Folding clutter suppression method based on frequency agility radar

Abstract

The invention discloses a folding clutter suppression method based on a frequency agility radar, and the method comprises the steps: setting the pulse number of a frequency agility pulse sequence, a frequency hopping interval and a frequency hopping coefficient of each frequency agility pulse signal, and transmitting a plurality of frequency agility pulse signals; calculating the carrier frequency of the echo signal received by the frequency agility radar according to the frequency hopping interval and the frequency hopping coefficient; filtering the echo signal by using a frequency domain filter corresponding to the echo signal carrier frequency, and outputting the filtered echo signal; respectively performing impulse response and convolution processing on the time domain and the frequency domain of the filtered echo signal by using a matched filter, and outputting the echo signal after matched filtering; and sparse reconstruction is carried out on observation signals in the sparse reconstruction model by using an orthogonal matching pursuit algorithm or an alternating direction multiplier method to obtain sparse vectors, so that target signal energy is enhanced, non-matching interference components are suppressed, significant enhancement of weak and small targets is realized, and folding clutters and noise are suppressed.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing technology, and in particular to a folding clutter suppression method based on frequency agile radar. Background Technology

[0002] Folded clutter refers to a phenomenon in radar systems where, due to improper Pulse Repetition Frequency (PRF) settings or a target echo signal time delay exceeding one PRF cycle, clutter signals that should appear at long distances are "folded" to appear at close range, creating a false clutter image on the radar screen. Alternatively, when the radar's PRF illuminates a ground object (usually moving at high speed), the reflected clutter frequency is high due to the relatively rapid movement of the ground object relative to the radar. If the reflected clutter frequency exceeds the Nyquist frequency of the radar sampling system, a false clutter image will be formed on the radar screen.

[0003] Existing low-pass filters can only filter out low-frequency and zero-frequency clutter, i.e., clutter reflected from ground objects (usually stationary or moving at low speeds) whose echo frequencies are close to zero (stationary clutter) or in the low-frequency range (low-speed clutter). These low-frequency and zero-frequency clutter have a clear boundary with the higher frequencies of the echo signal reflected from the target (moving at high speeds). The aforementioned methods are ill-suited to range folding caused by high pulse repetition frequencies or complex motion conditions, making it difficult to accurately estimate or distinguish folded clutter. The overlap between the folded clutter and the signal echo spectrum makes it easy to misjudge or miss the target signal. Especially in folded clutter scenarios, the spectrum of folded clutter often overlaps with the true target echo, making it difficult for traditional filtering methods to effectively distinguish between the target and clutter. They may even misidentify folded clutter as the target or suppress the target signal, reducing the detection performance of the radar system. Summary of the Invention

[0004] The purpose of this invention is to provide a method for suppressing folded clutter based on frequency agile radar. Starting from four aspects, namely, transmitter signal design, frequency domain filtering, matched filtering and sparse reconstruction, a folded clutter suppression mechanism is constructed from the transmitter to the receiver. This enhances the target signal energy and suppresses unmatched interference components, achieving significant enhancement for weak targets and suppressing folded clutter and noise.

[0005] This invention is implemented by the following technical solution: a method for suppressing folded clutter based on frequency agile radar, comprising: Step S1: Set the number of pulses in the frequency agile pulse sequence, the frequency hopping interval between adjacent frequency agile pulse signals, and the frequency hopping coefficient of each frequency agile pulse signal, and transmit multiple frequency agile pulse signals. Step S2: Calculate the carrier frequency of the echo signal received by the frequency-agile radar based on the frequency hopping interval and frequency hopping coefficient; set the passband of the frequency domain filter, use the frequency domain filter corresponding to the echo signal carrier frequency to filter the echo signal, and output the filtered echo signal. Step S3: Use a matched filter to process the filtered echo signal by impulse response and convolution, and output the matched filtered echo signal. Step S4: Construct a sparse reconstruction model based on the echo signal after matched filtering, and use the orthogonal matching pursuit algorithm or the alternating direction multiplier method to sparsely reconstruct the observed signal in the sparse reconstruction model to obtain a sparse vector.

