CN111487593B - Incomplete radar signal restoration method - Google Patents

Incomplete radar signal restoration method Download PDF

Info

Publication number
CN111487593B
CN111487593B CN202010188653.2A CN202010188653A CN111487593B CN 111487593 B CN111487593 B CN 111487593B CN 202010188653 A CN202010188653 A CN 202010188653A CN 111487593 B CN111487593 B CN 111487593B
Authority
CN
China
Prior art keywords
signal
epsilon
data
matrix
sparse
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202010188653.2A
Other languages
Chinese (zh)
Other versions
CN111487593A (en
Inventor
刘方正
韩振中
潘继飞
曾瑞琪
王杰贵
姜秋喜
刘鑫
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
National University of Defense Technology
Original Assignee
National University of Defense Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by National University of Defense Technology filed Critical National University of Defense Technology
Priority to CN202010188653.2A priority Critical patent/CN111487593B/en
Publication of CN111487593A publication Critical patent/CN111487593A/en
Application granted granted Critical
Publication of CN111487593B publication Critical patent/CN111487593B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/28—Details of pulse systems
    • G01S7/285—Receivers
    • G01S7/292—Extracting wanted echo-signals

Landscapes

  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Radar Systems Or Details Thereof (AREA)

Abstract

The invention discloses a incomplete radar signal restoration method, which comprises the following steps: firstly, acquiring acquisition signals y epsilon R M (M < N) and an index set Z; secondly, setting I n∈RN*N as an identity matrix, deleting the j-th row (j epsilon Z) In, and keeping the sequence and the size of other rows unchanged to obtain an observation matrix phi epsilon R M*N; then constructing a sparse dictionary matrix C epsilon R N*N by DCT according to the formula (6); then, the sparse vector Θ is reconstructed by using an orthogonal matching pursuit algorithm to obtain an estimated valueFinally, the restoration signal is obtained by inverse DCT transformationCompared with the prior art, the method can reconstruct the complete original signal better under the condition of continuous loss or random loss, and the repaired signal is quite similar to the original signal in the aspects of time domain, frequency domain, instantaneous frequency and the like.

