Iterative multi-target detection method based on pa-fda dual-mode radar

Abstract

This invention discloses an iterative multi-target detection method based on PA-FDA dual-mode radar, relating to the field of radar signal processing technology. The method includes: constructing a signal-level fusion model for the PA-FDA dual-mode radar; wherein the PA-FDA dual-mode radar signal-level fusion model is constructed based on target signals received by the PA antenna array and the FDA antenna array, and the target signals received by the PA antenna array and the FDA antenna array are doped with Gaussian white noise and noise-like interference; constructing a GLRT detector based on the PA-FDA dual-mode radar signal-level fusion model; constructing a CCBD-GLRT detector based on the PA-FDA dual-mode radar signal-level fusion model; using the GLRT detector to detect one of multiple targets and obtaining the detection result; based on the detection result, using the CCBD-GLRT detector to detect the remaining targets and obtaining the final detection result. This application can improve the performance of multi-target detection.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar signal processing, and particularly relates to an iterative multi-target detection method based on a PA-FDA dual-mode radar. BACKGROUND

[0002] Radar is a key equipment for battlefield information acquisition and situation awareness under modern informationized combat conditions, and target detection is an important function of a radar system, and modern radar systems may face the threat of cluster targets, such as unmanned aerial vehicle cluster combat, which requires the radar to have multi-target detection capability.

[0003] In the prior art, the radar used usually has the problems of small coverage range, long time consumption and low efficiency, and therefore, it is urgent to improve the radar system in the prior art to overcome the above problems. SUMMARY

[0004] In order to solve the above problems in the prior art, the application provides an iterative multi-target detection method based on a PA-FDA dual-mode radar.

[0005] In a first aspect, the application provides an iterative multi-target detection method based on a PA-FDA dual-mode radar, comprising:

[0006] A signal level fusion model of the PA-FDA dual-mode radar is constructed, wherein the signal level fusion model of the PA-FDA dual-mode radar is constructed based on target signals received by a PA antenna array and an FDA antenna array, and the target signals received by the PA antenna array and the FDA antenna array are mixed with Gaussian white noise and noise-like interference;

[0007] A GLRT detector is constructed based on the signal level fusion model of the PA-FDA dual-mode radar;

[0008] A CCBD-GLRT detector is constructed based on the signal level fusion model of the PA-FDA dual-mode radar;

[0009] One of the multiple targets is detected by using the GLRT detector, and a detection result is obtained, and then the remaining targets are detected by using the CCBD-GLRT detector according to the detection result, and a final detection result is obtained.

[0010] The application has the following beneficial effects:

[0011] The application provides an iterative multi-target detection method based on a PA-FDA dual-mode radar.

[0012] The application will be further described in detail below with reference to the drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 is a flow chart of the iterative multi-target detection method based on the PA-FDA dual-mode radar provided by the embodiment of the application;

[0014] Figure 2 is a structural schematic diagram of the PA-FDA dual-mode radar array element arrangement provided by the embodiment of the application;

[0015] Figure 3 is a relationship schematic diagram of the false alarm probability and the detection probability when the SNR is -7dB provided by the embodiment of the application;

[0016] Figure 4 is a relationship schematic diagram of the detection probability and the target angle under different radar systems provided by the embodiment of the application;

[0017] Figure 5 is a relationship schematic diagram of the corresponding detection probability and the signal-to-noise ratio under different radar systems provided by the embodiment of the application;

[0018] Figure 6 is a schematic diagram of the GLRT detector detection target result provided by the embodiment of the application;

[0019] Figure 7 is a schematic diagram of the CCBD-GLRT detector detection target result provided by the embodiment of the application;

[0020] Figure 8 is another schematic diagram of the CCBD-GLRT detector detection target result provided by the embodiment of the application;

[0021] Figure 9 is a schematic diagram of the CD optimization result provided by the embodiment of the application;

[0022] Figure 10 is a relationship curve schematic diagram of the PD and the SNR of different targets provided by the embodiment of the application;

[0023] Figure 11is a schematic diagram of the relationship between GLRT detection probability and target angle provided by an embodiment of the present application;

[0024] Figure 12 is another schematic diagram of the relationship between GLRT detection probability and target angle provided by an embodiment of the present application;

[0025] Figure 13 is another schematic diagram of the relationship between GLRT detection probability and target angle provided by an embodiment of the present application;

[0026] Figure 14 is a schematic diagram of the relationship between SNR of mismatched targets and detection probability under different radar systems provided by an embodiment of the present application. DETAILED DESCRIPTION

[0027] The present application will be further described in detail below with specific embodiments, but the embodiments of the present application are not limited thereto.

[0028] In the prior art, a conventional phased array (PA) radar system uses an angle-focused beam to detect targets in its main lobe, and the probability of detection (PD) is heavily dependent on the pointing direction of the transmit beam pattern. In order to cover a wide monitoring area, the PA radar transmits different pointing main beams one by one to cover a specific region of interest (ROI), so it takes a long time, which affects the target detection efficiency of the radar and reduces the working performance of the radar. In addition, a frequency diversity array (FDA) is widely studied due to its wide spatial coverage characteristics. Unlike a phased array (PA) radar using a phase shifter to scan a region of interest, the FDA radar forms a range / time-angle dependent transmit pattern by introducing a frequency increment between adjacent elements. Due to the time / range-dependent phase modulation, the FDA radar performs well in spatial coverage and can adjust the spatial coverage according to the frequency increment. Compared with the PA radar, the wide spatial coverage achieved by the FDA radar results in a certain loss of signal to noise ratio (SNR).

[0029] Therefore, the application uses a phased array (PA) radar system to sequentially guide a main beam to cover a specific wide monitoring area of interest, and combines the degrees of freedom of the FDA radar system and the high detection performance of the approximate maximum likelihood technique to propose a signal-level fusion mode, construct a PA-FDA dual-mode radar, use the high transmission power efficiency of the PA radar and the wide spatial coverage of the FDA radar to realize coverage of a wider ROI, combine the wide coverage advantage of the FDA radar with the high gain provided by the PA radar, and improve the target detection performance in a multi-target environment. In addition, for the needs of multi-target detection scenarios, an iterative multi-target detector is designed based on the dual-mode radar system, including a generalized likelihood ratio test (GLRT) and a detection-before-condition suppression generalized likelihood ratio test (CCBD-GLRT), and the corresponding analytical expressions of the detection probability and the false alarm probability are derived, promoting the application of the proposed detection algorithm in practice.

[0030] Please refer to Figure 1 , Figure 1 is a flowchart of the iterative multi-target detection method based on the PA-FDA dual-mode radar provided by the embodiment of the application, and the iterative multi-target detection method based on the PA-FDA dual-mode radar provided by the application comprises the following steps:

[0031] S101, a signal-level fusion model of the PA-FDA dual-mode radar is constructed, wherein the signal-level fusion model of the PA-FDA dual-mode radar is constructed based on target signals received by a PA antenna array and an FDA antenna array, and the target signals received by the PA antenna array and the FDA antenna array are mixed with Gaussian white noise and noise-like interference;

[0032] S102, a GLRT detector is constructed based on the signal-level fusion model of the PA-FDA dual-mode radar;

[0033] S103, a CCBD-GLRT detector is constructed based on the signal-level fusion model of the PA-FDA dual-mode radar;

[0034] S104, one of the multiple targets is detected using the GLRT detector, and a detection result is obtained, and then the remaining targets are detected using the CCBD-GLRT detector according to the detection result, and a final detection result is obtained.