[0006] Furthermore, in step S1, the frequency hopping interval is greater than the sub-bandwidth of the frequency agile pulse signal; the sub-bandwidth of the frequency agile pulse signal is greater than or equal to 2MHz and less than or equal to 10MHz.

[0007] Furthermore, the expression for the echo signal received by the frequency-agile radar in step 2 is:

[0008] In the formula, Indicates the echo signal. This represents the scattering coefficient of the i-th frequency agile pulse signal. Indicates the number of pulses. Indicates the width of the frequency-agile pulse signal. Indicates the linear frequency modulation slope. Indicates the frequency modulation sub-bandwidth. This represents the carrier frequency of the i-th frequency agile pulse signal. Let represent the frequency hopping coefficient of the i-th frequency agile pulse signal, and have , Indicates the number of selectable frequency points. Indicates the unit frequency hopping interval. Represents the window function.

[0009] Furthermore, the specific method for convolving the filtered echo signal using a matched filter in step S3 includes: A time-reversed conjugate frequency-agile pulse signal is generated by using a matched filter to induce an impulse response in the time domain of the signal, denoted as [missing information]. Furthermore, a matched filter is used to convolve the echo signal and the corresponding time-reversed conjugate frequency-agile pulse signal to obtain the time-domain matched-filtered echo signal, denoted as . In the formula, Indicates the echo signal. Indicates convolution processing; The time-domain signal of the frequency-agile pulse signal is transformed into a frequency-domain signal using a matched filter via Fourier transform. The impulse response of the frequency-domain signal is then applied to generate a frequency-agile pulse signal in a frequency-reversed conjugate form, denoted as [missing information]. Furthermore, a matched filter is used to convolve the echo signal and the corresponding frequency-agile pulse signal in its inverted conjugate form in the frequency domain, resulting in a matched-filtered echo signal in the frequency domain, denoted as . .

[0010] Furthermore, in step S4, a sparse reconstruction model is constructed based on the echo signal after matched filtering. The observed signal in the sparse reconstruction model is then sparsely reconstructed using the orthogonal matched pursuit algorithm or the alternating direction multiplier method to obtain the sparse vector. Specific methods include: Step S40: Obtain the observed signal based on the echo signal after matched filtering; Step S41: Construct the dictionary matrix; Step S42: Construct a sparse reconstruction model based on the dictionary matrix and the observed signals; Step S43: Use the orthogonal matching pursuit algorithm or the alternating direction multiplier method to sparsely reconstruct the observed signal in the sparse reconstruction model to obtain a sparse vector.

[0011] Furthermore, step S40, which involves obtaining the observed signal from the matched-filtered echo signal, specifically includes the following methods: Step S401: Discretize the matched-filtered echo signal to form a discretized echo signal, denoted as . ; Step S402: Define the set of orthogonal basis vectors Sparse vectors Based on the orthogonal basis vector set and sparse vector representation of the discretized echo mathematical signal, the expression for the discretized echo mathematical signal is: ; Step S403: Determine the sparsity of the sparse vector on the orthogonal basis vectors based on the number of non-zero elements and the number of impulses in the sparse vector. The sparsity can be expressed as: In the formula, Indicates sparsity. This represents the number of non-zero elements in a sparse vector. Indicates the number of pulses; Step S404: Define the observation matrix and calculate the observed signal based on the sparse vectors, the set of orthogonal basis vectors, and the observation matrix.

