CN112505665B - Space-time self-adaptive detection method and system suitable for partial uniform reverberation environment - Google Patents

Space-time self-adaptive detection method and system suitable for partial uniform reverberation environment Download PDF

Info

Publication number
CN112505665B
CN112505665B CN202011248227.XA CN202011248227A CN112505665B CN 112505665 B CN112505665 B CN 112505665B CN 202011248227 A CN202011248227 A CN 202011248227A CN 112505665 B CN112505665 B CN 112505665B
Authority
CN
China
Prior art keywords
matrix
data
detection
detected
target
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
CN202011248227.XA
Other languages
Chinese (zh)
Other versions
CN112505665A (en
Inventor
郝程鹏
闫林杰
刘明刚
侯朝焕
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.)
Institute of Acoustics CAS
Original Assignee
Institute of Acoustics CAS
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 Institute of Acoustics CAS filed Critical Institute of Acoustics CAS
Priority to CN202011248227.XA priority Critical patent/CN112505665B/en
Publication of CN112505665A publication Critical patent/CN112505665A/en
Application granted granted Critical
Publication of CN112505665B publication Critical patent/CN112505665B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

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
    • G01S7/52—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00
    • G01S7/52001—Auxiliary means for detecting or identifying sonar signals or the like, e.g. sonar jamming signals
    • 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
    • G01S7/52—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00
    • G01S7/539—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Data Mining & Analysis (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Mathematical Physics (AREA)
  • Mathematical Optimization (AREA)
  • Theoretical Computer Science (AREA)
  • Computational Mathematics (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Probability & Statistics with Applications (AREA)
  • Operations Research (AREA)
  • Bioinformatics & Cheminformatics (AREA)
  • Evolutionary Biology (AREA)
  • Algebra (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Bioinformatics & Computational Biology (AREA)
  • Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)

Abstract

The invention provides a space-time self-adaptive detection method and a space-time self-adaptive detection system suitable for a partial uniform reverberation environment, wherein the method comprises the following steps: acquiring a data matrix to be detected and an auxiliary data matrix of echo data received by a space symmetric linear array; combining the data to be detected and auxiliary data, and estimating parameters of the detection statistic constructed in advance by adopting maximum likelihood estimation; and inputting the estimated parameters into a pre-established space-time adaptive detector to finish the adaptive detection of the target. Compared with other detection methods of the same type, the method has better detection performance and distance estimation performance under the auxiliary data of a small sample, and greatly improves the efficiency in practical application.