[0035] Specifically, please continue to refer to Figure 1As shown, the PA-FDA dual-mode radar based iterative multi-target detection method provided by the embodiment has the following advantages. On the one hand, the PA-FDA dual-mode radar is constructed in a signal level fusion manner, and the joint information in the PA-FDA dual-mode radar is used for multi-target detection, so that the performance of detecting multi-targets is improved. On the other hand, the technical scheme of iterative multi-target detection is proposed, and the GLRT detector and the CCBD-GLRT detector are constructed, so that the detection accuracy and the detection efficiency are further improved.

[0036] In an optional embodiment of the present application, before constructing the signal level fusion model of the PA-FDA dual-mode radar, the following steps are further included:

[0037] The transmission signal of the PA antenna array is obtained, and the expression is as follows:

[0038]

[0039]

[0040] wherein rect(t) is a pulse function, t is time, t∈(0,T r ) is a variable time within a pulse repetition time T r , T p is a pulse width, Φ0(t) is an envelope of the transmission signal of the PA antenna array, f0 is a carrier frequency of the PA antenna array, e is Euler number, and j is an imaginary number;

[0041] The transmission signal of the FDA antenna array is obtained, and the expression is as follows:

[0042]

[0043]

[0044] wherein rect(t) is a pulse function, t is time, t∈(0,T r ) is a variable time within a pulse repetition time T r , T p is a pulse width, Φ m (t) is an envelope of the transmission signal corresponding to the mth array element of the FDA antenna array, f m is a carrier frequency of the mth array element of the FDA antenna array, f m =f0+(m-1)Δf, f0 is a reference carrier frequency of the mth array element of the FDA antenna array, m is the serial number of the FDA antenna array, Δf is a frequency increment value, and Δf<<f0, e is Euler number, and j is an imaginary number;

[0045] Suppose that an arbitrary target with a distance of R and an angle of θ, the echo data received by the n1th array element in the PA antenna array is as follows:

[0046]

[0047] where n1 = 1, 2, …, L, L is the number of elements in the PA antenna array, a is the complex scattering coefficient of the target, τ0= 2R / c is the time delay of the target signal, l is the lth element in the PA antenna array, ε l is the weight added to the lth element in the PA antenna array, ()*is the conjugate, is the two-way delay of the PA antenna array;

[0048] The echo data received by the nth2element in the FDA antenna array is:

[0049]

[0050] where n2 = 1, 2, …, M, M is the number of elements in the FDA antenna array, a is the complex scattering coefficient of the target, τ0= 2R / c is the time delay of the target signal, m is the mth element in the FDA antenna array, is the two-way delay of the FDA antenna array;

[0051] After the echo signal received by the PA-FDA dual-mode radar is processed by down-conversion, matching filtering and other related signal processing, the target signals of the PA antenna array and the FDA antenna array are obtained, respectively.

[0052] The expression of the target signal of the PA antenna array is:

[0053]

[0054] where a is the complex scattering coefficient of the target; η PA is the transmission gain term, b PA (θ) is the receiving steering vector of the PA antenna array, is a complex set of L dimensions;

[0055] The expression of the target signal of the FDA antenna array is:

[0056]

[0057] where a is the complex scattering coefficient of the target; η FDA is the phase shift term caused by the reference point, a(R, θ) is the transmitting steering vector of the FDA antenna array, b FDA (θ) is the receiving steering vector of the FDA antenna array, is a complex set of M 2 dimensions;

[0058] Considering that the received signal of radar contains noise and noise-like interference, the target signal of the PA antenna array is mixed with Gaussian noise and noise-like interference, and its expression is:

[0059] x PA =s PA +n PA ;

[0060] where n PA is the received interference of the PA antenna array, indicates that n PA obeys distribution, is a circularly symmetric complex Gaussian distribution with mean μ and variance σ 2 , R PA is the noise plus interference covariance matrix of the PA antenna array, is the noise power, n is the noise, L is an L-dimensional identity matrix, j PA is the noise-like interference signal received by the PA antenna array, j PA = α j b PA (θ j ), α j is the target complex scattering coefficient of the interference signal, b PA (θ j ) is the interference signal steering vector received by the PA antenna array, θ j is the angle of the interference signal, is the conjugate transpose operator;

[0061] Considering that the received signal of radar contains noise and noise-like interference, the target signal of the PA antenna array is mixed with Gaussian noise and noise-like interference, and its expression is:

[0062] x FDA =s FDA +n FDA ;

[0063] where n FDA is the received interference of the PA antenna array, indicates that n FDA obeys distribution, is a circularly symmetric complex Gaussian distribution with mean μ and variance σ 2 , R FDA is the noise plus interference covariance matrix of the PA antenna array, is the noise power, n is the noise, is an M 2 dimensional identity matrix, M is the number of elements of the FDA antenna array, jFDA This refers to noise-like interference signals received by the FDA antenna array. The complex coefficients of the interference signal obey distributed, For a given mean μ and variance σ 2 The circularly symmetric complex Gaussian distribution, For the interference power, θ j For the angle of the interference signal, Represents the Kronecker product, b FDA (θ j θ is the steering vector of the interference signal received by the FDA antenna array. j The angle of the interference signal.

[0064] In an optional embodiment of this application, a signal-level fusion model for a PA-FDA dual-mode radar is constructed based on the target signal from a noisy PA antenna array and the target signal from a noisy FDA antenna array, and its expression is as follows:

[0065]

[0066] Where V is the transmit-receive steering vector matrix of the PA-FDA dual-mode radar. diag{} is used to construct a diagonal matrix, b PA (θ) is the receive steering vector of the PA antenna array, and a(R,θ) is the transmit steering vector of the FDA antenna array. For Kronecker products, b FDA (θ) is the FDA antenna array receive steering vector. Let R be a complex set of D×2 dimensions, and θ be the target range and angle, respectively, and η be the coefficient vector of the PA-FDA dual-mode radar. Where η1 and η2 are constant complex coefficient vectors of the received signals from the PA and FDA antenna arrays, respectively, and η1 = αη PA η PA For the transmission gain term of the PA radar, η2 = αη FDA η FDA Let α be the phase shift term caused by the reference point in the FDA radar, and α be the complex scattering coefficient of the target. T For transpose operation, It is a set of complex numbers with dimensions of 2×1.

[0067] In one optional embodiment of this application, the process of constructing a GLRT detector based on the signal-level fusion model of PA-FDA dual-mode radar includes:

[0068] A multi-objective hypothesis testing problem is proposed, and its expression is as follows:

[0069]

[0070] where x is the data to be detected, n is the noise component, x k is the kth training sample, n k is the noise in the kth training sample, k is the training sample serial number, K is the number of training samples, V is the PA-FDA dual-mode radar transmit-receive steering vector matrix, and η is the coefficient vector of the PA-FDA dual-mode radar;

[0071] Based on the generalized likelihood ratio test criterion, the decision criterion of the multi-target hypothesis test problem can be expressed as:

[0072]

[0073] where is the maximization with respect to R and η, R = diag{R PA ,R FDA}, R is the background signal matrix of the PA-FDA dual-mode radar, diag{} is a diagonal matrix, η is the coefficient vector of the PA-FDA dual-mode radar, f(x,X|H1) is the joint probability density function of x and X under the condition of H1, f(x,X|H0) is the joint probability density function of x and X under the condition of H0, x and X are the data to be detected and the training sample data, respectively, is the detection threshold;

[0074] When , the GLRT detector judges H1, and when , the GLRT detector judges H0;

[0075] Based on the generalized likelihood ratio test criterion, the GLRT detector is obtained, and its expression is:

[0076]

[0077] where T GLRT is the GLRT detection statistic of the PA-FDA dual-mode radar, ∑ is the summation symbol, S is the correlation matrix of the signal x k , x k represents the kth training sample, represents the conjugate transpose, () -1 is the inverse;

[0078] where is the comparison between the detection statistic and the threshold, when , the GLRT detector judges H1, and when , the GLRT detector judges H0.