[0012] Furthermore, the specific method for constructing the dictionary matrix in step S41 includes: Step S410: Obtain the composite scattering coefficient of the target from the observed signal; Step S411: Discretize the high-resolution range and velocity in the composite scattering coefficient of the target under test to obtain the discretized high-resolution range and discretized velocity; Step S412: Obtain the two-dimensional matrix of the composite scattering coefficients of the target under test based on the discretized high-resolution range and discretized velocity. The two-dimensional matrix of the composite scattering coefficients of the target under test can be expressed as: ,in, This represents the composite scattering coefficient of the target under test. Indicates the high-resolution range phase factor. The velocity phase factor is represented by P, which represents the number of points for discretizing the high-resolution distance, and Q represents the number of points for discretizing the velocity. Step S413: Rearrange the elements in the two-dimensional matrix of the composite scattering coefficients of the target in one dimension to construct a one-dimensional vector of composite scattering coefficients; the one-dimensional vector of composite scattering coefficients can be represented as... ,in, Let l represent a one-dimensional vector of composite scattering coefficients. The high-resolution range phase factor and velocity phase factor corresponding to the l-th element of the one-dimensional vector of composite scattering coefficients are denoted as l. , l represents the serial number; Step S414: Separate the index l in the l-th element into high-resolution distance indices. and speed The sequence number can be represented as In the formula, , , ; Step S415: Define the phase vector ,vector The phase relationship of l in the nth column of the one-dimensional vector of composite scattering coefficients can be expressed as: In the formula, dn represents the distance corresponding to the nth pulse, j represents the imaginary unit, and ln represents the index of the nth element; Step S416: Construct a dictionary matrix based on the phase vector. The dictionary matrix can be represented as: In the formula, Represents a dictionary matrix. This represents the frequency hopping coefficient of the i-th frequency agile pulse signal. Indicates the frequency hopping width. Indicates the high-resolution distance range. Indicates the carrier frequency. Indicates the speed range. This indicates the repetition period of the frequency-agile pulse signal.

[0013] Furthermore, the specific method of the orthogonal matching pursuit algorithm in step S43 includes: Input: Observation vector dictionary matrix sparsity ; Initialization: Residual vector The number of iterations t=0, the set of atomic indices index submatrix ; Step 1: Calculate the correlation between the residual vector and the column vectors in the dictionary matrix. , can be represented as: The index corresponding to the maximum value is placed into the atomic index set. In the index submatrix, the corresponding column vectors are placed into the index submatrix. middle; Step 2: Calculate the sparse vector corresponding to the current index submatrix. The formula for calculating the sparse vector corresponding to the current index submatrix is: ; Step 3: Update the residual vector ; Step 4: Update the iteration count t = t + 1. If t > S, stop the iteration; otherwise, go back to step 1 and continue iterating. Output: Sparse vector ; Furthermore, the specific method of alternating direction multipliers in step S43 includes: Input: Observation vector dictionary matrix ; Initialization: A two-dimensional matrix of the composite scattering coefficients of the target. Iteration step size Auxiliary vectors Error vector Iteration count t=0, Iteration termination condition and identity matrix; Step 1: Update the sparse vector: ; Step 2: Update auxiliary vectors: ; Step 3: Update the error vector: ; Step 4: Calculate the error between the sparse vector and the auxiliary vector. When the error is less than... If the iteration ends, exit the iteration; otherwise, update the iteration count t = t + 1. Output: Sparse vector .

[0014] Advantages of this invention: In this invention, by setting the frequency hopping coefficient of each frequency-agile pulse signal, the frequency-agile pulse signals emitted by the frequency-agile radar have non-overlapping spectral distributions. Furthermore, the frequency hopping interval of each frequency-agile pulse signal is set to be greater than the sub-bandwidth of the frequency-agile pulse signal, ensuring good distinguishability of the echo signals corresponding to the frequency-agile pulse signals in the frequency domain. By setting the passband of the rectangular bandpass filter, the passband of the rectangular bandpass filter covers the carrier frequency of the echo signals received by the frequency-agile radar. When folded clutter and the echo signals received by the frequency-agile radar pass through the rectangular bandpass filter, the echo signals received by the frequency-agile radar are allowed to pass through, suppressing folded clutter. Through the impulse response of the matched filter, each frequency-agile pulse signal is formed in both the time domain and the frequency domain into a time-reversed conjugate form of the frequency-agile pulse signal and a frequency-reversed conjugate form, respectively. The frequency-agile pulse signal is processed by convolution with a matched filter, which focuses the energy of the echo signal corresponding to the transmitted frequency-agile pulse signal. At the same time, it further suppresses mismatched interference components (such as residual clutter and background noise), thereby improving the signal-to-noise ratio of target detection. Furthermore, the observed signal in the sparse reconstruction model is sparsely reconstructed using an orthogonal matched pursuit algorithm or an alternating direction multiplier method, realizing the reconstruction of the original sparse echo signal (i.e., sparse vector) from the observed signal. After sparse reconstruction, the sparse vector is obtained, and then the velocity-range information of the target under test can be extracted from the sparse vector. Sparse reconstruction not only enhances the detectability of weak targets in a strong clutter background, but also further suppresses residual clutter and noise, realizing the distinction between folded clutter and echo signal, thereby significantly improving the overall detection performance and anti-interference capability of the radar system. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a flowchart illustrating a folding clutter suppression method based on frequency-agile radar provided in an embodiment of the present invention. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] Example Figure 1 This is a flowchart of a folding clutter suppression method based on frequency-agile radar provided in an embodiment of the present invention. See also... Figure 1 The method for suppressing clutter based on frequency agile radar folding includes: Step S1: Set the number of pulses in the frequency agile pulse sequence, the frequency hopping interval between adjacent frequency agile pulse signals, and the frequency hopping coefficient of each frequency agile pulse signal, and transmit multiple frequency agile pulse signals.