Description

Space-time self-adaptive detection method and system suitable for partial uniform reverberation environment
Technical Field
The invention relates to the technical field of underwater sound, in particular to a space-time self-adaptive detection method and system suitable for a partial uniform reverberation environment.
Background
The underwater target detection technology is used for detecting whether targets exist in an underwater sound field or not based on a signal detection and estimation theory. In shallow sea active sonar signal detection, reverberation as a main interfering factor will directly threaten the target detection performance of the system. In particular to a sonar carrier with a certain movement speed, reverberations in different directions have different Doppler frequency shifts, so that a reverberant spectrum spreads in a Doppler-angle domain, and the reverberant spectrum is difficult to effectively inhibit by traditional methods such as wave beam forming, matched filtering and the like. In the 90 s of the 20 th century, jaffer applied a space-time adaptive processing (STAP) technique based on space-time domain joint filtering to active sonar reverberation suppression for the first time. On the basis of STAP, a space-time adaptive detection (STAD) technology aiming at reverberation suppression and target detection is developed, wherein more classical detection methods mainly comprise generalized likelihood ratio detection (GLRT), adaptive matched filter detection (AMF), wald detection methods and the like.
However, the conventional STAD method still suffers from two drawbacks: firstly, estimating and inverting a high-dimensional interference covariance matrix, and having large demand for uniform auxiliary data; and secondly, an ideal target sampling model is mostly adopted, namely, the sampling point is considered to be exactly consistent with the peak position of the target matched filtering output, and the condition of target energy leakage is ignored. For the first disadvantage, nitzberg teaches that the aim of reducing the amount of auxiliary data can be achieved by using the oblique symmetry characteristics of the reverberation covariance matrix in a spatially symmetric linear array system. Aiming at the second deficiency, the institute of acoustic science Hao Chengpeng team and italian scholars Orlando developed researches on detection methods based on the target energy leakage sampling model. In recent years, a method for detecting a skew-symmetric AMF (PM-AMF-PHE) based on a skew-symmetric characteristic and a target energy leakage sampling model in a partially uniform reverberant environment has been proposed. Here, partial uniformity means that the reverberation covariance matrix structure of the data to be detected and the auxiliary data is identical, only one unknown energy scale factor is worse, and research proves that the environment is closer to the actual working scene of sonar. The PM-AMF-PHE method effectively compensates the target energy leakage loss and improves the target detection performance under the condition of limited auxiliary data quantity.
In an actual environment, even auxiliary data are extremely limited or even cannot be acquired under the influence of factors such as underwater interface fluctuation, channel variation and the like, so that a detection method under a partial even reverberation environment is provided. The existing PM-AMF-PHE method considers the oblique symmetry characteristic of a reverberation covariance matrix and a target energy leakage sampling model at the same time when receiving data modeling, but adopts a two-step GLRT criterion to design a detection method, namely data to be detected and auxiliary data are used separately to realize derivation of detection statistics and Maximum Likelihood Estimation (MLE) of unknown parameters, joint utilization of the data to be detected and the auxiliary data cannot be realized, the data utilization rate of received echoes is low, and the detection performance is restricted.
The existing PM-AMF-PHE adopts a two-step GLRT criterion, the combined use of data to be detected and auxiliary data cannot be realized in the design process of a detection method, the utilization rate of the received data is low, and the detection performance of the PM-AMF-PHE cannot meet the requirements under the condition of limited auxiliary data quantity.
Disclosure of Invention
The invention aims to overcome the technical defects and provides a high-performance space-time self-adaptive detection method suitable for a partially uniform reverberation environment, wherein a target energy leakage sampling model is adopted to compensate leakage loss, the requirement for auxiliary data is reduced by utilizing the oblique symmetry characteristic of a reverberation covariance matrix in a space symmetric linear array, unknown parameter estimation and detection statistic deduction are carried out by jointly using data to be detected and auxiliary data, the utilization rate of received echo data is improved, and the method has obvious target detection advantages under the condition of limited auxiliary data quantity, and is beneficial to practical application.
To achieve the above object, embodiment 1 of the present invention proposes a space-time adaptive detection method suitable for a partially uniform reverberant environment, the method comprising:
acquiring a data matrix to be detected and an auxiliary data matrix of echo data received by a space symmetric linear array;
combining the data to be detected and auxiliary data, and estimating parameters of the detection statistic constructed in advance by adopting maximum likelihood estimation;
and inputting the estimated parameters into a pre-established space-time adaptive detector to finish the adaptive detection of the target.
As an improvement of the above method, the acquiring the data matrix to be detected and the auxiliary data matrix of the echo data received by the space symmetric linear array specifically includes:
the space symmetric linear array consists of N array elements, and the received echo signal is processed to obtain a discrete space time processing N-dimensional echo complex vector z i The received echo vector z to be detected of the ith distance unit i Expressed as:
z i ＝s i +n i ∈C N×1 (1)
wherein C represents a complex domain, n i Representing complex Gaussian interference vectors, s i Representing a leakage target signal vector, and when the target has energy leakage, the signal energy can leak into a left distance unit and a right distance unit to obtain a target energy leakage model consisting of three adjacent distance units, and s i Expressed as:
Figure BDA0002770766810000031
wherein alpha is the complex amplitude factor of the received target echo signal and is an unknown determined parameter; x-shaped articles p (. Cndot.) is the complex ambiguity function of the transmitted signal; epsilon 0 ∈[0,T p ]To measure the severity of the target energy leakage, T, for the residual time delay p Is pulse width; v is a target normalized airspace guide vector; f is Doppler shift introduced by the target and v; l represents the serial number of the sample to be detected;