[0079] In an alternative embodiment of the present application, based on the signal level fusion model of the PA-FDA dual-mode radar, the process of constructing the CCBD-GLRT detector includes:

[0080] Based on the target information detected by the GLRT detector, an iterative steering matrix is constructed, and the multi-target hypothesis testing detection problem is updated, which is expressed as:

[0081]

[0082] wherein, is a steering matrix including 2(S+1) columns, is a matrix constructed by the transmit-receive steering vectors of the known S targets, V S+1 is the steering vector of the search target, B S = [η1,...,η S ] T is a coefficient matrix of 2×S dimensions, B S+1 = [B S ,...,η S+1 ] T is a coefficient matrix of 2×(S+1) dimensions, η s is a complex coefficient vector of the s-th target, η S+1 represents a complex coefficient vector of the search target, n is a noise component;

[0083] The iterative steering matrix is decomposed, which is expressed as:

[0084]

[0085] wherein, is a semi-unitary matrix, is a Hermitian matrix, Sp() is a generating subspace, is an augmented unitary matrix, composed of the last D-2S columns of the unitary matrix obtained by singular value decomposition of , then the orthogonal transformation matrix is

[0086] The orthogonal transformation matrix is used to update the multi-target hypothesis testing detection problem in the previous step, and the hypothesis testing detection problem is expressed as:

[0087]

[0088] wherein, y is the data to be detected, w is the noise n after transformation using the orthogonal transformation matrix , and is the expression of the noise n after transformation using the orthogonal transformation matrix transformed search target steering vector, that is

[0089] using the orthogonal transformation matrix Transform the training sample data, the expression is:

[0090] X = [x1, x2, …, x k ];

[0091]

[0092] where x k is the kth training sample, w K is the kth training sample after orthogonal transformation matrix transformation, is a complex set of (D-2S) × K, D is the dimension of PA-FDA dual-mode radar receiving signal, S is the number of known targets, K represents the number of training samples;

[0093] Based on the generalized likelihood ratio test criterion, using the orthogonal transformation matrix transformed hypothesis test detection problem, construct CCBD-GLRT detector, the expression is:

[0094]

[0095]

[0096] where y is the transformed data to be detected, is the conjugate transpose, M is the correlation matrix of the transformed training sample, S is the signal covariance matrix of the S targets, () -1 is the inverse, is the kth training sample after orthogonal transformation matrix transformation of the search target steering vector;

[0097] wherein is judged with the second detection threshold, when T CCBD > ζ, the detector judges H1, when T CCBD < ζ, the detector judges H0.

[0098] In an optional embodiment of the present application, further comprising: using the coordinate descent algorithm to optimize the parameters, the process includes:

[0099] optimizing the Q target parameters [θ1, …, θ Q ] output by the GLRT detector and the CCBD-GLRT detector; wherein the target parameters to be optimized are angles θ;

[0100] optimizing the target parameters θ1 to θQ Among them, the objective parameter θ1 is optimized using the objective parameters [θ2, ..., θ1]. Q [The known target transmit-receive steering matrix in the iterative steering matrix of the CCBD-GLRT detector] Based on the CCBD-GLRT detector, via the guide vector V S+1 Optimize the search objective θ1 to obtain the optimization parameters. Replace θ1 to optimize objective θ1; optimize objective θ2 by utilizing the already optimized objective. and target [θ3,…,θ Q ], optimize the objective θ2 to obtain the optimized objective. Optimize the remaining objectives sequentially, performing Q+1 iterations of detection on the Q objectives to obtain the optimized objectives.

[0101] In one optional embodiment of this application, the PA-FDA dual-mode radar includes a PA antenna array and an FDA antenna array, wherein the PA antenna array includes 8 transmitting elements and the FDA antenna array includes 8 transmitting elements. The elements in the PA antenna array and the elements in the FDA antenna array are arranged in an array, and the spacing between adjacent elements is 0.1m to 0.2m.

[0102] In one alternative embodiment of this application, please refer to Figure 2 , Figure 2 This is a schematic diagram of a PA-FDA dual-mode radar array element arrangement provided in an embodiment of the present invention. The multi-target detection process is achieved through the following steps:

[0103] S101. Construct a signal-level fusion model for PA-FDA dual-mode radar.

[0104] The array is configured with a uniform linear array (ULA), which includes a PA antenna array and an FDA antenna array. Figure 2 As can be seen, the left side has a PA antenna array with L array elements, and the right side has an FDA antenna array with M array elements. The spacing between adjacent array elements is the same.

[0105] The transmitted signal of the PA antenna array is represented as:

[0106]

[0107]

[0108] Where rect(t) is the impulse function, t is time, and t∈(0,T) r ) represents the pulse repetition time T r The variable time within T pwhere T is the pulse repetition time, T is the pulse width, Φ0(t) is the envelope of the transmit signal of the PA antenna array, f0is the carrier frequency of the PA antenna array, e is the Euler number, and j is the imaginary number;

[0109] The transmit signal of the FDA antenna array is represented as:

[0110]

[0111]

[0112] where rect(t) is a pulse function, t is time, t ∈ (0, T r ) is a variable time within the pulse repetition time T r , T p is the pulse width, Φ m (t) is the envelope of the transmit signal corresponding to the mth element of the FDA antenna array, f m is the carrier frequency of the mth element of the FDA antenna array, f m = f0+ (m-1) Δf, f0is the reference carrier frequency of the mth element of the FDA antenna array, m is the serial number of the FDA antenna array, Δf is the frequency increment value, and Δf << f0, e is the Euler number, and j is the imaginary number;

[0113] The transmit signal of the PA antenna array and the transmit signal of the FDA antenna array are set as orthogonal signals, which can be represented as:

[0114]

[0115] where δ mm′ (τ) is a Dirac function, τ is an arbitrary time offset, m, m' ∈ [0, M];

[0116] An arbitrary target with a distance of R and an angle of θ in the PA-FDA dual-mode radar is set, and the echo data received by the elements in the PA-FDA dual-mode radar can be represented as follows:

[0117] The echo data received by the nth1 element in the PA antenna array is:

[0118]

[0119] where n1 = 1, 2, …, L, L is the number of elements in the PA antenna array, α is the complex scattering coefficient of the target, τ0= 2R / c is the time delay of the target signal, l is the lth element in the PA antenna array, ε l is the weight added to the lth element in the PA antenna array, ()*is the conjugate, is the two-way delay of the PA antenna array;

[0120] The echo data received by the nth2 array element in the FDA antenna array is:

[0121]

[0122] wherein n2 = 1, 2, …, M, M is the number of array elements in the FDA antenna array, a is the complex scattering coefficient of the target, τ0= 2R / c is the time delay of the target signal, m is the mth array element in the FDA antenna array, is the two-way delay of the FDA antenna array;

[0123] In the above, the weight of the array element can be obtained in a vector, wherein the expression of the vector is:

[0124]

[0125] wherein θ0is the direction in which the PA antenna array is directed, and d is the array element spacing;

[0126] In the above, the two-way delay of the PA antenna array is expressed as:

[0127]

[0128] In the above, the two-way delay of the FDA antenna array is expressed as:

[0129]

[0130] The receiver of the PA-FDA dual-mode radar processes the echo data, including down-conversion, matched filtering and storage, to obtain the target signal of the PA antenna array and the target signal of the FDA antenna array.

