CN111487593A - Incomplete radar signal repairing method - Google Patents
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Abstract
The invention discloses a method for repairing a defective radar signal, which comprises the following steps of firstly obtaining an acquired signal y ∈ RM(M<N) and an index set Z; secondly is provided with In∈RN*NDeleting the jth row (j ∈ Z) In the In as a unit matrix, and keeping the sequence and the size of other rows unchanged to obtain an observation matrix phi ∈ RM*NSecondly, constructing a sparse dictionary matrix C ∈ R by DCT transformation according to formula (6)N*N(ii) a Then, an orthogonal matching pursuit algorithm is used for reconstructing the sparse vector theta to obtain an estimated value of the sparse vector theta
Finally, the repair signal is obtained by inverse DCT
The invention can realize that under the condition of continuous loss or random loss, compared with the prior art, the method can better reconstruct the complete original signal and the repaired signal in time domain and frequency domainThe domain and instantaneous frequency are quite close to the original signal.
Description
Technical Field
The invention belongs to the field of radar signal analysis, relates to a defective radar signal repairing technology, and particularly relates to a defective radar signal repairing method.
Background
The accurate analysis and processing of radar signals are one of the core tasks of radar countermeasure, and the conventional reconnaissance acquisition equipment, particularly lift-off equipment, is influenced by a series of weak observation factors (such as low signal-to-noise ratio, short faults of signal transmission and storage, discontinuous alignment of attitude of a reconnaissance platform to a target and the like) in the real-time signal acquisition process, so that the acquired data is continuously lost or randomly lost in part of time, the integrity of the acquired signals is seriously influenced, and the accuracy and reliability of subsequent signal processing results are further influenced. If the data lost in the acquisition process can be repaired by using the actually acquired data to repair the radar signal, the correctness of the signal processing result can be effectively improved.
For the radar signal restoration problem under weak observation conditions, the prior solution methods mainly comprise an interpolation method, a curve fitting method and the like. The method extracts the distribution rule or trend of data by using the existing data information, estimates the missing data according to the rule, often needs to solve a series of equations or high-dimensional equation sets, the solving process is more and more difficult along with the increase of data quantity, and the method does not combine the data characteristics of radar signals, the difference between the signals repaired by the method and the original signals in time domain and frequency domain is larger, the signal fine analysis and processing requirements are difficult to meet, and the judgment and parameter estimation of key characteristics such as pulse width, repetition frequency, intra-pulse modulation type, code element width, coding rule and the like of the radar signals are influenced particularly in the aspect of time-frequency characteristic analysis.
Disclosure of Invention
The invention aims to provide a defective radar signal repairing method.
The purpose of the invention can be realized by the following technical scheme:
a method for repairing a defective radar signal, comprising the steps of:
step one, acquiring and obtaining an acquisition signal y ∈ RM(M<N) and an index set Z;
step two: let In∈RN*NDeleting the jth row (j ∈ Z) In the In as a unit matrix, and keeping the sequence and the size of other rows unchanged to obtain an observation matrix phi ∈ RM*N；
Thirdly, constructing a sparse dictionary matrix C ∈ R by utilizing DCT (discrete cosine transformation) according to the formula (6)N*N；
Step four: the orthogonal matching pursuit algorithm is used for reconstructing the sparse vector theta to obtain the estimated value thereof
Step five: recovery signal using inverse DCT transform
Further, the acquisition signal y ∈ R is obtained in the step oneM(M<N) and the index set Z comprises the following specific steps:
s1, setting the observed collected signal as y ∈ RM(M<N), wherein M represents the number of data points actually acquired, and N represents the number of original data points under the condition of no loss;
s2: setting the numerical value of the lost N-M point data as zero, reconstructing a group of N point data by the actually acquired M point data and the supplemented N-M zero data, and marking the N point data as x0, wherein the data value corresponding to the data loss position is zero;
s3, marking the index of the lost position as a set Z, removing N-M zero values of the index position of the set Z in x0, and keeping the sequence and the size of other element values unchanged to obtain an observed signal y ∈ RM(M<N)。