taking the ith distance unit to be detected as the center, delaying the residual time epsilon-T p /2,T p /2]Redefined as:
Figure BDA0002770766810000032
z k ∈C N×1 k uniform auxiliary data collected from distance units adjacent to the data to be detected are represented, and only two interference components of white noise and reverberation are contained;
Z L ＝[z l-1 ,z l ,z l+1 ]∈C N×3 for the data matrix to be detected, Z K ＝[z 1 ,...,z K ]∈C N×K As an auxiliary data matrix, z= [ Z L ,Z K ]∈C N×(3+K) Is a joint data matrix.
As an improvement of the method, the data to be detected and the auxiliary data are combined, and the maximum likelihood estimation is adopted to estimate the parameters of the pre-constructed detection statistic; the method specifically comprises the following steps:
step 2-1) constructing a detection statistic T based on GLRT criterion:
Figure BDA0002770766810000033
wherein, gamma > 0 represents unknown energy scale factor, M is covariance matrix of symmetric linear array; v is a normalized airspace guide vector, and M and v have oblique symmetry characteristics, namely:
M＝J N M * J N ,v＝J N v *
wherein J is N ∈R N×N For permutation matrices, (. Cndot.) * For conjugate operation, R is the real number domain, where the permutation matrix J N ∈R N×N Is a square matrix with the diagonal line of 1 and other elements of 0;
step 2-2) based on the oblique symmetry properties of M and v, f j (Z; j epsilon, j alpha, gamma, M) is represented by H j J=0, 1 assumes a probability density function of the joint data matrix Z:
Figure BDA0002770766810000041
where det (·) represents the determinant operation of the matrix, tr (·) represents the trace of the matrix, (·) T And ( H Representing the transpose and conjugate transpose of the matrix, the intermediate variable S and the interference data matrix F (jα) are:
Figure BDA0002770766810000042
x is a data matrix generated from the data to be detected:
Figure BDA0002770766810000043
vector quantity
Figure BDA0002770766810000044
And->
Figure BDA0002770766810000045
The method comprises the following steps:
Figure BDA0002770766810000046
the fuzzy function matrix D is:
Figure BDA0002770766810000047
wherein t is 1 ,t 2 ,t 3 All are time delays: t is t 1 ＝-T p -ε,t 2 ＝-ε,t 3 ＝T p -ε；
Step 2-3) Using maximum likelihood estimation pair H j Estimating M under the assumption that j=0, 1 to obtain an estimation result
Figure BDA0002770766810000048
The method comprises the following steps:
Figure BDA0002770766810000049
after substituting (9) into equation (6), the detection statistic is:
Figure BDA00027707668100000410
step 2-4) based on equation (10), the maximum likelihood estimate of α is:
Figure BDA0002770766810000051
and (3) solving the first partial derivative of alpha in the formula (11) and setting zero to obtain the estimation result of alpha, wherein the estimation result is as follows:
Figure BDA0002770766810000052
wherein Q is an intermediate variable matrix:
Figure BDA0002770766810000053
Figure BDA0002770766810000054
represent S -1/2 v Zhang Chengzi spatial matrix->
Figure BDA0002770766810000055
Orthogonal complement of I N Is an N-dimensional identity matrix;
step 2-5) will
Figure BDA0002770766810000056
Substitution (10), solving for H 1 Let maximum likelihood estimation of gamma +.>
Figure BDA0002770766810000057
The method comprises the following steps:
Figure BDA0002770766810000058
the intermediate matrices B and C are:
Figure BDA0002770766810000059
Figure BDA00027707668100000510
wherein the matrix Q can be characterized as q=u (γ 1 I 6 +Λ)U H Wherein U is C 6×6 For unitary matrix, Λ is eigenvalue λ 1 ,...,λ 6 Is a diagonal array of (a);
the intermediate matrices E and G are:
Figure BDA00027707668100000511
Figure BDA0002770766810000061
the matrices W and V are:
Figure BDA0002770766810000062
Figure BDA0002770766810000063
substituting the characteristic decomposition of Q into (14),
Figure BDA0002770766810000064
wherein,,
Figure BDA0002770766810000065
Figure BDA0002770766810000066
**m＝p * ，n＝q * ；
for h 1 (γ 1 ) Gamma determination 1 And setting zero to obtain gamma 1 Estimate of (2)
Figure BDA0002770766810000067
Solving for this nonlinearity using fsive functionAn equation;
step 2-6) based on equation (10), at H 0 The maximum likelihood estimate for gamma is assumed to be:
Figure BDA0002770766810000068
simplifying to obtain
Figure BDA0002770766810000069
For X H S -1 X is subjected to characteristic decomposition to obtain
Figure BDA00027707668100000610
Wherein U is 0 ∈C 6×6 As unitary matrix, Λ 0 Is characterized by lambda 0,1 ,...,λ 0,6 Is a diagonal array of (a); and (3) substituting (19) and then simplifying to obtain:
Figure BDA00027707668100000611
for h 0 (γ 0 ) Gamma determination 0 And zero setting the first partial derivative of (2) to obtain the gamma 0 Estimate of (2)
Figure BDA00027707668100000612
Here->
Figure BDA00027707668100000613
And solving by adopting a numerical method.
As an improvement of the above method, the space-time adaptive detector is:
Figure BDA0002770766810000071
wherein H is 1 And H 0 Representing targeted and non-targeted hypotheses, respectively; η represents the correspondence under a certain false alarm probabilityIs provided.
As an improvement of the above method, the inputting the estimated parameters into the pre-established space-time adaptive detector, and completing the adaptive detection of the target specifically includes:
step 3-1) calculating a detection statistic T:
Figure BDA0002770766810000072
step 3-2) when the test statistic T is greater than the detection threshold eta, testing H 1 If yes, the detection result is a target, otherwise, check H 0 And (3) if the result is true, the detection result is no target.
Embodiment 2 of the present invention proposes a space-time adaptive detection system suitable for a partially uniform reverberant environment, the system comprising: the system comprises a space-time adaptive detector, a data acquisition module, a parameter estimation module and a detection module which are established in advance;
the data acquisition module is used for acquiring a data matrix to be detected and an auxiliary data matrix of echo data received by the space symmetry linear array;
the parameter estimation module is used for combining the data to be detected and the auxiliary data, and estimating the parameters of the pre-constructed detection statistic by adopting maximum likelihood estimation;
the detection module is used for inputting the estimated parameters into the space-time adaptive detector to finish the adaptive detection of the target.
The invention has the advantages that:
the method disclosed by the invention realizes the derivation of the detection statistics and MLE of all unknown parameters by combining the data to be detected and the auxiliary data, replaces the traditional derivation method of only using the data to be detected or the auxiliary data in the two-step GLRT criterion, greatly improves the utilization rate of echo data, has better detection performance and distance estimation performance under small sample auxiliary data compared with other detection methods of the same type, and greatly improves the efficiency in practical application.