Description

Incomplete radar signal restoration method
Technical Field
The invention belongs to the field of radar signal analysis, relates to a repair technology of incomplete radar signals, and particularly relates to a repair method of incomplete radar signals.
Background
The accurate analysis and processing of radar signals are one of the core tasks of radar countermeasure, and the existing reconnaissance acquisition equipment, particularly the lift-off equipment, is influenced by a series of weak observation factors (such as low signal-to-noise ratio, short signal transmission and storage faults, intermittent alignment of the attitude of a reconnaissance platform to a target and the like) in the real-time acquisition process of signals, so that acquired data are continuously lost or randomly lost in part of time, the integrity of the acquired signals is seriously influenced, and the accuracy and the reliability of subsequent signal processing results are further influenced. If the data lost in the acquisition process can be repaired by using the actual acquired data, the radar signal is repaired, and the correctness of the signal processing result is effectively improved.
For the problem of radar signal restoration under weak observation conditions, the previous solutions mainly include interpolation methods, curve fitting methods and the like. The method utilizes the existing data information to extract the distribution rule or trend of the data, estimates the missing data according to the rule, often needs to solve a series of equations or a high-dimensional equation set, and along with the increase of the data volume, the solving process becomes more difficult, the method does not combine the data characteristics of the radar signal, the signal repaired by the method has larger phase difference with the original signal in the time domain and the frequency domain, the signal fine analysis processing requirement is difficult to meet, and particularly the key feature judgment and parameter estimation such as the pulse width, the repetition frequency, the pulse modulation type, the code element width, the coding rule and the like of the radar signal can be influenced in the aspect of time-frequency feature analysis.
Disclosure of Invention
The invention aims to provide a method for repairing incomplete radar signals.
The aim of the invention can be achieved by the following technical scheme:
A method of repairing a malformed radar signal, the method comprising the steps of:
step one: acquiring acquired acquisition signals y epsilon R M (M < N) and an index set Z;
Step two: setting I n∈RN*N as an identity matrix, deleting the j-th row (j epsilon Z) In, and keeping the sequence and the size of other rows unchanged to obtain an observation matrix phi epsilon R M*N;
Step three: constructing a sparse dictionary matrix C epsilon R N*N by utilizing DCT according to a formula (6);
step four: reconstructing sparse vector Θ to obtain its estimated value by using orthogonal matching pursuit algorithm
Step five: obtaining a repair signal using an inverse DCT transform
Further, the specific steps of obtaining the acquisition signal y e R M (M < N) and the index set Z in the first step are:
s1: setting the observed acquisition signal as y epsilon R M (M < N), wherein M represents the number of data points acquired in practice and N represents the number of original data points without loss;
S2: the value of the lost N-M point data is set to be zero, and a group of N point data is reconstructed by the actually collected M point data and the N-M zero data which are supplemented, and is marked as x0, and the data value corresponding to the data loss position is set to be zero;
S3: and (3) marking the index of the lost position as a set Z, removing N-M zero values corresponding to the index position of the set Z in x0, and keeping the sequence and the size of other element values unchanged to obtain an observation signal y epsilon R M (M < N).
Further, in the third step, the specific steps of constructing the sparse dictionary matrix by using the DCT according to the formula (6) are as follows:
the DCT matrix is adopted as a sparse dictionary matrix, and is set as C epsilon R N*N, and the element calculation method of the ith row and j columns of the matrix C is shown as a formula (6);
Further, the sparse vector Θ in the fourth step is specifically expressed as:
Θ＝C-1x (7)。
the invention has the beneficial effects that:
Compared with the prior art, the method can reconstruct the complete original signal better under the condition of continuous loss or random loss, and the repaired signal is quite similar 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 the data is not higher than 30%, the method can better repair the original signal; under the random loss condition, the signal restoration effect is obviously superior to the continuous loss condition, and when the random loss rate of data is not higher than 60%, the average relative error of the acquired signal restored by the method is close to 0 compared with the original real signal. The conventional interpolation algorithm is used for processing the acquisition signals with the continuous loss rate reaching 10% or more or processing the acquisition signals with the random loss rate reaching 40% or more, and the time domain and the frequency domain of the result are severely distorted, and particularly the original characteristics of the signals are completely not reflected by the processing result due to the serious distortion of the instantaneous frequency. It should also be noted that the interpolation algorithm takes about 2 times as much time as the present invention in terms of calculation time.
Drawings
The present invention is further described below with reference to the accompanying drawings for the convenience of understanding by those skilled in the art.
FIG. 1 is a flow chart of a method for repairing an anti-scout signal of a incomplete radar according to the present invention;
FIG. 2.1 is a signal time domain comparison chart of the repair result under the condition of continuously losing data according to the invention;
FIG. 2.2 is a signal frequency domain comparison chart of the repair result under the condition of continuously losing data according to the invention;
FIG. 2.3 is a graph showing the comparison of signal time-frequency domains of the repair result under the condition of continuously losing data according to the present invention;
FIG. 2.4 shows the average relative error of the repair signals for different data loss rates in the case of continuous loss according to the present invention;
FIG. 3.1 is a signal time domain comparison chart of the repair result under the random data loss condition of the present invention;
FIG. 3.2 is a signal frequency domain comparison chart of the repair result under the random data loss condition of the invention;
FIG. 3.3 is a graph showing the comparison of signal time-frequency domains of the repair result under the random data loss condition of the present invention;
Fig. 3.4 shows the average relative error of the repair signal for different data loss rates in the random loss situation of the present invention.
Detailed Description
1-3.4, The method transforms the incomplete signal into a sparse domain based on a compressed sensing theory to obtain sparse domain representation of the signal, and then uses an orthogonal matching pursuit algorithm and a cosine discrete transformation algorithm to repair the original signal.
1) Constructing an observation matrix of the incomplete signals;
