CN109932716B - Low-altitude target micro Doppler feature extraction method - Google Patents
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Abstract
Disclosed is a low-altitude target micro Doppler feature extraction method, which comprises the following steps: receiving and preprocessing a target echo signal irradiated by an external radiation source; extracting target micro-motion frequency and constructing a multiple observation vector model; constructing a target micro Doppler characteristic parameter dictionary; and extracting the micro Doppler features of the low-altitude target. On the premise that ground clutter and other clutter can be well filtered, the method can realize good micro-Doppler characteristic extraction on the low-altitude target under the condition of a Gaussian white noise channel.
Description
Technical Field
The invention relates to an external radiation source radar signal processing technology, in particular to a low-altitude target micro Doppler feature extraction method.
Background
At present, low-altitude areas are gradually opened, a large number of general aircrafts, especially unmanned aerial vehicles, enter the low-altitude field, the war electromagnetic environment is gradually complicated, and huge pressure is caused to air defense early warning and air training in important areas. The external radiation source radar has good four-resistant (anti-radiation missile, anti-interference, stealth resistance and low-altitude penetration resistance) capability. Especially, the civil communication signal-based external radiation source radar can make full use of the existing mobile communication facilities to construct a large-range passive detection network and has strong survivability in war environments. In order to maintain the national ownership and the state-of-the-earth defense space, the micro Doppler feature of the low-altitude target is effectively extracted, so that the low-altitude and ultra-low-altitude penetration target can be effectively tracked and imaged, the attribute, intention and threat degree of the low-altitude target are judged, and the method is one of the key factors for realizing more effective low-altitude monitoring and obtaining the war initiative.
The currently common micro-doppler feature extraction methods include: the time-frequency analysis is combined with a Hough Transform (HT) method, and the method is a common micro Doppler feature extraction method due to the characteristics of simplicity, effectiveness and the like. However, the extraction precision is influenced by the size of the radar echo data matrix, the window length of time-frequency analysis and the resolution of time-frequency analysis images. An orthogonal matching pursuit method is an efficient feature extraction technology proposed by y.c. Pati in 1993. The method is based on a matching pursuit algorithm, atoms in a dictionary are subjected to orthogonalization processing according to a Shi Mi special orthogonalization method, and iterative decomposition of signals is achieved on the basis that the signals are decomposed into overcomplete orthogonal bases. The method has high decomposition efficiency, high convergence rate, simplicity and feasibility, and is still applicable under the undersampling condition. However, the greatest disadvantage of the method is that when the extracted characteristic parameters are increased, the number of atoms in the dictionary is greatly increased, and the calculation amount of algorithm decomposition is increased in a geometric series manner.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a low-altitude target micro Doppler feature extraction method, which comprises the following steps:
the first step is as follows: reception and preprocessing of target echo signals illuminated by external radiation sources
The external radiation source transmits LTE communication signals, after the LTE communication signals irradiate a target, the signals reflected by the target are called target echo signals, and after the receiver receives the signals, the receiver samples and receives the signals and outputs received signals;
the communication signal output by the external radiation source is
Wherein N is a memberCarrier frequency number, K is code length, n is index of sub-carrier frequency, K is index of code length, a n Is the weighting factor of the nth sub-carrier frequency, A re Is a real part modulation coefficient, A im Is the imaginary modulation coefficient, T p For Orthogonal Frequency Division Multiplexing (OFDM) symbol duration, f 0 Is the carrier frequency, and Δ f is the sub-carrier frequency interval; wherein Δ f satisfies the OFDM orthogonality condition
Wherein, i, j is the number of the sub-carrier frequency, which means that any two sub-carrier frequencies satisfy the orthogonality condition, that is
Δf＝1/T p (3)
The received target echo signal is
Wherein, t m Is a slow time, t k For fast time, σ is the scattering coefficient of the target, r (t) m ) The sum of the distances between the target and the external radiation source and the distance between the target and the receiver are respectively, and c is the speed of light in vacuum;
the reference signal is a direct wave signal from a receiver to an external radiation source and can be expressed as
Wherein D is the distance between the external radiation source and the receiver;
assuming that the multipath clutter in the received signal is better suppressed and the clean target echo and direct wave are obtained, the echo signal is conjugate multiplied by the reference signal to obtain the baseband echo which can be expressed as
Wherein the content of the first and second substances,
is s is r (t k ，t m ) The conjugate signal of (a);
the second step is that: extracting target micro-motion frequency and constructing multiple observation vector model
(a) Multiple observation vector model
Let there be a one-dimensional vector x = [ x (1), …, x (U)] T The coordinate alpha under the U-dimensional normal orthogonal base psi only contains B nonzero elements, and if B & lt U, the alpha is called B sparse; wherein x (1), …, x (U) is a coordinate in a conventional coordinate system; Ψ is a sparse basis matrix called x; let us assume that there is an observation matrix phi that is independent of Ψ V×U (V < U) performing a linear observation on the vector x, and recording the observation result as y = Φ x = Φ Ψ α = Θ α, where Θ = Φ Ψ is referred to as a sensing matrix; reducing an original N-dimensional signal vector x into an M-dimensional vector y; when the constrained isometry condition is satisfied, the sparse representation of the signal vector x can be obtained by solving for the minimum l 0 Norm resolution, i.e.