Drawings
FIG. 1 is a flow chart of a method of the present invention for space-time adaptive detection for a partially uniform reverberant environment;
FIG. 2 shows P of different detection methods d A profile as a function of SRNR;
FIG. 3 shows delta of different detection methods rms Change with SRNR.
Detailed Description
The technical scheme of the invention is described in detail below with reference to the accompanying drawings.
The invention designs an adaptive solution under a partial uniform reverberation environment based on a GLRT test criterion. Assuming that a sonar system adopts a space symmetric linear array to receive echoes, a target signal adopts a target energy leakage sampling model, and a reverberation signal adopts an oblique symmetric priori structure; taking the target energy leakage phenomenon existing during sampling into consideration, an energy leakage sampling model is adopted during modeling of the received signal to compensate leakage loss, and the oblique symmetry characteristic of a reverberation covariance matrix is utilized during modeling of the reverberation signal to reduce the requirement for auxiliary data. The derivation process of the detection method only needs one step, namely MLE of the parameters is realized by directly adopting the combination of the data to be detected and the auxiliary data. And substituting the estimated value into the detection statistic instead of the theoretical value to obtain the fully self-adaptive PM-GLRT-PHE detection method.
As shown in fig. 1, embodiment 1 of the present invention proposes a space-time adaptive detection method suitable for a partially uniform reverberant environment, where the method includes:
step 1), acquiring a data matrix to be detected and an auxiliary data matrix of echo data received by a space symmetric linear array;
step 2) combining the data to be detected and auxiliary data, and estimating parameters of pre-constructed detection statistics by using maximum likelihood estimation;
and 3) inputting the estimated parameters into a pre-established space-time adaptive detector to finish the adaptive detection of the target.
The method of the present invention will be described in detail.
1. Description of the problem
Firstly, introducing a multi-channel discrete time signal model of a target and an interference echo, and giving out a binary hypothesis testing problem of a detection target under a target energy leakage sampling model on the basis.
1.1, received Signal model
Assuming that a uniform linear array is composed of N array elements, after a series of signal processing is carried out on the received echo signals, a discrete space-time processing N-dimensional echo complex vector z is obtained i The received echo vector z to be detected of the ith distance unit i Can be expressed as
z i ＝s i +n i ∈C N×1 (1)
Wherein C represents a complex domain, n i Representing complex Gaussian interference vectors, s i Representing a leakage target signal vector, and when the target has energy leakage, the signal energy can leak into a left distance unit and a right distance unit to obtain a target energy leakage model consisting of three adjacent distance units, and s i Can be expressed as:
Figure BDA0002770766810000091
wherein alpha represents the complex amplitude factor of the received target echo signal and is an unknown determined parameter; x-shaped articles p (-) represents the complex ambiguity function of the transmitted signal; epsilon 0 ∈[0,T p ]Representing the residual time delay, can measure the severity of the target energy leakage, T p Is pulse width; v represents a target normalized airspace guide vector; f represents Doppler shift introduced by the target and v; l represents the serial number of the sample to be detected.
For convenience of description, the residual time delay epsilon-T is centered on the ith distance unit to be detected p /2,T p /2]Redefined as:
Figure BDA0002770766810000092
1.2 hypothesis test problem
From the received signal model in 1.2, the binary hypothesis testing problem for leakage target detection can be written as:
Figure BDA0002770766810000093
wherein H is 1 And H 0 Representing targeted and non-targeted hypotheses, respectively. z i ∈C N×1 Representing the data vector to be detected, z k ∈C N ×1 K uniform auxiliary data collected from distance units adjacent to the data to be detected are represented, and only two interference components of white noise and reverberation are contained. n is n i For the interference component in the data to be detected, the interference component is mixed with z in a partial uniform reverberation background k Are mutually independent in statistics, and are both zero-mean complex Gaussian random processes, namely n i ～CN N (0, γM) and z k ～CN N (0, M). Gamma > 0 represents an unknown energy scale factor.
In an active sonar system, the covariance matrix M of the symmetrical linear array and the normalized airspace guiding vector v both have important characteristics of oblique symmetry, namely
M＝J N M * J N ,v＝J N v * (5)
Wherein J is N ∈R N×N For permutation matrices, (. Cndot.) * For conjugate operation, R is the real number domain, where the permutation matrix J N ∈R N×N Is a square matrix with a diagonal line of 1 and other elements of 0.
2. Design of detection method
The hypothesis testing problem in (4) is solved by adopting GLRT testing criteria. Let Z be L ＝[z l-1 ,z l ,z l+1 ]∈C N×3 For the data matrix to be detected, Z K ＝[z 1 ,...,z K ]∈C N×K As an auxiliary data matrix, z= [ Z L ,Z K ]∈C N×(3+K) For the joint data matrix, the detection expression based on the GLRT criterion is as follows:
Figure BDA0002770766810000101
wherein eta represents a certain false alarm probability (P fa ) A detection threshold value below. Based on the oblique symmetry characteristic of M, v, f j (Z; j epsilon, j alpha, gamma, M) is represented by H j J=0, 1 assumes a probability density function of the joint data matrix z:
Figure BDA0002770766810000102
where det (. Cndot.) represents the determinant operation of the matrix, tr (. Cndot.) represents the trace of the matrix, (. Cndot.) T And ( H Representing the transpose and conjugate transpose of the matrix,
Figure BDA0002770766810000103
Figure BDA0002770766810000104
Figure BDA0002770766810000111
Figure BDA0002770766810000112
the fuzzy function matrix D is:
Figure BDA0002770766810000113
wherein t is 1 ,t 2 ,t 3 All are time delays: t is t 1 ＝-T p -ε,t 2 ＝-ε,t 3 ＝T p -ε；
Estimating H by MLE method j M under the assumption that j=0, 1, the estimation result is
Figure BDA0002770766810000114
After substituting (9) into formula (6), GLRT detection decision type is equivalent to
Figure BDA0002770766810000115
Based on (10), the MLE equivalent of α is:
Figure BDA0002770766810000116
and (3) solving the first partial derivative of alpha in the formula (11) and setting zero to obtain the estimated result of alpha, wherein the estimated result is as follows:
Figure BDA0002770766810000117
wherein Q is an intermediate variable matrix:
Figure BDA0002770766810000118
Figure BDA0002770766810000119