[0131] The expression of the target signal of the PA antenna array is:

[0132]

[0133] wherein a is the complex scattering coefficient of the target, η PA is the transmission gain term, b PA (θ) is the receiving steering vector of the PA antenna array, is a complex set of L dimensions;

[0134] The expression of the target signal of the FDA antenna array is:

[0135]

[0136] wherein a is the complex scattering coefficient of the target, η FDA is the phase shift term caused by the reference point, a(R, θ) is the transmitting steering vector of the FDA antenna array, b FDA(θ) is the receive steering vector of the FDA antenna array, M 2 is the complex set of dimensions,

[0137] In the above, the transmission gain term η PA is expressed as:

[0138]

[0139] In the above, the phase shift term η FDA caused by the reference point is expressed as:

[0140]

[0141] In the above, the receive steering vector b PA (θ) of the PA antenna array is expressed as:

[0142]

[0143] In the above, the transmit steering vector a(R, θ) of the FDA antenna array is expressed as:

[0144]

[0145] In the above, the receive steering vector b FDA (θ) of the FDA antenna array is expressed as:

[0146]

[0147] where f θ = dsinθ / λ0 is the spatial frequency, and f R = 2ΔfR / c is the range frequency.

[0148] The setting background consists of Gaussian white noise and noise-like interference, the interference range is R j , and the angle is θ j . The target signal mixed with noise can be expressed as follows:

[0149] The target signal of the PA antenna array mixed with Gaussian white noise and noise-like interference is expressed as:

[0150] x PA = s PA + n PA ;

[0151] where n PA is the received interference of the PA antenna array, n PA obeys the distribution, with mean μ and variance σ2 a circularly symmetric complex Gaussian distribution, R PA is the noise plus interference covariance matrix of the PA antenna array, is the noise power, n is the noise, L is the L-dimensional identity matrix, j PA is the interference signal of the PA antenna array, j PA = a j b PA (0 j ), a j is the target complex scattering coefficient of the interference signal, b PA (0 j ) is the steering vector of the interference signal received by the PA antenna array, 0 j is the angle of the interference signal, is the conjugate transpose operator;

[0152] The target signal of the FDA antenna array is contaminated by Gaussian noise and similar noise, which is expressed as:

[0153] x FDA = s FDA + n FDA ;

[0154] where n FDA is the interference received by the FDA antenna array, denotes that n FDA obeys distribution, is a circularly symmetric complex Gaussian distribution with mean μ and variance σ 2 , R FDA is the noise plus interference covariance matrix of the FDA antenna array, is the noise power, n is the noise, is the M 2 -dimensional identity matrix, M is the number of elements of the FDA antenna array, j FDA is the similar noise interference signal received by the FDA antenna array, obeys distribution, is a circularly symmetric complex Gaussian distribution with mean μ and variance σ 2 , is the interference power, 0 j is the angle of the interference signal, denotes the Kronecker product, b FDA (0 j ) is the steering vector of the interference signal received by the FDA antenna array, 0 j is the angle of the interference signal.

[0155] Based on the target signal of the PA antenna array with noise and the target signal of the FDA antenna array with noise, a signal level fusion model of the PA-FDA dual-mode radar is constructed, and the expression is:

[0156]

[0157] Wherein, V is the transmitting-receiving steering vector matrix of the PA-FDA dual-mode radar, diag{} is a diagonal matrix, b PA (θ) is the receiving steering vector of the PA antenna array, a(R,θ) is the transmitting steering vector of the FDA antenna array, is the Kronecker product, b FDA (θ) is the receiving steering vector of the FDA antenna array, is a complex set of D×2 dimensions, R and θ are the target distance and angle respectively, and η is the coefficient vector of the PA-FDA dual-mode radar, Wherein, η1 and η2 are constant complex coefficient vectors of the PA and FDA antenna array receiving signals respectively, η1=αη PA , η PA is the transmission gain term of the PA radar, η2=αη FDA , η FDA is the phase shift term of the FDA radar caused by the reference point, α is the complex scattering coefficient of the target, [] T is the transposition operation, is a complex set of 2×1 dimensions.

[0158] Based on the Neyman-Pearson criterion, the target signal of the PA antenna array with noise and interference and the target signal of the FDA antenna array with noise and interference are combined to obtain the general expression of the decision of the PA-FDA dual-mode radar system multi-target hypothesis testing detection problem:

[0159]

[0160] Wherein, ω is the detection threshold, f(x PA ,x FDA |H1) and f(x PA ,x FDA |H0) are the joint probability density functions, H1 is the alternative hypothesis, H0 is the zero hypothesis, f(x PA ,x FDA |H1) is the joint probability density function of x PA ,x FDA under the condition of H1, and f(x PA ,x FDA |H0) is the joint probability density function of x PA,x FDA The joint probability density function, log is the logarithmic operation. When T > ω, the PA-FDA dual-mode radar detector judges it as H1, and when T < ω, the PA-FDA dual-mode radar detector judges it as H0.

[0161] It should be noted that the following process is an analysis of the detection performance of the signal-level fusion model of the PA-FDA dual-mode radar, specifically:

[0162] The expressions for updating the joint probability density function of the PA antenna array and the FDA antenna array under the alternative and null hypotheses, respectively, are as follows:

[0163]

[0164] Where, f(x) PA ,x FDA |H i ) is H i under the condition x PA ,x FDA The joint probability density function, where when i = 0 or i = 1, H0 is the null hypothesis and H1 is the alternative hypothesis, x PA For the PA antenna array to receive signals, x FDA For the FDA antenna array receiving signal, det() is used to retrieve the determinant of the matrix, where D = M. 2 +L, D is the dimension of the PA-FDA dual-mode radar received signal, M is the number of FDA antenna arrays, L is the number of PA antenna array elements; R = diag{R PA ,R FDA Let R be the noise plus interference background covariance matrix of the PA-FDA dual-mode radar, and diag{} be the constructed diagonal matrix. PA The noise plus interference covariance matrix of the PA antenna array. Let I be the noise power, n represent the noise, and I be the noise level. L Let j be an L-dimensional identity matrix. PA j represents the interference signal of the PA antenna array. PA =α j b PA (θ j );α j Let b be the target complex scattering coefficient of the interference signal. PA (θ j θ is the steering vector for the PA antenna array to receive interference signals. j For the angle of the interference signal, Represents the conjugate transpose operator; R FDA The noise plus interference covariance matrix of the FDA antenna array. is the noise power, n is the noise, is M 2 is the identity matrix of dimension M is the number of elements of the FDA antenna array, j FDA is the noise-like interference signal received by the FDA antenna array, is the complex coefficient of the interference signal, which obeys distribution, is the circularly symmetric complex Gaussian distribution with mean μ and variance σ 2 , is the interference power, θ j is the angle of the interference signal, denotes the Kronecker product, b FDA (θ j ) is the received interference signal steering vector of the FDA antenna array, θ j is the angle of the interference signal; is the signal level fusion model of the PA-FDA dual-mode radar, α is the complex scattering coefficient of the target, is the transmit-receive steering vector space of the PA-FDA dual-mode radar, diag{} is the diagonal matrix construction, b PA (θ) is the receive steering vector of the PA antenna array, a(R, θ) is the transmit steering vector of the FDA antenna array, denotes the Kronecker product, b FDA (θ) is the receive steering vector of the FDA antenna array, is a complex set of dimension D x 2, is the constant coefficient vector of the PA-FDA dual-mode radar, η1 and η2 are the constant coefficients of the PA antenna array and the FDA antenna array respectively, T is the transpose operation, is a complex set of dimension 2 x 1;

[0165]

[0166] where i represents the hypothesis number, H0 when it takes 0 represents the null hypothesis, and H1 when it takes 1 represents the alternative hypothesis, n is the noise vector, M is the number of elements of the FDA antenna array in the PA-FDA dual-mode radar, L is the number of PA antenna elements in the PA-FDA dual-mode radar, b PA (θ) is the receive steering vector of the PA antenna array, a(R, θ) is the transmit steering vector of the FDA antenna array, where R and θ are the target distance and angle respectively, b FDA (θ) is the receive steering vector of the FDA antenna array;

[0167] The PA-FDA dual-mode radar system decision criterion is updated as:

[0168]

[0169] wherein, n is a noise component;

[0170] The hypothesis testing detection problem of the updated PA-FDA dual-mode radar system is distributed as:

[0171]

[0172] wherein, Re() is the real part of the output complex number; the false alarm probability and the detection probability of the PA-FDA dual-mode radar system are respectively expressed as:

[0173]

[0174]

[0175] wherein, P fa is the false alarm probability, P d is the detection probability, is an error function.