α＝arg min||α|| 0 (8)
Where α is a sparse representation of the vector x, and α satisfies the condition y = Φ Ψ α;
consider that if there are L sources with the same sparse structure, it is written X = [ X = 1 ，…，x L ] T X is a number of L X, i.e. X 1 ，…，x L The formed matrix can adopt the same observation matrix, and the observation result can be expressed as
Y＝ΦX＝Φ[x 1 ，…，x L ] (9)
The model is called a multiple observation vector MMV model, and the multiplicity is L; the prior information that the signals have the same sparse structure is utilized, and the solution is carried out by the minimum of the sparse matrix rank, namely, the following equation sets are connected
Wherein A is a sparse representation of X, α l Represents the coordinates of the l-th source under the U-dimensional orthonormal basis and satisfies the condition Y = phi psi [ alpha ] 1 ，…，α L ]；
(b) Construction of multiple observation vector model
Aiming at the baseband echo signal output in the first step, if the time is t m And a fast time t k Respectively sampling M 'and N', the echo signal can be expressed in a matrix form S r ∈R N′×M′ Wherein R represents a real number matrix; due to the change of the target attitude, the observed echo matrix can not be directly used as a multiple observation vector S r (ii) a Therefore, a fast time t 'of the same target attitude is extracted' s The baseband echo of (3) is used for constructing a multiple observation vector model with the same sparse structure, so that the sparse expression of the multiple observation vector model can be solved;
because the echo at a certain fast time needs to be extracted, the prior information of the target micro-motion frequency is needed; extracting a target micro-motion frequency f by utilizing sinusoidal frequency modulation Fourier Bessel transformation; constructing a multiple observation vector model of the baseband echo by using the extracted micro-motion frequency f ', wherein f' is the estimation result of the extracted target micro-motion frequency
S(f′)＝[s b (t′ s1 ，t′ m1 )，s b (t′ s2 ，t′ m2 )，…，s b (t′ sN′ ，t′ mN′ )] (11)
Wherein T =1/f 'is a target inching period, T' si Is a marked fast time instant, t' mi Is a fast time t' si Corresponding slow time series, i.e. t' mi ＝t′ si ，t′ si +T，...，t′ si +LT，
The number of occurrences of the same attitude at the radar irradiation time t,
represents rounding down，s b (t′ si ，t′ mi ) Is represented by t' si ，t′ mi Is a parametric baseband echo signal, i =1,2, ·, N';
the third step: constructing a target micro Doppler feature parameter dictionary
For a specific external radiation source signal, a received signal in practical application contains a target echo signal, a direct wave signal and other clutter, wherein the clutter signal is filtered by an existing clutter suppression method;
for the preprocessed target echo signal, a multiple observation vector model is constructed according to the second step, the orthogonality of OFDM signals is utilized to extract the echo of a certain sub-carrier frequency for processing, and then the carrier frequency of the target in the baseband echo is a known quantity; assuming that the number of signal amplitudes and phases in the sparse dictionary are P terms and Q terms respectively, the sparse dictionary can be expressed as { A } 1 ，…，A P And { theta } - } and 1 ，…，θ Q h, the sparse dictionary Ψ (f ') with f' as parameter can be expressed as a matrix
Wherein the sparse dictionary matrix Ψ (f ') has a size of M' × PQ,
for decimated slow time instants, row vectors in the matrix
A feature vector representing the target micro-Doppler, where m =1, …, L, and
wherein the content of the first and second substances,
the fourth step: micro-Doppler feature extraction of low-altitude targets
After the communication radiation source signal feature data set dictionary construction is completed, for a target baseband echo signal, the micro Doppler feature extraction of a low-altitude target is realized by adopting an orthogonal matching tracking algorithm;
using the micro-doppler feature parameter dictionary constructed in the third step, x = Ψ α can be rewritten as
S(f′)＝Ψ(f′)X (15)
The size of the source matrix S (f ') is M multiplied by L, the size of the sparse representation matrix X is PQ multiplied by L, and the size of the sparse base matrix psi (f ') is M ' multiplied by PQ;
defining a down-sampling rate of
η＝L/M′ (16)
Where M' is the number of slow time sample points;
under the condition of noise, the sparse expression solution of the MMV model of the multiple observation vectors can be solved through l 0 Norm minimization for solving
X＝arg min||X|| 0 (17)
Wherein X satisfies the condition
ε is the allowable error;
in the solving process, if and only if the formulas (13) and (14) satisfy A p ＝A i And theta q ＝θ i X tintin matrix Ψ (f)', a q+(p-1)Q If the row is not zero, extracting information such as amplitude, phase and the like of the target echo signal from the non-zero row vector in the matrix, and obtaining information such as the rotation radius, the initial phase and the like of the target through formula conversion, namely realizing the extraction of the low-altitude target micro Doppler characteristic.