represent S -1/2 v Zhang Chengzi spatial matrix->
Figure BDA00027707668100001110
Orthogonal complement of I N Is an N-dimensional identity matrix;
will be
Figure BDA00027707668100001111
Substitution (10), solving for H 1 Let maximum likelihood estimation of gamma +.>
Figure BDA00027707668100001112
The method comprises the following steps:
Figure BDA0002770766810000121
the intermediate matrices B and C are:
Figure BDA0002770766810000122
Figure BDA0002770766810000123
wherein the matrix Q can be characterized as q=u (γ 1 I 6 +Λ)U H Wherein U is C 6×6 For unitary matrix, Λ is eigenvalue λ 1 ,...,λ 6 Is a diagonal array of (a);
the intermediate matrices E and G are:
Figure BDA0002770766810000124
Figure BDA0002770766810000125
the matrices W and V are:
Figure BDA0002770766810000126
Figure BDA0002770766810000127
substituting the characteristic decomposition of Q into (14),
Figure BDA0002770766810000128
wherein,,
Figure BDA0002770766810000131
Figure BDA0002770766810000132
**
m＝p * ，n＝q * ；
for h 1 (γ 1 ) Gamma determination 1 And zero setting to obtain gamma 1 Estimate of (2)
Figure BDA0002770766810000133
Figure BDA0002770766810000134
The form of the analytical solution is not given and therefore a numerical solution is required, for example the non-linear equation can be solved using the fsolve function.
Also based on formula (10), in H 0 Let the MLE for gamma be
Figure BDA0002770766810000135
Simplifying to obtain
Figure BDA0002770766810000136
For X H S -1 X is subjected to characteristic decomposition to obtain
Figure BDA0002770766810000137
Wherein U is 0 ∈C 6×6 As unitary matrix, Λ 0 Is characterized by lambda 0,1 ,...,λ 0,6 Is a diagonal array of (a) pairs. Substituting (19) and then simplifying to obtain
Figure BDA0002770766810000138
For h 0 (γ 0 ) Gamma determination 0 And zero setting the first partial derivative of (2) to obtain the gamma 0 Estimate of (2)
Figure BDA0002770766810000139
Here->
Figure BDA00027707668100001310
Numerical methods are still needed to solve.
Finally, substituting all obtained unknown parameter estimated values into the step (14) to deduce PM-GLRT-PHE under the partial uniform reverberation environment:
Figure BDA00027707668100001311
it is noted that since the residual delay epsilon estimation here does not have an analytical solution, it is estimated using a grid search method. Finally, the process is carried out,
Figure BDA00027707668100001312
the estimation accuracy of (2) is reflected on the estimation accuracy of the target distance in the distance unit to be detected, where the distance root mean square error +.>
Figure BDA00027707668100001313
To represent.
Detection probability P of PM-GLRT-PHE by adopting Monte Carlo method d And the target distance estimation performance is evaluated and compared with the existing PM-AMF-PHE, GLRT-LC-PHE and P-GLRT detection methods. Let false alarm probability P fa ＝10 -4 ，P d And delta rms The number of independent simulations was 10 3 N=12, γ=2. Consider the case where the amount of auxiliary data is limited, i.e., the amount of auxiliary data is k=n+1. The reverberation model typically employs an exponentially related complex gaussian model, i.e. M i,j ＝ρ |i-j| ρ=0.9 is a lag correlation coefficient. Signal to reverberation noise ratio srnr= |α| 2 v H M -1 v/γ。
FIG. 2 shows P for four detection methods d Graph of change with SRNR. Simulation results show that P of four detection methods d All increase with SRNR and PM-GLRT-PHP of E d Is obviously superior to other existing detection methods of the same type. For example at P d At=0.8, PM-GLRT-PHE outperforms PM-AMF-GLRT, GLRT-LC-PHE, and P-GLRT by about 1.5dB, 4.5dB, and 8.5dB performance gains, respectively. Similarly, FIG. 3 shows the target distance root mean square error δ for each detection method under the same parameters rms Wherein the P-GLRT is not evaluated for distance estimation accuracy because it does not have a distance estimation capability. As can be seen from the figure, the distance estimation accuracy of PM-GLRT-PHE and PM-AMF-GLRT is approximately the same, and is superior to that of GLRT-LC-PHE. This is because the PM-GLRT-PHE and PM-AMF-PHE detection methods have close estimation accuracy to epsilon, and the application of the oblique symmetry characteristics greatly improves the estimation accuracy to epsilon under the condition of limited auxiliary data.
The method of the invention is creative in that:
1. the invention provides a high-performance space-time self-adaptive detection method suitable for a partial uniform reverberation environment, which is characterized in that when the detection method is designed, the estimation of all unknown parameters and the derivation of detection statistics are completed by using data to be detected and auxiliary data in a combined way, so that the utilization rate of echo data is greatly improved, and the detection performance and the excellent distance estimation performance are better under the condition that the quantity of the auxiliary data is limited.
2. The invention provides the numerical value estimation form of the unknown parameter gamma based on the data to be detected and the auxiliary data, can adopt the numerical value solving method such as the fsolve function and the like, and has accurate parameter estimation precision.
3. The invention aims at an active sonar system with a space symmetric linear array in a partial uniform reverberation environment, when a received signal is modeled, a target energy leakage sampling model is adopted for a target signal echo to compensate energy leakage loss, and the requirement for auxiliary data is reduced by adopting the oblique symmetry characteristic of a covariance matrix for reverberation, so that the detection performance when the quantity of the auxiliary data is limited is improved.
4. The invention assumes that the Doppler of the detected target is known, and is used for calculating the airspace guide vector.
Embodiment 2 of the present invention proposes a space-time adaptive detection system suitable for a partially uniform reverberant environment, the system comprising: the system comprises a space-time adaptive detector, a data acquisition module, a parameter estimation module and a detection module which are established in advance;
the data acquisition module is used for acquiring a data matrix to be detected and an auxiliary data matrix of echo data received by the space symmetry linear array;
the parameter estimation module is used for combining the data to be detected and the auxiliary data, and estimating the parameters of the pre-constructed detection statistic by adopting maximum likelihood estimation;
and the detection module is used for inputting the estimated parameters into the space-time adaptive detector to finish the adaptive detection of the target.
Finally, it should be noted that the above embodiments are only for illustrating the technical solution of the present invention and are not limiting. Although the present invention has been described in detail with reference to the embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the present invention, which is intended to be covered by the appended claims.