[0176] S102, constructing a GLRT detector

[0177] S1021, proposing a multi-target hypothesis testing problem

[0178] In order to detect whether there is a target in the detected distance unit, first, a multi-target hypothesis testing detection problem is proposed, which is expressed as:

[0179]

[0180] wherein, x is the data to be detected, n is a noise component, x k is the kth training sample, n k is the noise in the kth training sample, k is the training sample serial number, K is the number of training samples, V is the PA-FDA dual-mode radar transmitting-receiving steering vector matrix, and η is the coefficient vector of the PA-FDA dual-mode radar;

[0181] S1022, proposing a multi-target hypothesis testing detection problem decision criterion based on a generalized likelihood ratio test criterion

[0182] In the above step S1021, n and n k are independent and identically distributed, and are zero-mean complex circularly symmetric Gaussian distributions with R is a positive definite covariance matrix, and according to the generalized likelihood ratio test criterion, the GLRT detector can be obtained in the following manner, and its expression is:

[0183]

[0184] wherein, is the maximum of R and η, R = diag{R PA ,R FDA}, R is the PA-FDA dual-mode radar background covariance matrix, diag{} is a diagonal matrix, η is the coefficient vector of the PA-FDA dual-mode radar, f(x,X|H1) is the joint probability density function of x and X under the condition of H1, f(x,X|H0) is the joint probability density function of x and X under the condition of H0, x and X are respectively the to-be-detected data and the training sample data, and it can be understood that the to-be-detected data is the measured data, the echo signal received by the PA-FDA radar, and the training sample data is the detection background data composed of Monte Carlo experiments according to the relevant distribution, is a detection threshold value;

[0185] When GLRT(x, X) > T , the GLRT detector judges H1, and when GLRT(x, X) < T , the GLRT detector judges H0.

[0186] It should be noted that the PA antenna array and the FDA antenna array are respectively under the alternative hypothesis and the null hypothesis, and the PDFs of x and X under H i (i = 0, 1) are as follows:

[0187]

[0188] Based on the generalized likelihood ratio test criterion, the GLRT detector is obtained, and the expression is as follows:

[0189]

[0190] In the above, T GLRT is the GLRT detection statistic of the PA-FDA dual-mode radar, ∑ is a summation symbol, S is the correlation matrix of the signal x k , x k represents the kth training sample, represents the conjugate transpose, and () -1 is the inverse;

[0191] wherein, is a comparison between the detection statistic and the threshold value, when GLRT(x, X) > T , the GLRT detector judges H1, and when GLRT(x, X) < T , the GLRT detector judges H0;

[0192] In the above, there is a mismatch between x and V η in the above, x is composed of multi-target signals, and the mismatch between the GLRT detector and the echo data can be regarded as s0 = V ηthe mismatch between s and s;

[0193] wherein wherein Q is the number of targets, and when a mismatch occurs, the information distribution of the GLRT detector is updated as

[0194]

[0195] wherein ρ GLRTmis is the loss factor, whose distribution is

[0196] S1023, PFA and PD derivation

[0197] ρ GLRTmis The PDF of ρ can be expressed as

[0198]

[0199]

[0200] According to the above analysis, in the first step of multi-target detection, the probability of false alarm (PFA) and the probability of detection (PD) of the GLRT detector are respectively

[0201]

[0202]

[0203]

[0204] When there is only one target in the measured distance unit, i.e. there is no mismatch, the information distribution of the GLRT detector is updated as

[0205]

[0206] wherein the non-centrality parameter δ GLRTmis is reduced to ρ GLRT As the loss factor of the complex beta distribution, has K-(D-2)+1 and D-2 degrees of freedom, and its PDF is expressed as

[0207]

[0208] From the above formula, it can be seen that although there is a mismatch between the GLRT detector and the echo data, the determination of the threshold still has the constant false alarm rate (CFAR) characteristic; in addition, and ρ GLRTmisIn the first step, the PD is determined jointly, thus, the GLRT detector PD is related to the signal-to-noise ratio of multiple targets and the angle difference between the detected target and the mismatched target, it is pointed out that, since the steering matrix is Vandermonde structure, the target with angle difference greater than 3dB beam width can be regarded as approximately orthogonal, especially for the target with low signal-to-noise ratio;

[0209] Considering that multiple targets in the embodiment are located on different beams, it can be obtained that:

[0210]

[0211]

[0212] wherein, and s i = V i η i define the signal of the ith target.

[0213] When the SNR of the mismatched target is low, the non-centrality parameter and are related to the mismatched signal and the assumed signal respectively, so that the GLRT detector PD is approximately related to the whitened power of the mismatched signal and the assumed signal. It is pointed out that, the mismatched signal in the GLRT not only exists in but also exists in

[0214] S103, constructing a CCBD-GLRT detector

[0215] S1031, constructing an iterative steering matrix based on the target information detected by the GLRT detector, and updating the multiple target hypothesis testing detection problem, the expression of which is:

[0216]

[0217] wherein, is a steering vector with 2(S+1 columns, B S = [η1,...,η S ] T and B S+1 = [B S ,...,η S+1 ] T are coefficient vectors with 2S and 2(S+1) elements respectively;

[0218] It is noted that the detection problem is similar to the target detection problem in a subspace interference environment, where the subspace interference corresponds to the previously detected target in our work. Since the interference can be suppressed before detection, the previously detected target can be cancelled to avoid affecting the detection of other possible targets. In the above equation, the detection problem is transformed by a unitary matrix, which is constructed based on the previously detected target; according to the polar decomposition property, a full column rank matrix can be decomposed into the product of a semi-unitary matrix and a Hermitian matrix. Therefore, the steering vector can be decomposed as

[0219]

[0220] where, is a steering matrix with 2S rows, is a semi-unitary matrix, is a Hermitian matrix; in this way, the augmented matrix is a unitary matrix, where, is composed of the last D-2S columns of the unitary matrix obtained by singular value decomposition of , and the orthogonal transformation matrix is obtained as

[0221] S1032, constructing a CCBD-GLRT detector

[0222] Using the constructed The previously detected target can be cancelled before another target is detected; the above hypothesis testing detection problem is converted into

[0223]

[0224] where, Similarly, the training sample data is transformed by the orthogonal transformation matrix , and the expression is

[0225]

[0226] X = [x1, x2,..., x k ];

[0227] where x k is the kth training sample, w K is the kth training sample after being transformed by the orthogonal transformation matrix, is a complex set of (D-2S) x K dimensions, D is the dimension of the PA-FDA dual-mode radar received signal, S is the number of known targets, and K represents the number of training samples; in the above equation, ​To ensure nonsingularity, the number of secondary data is limited, i.e. the CCBD-GLRT detector is valid.