The method has the advantages that the micro Doppler characteristic information of the target can be obtained by directly processing the echo signal without carrying out characteristic extraction from the image, and the problem that the resolution of the image influences the extraction precision of the characteristic parameters is solved; the multi-observation vector model is adopted to process the target baseband echo signal, the extraction precision of the characteristic parameter is improved along with the increase of the weight of the model, and meanwhile, a better low-altitude target micro Doppler characteristic extraction function can be realized under the condition that the weight reaches a certain value; compared with a method adopting a single observation vector model, the method has the advantage that the time consumption for extracting the target characteristic parameters is less. Therefore, the method has stronger robustness on the micro Doppler feature extraction of the low-altitude target under different signal-to-noise ratios.
Drawings
FIG. 1 is a diagram showing the positional relationship between an object and external radiation sources and receivers;
FIG. 2 shows a graph of the target baseband echo signal sparse solution results;
FIG. 3 shows a Doppler curve of scattering points of a target, wherein FIG. 3 (a) shows a target micro-Doppler theoretical curve and FIG. 3 (b) shows a target micro-Doppler reconstruction curve;
FIG. 4 illustrates normalized mean square error at different multiplicity, where FIG. 4 (a) illustrates normalized mean square error of radius of rotation at different multiplicity and FIG. 4 (b) illustrates normalized mean square error of initial phase at different multiplicity;
FIG. 5 shows the time consumption of the low-altitude target micro-Doppler feature extraction method of the invention under different multiples;
fig. 6 shows a schematic flow diagram of the method of the invention.
Detailed Description
The technical scheme and the implementation process of the invention are described in detail by combining specific examples.
The low-altitude target micro Doppler feature extraction method comprises the following steps:
the first step is as follows: receiving and preprocessing a target echo signal irradiated by an external radiation source;
a position relation diagram among the target, the external radiation source and the receiver is shown in fig. 1, the selected external radiation source transmits Long Term Evolution (LTE) communication signals, after the signals irradiate the target, the signals reflected by the target are called target echo signals, and after the signals are received by the receiver, the signals are sampled and received signals are output;
the communication signal output by the external radiation source is
Where N is the subcarrier number, K is the code length (related to the modulation scheme), N is the index of the subcarrier frequency, K is the index of the code length, a n Is the weighting factor of the nth sub-carrier frequency, A re Is a real part modulation coefficient, A im Is the imaginary modulation coefficient, T p For Orthogonal Frequency Division Multiplexing (OFDM) symbol duration, f 0 Is the carrier frequency, and Δ f is the sub-carrier frequency interval;
wherein Δ f satisfies the OFDM orthogonality condition
Where i, j is the number of the sub-carrier frequency, which means that any two sub-carrier frequencies satisfy the orthogonality condition, i.e. it is
Δf＝1/T p (3)
The received target echo signal is
Wherein, t m Is a slow time, t k For fast time, σ is the scattering coefficient of the target, r (t) m ) The sum of the distances between the target and the external radiation source and the distance between the target and the receiver are respectively, and c is the speed of light in vacuum;
the reference signal is a direct wave signal from a receiver to an external radiation source and can be expressed as
Wherein D is the distance between the external radiation source and the receiver;
assuming that the multipath clutter in the received signal is better suppressed and the clean target echo and direct wave are obtained, the echo signal is conjugate multiplied by the reference signal to obtain the baseband echo which can be expressed as
Wherein the content of the first and second substances,
is s is r (t k ，t m ) The conjugate signal of (a);
the second step is that: extracting target micro-motion frequency and constructing a multiple observation vector model;