Further, the specific step of constructing the sparse dictionary matrix by using DCT transform according to formula (6) in the third step is:
the DCT matrix is adopted as a sparse dictionary matrix and is set as C ∈ RN*NThe calculation method of the ith row and j column elements of the matrix C is shown as formula (6);
further, the sparse vector Θ in step four is specifically expressed as:
Θ＝C-1x (7)。
the invention has the beneficial effects that:
the invention can realize that under the condition of continuous loss or random loss, compared with the prior art, the method can better reconstruct a complete original signal, and the restored signal is quite close to the original signal in the aspects of time domain, frequency domain, instantaneous frequency and the like. Under the condition of continuous loss, when the random loss rate of data is not higher than 30%, the method can better restore the original signal; under the condition of random loss, the signal repairing effect is obviously better than that of the continuous loss, and when the random loss rate of data is not higher than 60%, the average relative error of the repaired acquired signal is close to 0 compared with the original real signal. However, in the conventional interpolation algorithm, after processing the acquired signals with a continuous loss rate of 10% or more or processing the acquired signals with a random loss rate of 40% or more, the time domain and the frequency domain of the result are severely distorted, and particularly, the processing result can not show the original characteristics of the signals completely due to the severe distortion of the instantaneous frequency. It should also be noted that, in terms of computation time, the interpolation algorithm takes about 2 times as long as the present invention.
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In order to facilitate understanding for those skilled in the art, the present invention will be further described with reference to the accompanying drawings.
FIG. 1 is a flow chart of a method for repairing an anti-surveillance signal of a defective radar according to the present invention;
FIG. 2.1 is a signal time domain comparison diagram of the repair result under the condition of continuous data loss according to the present invention;
FIG. 2.2 is a signal frequency domain comparison diagram of the repair result under the condition of continuous data loss according to the present invention;
FIG. 2.3 is a comparison graph of the time-frequency domain of the signal of the repair result under the condition of continuous data loss according to the present invention;
FIG. 2.4 is the average relative error of the recovery signals at different data loss rates under the continuous loss condition of the present invention;
FIG. 3.1 is a signal time domain comparison diagram of the repair result under the condition of random data loss in the present invention;
FIG. 3.2 is a signal frequency domain comparison diagram of the repair result under the condition of random data loss in the present invention;
FIG. 3.3 is a comparison graph of the time-frequency domain of the signal of the repair result under the condition of random data loss according to the present invention;
fig. 3.4 shows the average relative error of the recovery signals for different data loss rates under the random loss condition of the present invention.
Detailed Description
As shown in fig. 1-3.4, a method for repairing a defective radar signal transforms a defective signal into a sparse domain based on a compressive sensing theory to obtain a sparse domain representation of the signal, and then uses an orthogonal matching pursuit algorithm and a cosine discrete transform algorithm to repair the original signal.
1) Constructing an observation matrix of the incomplete signals;
let the observed acquisition signal be y ∈ RM(M<N), wherein M represents the number of data points obtained by actual acquisition, and N represents the number of original data points under the condition of no loss, namely the data points of N-M which discard the original complete signals in the actual acquisition process of the acquisition equipment are defaulted to be not particularly important;
the value of the lost N-M point data is set to zero, because the N-M point data fails to acquire a signal at the corresponding time, a group of N point data, denoted as x0, can be reconstructed from the actually acquired M point data and the supplemented N-M zero data, and the data value corresponding to the data loss position is set to zero. Recording the index of the lost position as a set Z, removing N-M zero values of the index position of the corresponding set Z in x0, and keeping the sequence and the size of other element values unchanged to obtain the index of the lost positionObserved Signal y ∈ RM(M<N)。
2) Signal restoration principle;
let In∈RN*NDeleting the jth row (j ∈ Z) In as a unit matrix, and keeping the sequence and the size of other rows unchanged to obtain an observation matrix phi ∈ RM*NAnd then applying a CS repair algorithm to reconstruct an estimated value of the original signal N point data.