Claims (4)

1. A space-time adaptive detection method suitable for a partially uniform reverberant environment, the method comprising:
acquiring a data matrix to be detected and an auxiliary data matrix of echo data received by a space symmetric linear array;
combining the data to be detected and auxiliary data, and estimating parameters of the detection statistic constructed in advance by adopting maximum likelihood estimation;
inputting the estimated parameters into a pre-established space-time adaptive detector to finish the adaptive detection of the target;
the method for acquiring the data matrix to be detected and the auxiliary data matrix of the echo data received by the space symmetry linear array specifically comprises the following steps:
the space symmetric linear array consists of N array elements, and the received echo signal is processed to obtain a discrete space time processing N-dimensional echo complex vector z i The received echo vector z to be detected of the ith distance unit i Expressed as:
z i ＝s i +n i ∈C N×1 (1)
wherein C represents a complex domain, n i Representing complex Gaussian interference vectors, s i Representing a leakage target signal vector, and when the target has energy leakage, the signal energy can leak into a left distance unit and a right distance unit to obtain a target energy leakage model consisting of three adjacent distance units, and s i Expressed as:
Figure FDA0004228498310000011
wherein alpha is the complex amplitude factor of the received target echo signal and is an unknown determined parameter; x-shaped articles p (. Cndot.) is the complex ambiguity function of the transmitted signal; epsilon 0 ∈[0,T p ]To measure the severity of the target energy leakage, T, for the residual time delay p Is pulse width; v is a target normalized airspace guide vector; f is Doppler shift introduced by the target and v; l represents the serial number of the sample to be detected;
taking the ith distance unit to be detected as the center, delaying the residual time epsilon-T p /2,T p /2]Redefined as:
Figure FDA0004228498310000012
z k ∈C N×1 k uniform auxiliary data collected from distance units adjacent to the data to be detected are represented, and only two interference components of white noise and reverberation are contained;
Z L ＝[z l-1 ,z l ,z l+1 ]∈C N×3 for the data matrix to be detected, Z K ＝[z 1 ,...,z K ]∈C N×K As an auxiliary data matrix, z= [ Z L ,Z K ]∈C N×(3+K) Is a joint data matrix;
combining the data to be detected and auxiliary data, and estimating parameters of pre-constructed detection statistics by using maximum likelihood estimation; the method specifically comprises the following steps:
step 2-1) constructing a detection statistic T based on GLRT criterion:
Figure FDA0004228498310000021
wherein, gamma > 0 represents unknown energy scale factor, M is covariance matrix of symmetric linear array; v is a normalized airspace guide vector, and M and v have oblique symmetry characteristics, namely:
M＝J N M * J N ,v＝J N v *
wherein J is N ∈R N×N For permutation matrices, (. Cndot.) * For conjugate operation, R is the real number domain, where the permutation matrix J N ∈R N×N Is a square matrix with the diagonal line of 1 and other elements of 0;
step 2-2) based on the oblique symmetry properties of M and v, f j (Z; j epsilon, j alpha, gamma, M) is represented by H j J=0, 1 assumes a probability density function of the joint data matrix Z:
Figure FDA0004228498310000022
where det (·) represents the determinant operation of the matrix, tr (·) represents the trace of the matrix, (·) T And ( H Representing the transpose and conjugate transpose of the matrix, the intermediate variable S and the interference data matrix F (jα) are:
Figure FDA0004228498310000023
x is a data matrix generated from the data to be detected:
Figure FDA0004228498310000024
vector quantity
Figure FDA0004228498310000025
And->
Figure FDA0004228498310000026
The method comprises the following steps:
Figure FDA0004228498310000027
the fuzzy function matrix D is:
Figure FDA0004228498310000031
wherein t is 1 ,t 2 ,t 3 All are time delays: t is t 1 ＝-T p -ε,t 2 ＝-ε,t 3 ＝T p -ε；
Step 2-3) Using maximum likelihood estimation pair H j Estimating M under the assumption that j=0, 1 to obtain an estimation result
Figure FDA00042284983100000311
The method comprises the following steps:
Figure FDA0004228498310000032
after substituting (9) into equation (6), the detection statistic is:
Figure FDA0004228498310000033
step 2-4) based on equation (10), the maximum likelihood estimate of α is:
Figure FDA0004228498310000034
and (3) solving the first partial derivative of alpha in the formula (11) and setting zero to obtain the estimation result of alpha, wherein the estimation result is as follows:
Figure FDA0004228498310000035
wherein Q is an intermediate variable matrix:
Figure FDA0004228498310000036
represent S -1/2 v Zhang Chengzi spatial matrix->
Figure FDA0004228498310000037
Orthogonal complement of I N Is an N-dimensional identity matrix;
step 2-5) will
Figure FDA0004228498310000038
Substitution (10), solving for H 1 Let maximum likelihood estimation of gamma +.>
Figure FDA0004228498310000039
The method comprises the following steps:
Figure FDA00042284983100000310
Figure FDA0004228498310000041
the intermediate matrices B and C are:
Figure FDA0004228498310000042
Figure FDA0004228498310000043
wherein the matrix Q can be characterized as q=u (γ 1 I 6 +Λ)U H Wherein U is C 6×6 For unitary matrix, Λ is eigenvalue λ 1 ,...,λ 6 Is a diagonal array of (a);
the intermediate matrices E and G are:
Figure FDA0004228498310000044
Figure FDA0004228498310000045
the matrices W and V are:
Figure FDA0004228498310000046
Figure FDA0004228498310000047
substituting the characteristic decomposition of Q into (14),
Figure FDA0004228498310000048
wherein,,
Figure FDA0004228498310000049
Figure FDA0004228498310000051
for h 1 (γ 1 ) Gamma determination 1 And setting zero to obtain gamma 1 Estimate of (2)
Figure FDA0004228498310000052
Solving the nonlinear equation by adopting an fsive function;
step 2-6) based on equation (10), at H 0 The maximum likelihood estimate for gamma is assumed to be:
Figure FDA0004228498310000053
simplifying to obtain
Figure FDA0004228498310000054
For X H S -1 X is subjected to characteristic decomposition to obtain
Figure FDA0004228498310000055
Wherein U is 0 ∈C 6×6 As unitary matrix, Λ 0 Is characterized by lambda 0,1 ,...,λ 0,6 Is a diagonal array of (a); and (3) substituting (19) and then simplifying to obtain:
Figure FDA0004228498310000056
for h 0 (γ 0 ) Gamma determination 0 And zero setting the first partial derivative of (2) to obtain the gamma 0 Estimate of (2)
Figure FDA0004228498310000057
Here->
Figure FDA0004228498310000058
And solving by adopting a numerical method.
2. The method for space-time adaptive detection of a partially uniform reverberant environment according to claim 1, wherein the space-time adaptive detector is:
Figure FDA0004228498310000059
wherein H is 1 And H 0 Representing targeted and non-targeted hypotheses, respectively; η represents a corresponding detection threshold under a certain false alarm probability.
3. The method for space-time adaptive detection of a partially uniform reverberant environment according to claim 2, wherein the inputting the estimated parameters into a pre-established space-time adaptive detector, performing adaptive detection of the target specifically comprises:
step 3-1) calculating a detection statistic T:
Figure FDA0004228498310000061