in a practical environment, strong scattering points on aerial targets and spatial targets are always limited, so that echoes of the aerial targets and the spatial targets have sparsity per se. The invention constructs a multiple observation vector model for the baseband echo, and reduces the data volume of the echo matrix, thereby reducing the operation amount of the feature extraction algorithm. The multiple observation vector model is a general popularization of a single observation vector model, and is used for observing signals with the same sparse structure for multiple times, namely, each column of the signals is sparse, the positions of non-zero elements are the same, and the multiple observation vector model has higher reconstruction accuracy and better anti-noise capability than the single observation vector model;
(a) Multiple observation vector model
Let there be a one-dimensional vector x = [ x (1), …, x (U)] T The coordinate alpha under the U-dimensional orthonormal base psi only contains B (B < U) nonzero elements, and alpha is called B sparse. Where x (1), …, x (U) are coordinates in a conventional coordinate system. Ψ is referred to as a sparse basis matrix for x. Setting the existence of an observation matrix phi which is not related to psi V×U (V < U) a linear observation is made of vector x, and the observation can be noted as y = Φ x = Φ Ψ α = Θ α, where Θ = Φ Ψ is referred to as the perceptual matrix. The original N-dimensional signal vector x is reduced to an M-dimensional vector y. When the constrained isometry condition (which is well known to those skilled in the art) is satisfied, the sparse representation of the signal vector x can be obtained by solving for the minimum l 0 Norm resolution, i.e.
α＝arg min||α|| 0 (8)
Where α is a sparse representation of the vector x, and α satisfies the condition y = Φ Ψ α;
consider that if there are L sources with the same sparse structure, it is written X = [ X ] 1 ，…，x L ] T (X is a number of X's, i.e. X 1 ，…，x L Formed matrix), the same observation matrix may be used and the observations may be represented as
Y＝ΦX＝Φ[x 1 ，…，x L ] (9)
This model is called the multiple observation vector (MMV) model, with a multiplicity of L. By using the prior information that the signals have the same sparse structure, the solution can be carried out by the minimum of the sparse matrix rank, namely, the following equations are combined
Wherein A is a sparse representation of X, α l Represents the coordinates of the l-th source under the U-dimensional orthonormal basis and satisfies the condition Y = phi psi [ alpha ] 1 ，…，α L ]；
(b) Construction of multiple observation vector model
Aiming at the baseband echo signal output in the first step, if the time is t m And a fast time t k M 'and N' samples are respectively taken, the echo signal can be expressed in a matrix form S r ∈R N′×M′ Where R represents a real number matrix. Due to the change of the target attitude, the observed echo matrix can not be directly used as a multiple observation vector S r . Therefore, a fast time t 'of the same target attitude is extracted' s The baseband echo of (1) constructs a multiple observation vector model with the same sparse structure, so that the sparse expression of the multiple observation vector model can be solved;
since echoes at a certain fast time instant need to be extracted, a priori information on the target micro-motion frequency is needed. The method extracts the target micro-motion frequency f by using the sinusoidal frequency modulation Fourier Bessel transformation, can directly calculate the baseband echo, extracts the target micro-motion frequency, and has higher precision. Constructing a multiple observation vector model of the baseband echo by using the extracted micro-motion frequency f ', wherein f' is the estimation result of the extracted target micro-motion frequency
S(f′)＝[s b (t′ s1 ，t′ m1 )，s b (t′ s2 ，t′ m2 )，…，s b (t′ sN′ ，t′ mN′ )] (11)
Wherein T =1/f 'is a target inching period, T' st Is a marked fast time instant, t' mi Is a fast time t' si Corresponding slow time sequence, i.e. t' mi ＝t′ si ，t′ si +T，...，t′ si +LT，
The number of occurrences of the same attitude at the radar irradiation time t,
denotes rounding down, s b (t′ si ，t′ mi ) Is represented by t' si ，t′ mi Is a parametric baseband echo signal, i =1,2, ·, N';
the third step: constructing a target micro Doppler characteristic parameter dictionary;
after a baseband echo multiple observation vector model is constructed, feature extraction needs to be carried out on the model, and a target micro Doppler feature parameter dictionary is constructed; the amplitude, the initial phase and the micro-motion frequency of the target baseband echo signal are used as micro-Doppler characteristic parameters of a target, and the micro-motion frequency of the target is obtained by other methods, so that the amplitude and the initial phase of the target baseband echo signal form a characteristic vector;