[0228] To simplify the process, the detection problem can be updated as:

[0229]

[0230] where y is the data to be detected, w is the transformed data using the orthogonal transformation matrix The expression of the transformed noise n, is the transformed search target steering vector using the orthogonal transformation matrix The transformed search target steering vector, i.e.

[0231] S1033, deriving the CCBD-GLRT detector based on the generalized likelihood ratio test criterion

[0232] In the above step S1032, According to the generalized likelihood ratio test criterion, the CCBD-GLRT detector can be expressed as:

[0233]

[0234] where, When S = 0, the CCBD-GLRT detector is reduced to the GLRT detector;

[0235] Since the CCBD-GLRT detector is similar to the target detection detector in the subspace interference, when K ≥ D, the CCBD-GLRT detector is equivalent in performance to the cGLRT detector. It should be noted that when Q > S + 1, there is a mismatch between the CCBD-GLRT detector and the echo data; the distribution of the detection statistic T CCBD The mismatch between the CCBD-GLRT detector and the echo data can be seen as the mismatch between t0 = Tη S+1 and

[0236] where, defines the multi-target signal transformed by Q,

[0237] S1034, PFA and PD derivation

[0238] Similar to the cGLRT detector, the distribution of the CCBD-GLRT detector is:

[0239]

[0240] where, p​CCBDmis For the loss factor distribution being comprises p CCBDmis The PDF of

[0241]

[0242]

[0243] The PFA of the CCBD-GLRT detector is

[0244]

[0245] The PD of the CCBD-GLRT detector is

[0246]

[0247]

[0248] When the number of targets is S+1, that is, there is no mismatch, T CCBD The distribution of

[0249]

[0250] where, The loss factor p CCBD The distribution is The PDF of

[0251]

[0252] and is updated as

[0253]

[0254]

[0255] It can be seen that the PD is related to the whitening power of the signal, where the detected target passes through and the mismatched target passes through It should be noted that the number of targets in the CCBD-GLRT detector is less than that in the GLRT detector, and the performance loss will decrease with the increase of the number of known targets.

[0256] S104, iterative multi-target detection

[0257] Based on the designed GLRT detector and CCBD-GLRT detector, multi-target detection is carried out in an iterative detection scheme.

[0258] The GLRT detector based on design detects one target (the target with the largest SNR) in the multiple targets, then uses the CCBD-GLRT detector to detect the second target based on the previously detected target, and detects the remaining targets according to the knowledge of the previous detection.

[0259] The number of iterations required for Q targets is Q+1, and the number of targets does not need to be known in the process of detecting multiple targets; when the condition is maintained in the entire spatial angle domain CCBD (θ i ) < ζ, the iterative detection process will stop, and the iterative algorithm includes the following flow:

[0260] 1. Input x, X, PFA parameter value; 2. Initialization: S = 0, θ = Null; 3. Calculate T GLRT and 4. Perform the following iterative process, then, S = S + 1; Calculate T CCBD and θ S ; determine ζ and S; while max[T CCBD (θ i )] > ζ, do, S = S + 1; Update T CCBD , update [θ1,..., θ S ]; update ζ, update S; end while, end if; 5. θ = [θ1, θ2,..., θ S ]; 6. Output θ.

[0261] S105. Parameter optimization based on CD algorithm

[0262] In the Q-1 steps of execution, as the number of iterations increases, the mismatch between the detector and the echo data becomes smaller and smaller; after all the targets θ = [θ1, θ2,..., θ Q ] are found, the detected targets θ can be updated based on the coordinates down (CD) algorithm to obtain better performance.

[0263] The targets detected through the Q update steps can be sequentially updated as For example, in the first step, θ1 can be updated as where T CCBD is calculated through [θ2,..., θ Q ].

[0264] CD-based optimization algorithm includes the following flow:

[0265] 1. Input the θ parameter value; 2. Initialize q = 1, θ′ = [θ2,...,θ Q 3. Calculate ζ, S = Q - 1; 4. Execute the following parameter optimization algorithm, while q ≤ Q, do, calculate T CCB Calculate θ′; q = q + 1; if q ≤ Q - 1 then, else end if, end while 5. Output

[0266] In one optional embodiment of this application, the effects of the present invention are further illustrated by combining simulation experiments.

[0267] Considering the PA-FDA dual-mode radar system, and using its optimal detection performance as a reference, the effectiveness of the proposed multi-target detection method was verified through numerical results. The simulation parameters of the radar system are shown in Table 1.

[0268] Table 1 PA-FDA Dual-Mode Radar Parameters

[0269]

[0270] Three targets at the same distance but different angles were considered, and the parameters are shown in Table 2.

[0271] Table 2 Target Parameters

[0272]

[0273] For the interfering environment, the background consists of Gaussian white noise and noise-like interfering devices, and their distribution... in j is the turning vector of the jammer (j = j PA Let PA be the expression, and j = j FDA (Referring to FDA). It is assumed that the jammer considered here is within the same range as the target at a 45-degree angle.

[0274] Please see Figure 3 , Figure 3 This is a schematic diagram illustrating the relationship between false alarm probability and detection probability when the SNR is -7dB, provided in an embodiment of the present invention. As shown in the figure, the optimal receiver operating curves (ROCs) for three targets—PA radar system, FDA radar system, and PA-FDA dual-mode radar system—are displayed, where the numbers "1", "2", and "3" represent the target index, respectively. The signal-to-noise ratio in this embodiment is ||α||. 2 noise power Essentially, it's the input signal-to-noise ratio that doesn't match the beammap gain; byFigure 2 As can be seen, the ROC of the mainlobe target is much higher than that of the sidelobe target; when PFA is 1e -4 -7dB, the optimal PD of FDA is 0.9, which is lower than that of the mainlobe target with PA; it can be seen that the wide coverage of FDA in a single pulse is at the cost of a certain PD loss; it should be noted that when SNR is-7dB, the PDs of the first target with PA and PA-FDA dual-mode radar are both first when PFA is higher than 10-8, because the PD is related to the received signal-to-noise ratio after beamforming, and depends on the signal-to-noise ratio of the target and the aperture of the radar.

[0275] Please refer to Figure 4 , Figure 4 is a relationship diagram between detection probability and target angle under different radar systems provided by the embodiment of the application, Figure 4 shows the optimal PDs in the full spatial angle domain, and SNR and PFA are set to-7dB and 10 -4 -8 respectively; as shown in Figure 4 , the optimal detection performance of the PA-FDA dual-mode radar in the full spatial angle domain is higher than that of PA and FDA; thus, the PA-FDA dual-mode radar provided in the embodiment can enhance the PD (Probability of detection).

[0276] Please refer to Figure 5 , Figure 5 is a relationship diagram between corresponding detection probability and signal-to-noise ratio under different radar systems provided by the embodiment of the application, Figure 5 shows the detection probability and signal-to-noise ratio of PA radar system, FDA radar system and PA-FDA dual-mode radar system; as shown in Figure 4 , when SNR is-7dB, the PDs of all targets from different directions are 0.9, which is 9dB higher than that of FDA for the mainlobe target of PA radar; compared with the target in the mainlobe of PA, the PDs of the second and third targets are lower, which are 14dB and 18dB respectively; thus, PA is not conducive to detecting multiple targets at the same time; in the developed PA-FDA dual-mode radar, the optimal performance of PA-FDA dual-mode for the mainlobe target is 0.5dB higher than that of PA, and the optimal performance for the sidelobe target is slightly better than that of FDA; thus, the PA-FDA dual-mode radar provided in the embodiment has better detection capability in a multi-target scenario.

