppressing the clutter of the meteorological radar wind power plant based on the low-rank matrix sparse recovery is characterized by comprising the following specific steps of:

step 1, inputting a meteorological radar echo signal, wherein an input signal under the mth pulse of the ith distance unit is as follows:

x_i(m)＝s_i(m)+c_i(m)+w_i(m)+n_i(m)

where i 1, L is the number of distance elements, M1, M is the number of coherent integration pulses, s_i(m)、c_i(m)、w_i(m) and n_i(m) are respectively the ith distanceMeteorological signals, ground clutter signals, wind turbine clutter WTC signals and noise signals at the mth pulse of the unit;

step 2, constructing a low-rank snapshot matrix of random sampling, specifically:

respectively taking 40 range cells at both sides of the ith range cell, and converting the echo signal [ x ] in the ith range cell_i(1),x_i(2),..,x_i(M)]Setting zero to obtain an observation matrix X_L×M：

From X_L×MConstructing a randomly sampled low-rank snapshot matrix, wherein the construction criterion is as follows: successive approximation observation matrix X_L×MVector [ x ] under mth pulse₁(m),x₂(m),...,x_L(m)]^TBuild up of a snap matrix

Wherein m is₁And m₂Respectively representing the number of rows and columns, m, of the snap-shot matrix₁×m₂＝L，m₁＝m₂Elements of the p-th row and q-th column of the snapshot matrix

Echo signal x_i(m) constructing a low-rank snapshot matrix X as follows:

defining meteorological signals s by X_i(m) the low-rank snapshot matrix S constructed after zeroing the ith distance unit is as follows:

definition of ground clutter signal c by X_i(m) the low-rank snapshot matrix C constructed after zeroing the ith distance unit is as follows:

defining the noise signal n by X_i(m) the low-rank snapshot matrix N constructed after zeroing the ith distance unit is as follows:

WTC signal w_i(m) the constructed low-rank snapshot matrix W is a zero matrix;

and 3, recovering the meteorological signals after the WTC is restrained through a matrix completion model:

s.t.P_Ω(X)＝P_Ω(S+N)

wherein min (·) represents the minimization process, | | · | | | purple_*Denotes the nuclear norm, P_ΩRepresents a mapping projected onto a sparse matrix subspace that is non-zero only in the index set omega, which leaves the elements of the matrix in omega unchanged, the elements outside omega zeroed out,

step 4, solving a matrix completion model by using an inaccurate augmented Lagrange multiplier method IALM, and outputting a signal after the WTC is inhibited, wherein the method specifically comprises the following steps:

the lagrange function is:

wherein Y is Y₀+ mu (X-S-N-W) is Lagrangian multiplicationA sub-matrix; y is₀The initial value of the Lagrange multiplier matrix is 0; mu is a penalty factor, | ·| non-woven phosphor powder_FRepresents F norm, | ·| non-conducting phosphor_FThe number of the F-norm is shown,

tr (-) denotes taking the trace of the matrix,

the representation takes the real part of the complex number,<·,·>representing the inner product of the matrix;

the method for solving the problem by using the non-precise augmented Lagrange multiplier method IALM comprises the following steps:

1) let Y₀＝0、W₀＝0，N＝0，μ₀＞0，ρ＞1，k＝0，η＝10^-3Wherein W is₀0 denotes the initial value of the wind turbine clutter to be suppressed;

2) using the formula (U, sigma, V)^H)＝svd(X-N_k-W_k+μ_k ^-1Y_k) And

and (4) updating S:

wherein S_k+1And S_kRespectively representing the k +1 and k updates, W, of the meteorological signal S_kRepresents the kth update, N, of the WTC signal W_kIndicating the kth update of noise N, Y_kRepresents the kth update, μ, of the Lagrangian multiplier matrix Y_kA kth update representing a penalty factor μ;

3) updating W:

wherein

Indicating index sets except omega;

4)

5) updating Y_k：Y_k+1＝Y_k+μ_k(X-S_k+1-N_k+1-W_k+1)；

6) Updating mu_kTo mu_k+1：μ_k+1＝ρμ_k；

7) If the following formula is not satisfied, the algorithm is not converged, let k ← k +1, go to step 2, otherwise go to step 8:

||S_k-S_k-1||_F/||S_k||_F≤η；

8) and (4) ending the circulation and outputting:

snap matrix for recovering echo signals under each pulse by using IALM (analog-to-digital converter) successive output completion

Sequentially extracting the first column and the last row in each matrix, and forming M L multiplied by 1-dimensional vectors by the first column and the last row

Then, the M L multiplied by 1 dimensional vectors form an M multiplied by L dimensional echo signal recovery matrix

Get

The ith row vector in the space is used as the meteorological signal of the ith distance unit which is recovered sparsely

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