for a specific external radiation source signal, a received signal in practical application contains a target echo signal, a direct wave signal and other clutter, wherein the clutter signal is filtered by an existing clutter suppression method;
for the preprocessed target echo signal, the methodAnd constructing a multiple observation vector model according to the second step, and extracting the echo of a certain sub-carrier frequency by utilizing the orthogonality of Orthogonal Frequency Division Multiplexing (OFDM) signals for processing, wherein the carrier frequency of the target in the baseband echo is a known quantity. Assuming that the number of signal amplitudes and phases in the sparse dictionary are P terms and Q terms respectively, the sparse dictionary can be expressed as { A } 1 ，…，A P And { theta } - } and 1 ，…，θ Q f ' is used as a parameter, and the sparse dictionary Ψ (f ') with f ' as a parameter can be expressed as a matrix
Wherein the sparse dictionary matrix Ψ (f ') has a size of M' × PQ,
for extracted slow time instants, row vectors in the matrix
A feature vector representing the target micro-Doppler, where m =1, …, L, and
wherein the content of the first and second substances,
the fourth step: extracting micro Doppler features of the low-altitude target;
after the construction of a communication radiation source signal feature data set dictionary is completed, for a target baseband echo signal, the invention adopts an orthogonal matching tracking algorithm to realize the extraction of the micro Doppler feature of a low-altitude target;
using the micro-doppler feature parameter dictionary constructed in the third step, x = Ψ α can be rewritten as
S(f′)＝Ψ(f′)X (15)
The size of the source matrix S (f ') is M multiplied by L, the size of the sparse representation matrix X is PQ multiplied by L, and the size of the sparse base matrix psi (f ') is M ' multiplied by PQ;
defining a down-sampling rate of
η＝L/M′ (16)
Where M' is the number of slow time sample points;
under noisy conditions, the sparse representation of the multiple observation vector (MMV) model can be solved by l 0 Norm minimization for solving
X＝arg min||X|| 0 (17)
Wherein X satisfies the condition
ε is the allowable error;
in the solving process, if and only if the formulas (13) and (14) satisfy A p ＝A i And theta q ＝θ i X in the matrix Ψ (f'), of |q+(p-1)Q If the row is not zero, information such as amplitude, phase and the like of the target echo signal can be extracted from the non-zero row vector in the matrix, and information such as the rotation radius, the initial phase and the like of the target is obtained through formula conversion, namely extraction of the low-altitude target micro Doppler features is achieved.
Example testing
In order to verify the feasibility and robustness of the method in target micro Doppler feature extraction, the experiment carries out computer simulation verification on the micro Doppler features of a plurality of scattering points on a rotating target, the rotating frequency of the micro Doppler features is 25Hz, and the simulation result is analyzed.
Testing one: feasibility test for low-altitude target micro Doppler theoretical feature extraction
3 target rotation points to be subjected to feature extraction are provided, the initial phases are pi/2,5 pi/3,4 pi/3 respectively, the rotation radiuses are 0.68m,3.12m and 2.94m respectively, the feasibility of the method for extracting the low-altitude target micro Doppler features is tested, and the test result is shown in figure 2. And reconstructing a micro Doppler curve of the scattering point of the rotating target by using the extraction result and comparing the micro Doppler curve with a micro Doppler theoretical curve of the scattering point of the rotating target, wherein the result is shown in fig. 3.
As can be seen from the test results in FIG. 2, the target has three rotational scattering points, and the rotational radius and the initial phase of the target are calculated as {0.680m,1.571rad }, {2.932m,5.759rad }, and {3.136m,3.884rad }, respectively. From the result of fig. 3, it can be seen that the micro doppler reconstruction curve of the scattering point of the target is relatively close to the theoretical curve thereof, and although there is a certain deviation on the initial phase, the rotation period and the amplitude are relatively close, so that a better function of extracting the micro doppler feature of the low altitude target can be realized. The test results prove the feasibility of extracting the low-altitude target micro Doppler features.