[0277] Please refer to Figures 6-8 as shown, Figure 6is a schematic diagram of a GLRT detector detecting a target according to an embodiment of the present application, Figure 7 is a schematic diagram of a CCBD-GLRT detector detecting a target according to an embodiment of the present application, Figure 8 is another schematic diagram of a CCBD-GLRT detector detecting a target according to an embodiment of the present application; Figure 6 shows the result of detecting a target using a GLRT detector, Figure 7 shows the result of detecting a target using a GLRT detector, and detecting a target using a CCBD-GLRT detector, Figure 8 shows the result of detecting a target using a CCBD-GLRT detector, and detecting a target using a CCBD-GLRT detector again; wherein "mc" and "th" represent PDs obtained using Monte Carlo simulation threshold and theoretical result, respectively; Figure 6 is a result of detecting a target using a GLRT detector in the first step of iterative multi-target detection, and it can be seen that the PDs of the PA and PA-FDA dual-mode array are higher than that of the FDA; Figure 7 is a result of detecting a target using a CCBD-GLRT detector in the second step of iterative multi-target detection based on the target detected in step one, and the FDA detects a second target with a PD of 0.6, while the PA detects a second target with a PD of 0.06 because it cannot detect the target of the sidelobe; Figure 8 is a result of detecting a target based on the targets detected in the previous two steps, and the FDA detects a third target with a PD of 0.62, while the PA does not detect the third target, and thus the PA-FDA dual-mode radar detects a third target with a PD of 0.6.

[0278] Please refer to Figure 9 , Figure 9 is a schematic diagram of a result based on CD optimization according to an embodiment of the present application, wherein "initial" is a result obtained by Figure 6 , Figure 7 and Figure 8 , and "CD" represents the "initial" result optimized using CD; it can be seen from Figure 6 , Figure 7 and Figure 8 that the performance of the initial optimization result and the optimization result based on CD is the same for the target at -35 degrees, because there is no mismatch in the third step; thus, because the mismatch in the model is eliminated, the target detection probability at 0 degrees and 20 degrees is improved.

[0279] Please refer to Figure 10 , Figure 10 is a schematic diagram of a relationship curve of PD and SNR of different targets according to an embodiment of the present application; wherein, Figure 10The schematic diagram of θ1=0deg is shown, θ1 can also be 20deg and-35deg, which are not limited in the present application; the Monte Carlo results of the CCBD-GLRT detector and the cGLRT are consistent, when we detect the first and second targets, mismatching occurs because there are three targets; in Figure 10 As shown in the figure, the performance of the PA-FDA dual-mode radar is close to that of the PA, and is about 8dB better than that of the FDA.

[0280] Please refer to Figures 11-13 As shown in the figure, Figure 11 is a schematic diagram of the relationship between the GLRT detection probability and the target angle provided by the embodiment of the present application, Figure 12 is another schematic diagram of the relationship between the GLRT detection probability and the target angle provided by the embodiment of the present application, Figure 13 is another schematic diagram of the relationship between the GLRT detection probability and the target angle provided by the embodiment of the present application; Figure 11 The full spatial angle domain PD is shown in the figure, it can be seen that the PD loss is caused by the mismatch between the detection model and the test data; Figure 12 The result figure of the CCBD-GLRT detector is shown in the figure, the target is at 0 degree, and the second step model is executed; obviously, the PD loss is lower than that of the first step model, because in the second step model, the number of mismatched targets is one, while in the first step model, the number is two; Figure 13 The CCBD-GLRT detector is executed in the third step model, the target is known to be at 0 degree and 20 degrees, there is no mismatch between the detection model and the test data, so there is no PD loss in the third step.

[0281] Please refer to Figure 14 As shown in the figure, Figure 14 is a schematic diagram of the relationship between the signal-to-noise ratio of the mismatched target and the detection probability under different radar systems provided by the embodiment of the present application, the PDs are obtained by 10 4 Monte Carlo trajectories, the angles of the detected target and the mismatched target are 20 degrees and-35 degrees respectively, and the SNRs of the detected target are 0dB and-7dB respectively; from Figure 14 It can be seen that when the SNR of the mismatched signal is low, the PD loss is very small; when the signal-to-noise ratio of the mismatched target is-7dB, the PD loss of the target with-7dB is less than 0.0341; with the increase of the signal-to-noise ratio of the mismatched target, the PD loss increases; for the same signal-to-noise ratio of the mismatched target, the performance loss of the PD is smaller for the detected target with higher signal-to-noise ratio.

[0282] The above is further detailed description of the present application in combination with specific preferred embodiments, and cannot be deemed as limitation of the specific implementation of the present application to these descriptions. For those skilled in the art to which the present application belongs, without departing from the concept of the present application, a number of simple deductions or substitutions can be made, and all should be deemed as falling within the protection scope of the present application.

Claims

1. An iterative multi-target detection method based on PA-FDA dual-mode radar, characterized in that, The method comprises the following steps: constructing a signal level fusion model of the PA-FDA dual-mode radar, wherein the signal level fusion model of the PA-FDA dual-mode radar is constructed based on target signals received by a PA antenna array and a FDA antenna array, and the target signals received by the PA antenna array and the FDA antenna array are mixed with Gaussian white noise and noise-like interference; constructing a GLRT detector based on the signal level fusion model of the PA-FDA dual-mode radar; constructing a CCBD-GLRT detector based on the signal level fusion model of the PA-FDA dual-mode radar; detecting one of the multiple targets by using the GLRT detector and obtaining a detection result, and then detecting the remaining targets by using the CCBD-GLRT detector according to the detection result to obtain a final detection result; the process of constructing the CCBD-GLRT detector based on the signal level fusion model of the PA-FDA dual-mode radar comprises: constructing an iterative steering matrix based on target information detected by the GLRT detector and updating the multiple target hypothesis testing detection problem, and the expression is as follows: ； wherein is a matrix comprising a steering matrix of columns, , is a matrix of known transmit-receive steering vectors of S targets, is a steering vector of a search target, is a coefficient matrix of dimension is a coefficient matrix of dimension is a complex coefficient vector of the s-th target, denotes a complex coefficient vector of a search target, is a noise component; decomposing the iterative steering matrix, and the expression is as follows: ； wherein, is a semi-unitary matrix, is a Hermitian matrix, , is a generating subspace, is an augmented unitary matrix, consists of the last D -2 S columns of a unitary matrix obtained by singular value decomposition of , then the orthogonal transformation matrix is ; Utilizing an orthogonal transformation matrix Update the multi-target hypothesis test detection problem in the previous step, which is expressed as: ； wherein is the data to be detected, , is transformed by a orthogonal transformation matrix noise after transformation expression, is the search target steering vector transformed by the orthogonal transformation matrix , , i.e. ; Utilizing an orthogonal transformation matrix The transformation of the training sample data is expressed as: ； ； wherein, is the i-th training sample, is the i-th training sample transformed by the orthogonal transformation matrix, is the i-th training sample transformed by the orthogonal transformation matrix, is the i-th training sample transformed by the orthogonal transformation matrix, is a set of complex numbers of dimension, is the number of known targets, is the dimension of the PA-FDA dual-mode radar received signal, is the number of known targets, denotes the number of training samples; Based on the generalized likelihood ratio test criterion, using orthogonal transformation matrix The transformed hypothesis test detection problem, the CCBD-GLRT detector is constructed, and its expression is: ； wherein is the transformed data to be detected, is the conjugate transpose, , is the correlation matrix of the transformed training samples, is the inverse, is the signal covariance matrix of the K targets, is the inverse, is the orthogonal transformed steering vector of the search target, is the orthogonal transformed steering vector of the search target; wherein, to determine if the second detection threshold, when the detector determines that when the detector determines that .