[0019] The frequency hopping interval is set to be greater than the sub-bandwidth of the frequency-agile pulse signal, which is the width of the frequency range occupied by the frequency-agile pulse signal itself. The frequency hopping interval is represented by the difference between the carrier frequencies used by adjacent frequency-agile pulse signals. The sub-bandwidth of the frequency-agile pulse signal is greater than or equal to 2MHz and less than or equal to 10MHz. Multiple frequency-agile pulse signals are programmed to transmit in a specific order, and the agile radar transmits each frequency-agile pulse signal according to this programmed sequence.

[0020] For a sequence of N frequency-agile pulse signals, its expression is:

[0021] In the formula, This represents a frequency-agile pulse signal sequence. This represents the scattering coefficient of the i-th frequency agile pulse signal. Indicates the number of pulses. Indicates the width of the frequency-agile pulse signal. Indicates the frequency modulation sub-bandwidth. Indicates the linear frequency modulation slope. This represents the carrier frequency of the i-th frequency agile pulse signal. Let represent the frequency hopping coefficient of the i-th frequency agile pulse signal, and have , Indicates the number of selectable frequency points. Indicates the unit frequency hopping interval. Represents the window function.

[0022] Frequency modulation sub-bandwidth refers to the width of the frequency range allocated to a single frequency modulation channel in a frequency modulation (FM) communication system. By setting the frequency hopping coefficient, each frequency agile pulse signal transmitted by the frequency agile radar has a non-overlapping spectral distribution, and the frequency hopping interval of each frequency agile pulse signal is set to be greater than the frequency agile pulse signal sub-bandwidth to ensure that the echo signal corresponding to the frequency agile pulse signal has good distinguishability in the frequency domain.

[0023] Step S2: Calculate the carrier frequency of the echo signal received by the frequency-agile radar based on the frequency hopping interval and the frequency hopping coefficient; set the passband of the frequency domain filter, and use the frequency domain filter corresponding to the echo signal carrier frequency to filter the echo signal, and output the filtered echo signal.

[0024] The frequency domain filter includes a rectangular bandpass filter. In this invention, the frequency domain filter used is a rectangular bandpass filter, which is a filter that only allows signals in a specific frequency band to pass through. The expression for the echo signal received by the frequency-agile radar is:

[0025] In the formula, Indicates the echo signal. This represents the scattering coefficient of the i-th frequency agile pulse signal. Indicates the number of pulses. Indicates the width of the frequency-agile pulse signal. Indicates the frequency modulation sub-bandwidth. Indicates the linear frequency modulation slope. This represents the carrier frequency of the i-th frequency agile pulse signal. Indicates the initial carrier frequency; Let represent the frequency hopping coefficient of the i-th frequency agile pulse signal, and have , Indicates the number of selectable frequency points. Indicates the unit frequency hopping interval. Represents the window function.

[0026] Given the frequency hopping interval and hopping coefficient of the frequency-agile pulse signal, the carrier frequency of the echo signal received by the frequency-agile radar can be calculated based on the expression of the echo signal received by the frequency-agile radar. The frequency distribution of folded clutter is offset from that of the echo signal received by the frequency-agile radar in the frequency domain. By setting the passband of the rectangular bandpass filter, the passband of the rectangular bandpass filter covers the carrier frequency of the echo signal received by the frequency-agile radar. When the folded clutter and the echo signal received by the frequency-agile radar pass through the rectangular bandpass filter, the echo signal received by the frequency-agile radar is allowed to pass through, thus suppressing the folded clutter.