And (2) testing: robustness test for low-altitude target micro-Doppler theoretical feature extraction
In order to verify the robustness of the method, the influence of Gaussian noise is considered, the SNR is changed from-10 dB to 20dB at equal intervals of 5dB, and 1000 Monte Carlo experiments are carried out. Fig. 4 shows the result of the feature extraction method for extracting the low-altitude target micro-doppler feature under different signal-to-noise ratios. From the test results of fig. 4, it can be known that the method can achieve a better function of extracting the low-altitude target micro doppler features when the feature parameter extraction accuracy is increased along with the increase of the model weight and the weight reaches a certain value. Fig. 5 shows the time-consuming result of the feature extraction method for extracting the low-altitude target micro-doppler features under different down-sampling rates. From the test results of fig. 5, compared with the method using a single observation vector model, the method has the advantages that the time consumption for extracting the target characteristic parameters is less, and the characteristic extraction can be performed more quickly and effectively. The test results also prove the robustness of the method for extracting the low-altitude target micro Doppler features under different signal to noise ratios.
For clarity of illustration, FIG. 6 shows a schematic flow diagram of the method of the present invention.
The invention provides a low-altitude target micro Doppler feature extraction method under the condition of a Gaussian white noise channel, which can be applied to automatic extraction of target micro Doppler features.
Claims (1)
1. A low-altitude target micro Doppler feature extraction method comprises the following steps:
the first step is as follows: reception and preprocessing of target echo signals illuminated by external radiation sources
The external radiation source transmits LTE communication signals, after the LTE communication signals irradiate a target, the signals reflected by the target are called target echo signals, and after the receiver receives the signals, the receiver samples and receives the signals and outputs received signals;
the communication signal output by the external radiation source is
Wherein N is the subcarrier frequency number, K is the code length, N is the index of the subcarrier frequency, K is the index of the code length, a n Is the weighting factor of the nth sub-carrier frequency, A re Is a real part modulation coefficient, A im For imaginary modulation factor, T p For Orthogonal Frequency Division Multiplexing (OFDM) symbol duration, f 0 Is the carrier frequency, and is the sub-carrier frequency interval; wherein Δ f satisfies the OFDM orthogonality condition
Wherein, i, j is the number of the sub-carrier frequency, which means that any two sub-carrier frequencies satisfy the orthogonality condition, that is
Δf＝1/T p (3)
The received target echo signal is
Wherein, t m Is a slow time, t k For fast time, σ is the scattering coefficient of the target, r (t) m ) Is composed ofThe sum of the distances between the target and the external radiation source and the distance between the target and the receiver are respectively, and c is the speed of light in vacuum;
the reference signal is a direct wave signal from the receiver to the external radiation source and can be expressed as
Wherein D is the distance between the external radiation source and the receiver;
assuming that the multipath clutter in the received signal is better suppressed and the clean target echo and direct wave are obtained, the echo signal is conjugate multiplied by the reference signal to obtain the baseband echo which can be expressed as
Wherein the content of the first and second substances,
is as s r (t k ，t m ) The conjugate signal of (a);
the second step is that: extracting target micro-motion frequency and constructing multiple observation vector model
(a) Multiple observation vector model
Let there be a one-dimensional vector x = [ x (1), …, x (U)] T The coordinate alpha under the U-dimensional orthonormal base psi only contains B nonzero elements, and if B & lt U, the alpha is called B sparse; wherein x (1), …, x (U) is the coordinate under the conventional coordinate system; Ψ is a sparse basis matrix called x; let us assume that there is an observation matrix phi that is independent of Ψ v×U (V < U) performing a linear observation on the vector x, and the observation result can be recorded as y = Φ x = Φ Ψ α = Θ α, where Θ = Φ Ψ is referred to as a perception matrix; reducing an original N-dimensional signal vector x into an M-dimensional vector y; when the constrained isometry condition is satisfied, the sparse representation of the signal vector x can be obtained by solving for the minimum l 0 Norm resolution, i.e.