step 3-2) when the test statistic T is greater than the detection threshold eta, testing H 1 If yes, the detection result is a target, otherwise, check H 0 And (3) if the result is true, the detection result is no target.
4. A space-time adaptive detection system adapted for use in a partially uniform reverberant environment, the system comprising: the system comprises a space-time adaptive detector, a data acquisition module, a parameter estimation module and a detection module which are established in advance;
the data acquisition module is used for acquiring a data matrix to be detected and an auxiliary data matrix of echo data received by the space symmetry linear array;
the parameter estimation module is used for combining the data to be detected and the auxiliary data, and estimating the parameters of the pre-constructed detection statistic by adopting maximum likelihood estimation;
the detection module is used for inputting the estimated parameters into the space-time adaptive detector to finish the adaptive detection of the target;
the processing procedure of the data acquisition module specifically comprises the following steps:
the space symmetric linear array consists of N array elements, and the received echo signal is processed to obtain a discrete space time processing N-dimensional echo complex vector z i The received echo vector z to be detected of the ith distance unit i Expressed as:
z i ＝s i +n i ∈C N×1 (1)
wherein C represents a complex domain, n i Representing complex Gaussian interference vectors, s i Representing a leakage target signal vector, and when the target has energy leakage, the signal energy can leak into a left distance unit and a right distance unit to obtain a target energy leakage model consisting of three adjacent distance units, and s i Expressed as:
Figure FDA0004228498310000062
wherein alpha is the complex amplitude factor of the received target echo signal and is an unknown determined parameter; x-shaped articles p (. Cndot.) is the complex ambiguity function of the transmitted signal; epsilon 0 ∈[0,T p ]To measure the severity of the target energy leakage, T, for the residual time delay p Is pulse width; v is a target normalized airspace guide vector; f is Doppler shift introduced by the target and v; l represents the serial number of the sample to be detected;
taking the ith distance unit to be detected as the center, delaying the residual time epsilon-T p /2,T p /2]Redefined as:
Figure FDA0004228498310000071
z k ∈C N×1 k uniform auxiliary data collected from distance units adjacent to the data to be detected are represented, and only two interference components of white noise and reverberation are contained;
Z L ＝[z l-1 ,z l ,z l+1 ]∈C N×3 for the data matrix to be detected, Z K ＝[z 1 ,...,z K ]∈C N×K As an auxiliary data matrix, z= [ Z L ,Z K ]∈C N×(3+K) Is a joint data matrix;
the processing procedure of the parameter estimation module specifically comprises the following steps:
step 2-1) constructing a detection statistic T based on GLRT criterion:
Figure FDA0004228498310000072
wherein, gamma > 0 represents unknown energy scale factor, M is covariance matrix of symmetric linear array; v is a normalized airspace guide vector, and M and v have oblique symmetry characteristics, namely:
M＝J N M * J N ,v＝J N v *
wherein J is N ∈R N×N For permutation matrices, (. Cndot.) * For conjugate operation, R is the real number domain, where the permutation matrix J N ∈R N×N Is a square matrix with the diagonal line of 1 and other elements of 0;
step 2-2) based on the oblique symmetry properties of M and v, f j (Z; j epsilon, j alpha, gamma, M) is represented by H j J=0, 1 assumes a probability density function of the joint data matrix Z:
Figure FDA0004228498310000073
where det (·) represents the determinant operation of the matrix, tr (·) represents the trace of the matrix, (·) T And ( H Representing the transpose and conjugate transpose of the matrix, the intermediate variable S and the interference data matrix F (jα) are:
Figure FDA0004228498310000074
x is a data matrix generated from the data to be detected:
Figure FDA0004228498310000075
vector quantity
Figure FDA0004228498310000081
And->
Figure FDA0004228498310000082
The method comprises the following steps:
Figure FDA0004228498310000083
the fuzzy function matrix D is:
Figure FDA0004228498310000084
wherein t is 1 ,t 2 ,t 3 All are time delays: t is t 1 ＝-T p -ε,t 2 ＝-ε,t 3 ＝T p -ε；
Step 2-3) Using maximum likelihood estimation pair H j Estimating M under the assumption that j=0, 1 to obtain an estimation result
Figure FDA00042284983100000811
The method comprises the following steps:
Figure FDA0004228498310000085
after substituting (9) into equation (6), the detection statistic is:
Figure FDA0004228498310000086
step 2-4) based on equation (10), the maximum likelihood estimate of α is:
Figure FDA0004228498310000087
and (3) solving the first partial derivative of alpha in the formula (11) and setting zero to obtain the estimation result of alpha, wherein the estimation result is as follows:
Figure FDA0004228498310000088
wherein Q is an intermediate variable matrix:
Figure FDA00042284983100000813
Figure FDA0004228498310000089
represent S -1/2 v Zhang Chengzi spatial matrix->
Figure FDA00042284983100000814
Orthogonal complement of I N Is an N-dimensional identity matrix;
step 2-5) will
Figure FDA00042284983100000812
Substitution (10), solving for H 1 Let maximum likelihood estimation of gamma +.>
Figure FDA00042284983100000810
The method comprises the following steps:
Figure FDA0004228498310000091
Figure FDA0004228498310000092
the intermediate matrices B and C are:
Figure FDA0004228498310000093
Figure FDA0004228498310000094
wherein the matrix Q can be characterized as q=u (γ 1 I 6 +Λ)U H Wherein U is C 6×6 For unitary matrix, Λ is eigenvalue λ 1 ,...,λ 6 Is a diagonal array of (a);
the intermediate matrices E and G are:
Figure FDA0004228498310000095
Figure FDA0004228498310000096
the matrices W and V are:
Figure FDA0004228498310000097
Figure FDA0004228498310000098
substituting the characteristic decomposition of Q into (14),
Figure FDA0004228498310000099
wherein,,
Figure FDA0004228498310000101
Figure FDA0004228498310000102
**
m＝p * ，n＝q * ；
for h 1 (γ 1 ) Gamma determination 1 And setting zero to obtain gamma 1 Estimate of (2)
Figure FDA0004228498310000103
Solving the nonlinear equation by adopting an fsive function;
step 2-6) based on equation (10), at H 0 The maximum likelihood estimate for gamma is assumed to be:
Figure FDA0004228498310000104
simplifying to obtain
Figure FDA0004228498310000105
For X H S -1 X is subjected to characteristic decomposition to obtain
Figure FDA0004228498310000106
Wherein U is 0 ∈C 6×6 As unitary matrix, Λ 0 Is characterized by lambda 0,1 ,...,λ 0,6 Is a diagonal array of (a); and (3) substituting (19) and then simplifying to obtain:
Figure FDA0004228498310000107
for h 0 (γ 0 ) Gamma determination 0 And zero setting the first partial derivative of (2) to obtain the gamma 0 Estimate of (2)
Figure FDA0004228498310000108
Here->
Figure FDA0004228498310000109
And solving by adopting a numerical method.
CN202011248227.XA 2020-11-10 2020-11-10 Space-time self-adaptive detection method and system suitable for partial uniform reverberation environment Active CN112505665B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202011248227.XA CN112505665B (en) 2020-11-10 2020-11-10 Space-time self-adaptive detection method and system suitable for partial uniform reverberation environment