[0027] Step S3: Use a matched filter to perform impulse response and convolution processing on the filtered echo signal, and output the matched filtered echo signal.

[0028] Specifically, a matched filter is used to induce an impulse response in the time domain of the frequency-agile pulse signal, forming a time-reversed conjugate form of the frequency-agile pulse signal, denoted as . Furthermore, a matched filter is used to convolve the echo signal and the corresponding time-reversed conjugate frequency-agile pulse signal to obtain the time-domain matched-filtered echo signal, denoted as . In the formula, Indicates the echo signal. Indicates convolution processing; Alternatively, a matched filter can be used to transform the time-domain signal of the frequency-agile pulse signal into a frequency-domain signal via Fourier transform. An impulse response is then applied to the frequency-domain signal to generate a frequency-agile pulse signal in a frequency-reversed conjugate form, denoted as... Furthermore, a matched filter is used to convolve the echo signal and the corresponding frequency-agile pulse signal in its inverted conjugate form in the frequency domain to obtain the echo signal after matched filtering in the frequency domain, denoted as . .

[0029] The impulse response of the matched filter enables the frequency agile pulse signals of each frequency to be converted into time-reversed conjugate form rate-frequency agile pulse signals and frequency-reversed conjugate form in the time and frequency domains, respectively. Furthermore, the convolution processing of the matched filter enables the energy of the echo signal corresponding to the transmitted frequency agile pulse signal to be focused, while further suppressing mismatched interference components (such as residual clutter and background noise), thereby improving the signal-to-noise ratio of target detection.

[0030] Step S4: Construct a sparse reconstruction model based on the echo signal after matched filtering, and use the orthogonal matching pursuit algorithm or the alternating direction multiplier method to sparsely reconstruct the observed signal in the sparse reconstruction model to obtain a sparse vector.

[0031] Sparse reconstruction is a processing technique for recovering sparse signals from an underdetermined observation system. By performing sparse reconstruction on undersampled data, the original signal can be inferred from a small number of observation signals.

[0032] Specifically, the observed signal is first obtained from the echo signal after matched filtering. Then, a dictionary matrix is ​​constructed. A sparse reconstruction model is constructed based on the dictionary matrix and the observed signal. Finally, the observed signal in the sparse reconstruction model is sparsely reconstructed using the orthogonal matching pursuit algorithm or the alternating direction multiplier method to obtain a sparse vector.

[0033] The specific method for obtaining the observed signal from the matched-filtered echo signal includes: first, discretizing the matched-filtered echo signal to form a discretized mathematical echo signal, and defining a set of orthogonal basis vectors. Sparse vectors Discretized echo mathematical signals can be derived from a set of orthogonal basis vectors and sparse vectors. It can be represented as Discretized echo mathematical signals are represented using orthogonal basis vector sets and sparse vectors, where the elements of the sparse vectors... , This represents the i-th element in the sparse vector. This represents the velocity and super-resolution distance characteristics of the discretized echo signal; Sparse vectors The sparsity on orthogonal basis vectors can be defined as: In the formula, Indicates sparsity. This represents the number of non-zero elements in a sparse vector. Represents the number of pulses, the number of non-zero elements. much smaller Then it is called a sparse vector. It is sparse; in this case, the discretized echo mathematical signal can be represented as: ; Sparsity is defined as follows: if a signal has only a small number of non-zero coefficients in a certain transform domain (such as Fourier transform or wavelet transform), and most of the other coefficients are approximately zero, then the signal is said to have sparsity in that domain.

[0034] Define an observation matrix , dimension Among them, satisfying , Indicates the number of measurements or the dimensions of measurement. The dimension of the discretized echo mathematical signal is represented by the observation vector, which is calculated from the sparse vector, the discretized echo mathematical signal, and the observation matrix. The expression for the observation vector is: The observation vector is low-dimensional data obtained by compressing the observation of the discretized echo mathematical signal, i.e., the discretized echo mathematical signal. Undersampling was performed at a sampling rate lower than the Nyquist sampling rate.