2. The PA-FDA dual-mode radar based iterative multi-target detection method according to claim 1, characterized in that, before the step of constructing the signal level fusion model of the PA-FDA dual-mode radar, the method further comprises the following steps: obtaining a transmitting signal of the PA antenna array, and the expression is as follows: ； ； wherein, is a pulse function, is time, is a pulse repetition time is a variable time within, is a pulse width, is an envelope of the PA antenna array transmit signal, is a carrier frequency of the PA antenna array, is Euler's number, is imaginary; obtaining a transmitting signal of the FDA antenna array, and the expression is as follows: ； ； wherein is a pulse function, is time, is a pulse repetition time is a variable time within, is a pulse width, is an envelope of a transmit signal corresponding to the th element of the FDA antenna array, is a carrier frequency of the th element of the FDA antenna array, , is a reference carrier frequency of the th element of the FDA antenna array, is a sequence number of the FDA antenna array, is a frequency increment value, satisfying , is Euler's number, is an imaginary number; Set the distance as and the angle as Any target, the echo data received by the first array element in the PA antenna array is: ； wherein, , N is the number of elements in the PA antenna array, is the complex scattering coefficient of the target, is the time delay of the target signal, is the element number of the PA antenna array, is the element number of the PA antenna array, is the weight added to the element number of the PA antenna array, is the weight added to the element number of the PA antenna array, is the conjugate, is the two-way delay of the PA antenna array; The echo data received by the Nth element in the FDA antenna array is: ​ ； in, , This represents the number of elements in the FDA antenna array. Let be the complex scattering coefficient of the target. For the target signal time delay, The first in the FDA antenna array Each array element, For the two-way delay of the FDA antenna array; after the echo signals received by the PA-FDA dual-mode radar are subjected to down-conversion and matched filtering related signal processing, target signals of the PA antenna array and the FDA antenna array are obtained respectively; the expression of the target signal of the PA antenna array is as follows: ； wherein, a target backscatter coefficient, a transmission gain term, a receive steering vector of the PA antenna array, is a set of complex numbers of dimension the expression of the target signal of the FDA antenna array is as follows: ； wherein, a target backscatter coefficient, a phase shift term due to a reference point, a transmit steering vector for the FDA antenna array, a receive steering vector for the FDA antenna array, is a set of complex numbers of dimension the target signal of the PA antenna array is mixed with Gaussian white noise and noise-like interference, and the expression is as follows: ； wherein is the received interference for the PA antenna array, denotes obeys is distributed, is a circularly symmetric complex Gaussian distribution with mean and variance , is the noise plus interference covariance matrix for the PA antenna array, , is the noise power, is the noise, is is the identity matrix of dimension is the noise-like interference signal received by the PA antenna array, , is the target complex scattering coefficient of the interference signal, is the interference signal steering vector received by the PA antenna array, is the angle of the interference signal, is the conjugate transpose operator; the target signal of the FDA antenna array is mixed with Gaussian white noise and noise-like interference, and the expression is as follows: ； where is the Gaussian white noise and the noise-like jamming received by the FDA antenna array, denotes obeys is distributed, is a circularly symmetric complex Gaussian distribution with mean and variance is a circularly symmetric complex Gaussian distribution with mean is the noise-plus-jamming covariance matrix of the FDA antenna array, , is the noise power, is the noise, is is the identity matrix of dimension M is the number of elements of the FDA antenna array, is the noise-like jamming signal received by the FDA antenna array, , is distributed, is a circularly symmetric complex Gaussian distribution with mean and variance is a circularly symmetric complex Gaussian distribution with mean and variance is the jamming power, is the jamming signal angle, denotes the Kronecker product, is the steering vector of the jamming signal received by the FDA antenna array, is the jamming signal angle.

3. The PA-FDA dual-mode radar based iterative multi-target detection method of claim 2, wherein, based on the target signal of the PA antenna array mixed with noise and the target signal of the FDA antenna array mixed with noise, the signal level fusion model of the PA-FDA dual-mode radar is constructed, and the expression is as follows: ； wherein is the transmit-receive steering vector matrix of the PA-FDA dual-mode radar, , is the diagonal matrix constructed, is the receive steering vector of the PA antenna array, is the transmit steering vector of the FDA antenna array, is the Kronecker product, is the receive steering vector of the FDA antenna array, is the is the set of complex numbers of dimension and are the target range and angle, respectively, is the coefficient vector of the PA-FDA dual-mode radar, wherein and are the constant complex coefficient vectors of the PA and FDA antenna array receive signals, respectively, , is the transmission gain term of the PA radar, , is the phase shift term of the FDA radar caused by the reference point, is the complex scattering coefficient of the target, is the transpose operation, is the is the set of complex numbers of dimension 4. The PA-FDA dual-mode radar based iterative multi-target detection method of claim 1, wherein, the process of constructing the GLRT detector based on the signal level fusion model of the PA-FDA dual-mode radar comprises: a multiple target hypothesis testing detection problem is proposed, and the expression is as follows: ； in, For the data to be tested, For noise components, For the first training samples, For the first Noise in each training sample The training sample number. The number of training samples, For PA-FDA dual-mode radar transmit-receive steering vector matrix, For the coefficient vector of the PA-FDA dual-mode radar; based on the generalized likelihood ratio test criterion, the decision criterion of the multiple target hypothesis testing detection problem can be expressed as: ； wherein, is the maximum of and , , is the PA-FDA dual-mode radar background signal matrix, is the constructed diagonal matrix, is the coefficient vector of the PA-FDA dual-mode radar, is the joint probability density function of under the condition is the joint probability density function of under the condition is the joint probability density function of under the condition and are the to-be-detected data and the training sample data, respectively, is a detection threshold. When the GLRT detector decides that When the GLRT detector decides that ; based on the generalized likelihood ratio test criterion, the GLRT detector is obtained, and the expression is as follows: ； wherein is the GLRT detection statistic for the PA-FDA dual-mode radar, , is the summation symbol, is the signal correlation matrix, denotes the k th training sample, denotes the conjugate transpose, is the inverse; wherein, For comparing the detection statistic and the threshold size, the GLRT detector determines that when the GLRT detector determines that when .

5. The PA-FDA dual-mode radar based iterative multi-target detection method of claim 1, wherein, the method further comprises the following steps: parameters are optimized by using a coordinate descent algorithm, and the process comprises the following steps: The target parameters outputted by the GLRT detector and the CCBD-GLRT detector are optimized; wherein the target parameters to be optimized are the angles ;​​ sequentially optimizing target parameters to ; wherein, optimizing target parameters , using target parameters as known target transmit-receive steering matrices in the CCBD-GLRT detector iterative steering matrix , optimizing search targets based on the CCBD-GLRT detector through steering vectors optimizing target parameters , obtaining optimized parameters , replacing , completing the optimization of the target ; optimizing targets , using the optimized target and target , optimizing the target , obtaining optimized target ; sequentially optimizing the remaining targets, completing the iteration of the targets times for detection, obtaining optimized target .

6. The PA-FDA dual-mode radar based iterative multi-target detection method of claim 1, wherein, the PA-FDA dual-mode radar comprises a PA antenna array and a FDA antenna array, wherein the PA antenna array comprises 8 transmitting elements, the FDA antenna array comprises 8 transmitting elements, the elements in the PA antenna array and the elements in the FDA antenna array are arranged in an array, and the spacing between adjacent elements is 0.1 m to 0.2 m.

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