Setting the observed acquisition signal as y epsilon R M (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 defaulting the N-M point data of which the acquisition equipment discards the original complete signal in the actual acquisition process to be not particularly important;
The value of the lost N-M point data is set to be zero, and because the N-M point data cannot successfully acquire signals at the corresponding moment, a group of N point data can be reconstructed from the actually acquired M point data and the N-M zero data which are supplemented by the N-M point data, and the N point data is marked as x0, and the data value corresponding to the data loss position is set to be zero. And (3) marking the index of the lost position as a set Z, removing N-M zero values corresponding to the index position of the set Z in x0, and keeping the sequence and the size of other element values unchanged to obtain an observation signal y epsilon R M (M < N).
2) A signal restoration principle;
By taking I n∈RN*N as an identity matrix, deleting the j-th row (j epsilon Z) In, keeping the sequence and the size of other rows unchanged, obtaining an observation matrix phi epsilon R M*N, and further, applying a CS repair algorithm, the estimated value of the N-point data of the original signal can be reconstructed.
From the above definition and assumptions, it is possible to:
y＝φx (1)
Wherein phi is an observation matrix;
the original signal x can be thinned through the sparse representation dictionary matrix psi epsilon R N*N, namely
x＝ψΘ (2)
Wherein Θ is a sparse representation coefficient vector;
Let a=φψ, then there is
y＝φψΘ＝AΘ (3)
At this time, the actual observed value, namely the acquired signal y and the measurement matrix A, is known, the sparse coefficient vector Θ needs to be reconstructed, and if Θ meets the sparsity, the signal repairing process under the CS framework can be realized.
The scholars prove that the signal can be repaired only by the fact that the measurement matrix A meets constraint equidistant property (RIP) or the observation matrix phi and the sparse representation dictionary matrix phi are uncorrelated.
The definition of RIP is as follows: for any k-sparse signal Θ and constant δ k e (0, 1), the following is satisfied:
Therefore, only the measurement matrix A is required to meet the RIP condition, or the observation matrix phi and the sparse representation dictionary matrix phi are not related, the estimated value of the sparse vector theta can be reconstructed And then the estimated value/>, of the complete acquisition signal x can be calculatedI.e.
The 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 Φ, the sparse dictionary matrix ψ, and the sparse representation coefficient vector Θ. The construction method of the observation matrix phi epsilon R M*N is described in detail above. Also because in order to achieve signal repair, the measurement matrix a must either satisfy the RIP condition or the observation matrix phi and the sparse representation dictionary matrix ψ are uncorrelated. Namely: signal restoration can be achieved by only selecting an appropriate dictionary matrix ψ. Generally, the dictionary matrix ψ which can make the original acquisition signal sufficiently sparse is not unique, and the dictionary matrix which can make the acquisition signal sparse can be used in signal restoration. Because the corresponding coefficient of the radar signal is sparse after Discrete Cosine Transform (DCT), the invention adopts DCT matrix as sparse dictionary matrix, and the DCT matrix is set as C epsilon R N*N, and the element calculation method of the ith row and j column of the matrix C is shown as formula (6).
The sparse representation vector Θ is:
Θ＝C-1x (7)；
based on compressed sensing method, the estimated value of sparse vector Θ is reconstructed Thereby obtaining the estimated value/>, of the original complete radar signal xThe present invention uses an Orthogonal Matching Pursuit (OMP) algorithm in signal restoration.
In summary, the incomplete radar signal restoration algorithm flow can be summarized as follows:
S1, observing acquired signals y epsilon R M (M < N) and an index set Z;
s2, setting I n∈RN*N as an identity matrix, deleting the j-th row (j epsilon Z) In, and keeping the sequence and the size of other rows unchanged to obtain an observation matrix phi epsilon R M*N;
s3, constructing a sparse dictionary matrix C epsilon R N*N by DCT according to the formula (6);
S4, reconstructing the sparse vector Θ by using an Orthogonal Matching Pursuit (OMP) algorithm to obtain an estimated value thereof
S5, obtaining a repair signal by utilizing inverse DCT (discrete cosine transform)
A correlation experiment was performed on a set of chirped signals. The signal has an intermediate frequency of 52MHz, a frequency modulation bandwidth of 4MHz, a forward incremental frequency modulation, an acquisition time length of 2us, a sampling frequency of 500MHz and a sampling point number of 1000. Signal restoration was performed with 5%, 10% continuous loss and 30%, 50% random loss of data, respectively, and comparative analysis experiments were performed with conventional interpolation methods. In order to intuitively compare the repair results, the repair effects are compared from the average relative error angles of the time domain, the frequency domain, the instantaneous frequency and the repair data with the original data respectively.
The method is found to reconstruct the original complete signal almost perfectly under the condition of continuously deleting 5% of data, the repair signal is quite close to the original complete signal in time domain and frequency domain, the instantaneous frequency characteristic is greatly improved, and the instantaneous frequency linear increase characteristic of the linear frequency modulation signal is reproduced. Under the condition of 10% missing, a good repair result is obtained, but as the number of missing points reaches 100, the general trend of the instantaneous frequency characteristic can be seen to be a linear frequency modulation signal, but the line fluctuates at the position corresponding to the missing, and the linearity is lost. However, the processing result of the conventional interpolation algorithm is severely distorted in the time-frequency domain, which seriously affects the subsequent signal analysis and processing.
And finding the average relative error of the repair 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 smaller, and the lost data can be perfectly repaired.
The method can repair the original complete signal almost perfectly under the condition of randomly deleting 30% and 50% of data, the repair signal is quite close to the original complete signal in the time domain and the frequency domain, and the instantaneous frequency linear increase characteristic of the linear frequency modulation signal is reproduced. In contrast, the processing result of the conventional interpolation algorithm is severely distorted in the time-frequency domain, and the linear frequency modulation characteristic of the signal is completely not shown.
And finding the average relative error of the repair signals with different data loss rates under the condition of random loss statistics. 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 smaller, and the lost data can be perfectly repaired.
The foregoing is merely illustrative of the structures of this invention and various modifications, additions and substitutions for those skilled in the art can be made to the described embodiments without departing from the scope of the invention or from the scope of the invention as defined in the accompanying claims.