[0035] The specific method for constructing the dictionary matrix includes: obtaining the composite scattering coefficients of the target from the echo signal after matched filtering, which can be expressed as... ,in, For high resolution distance, To obtain the velocity, the high-resolution range and velocity in the composite scattering coefficient of the target are discretized, resulting in discretized high-resolution range and discretized velocity. Based on the discretized high-resolution range and discretized velocity, a two-dimensional matrix of the composite scattering coefficient of the target is obtained. The two-dimensional matrix of the composite scattering coefficient of the target can be represented as:

[0036] in, This represents the composite scattering coefficient of the target under test. Indicates the high-resolution range phase factor. The velocity phase factor is represented by P, which represents the number of points for discretizing the high-resolution range, and Q represents the number of points for discretizing the velocity. The two-dimensional matrix of the composite scattering coefficients of the target under test represents all possible scenarios after discretization, and each element of this matrix represents the scattering coefficient of the corresponding scenario.

[0037] The elements of the two-dimensional matrix of the composite scattering coefficients of the target are rearranged in one dimension to construct a one-dimensional vector of composite scattering coefficients; this one-dimensional vector of composite scattering coefficients can be represented as... ,in, Let l represent a one-dimensional vector of composite scattering coefficients, and let l represent the high-resolution range phase factor and velocity phase factor corresponding to the l-th element of the one-dimensional vector of composite scattering coefficients. 'l' represents the index; the index 'l' in the 'l' element can be decomposed into high-resolution distance indexes. and speed The sequence number can be represented as In the formula, , , Define the phase vector ,vector The phase relationship of l in the nth column of the one-dimensional vector of composite scattering coefficients can be expressed as: In the formula, dn represents the distance corresponding to the nth pulse, j represents the imaginary unit, and ln represents the index of the nth element; a dictionary matrix is ​​constructed based on the phase vector, and the dictionary matrix can be represented as: In the formula, Represents a dictionary matrix. This represents the frequency hopping coefficient of the i-th frequency agile pulse signal. Indicates the frequency hopping width. Indicates the high-resolution distance range. Indicates the carrier frequency. Indicates the speed range. This indicates the repetition period of the frequency-agile pulse signal.

[0038] A sparse reconstruction model is constructed based on the dictionary matrix and the observed signal. The sparse reconstruction model can be expressed as follows: ; in, For observing signals, It is a dictionary matrix. The sparse target representation vector to be recovered. Observation noise or interference.

[0039] Specific methods for sparsely reconstructing the observed signals in a sparse reconstruction model using the orthogonal matching pursuit algorithm or the alternating direction multiplier method to obtain sparse vectors include: The core objective of sparse reconstruction is to minimize the sparsity of the sparse vector while satisfying the observation equation, expressed as: ; in, Representing sparse vectors of The norm of the problem is NP-hard, therefore the solution will be a sparse vector. Minimum The norm problem is equivalent to solving sparse vectors. Minimum Norm optimization problem: Solving sparse vectors of The norm (i.e., the sum of the absolute values ​​of all elements in a sparse vector) is expressed as: ; Solving sparse vectors using the orthogonal matching pursuit algorithm The specific method is as follows: Input: Observation vector dictionary matrix Sparsity S; Initialization: Residual vector The number of iterations t=0, the set of atomic indices index submatrix ; Step 1: Calculate the correlation between the residual vector and each column of the dictionary matrix. The index corresponding to the maximum value is placed into the atomic index set. In the index submatrix, the corresponding column vectors are placed into the index submatrix. middle; in, Represents the conjugate transpose of a dictionary matrix; Step 2: Calculate the sparse vector corresponding to the current index submatrix. The formula for calculating the sparse vector corresponding to the current index submatrix is: ; in, This represents the conjugate transpose of the index submatrix. The inverse matrix of the indexed submatrix; Step 3: Update the residual vector ; Step 4: Update the iteration count t = t + 1. If t > K, stop the iteration; otherwise, go back to step 1 and continue iterating. Output: Sparse vector ; Based on the solution of the sparse vector Calculate the sparse vector The sum of the absolute values ​​of the number of non-zero elements in the equation.