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202011248227.XA CN112505665B (en) 2020-11-10 2020-11-10 Space-time self-adaptive detection method and system suitable for partial uniform reverberation environment

Publications (2)

Publication Number Publication Date
CN112505665A CN112505665A (en) 2021-03-16
CN112505665B true CN112505665B (en) 2023-06-23

Family

ID=74957643

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202011248227.XA Active CN112505665B (en) 2020-11-10 2020-11-10 Space-time self-adaptive detection method and system suitable for partial uniform reverberation environment

Country Status (1)

Country Link
CN (1) CN112505665B (en)

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113589268B (en) * 2021-09-29 2021-12-21 中国人民解放军空军预警学院 Method, system and device for detecting double subspace signals in partially uniform environment
CN115575946B (en) * 2022-10-20 2024-06-04 中国人民解放军海军航空大学 Intelligent fusion detection method for radar target oblique symmetry subspace

Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6400306B1 (en) * 1999-12-17 2002-06-04 Sicom Systems, Ltd Multi-channel moving target radar detection and imaging apparatus and method
CN103033815A (en) * 2012-12-19 2013-04-10 中国科学院声学研究所 Detection Method and detection device of distance expansion target based on reverberation covariance matrix
CN104977579A (en) * 2015-07-03 2015-10-14 中国科学院声学研究所 Random-covariance-matrix-based multi-highlight target time space detection method
CN107479050A (en) * 2017-08-13 2017-12-15 中国科学院声学研究所 Object detection method and device based on symmetrical spectral property and sub-symmetry characteristic
CN107561540A (en) * 2017-08-13 2018-01-09 中国科学院声学研究所 The detection method and device of sonar leakage target based on the symmetrical spectral property of reverberation
CN108646249A (en) * 2018-05-11 2018-10-12 中国科学院声学研究所 A kind of parametrization leakage object detection method being suitable for the uniform Reverberation in part
CN111090088A (en) * 2018-10-24 2020-05-01 中国科学院声学研究所 Leakage target space-time detection method based on active sonar array skew symmetry characteristics
CN111090089A (en) * 2018-10-24 2020-05-01 中国科学院声学研究所 Space-time adaptive detection method based on two types of auxiliary data

Patent Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6400306B1 (en) * 1999-12-17 2002-06-04 Sicom Systems, Ltd Multi-channel moving target radar detection and imaging apparatus and method
CN103033815A (en) * 2012-12-19 2013-04-10 中国科学院声学研究所 Detection Method and detection device of distance expansion target based on reverberation covariance matrix
CN104977579A (en) * 2015-07-03 2015-10-14 中国科学院声学研究所 Random-covariance-matrix-based multi-highlight target time space detection method
CN107479050A (en) * 2017-08-13 2017-12-15 中国科学院声学研究所 Object detection method and device based on symmetrical spectral property and sub-symmetry characteristic
CN107561540A (en) * 2017-08-13 2018-01-09 中国科学院声学研究所 The detection method and device of sonar leakage target based on the symmetrical spectral property of reverberation
CN108646249A (en) * 2018-05-11 2018-10-12 中国科学院声学研究所 A kind of parametrization leakage object detection method being suitable for the uniform Reverberation in part
CN111090088A (en) * 2018-10-24 2020-05-01 中国科学院声学研究所 Leakage target space-time detection method based on active sonar array skew symmetry characteristics
CN111090089A (en) * 2018-10-24 2020-05-01 中国科学院声学研究所 Space-time adaptive detection method based on two types of auxiliary data

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
An Improved Adaptive Radar Detector based on Two Sets of Training Data;Linjie Yan et al.;《2019 IEEE Radar Conference (RadarConf)》;第1-6页 *
均匀混响背景下抗多目标干扰 恒虚警检测器设计;殷超然 等;《水下无人***学报》;第27卷(第4期);第434-441页 *
基于斜对称阵列的水下单脉冲降维空时自适应处理;王莎 等;《水下无人***学报》;第28卷(第2期);第168-173页 *

Also Published As

Publication number Publication date
CN112505665A (en) 2021-03-16

Similar Documents

Publication Publication Date Title
CN109031231B (en) Radar low-altitude target time reversal coherent angle estimation method
CN112505665B (en) Space-time self-adaptive detection method and system suitable for partial uniform reverberation environment
CN108732549A (en) A kind of array element defect MIMO radar DOA estimation method based on covariance matrix reconstruct
El-Keyi et al. Robust adaptive beamforming based on the Kalman filter
CN103984676A (en) Rectangular projection adaptive beamforming method based on covariance matrix reconstruction
CN109444896B (en) Underwater sound array positioning system and positioning method thereof
CN109459744B (en) Steady self-adaptive beam forming method for realizing multi-interference suppression
CN108646249B (en) Parameterized leakage target detection method suitable for partial uniform reverberation background
CN115508828B (en) Intelligent fusion detection method for radar target under subspace interference
CN109031227B (en) Conjugate gradient space-time adaptive processing method and system
CN109683151A (en) Tenth of the twelve Earthly Branches rooting MUSIC angle estimating method under non-uniform noise environment based on matrix completion
CN111090089B (en) Space-time adaptive detection method based on two types of auxiliary data
Jiang et al. Robust Matched Filtering in $\ell_ {p} $-Space
Tohidi et al. Compressed-domain detection and estimation for colocated MIMO radar
CN113884979A (en) Robust adaptive beam forming method for interference plus noise covariance matrix reconstruction
CN111090088B (en) Leakage target space-time detection method based on active sonar array skew symmetry characteristics
CN116106829B (en) Intelligent target detection method under partial uniform clutter and interference
CN110673118A (en) Active sonar single-frequency pulse train waveform design and detection algorithm
CN111665469A (en) Underwater multipath signal parameter estimation method based on space time-frequency distribution
CN116318296A (en) Robust beam forming method based on maximum posterior probability and covariance matrix reconstruction
CN114325570A (en) High-precision noise self-adaptive direction finding method
CN115524672A (en) Target robustness intelligent detection method under structured interference and clutter
CN111722178B (en) Far-field narrow-band signal incoming wave direction estimation method based on numerical solution of directivity model
CN109031211A (en) A kind of steady side lobe suppression method of cognition radar based on sequence optimisation
CN116299387B (en) Target intelligent detection method for interference orthogonal suppression under heterogeneous clutter

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
GR01 Patent grant