Claims (3)

1. A method for repairing a defective radar signal, comprising the steps of:
step one: acquiring acquisition signals y epsilon R M, M < N and an index set Z, wherein M represents the number of data points acquired in actual acquisition, and N represents the number of original data points under the condition of no loss;
Step two: setting I n∈RN*N as a unit matrix, deleting the j-th row in I n, wherein j epsilon Z, and other rows keep the sequence and the size unchanged to obtain an observation matrix phi epsilon R M*N;
Step three: the DCT matrix is adopted as a sparse dictionary matrix, and is set as C epsilon R N*N, and the element calculation method of the ith row and j columns of the matrix C is shown as the formula (6):
step four: reconstructing sparse vector Θ to obtain its estimated value by using orthogonal matching pursuit algorithm
Step five: obtaining a repair signal using an inverse DCT transform
2. The method for repairing a defective radar signal according to claim 1, wherein the acquiring signals y e R M, M < N, and the index set Z in the step one include the following specific steps:
S1: setting the acquired signal obtained by observation as y epsilon R M, M < N;
S2: the value of the lost N-M point data is set to be zero, and a group of N point data is reconstructed by the actually collected M point data and the N-M zero data which are supplemented, and is marked as x0, and the data value corresponding to the data loss position is set to be zero;
S3: and (3) marking the index of the lost position as a set Z, removing N-M zero values corresponding to the index position of the set Z in x0, and keeping the sequence and the size of other element values unchanged to obtain an observation signal y epsilon R M, wherein M < N.
3. The method for repairing a residual radar signal according to claim 1, wherein the sparse vector Θ in the fourth step is specifically expressed as:
Θ＝C-1x (7)。
CN202010188653.2A 2020-03-17 2020-03-17 Incomplete radar signal restoration method Active CN111487593B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010188653.2A CN111487593B (en) 2020-03-17 2020-03-17 Incomplete radar signal restoration method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010188653.2A CN111487593B (en) 2020-03-17 2020-03-17 Incomplete radar signal restoration method