[0040] Or sparse vectors using alternating direction multipliers The specific method is as follows: Input: Observation vector dictionary matrix ; Initialization: A two-dimensional matrix of the composite scattering coefficients of the target. Iteration step size Auxiliary vectors Error vector Iteration count t=0, Iteration termination condition and identity matrix; Step 1: Update the sparse vector: ; Step 2: Update auxiliary vectors: ; Step 3: Update the error vector: ; Step 4: Calculate the error between the sparse vector and the auxiliary vector. When the error is less than... If the iteration ends, exit the iteration; otherwise, update the iteration count t = t + 1. Output: Sparse vector ; Based on the solution of the sparse vector Calculate the sparse vector The sum of the absolute values ​​of the number of non-zero elements in the equation.

[0041] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for foldover clutter suppression based on agile frequency radar, characterized in that, The method comprises the following steps: Step S1: setting the number of pulses of a frequency agile pulse sequence, the frequency hopping interval of adjacent frequency agile pulse signals, and the frequency hopping coefficient of each frequency agile pulse signal, and transmitting a plurality of the frequency agile pulse signals; Step S2: calculating the carrier frequency of a received echo signal of the frequency agile radar according to the frequency hopping interval and the frequency hopping coefficient; setting the passband of a frequency domain filter; filtering the carrier frequency of the echo signal by using the frequency domain filter corresponding to the carrier frequency of the echo signal; and outputting the filtered echo signal; Step S3: performing impulse response and convolution processing on the filtered echo signal by using a matched filter, and outputting the matched filtered echo signal; Step S4: constructing a sparse reconstruction model according to the matched filtered echo signal; performing sparse reconstruction on the observation signal in the sparse reconstruction model by using an orthogonal matching pursuit algorithm or an alternating direction multiplier method, and obtaining a sparse vector.

2. The agile frequency-based folding clutter suppression method of claim 1, wherein, The frequency hopping interval in step S1 is greater than the subband width of the frequency agile pulse signal; the subband width of the frequency agile pulse signal is greater than or equal to 2 MHz and less than or equal to 10 MHz.

3. The agile frequency-based folding clutter suppression method of claim 1, wherein, The expression of the received echo signal of the frequency agile radar in step 2 is: wherein represents an echo signal, represents a scattering coefficient of the i-th frequency agile pulse signal, represents a pulse number, represents a sub-band width of the frequency agile pulse signal, represents a chirp rate, represents a frequency modulation sub-band width, represents a carrier frequency of the i-th frequency agile pulse signal, represents a frequency hopping coefficient of the i-th frequency agile pulse signal, and has , represents a number of optional frequency points, represents a unit frequency hopping interval, represents a window function.

4. The agile frequency-based folded spurs rejection method of claim 1, wherein, The specific method for performing convolution processing on the filtered echo signal by using a matched filter in step S3 comprises: The time domain signal of the frequency-agile pulse signal is convoluted with a matched filter to form a time-reversed conjugate form of the frequency-agile pulse signal, denoted as , and the echo signal and the corresponding time-reversed conjugate form of the frequency-agile pulse signal are convoluted with a matched filter to obtain a time domain matched filtered echo signal, denoted as , wherein, represents the echo signal, represents the convolution processing; Or using a matched filter to Fourier transform the frequency agile pulse signal time domain signal into a frequency domain signal, and forming a frequency agile pulse signal in the form of frequency domain inverse conjugate impulse response, denoted as ; and using a matched filter to convolve the echo signal and the corresponding frequency agile pulse signal in the form of frequency domain inverse conjugate, to obtain a matched filtered echo signal in the frequency domain, denoted as .

5. The agile frequency-based folded spurs rejection method of claim 1, wherein, The specific method for constructing a sparse reconstruction model according to the matched filtered echo signal in step S4 comprises: Step S40: obtaining an observation signal according to the matched filtered echo signal; Step S41: constructing a dictionary matrix; Step S42: constructing a sparse reconstruction model according to the dictionary matrix and the observation signal; Step S43: performing sparse reconstruction on the observation signal in the sparse reconstruction model by using an orthogonal matching pursuit algorithm or an alternating direction multiplier method, and obtaining a sparse vector.

6. The agile frequency-based folded spurs rejection method of claim 5, wherein, The specific method for obtaining an observation signal according to the matched filtered echo signal in step S40 comprises: Step S401: discretize the matched filtered echo signal to form a discrete echo mathematical signal, denoted as ; Step S402: defining a set of orthogonal basis vectors and a sparse vector , the discretized echo mathematical signal is represented according to the set of orthogonal basis vectors and the sparse vector, and the expression of the discretized echo mathematical signal is: ; Step S403: determining the sparsity of the sparse vector on the orthogonal basis vectors according to the number of non-zero elements in the sparse vector and the number of pulses, and the sparsity can be expressed as: , wherein, represents the sparsity, represents the number of non-zero elements in the sparse vector, represents the number of pulses; Step S404: defining an observation matrix, and calculating the observation signal according to the sparse vector, the discretized mathematical signal and the observation matrix.

7. The agile frequency based folding spurs rejection method according to claim 5, characterized in that, The specific method for constructing a dictionary matrix in step S41 comprises: Step S410: obtaining a complex scattering coefficient of a to-be-detected target from the matched filtered echo signal; Step S411: discretizing the high-resolution range and velocity in the complex scattering coefficient of the to-be-detected target to obtain a discretized high-resolution range and a discretized velocity; Step S412: obtaining a two-dimensional matrix of the complex scattering coefficient of the target to be measured according to the discretized high-resolution distance and the discretized velocity, which can be expressed as: wherein, represents the complex scattering coefficient of the target to be measured, represents a high-resolution distance phase factor, represents a velocity phase factor, P represents the number of points of the discretized high-resolution distance, and Q represents the number of points of the discretized velocity; Step S413: one-dimensional rearrangement is performed on the elements in the two-dimensional matrix of the composite scattering coefficient of the to-be-tested target, to construct a one-dimensional vector of the composite scattering coefficient; the one-dimensional vector of the composite scattering coefficient can be expressed as , wherein, represents the one-dimensional vector of the composite scattering coefficient, and the high-resolution range phase factor and the velocity phase factor corresponding to the lth element in the one-dimensional vector of the composite scattering coefficient are denoted as , and l represents a serial number; Step S414: the sequence number I in the Ith element can be split into a high resolution range sequence number and a velocity sequence number , which can be expressed as , wherein , , ; Step S415: defining a phase vector , vector represents the l phase relationship when the nth column in the one-dimensional vector of the complex scattering coefficient, which can be expressed as: , where dn represents the distance corresponding to the nth pulse, j represents the imaginary unit, and ln represents the serial number of the nth element. Step S416: constructing a dictionary matrix according to the phase vector, which can be expressed as: , wherein, represents the dictionary matrix, represents the frequency hopping coefficient of the i-th frequency agile pulse signal, represents the frequency hopping width, represents the high-resolution distance range, represents the carrier frequency, represents the velocity range, represents the frequency agile pulse signal repetition period.

8. The agile frequency based foldover clutter rejection method of claim 5, wherein, The specific method for the orthogonal matching pursuit algorithm in step S43 comprises: Input: observation vector , dictionary matrix , sparsity ; Initialization: Residual vector , iteration number t = 0, atom index set , index sub-matrix ; Step 1: Calculate the residual vector and the correlation degree of column vectors in the dictionary matrix , which can be expressed as: , where the index corresponding to the maximum value is put into the atomic index set , and the corresponding column vector is put into the index sub-matrix . Step 2: calculate the corresponding sparse vector under the current index sub-matrix, the calculation formula of the corresponding sparse vector under the current index sub-matrix is: ; Step 3: Update the residual vector ; Step 4: updating the iteration number t = t + 1, and if t > S, stopping iteration, otherwise, continuing to go to step 1 to continue iteration; Output: Sparse vector .

9. The method of foldover spurs rejection based on agile frequency radar according to claim 5, characterized in that, The specific method for the alternating direction multiplier method in step S43 comprises: Input: observation vector , dictionary matrix ; Initialization: 2D matrix of complex scattering coefficients of the object under test Iteration step Auxiliary vector Error vector Iteration number t=0, iteration termination condition And Identity matrix; Step 1: Update the sparse vector: ; Step 2: Update the auxiliary vector: ; Step 3: Update the error vector: ; Step 4: Calculate the error between the sparse vector and the auxiliary vector, exit the iteration when the error is less than t = t + 1; otherwise update the iteration number Output: Sparse vector .

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