According to the above definitions and assumptions, it is possible to obtain:
y＝φx (1)
wherein phi is an observation matrix;
the original signal x may be represented by a sparse representation dictionary matrix ψ ∈ RN*NTo make sparseness, i.e.
x＝ψΘ (2)
Wherein, theta is a sparse representation coefficient vector;
let A be phi psi, then
y＝φψΘ＝AΘ (3)
At this time, knowing the actual observed value, namely the acquisition signal y and the measurement matrix A, the sparse coefficient vector theta needs to be reconstructed, and if the theta meets the sparsity, the signal restoration process under the CS framework can be realized.
The scholars prove that the signal restoration can be realized only by measuring that the matrix A meets the constraint equidistant property (RIP) or that the observation matrix phi and the sparse representation dictionary matrix psi are not related.
RIP is defined as follows: for arbitrary k-sparse signals Θ and constantsk∈ (0,1), satisfying:
therefore, the estimated value of the sparse vector theta can be reconstructed only by ensuring that the measurement matrix A meets the RIP condition or that the observation matrix phi and the sparse representation dictionary matrix psi are uncorrelated
And then the estimated value of the complete acquisition signal x can be calculated
Namely, it is
So far, reconstruction and repair of the signal x0 are realized.
3) Repairing radar signals;
as described above, the radar signal restoration process is mainly related to the observation matrix phi, the sparse dictionary matrix psi and the sparse representation coefficient vector theta, wherein the observation matrix phi ∈ RM*NThe method for constructing the sparse dictionary matrix comprises the steps of obtaining a sparse dictionary matrix and a measurement matrix A, obtaining an observation matrix phi, obtaining a sparse representation dictionary matrix psi, and constructing a sparse dictionary matrix C ∈ R sparse dictionary matrix according to the sparse dictionary matrix A, wherein the measurement matrix A needs to meet RIP conditions or the observation matrix phi and the sparse representation dictionary matrix psi are irrelevant to realize signal restorationN*NThe calculation method of the ith row and j column elements of the matrix C is shown in formula (6).
The sparse representation vector Θ is:
Θ＝C-1x (7)；
reconstructing an estimated value of a sparse vector theta based on a compressive sensing method
Further obtaining the estimated value of the original complete radar signal x
The present invention uses an Orthogonal Matching Pursuit (OMP) algorithm in signal repair.
In summary, the incomplete radar signal restoration algorithm flow can be summarized as follows:
s1 observing and obtaining an acquisition signal y ∈ RM(M<N) and an index set Z;
s2, set In∈RN*NDeleting the jth row (j ∈ Z) In the In as a unit matrix, and keeping the sequence and the size of other rows unchanged to obtain an observation matrix phi ∈ RM*N；
S3, constructing sparse dictionary matrix C ∈ R by DCT transformation according to formula (6)N*N；
S4, reconstructing the sparse vector theta by using an Orthogonal Matching Pursuit (OMP) algorithm to obtain an estimated value of the sparse vector theta
S5, obtaining the repair signal by inverse DCT
Correlation experiments were performed on a set of chirped signals. The intermediate frequency of the signal is 52MHz, the frequency modulation bandwidth is a forward incremental frequency modulation of 4MHz, the acquisition duration is 2us, the sampling frequency is 500MHz, and the number of sampling points is 1000. Signal repair was performed with 5%, 10% continuous loss and 30%, 50% random loss, respectively, and comparative analysis experiments were performed with conventional interpolation. In order to visually compare the repairing results, the repairing effects are compared from the time domain, the frequency domain, the instantaneous frequency and the average relative error angle of the repairing data and the original data.
The method is found out that under the condition of continuous missing of 5% of data, the original complete signal is almost perfectly reconstructed, the restored signal is quite close to the original complete signal in a time domain and a frequency domain, the instantaneous frequency characteristic is greatly improved, and the linear increasing characteristic of the instantaneous frequency of the linear frequency modulation signal is reproduced. Under the condition of 10% of deficiency, a better repairing result is obtained, but as the number of the deficiency points reaches 100, the overall trend of the instantaneous frequency characteristic can be seen as a linear frequency modulation signal, but the line fluctuates at the position corresponding to the deficiency, and the linearity degree is lost. However, the processing result of the conventional interpolation algorithm is distorted in the time-frequency domain, which seriously affects the subsequent signal analysis and processing.
And (4) finding the average relative error of the recovery signals with different data loss rates by counting the continuous loss conditions. Under the condition that the data loss rate is not higher than 30%, the average relative error between the signal repaired by the method and the original real signal is small, and the lost data can be repaired more perfectly.
It is found that under the condition of random missing of 30% and 50% of data, the method can almost perfectly restore the original complete signal, the restored signal is quite close to the original complete signal in the time domain and the frequency domain, and simultaneously, the linear increasing characteristic of the instantaneous frequency of the linear frequency modulation signal is reproduced. On the contrary, the processing result of the conventional interpolation algorithm generates more serious distortion in the time-frequency domain, and the linear frequency modulation characteristic of the signal can not be completely reflected.
The average relative error of the signals is found by counting the average relative error of the recovery signals with different data loss rates under the condition of random loss. Under the condition that the data loss rate is not higher than 60%, the average relative error between the signal repaired by the method and the original real signal is small, and the lost data can be repaired more perfectly.
The foregoing is merely exemplary and illustrative of the present invention and various modifications, additions and substitutions may be made by those skilled in the art to the specific embodiments described without departing from the scope of the invention as defined in the following claims.
Claims (4)
1. A method for repairing a defective radar signal, the method comprising the steps of:
step one, acquiring and obtaining an acquisition signal y ∈ RM(M<N) and an index set Z;
step two: let In∈RN*NDeleting the jth row (j ∈ Z) In the In as a unit matrix, and keeping the sequence and the size of other rows unchanged to obtain an observation matrix phi ∈ RM*N；
Thirdly, constructing a sparse dictionary matrix C ∈ R by utilizing DCT (discrete cosine transformation) according to the formula (6)N*N；
Step four: the orthogonal matching pursuit algorithm is used for reconstructing the sparse vector theta to obtain the estimated value thereof
Step five: recovery signal using inverse DCT transform
2. The method for repairing defective radar signals according to claim 1, wherein the acquisition signal y ∈ R is obtained in the first stepM(M<N) and the index set Z comprises the following specific steps:
s1, setting the observed collected signal as y ∈ RM(M<N), wherein M represents the number of data points actually acquired, and N represents the number of original data points under the condition of no loss;
s2: setting the numerical value of the lost N-M point data as zero, reconstructing a group of N point data by the actually acquired M point data and the supplemented N-M zero data, and marking the N point data as x0, wherein the data value corresponding to the data loss position is zero;
s3, marking the index of the lost position as a set Z, removing N-M zero values of the index position of the set Z in x0, and keeping the sequence and the size of other element values unchanged to obtain an observed signal y ∈ RM(M<N)。
3. The method for repairing a defective radar signal according to claim 1, wherein the step three of constructing the sparse dictionary matrix by using DCT transform according to formula (6) comprises the specific steps of:
the DCT matrix is adopted as a sparse dictionary matrix and is set as C ∈ RN*NThe calculation method of the ith row and j column elements of the matrix C is shown as formula (6);
4. the method for repairing a defective radar signal according to claim 1, wherein the sparse vector Θ in step four is specifically expressed as:
Θ＝C-1x (7)。
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| CN114755654A (en) * | 2022-06-14 | 2022-07-15 | 中达天昇(江苏)电子科技有限公司 | Damaged radar signal restoration method based on image mimicry technology |
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