α＝arg min||α|| 0 (8)
Where α is a sparse representation of the vector x, and α satisfies the condition y = Φ Ψ α;
consider that if there are L sources with the same sparse structure, it is written X = [ X ] 1 ，…，x L ] T X is a number of L X, i.e. X 1 ，…，x L The formed matrix can adopt the same observation matrix, and the observation result can be expressed as
Y＝ΦX＝Φ[x 1 ，…，x L ] (9)
The model is called a multiple observation vector MMV model, and the multiplicity is L; solving is carried out by sparse matrix rank minimization by using the prior information that signals have the same sparse structure, namely the following equation sets are combined
Wherein A is a sparse representation of X, α l Represents the coordinates of the l-th source under the U-dimensional orthonormal basis and satisfies the condition Y = phi psi [ alpha ] 1 ，…，α L ]；
(b) Construction of multiple observation vector model
Aiming at the baseband echo signal output in the first step, if the time is t m And a fast time t k Respectively sampling M 'and N', the echo signal can be expressed in a matrix form S r ∈R N′×M′ Wherein R represents a real number matrix; due to the change of the target attitude, the observed echo matrix can not be directly used as a multiple observation vector S r (ii) a Therefore, a fast time t 'of the same target attitude is extracted' s The baseband echo of (1) constructs a multiple observation vector model with the same sparse structure, so that the sparse expression of the multiple observation vector model can be solved;
because the echo at a certain fast time needs to be extracted, the prior information of the target micro-motion frequency is needed; extracting a target micro-motion frequency f by utilizing sinusoidal frequency modulation Fourier Bessel transformation; constructing a multiple observation vector model of the baseband echo by using the extracted micro-motion frequency f ', wherein f' is the estimation result of the extracted target micro-motion frequency
S(f′)＝[s b (t′ s1 ，t′ m1 )，s b (t′ s2 ，t′ m2 )，…，s b (t′ sN′ ，t′ mN′ )] (11)
Wherein T =1/f 'is a target inching period, T' si Is a marked fast time instant, t' mi Is a fast time t' si Corresponding slow time series, i.e. t' mi ＝t′ si ，t′ si +T，...，t′ si +LT，
The number of occurrences of the same attitude at the radar illumination time t,
denotes rounding down, s b (t′ si ，t′ mi ) Is represented by t' si ，t′ mi Is a parametric baseband echo signal, i =1,2, ·, N';
the third step: constructing a target micro Doppler feature parameter dictionary
For a specific external radiation source signal, a received signal in practical application contains a target echo signal, a direct wave signal and other clutter, wherein the clutter signal is filtered by an existing clutter suppression method;
for the preprocessed target echo signal, a multiple observation vector model is constructed according to the second step, the orthogonality of OFDM signals is utilized to extract the echo of a certain sub-carrier frequency for processing, and then the carrier frequency of the target in the baseband echo is a known quantity; assuming that the number of signal amplitudes and phases in the sparse dictionary are P terms and Q terms respectively, the sparse dictionary can be expressed as { A } 1 ，…，A P And { theta } 1 ，…，θ Q F ' is used as a parameter, and the sparse dictionary Ψ (f ') with f ' as a parameter can be expressed as a matrix
Wherein the sparse dictionary matrix Ψ (f ') has a size of M' × PQ,
for decimated slow time instants, row vectors in the matrix
A feature vector representing the target micro-Doppler, where m =1, …, L, and
wherein the content of the first and second substances,
the fourth step: micro-Doppler feature extraction of low-altitude targets
After the communication radiation source signal feature data set dictionary construction is completed, for a target baseband echo signal, the micro Doppler feature extraction of a low-altitude target is realized by adopting an orthogonal matching tracking algorithm;
using the micro-doppler feature parameter dictionary constructed in the third step, x = Ψ α can be rewritten as
S(f′)＝Ψ(f′)X (15)
The size of the source matrix S (f ') is M multiplied by L, the size of the sparse representation matrix X is PQ multiplied by L, and the size of the sparse base matrix psi (f ') is M ' multiplied by PQ;
defining a down-sampling rate of
η＝L/M′ (16)
Where M' is the number of slow time sample points;
under the condition of noise, the sparse expression solution of the MMV model with multiple observation vectors can pass through l 0 Norm minimization for solving
X＝arg min||X|| 0 (17)
WhereinX satisfies the condition
ε is the allowable error;
in the solving process, if and only if the formulas (13) and (14) satisfy A p ＝A i And theta q ＝θ i X tintin matrix Ψ (f)', a q+(p-1)Q If the row is not zero, extracting information such as amplitude, phase and the like of a target echo signal from the non-zero row vector in the matrix, and obtaining information such as the rotation radius, the initial phase and the like of the target through formula conversion, namely realizing the extraction of the low-altitude target micro Doppler characteristic.
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