Publications (2)

Publication Number Publication Date
CN111487593A CN111487593A (en) 2020-08-04
CN111487593B true CN111487593B (en) 2024-06-11

Family

ID=71794525

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010188653.2A Active CN111487593B (en) 2020-03-17 2020-03-17 Incomplete radar signal restoration method

Country Status (1)

Country Link
CN (1) CN111487593B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114755654B (en) * 2022-06-14 2022-11-18 中达天昇(江苏)电子科技有限公司 Damaged radar signal restoration method based on image mimicry technology

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106068645A (en) * 2014-01-10 2016-11-02 奥斯坦多科技公司 Method for full parallax squeezed light field 3D imaging system

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP6857971B2 (en) * 2016-06-13 2021-04-14 株式会社デンソーテン Radar device and signal processing method

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106068645A (en) * 2014-01-10 2016-11-02 奥斯坦多科技公司 Method for full parallax squeezed light field 3D imaging system

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
Repair wind field in oil contaminated areas with SAR images;Jie Guo;Chinese Journal of Oceanology and Limnology;20141203;全文 *
基于变分模态分解和压缩感知的弱观测条件下雷达信号重构方法;刘方正;电子与信息学报;20210615;全文 *

Also Published As

Publication number Publication date
CN111487593A (en) 2020-08-04

Similar Documents

Publication Publication Date Title
Yan et al. Robust 1-bit compressive sensing using adaptive outlier pursuit
US11082153B2 (en) Signal sampling and recovery method and apparatus applicable to OvXDM system, and OvXDM system
CN111337893B (en) Off-grid DOA estimation method based on real-value sparse Bayesian learning
CN107666322B (en) Self-adaptive microseismic data compression sensing method based on dictionary learning
CN102998673B (en) Compressive sensing imaging method for synthetic aperture radar
US6772185B1 (en) Time-series predicting method using wavelet number series and device thereof
CN111487593B (en) Incomplete radar signal restoration method
CN111337873B (en) DOA estimation method based on sparse array
CN112162152B (en) Sine wave coherent pulse train signal frequency estimation method based on phase straight line fitting
CN108572352B (en) Parameter estimation method of phase coding signal based on undersampling
CN108132383B (en) Time-interleaved multi-harmonic signal undersampling method
CN113362405B (en) Construction method of image reconstruction system based on StOMP compressed sensing
CN104459695B (en) Sparsity microwave imaging method based on compression phase restoring
CN108629371B (en) Data dimension reduction method for two-dimensional time-frequency data
CN114519384B (en) Target classification method based on sparse SAR amplitude-phase image dataset
CN116389198A (en) Multi-target time delay sparse reconstruction estimation method based on exponential filter
CN113705335B (en) Time-frequency super-resolution extraction method for low-frequency sparse line spectrum signal
Mourad et al. Orthogonal matching pursuit with correction
CN107784278B (en) Sparse image reconstruction accuracy reduction complexity method is improved with structuring is prior-constrained
Wang et al. A modified image reconstruction algorithm based on compressed sensing
CN111242082A (en) Face super-resolution reconstruction identification method based on fractional order orthogonal partial least square
Prabhavathi et al. Compressive Sensing and its Application to Speech Signal Processing
Su et al. A DOA estimation algorithm based on greedy recovery under the condition of array element failure
CN113156416B (en) Unknown target discrimination method based on multi-kernel dictionary learning
CN112731395B (en) SAR imaging method based on non-convex and total variation regularization

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant