CN107390197B - Radar self-adaption sum-difference beam angle measurement method based on feature space - Google Patents

Radar self-adaption sum-difference beam angle measurement method based on feature space Download PDF

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CN107390197B
CN107390197B CN201710660475.7A CN201710660475A CN107390197B CN 107390197 B CN107390197 B CN 107390197B CN 201710660475 A CN201710660475 A CN 201710660475A CN 107390197 B CN107390197 B CN 107390197B
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CN107390197A (en
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曹运合
曾丽
凤宏晓
周生华
谢荣
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Xi'an Thunder Driven Electronic Technology Co ltd
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Xidian University
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    • 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
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Abstract

The invention discloses a radar self-adaption sum and difference beam angle measurement method based on a characteristic space, which mainly comprises the following steps: determining an even linear array, wherein the even linear array comprises M array elements, J +1 signal sources exist in the detection range of the even linear array, the J +1 signal sources transmit J +1 incident signals to the even linear array, and the J +1 incident signals comprise target signals; further determining M-dimensional signals received by the uniform linear array at the time t; dividing the uniform linear arrays of M array elements into L sub-arrays, and obtaining L-dimensional dimensionality reduction signal output of the uniform linear arrays at the time t according to M-dimensional signals received by the uniform linear arrays at the time t; calculating to obtain the sum beam weight of J +1 incident signals received by L sub-arrays; calculating to obtain the difference beam weight W of J +1 incident signals received by L sub-arraysdiff(ii) a Receiving the sum beam weight W of J +1 incident signals according to L sub-arrayssumL subarrays receive difference beam weight W of J +1 incident signalsdiffAnd outputting the L-dimensional dimensionality reduction signal of the uniform linear array at the time t, and calculating to obtain the actual incoming wave direction of the target signal.

Description

Radar self-adaption sum-difference beam angle measurement method based on feature space
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a radar self-adaption and difference beam angle measurement method based on a feature space, which is suitable for detecting the actual position of a target by a radar under the condition of interference.
Background
Due to the wide application prospect of the array signal processing algorithm, the array signal processing algorithm is developed quite rapidly in recent years, and the self-adaptive beam forming also receives more attention; under ideal conditions, the adaptive beam forming can effectively reserve a desired signal, suppress interference signals and clutter and enable the output signal-to-interference-and-noise ratio of the array to be maximum. However, various errors exist in the actual system, including covariance estimation error caused by limited adaptive samples, pointing error of constrained steering vectors, and various system errors, such as array element position error, array element amplitude-phase error, mutual coupling between array elements, channel frequency characteristic mismatch, etc., where the adaptive beam performance is greatly degraded or even completely failed, which is more obvious especially when the covariance matrix contains a desired signal.
Most of the traditional adaptive beam forming methods are researched based on array element-level antenna arrays to form array element-level beam forming methods, but with the popularization and use of large radar arrays, the disadvantages of the array element-level beam forming methods are gradually highlighted: the computation amount is quite large, and the cost of software and hardware for realizing the system is also quite high; because the sum and difference beam patterns play a unique role in realizing angle estimation and tracking, the sum and difference beam patterns are widely applied to phased array radar and synthetic aperture sonar, so that the technology is always valued by a plurality of scholars and has a plurality of results. However, when there is interference, the adaptive signal processing affects the weight vectors of the sum and difference beams while suppressing the interference, so that the sum and difference directional diagram is distorted near the main lobe, resulting in a difference between the adaptive angle finding curve and the normal sum and difference angle finding curve, and bringing a deviation to the angle measurement, thereby causing the performance of the sum and difference angle measurement to be reduced or even to be invalid.
Disclosure of Invention
In view of the above-mentioned deficiencies of the prior art, the present invention aims to provide a radar adaptive and difference beam angle measurement method based on a feature space, which can reduce the complexity of an array by using a sub-array, and can maintain a monopulse angle measurement in the presence of interference, thereby maintaining good angle measurement performance; and a new method is used for obtaining the difference beam weight, so that the actual direction of the target is easy to obtain, and the engineering is easy to realize.
The main ideas of the invention are as follows: carrying out dimensionality reduction processing on the received signals of the uniform linear array to obtain sub-array received signals, and carrying out eigenvalue decomposition on a covariance matrix of the sub-array received signals to obtain a signal subspace and a noise subspace; under the condition that an output expected signal is unchanged, the variance output by the uniform linear array is minimized, the optimal weight of the submatrix after dimension reduction is solved, and then the optimal weight is projected to a signal subspace to obtain a self-adaption and a beam optimal weight based on a feature space; then, considering the condition of interference, in order to maintain the single pulse angle measurement performance, a new linear relation of the difference beam weight is provided as a constraint condition for calculating the difference beam weight, the minimum power of the output signal of the difference beam is taken as a target function, and the difference beam weight and a single pulse ratio curve are calculated, so that the actual direction of the target is easy to obtain.
In order to achieve the technical purpose, the invention is realized by adopting the following technical scheme.
A radar self-adaption sum and difference beam angle measurement method based on feature space comprises the following steps:
step 1, determining an even linear array, wherein the even linear array comprises M array elements, J +1 signal sources exist in a detection range of the even linear array, the J +1 signal sources transmit J +1 incident signals to the even linear array, and the J +1 incident signals comprise target signals; further determining M-dimensional signals received by the uniform linear array at the time t;
wherein t represents a time variable, M represents the number of array elements included in the uniform linear array, and M, J are positive integers greater than 0 respectively;
step 2, dividing the uniform linear arrays of M array elements into L sub-arrays, and obtaining L-dimensional dimensionality reduction signal output of the uniform linear arrays at the time t according to M-dimensional signals received by the uniform linear arrays at the time t;
wherein, L represents the number of sub-arrays contained after the uniform linear array of M array elements is divided, and L is a positive integer greater than 0;
step 3, calculating to obtain the sum beam weight W of J +1 incident signals received by L sub-arrayssum；
Step 4, calculating to obtain the difference beam weight W of J +1 incident signals received by L sub-arraysdiff；
Step 5, receiving the sum beam weight W of J +1 incident signals according to L sub-arrayssumL subarrays receive difference beam weight W of J +1 incident signalsdiffAnd outputting the L-dimensional dimensionality reduction signal of the uniform linear array at the time t, and calculating to obtain the actual incoming wave direction of the target signal.
Compared with the prior art, the invention has the following advantages:
under the condition of interference, the existing sum and difference beam angle measurement method has the advantages that adaptive signal processing influences the weight vectors of sum and difference beams while inhibiting interference, so that a sum and difference directional diagram is distorted, an adaptive angle identification curve is different from a common sum and difference angle identification curve, and larger deviation is brought to angle measurement, and the performance of the sum and difference angle measurement is reduced or even fails; the invention uses the sub-array, thereby reducing the complexity of the array, not only having small operand and fast convergence speed, but also greatly reducing the cost of hardware and software; the key point is that under the condition of interference, the single-pulse angle measurement method can be maintained, the robustness is good, the correct angle measurement performance is kept, and the actual position of the target can be effectively and accurately measured under the interference environment.
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The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
FIG. 1 is a flow chart of a radar adaptive sum and difference beam angle measurement method based on feature space according to the present invention;
FIG. 2 is a sum and difference beam pattern of the method of the present invention;
FIG. 3 is a graph of single pulse ratio obtained by the method of the present invention;
FIG. 4 is a sum and difference beam pattern of the method of the present invention under amplitude and phase error conditions;
FIG. 5 is a graph of single pulse ratio obtained by the method of the present invention under amplitude-phase error conditions.
Detailed Description
Referring to fig. 1, it is a flow chart of a radar adaptive sum difference beam angle measurement method based on feature space of the present invention; the radar self-adaption and difference beam angle measurement method based on the feature space comprises the following steps:
step 1, determining an even linear array, wherein the even linear array comprises M array elements, the spacing between the array elements is d, the directional diagram of the M array elements is isotropic, J +1 signal sources exist in the detection range of the even linear array, the J +1 signal sources transmit J +1 incident signals to the even linear array, the J +1 incident signals comprise a target signal and J interference signals, and the J +1 incident signalsThe signals are narrow-band signals respectively, the wavelengths of the signals are lambda, and the incoming wave direction of the ith incident signal is thetaiI ∈ {1,2, …, J +1}, the incoming wave directions of J +1 incident signals are different and are respectively theta1,θ2,…,θi,…,θJ+1。
J +1 signal sources transmit J +1 incident signals to the uniform linear array, each array element receives J +1 irrelevant narrowband signals respectively, and the J +1 irrelevant narrowband signals received by the mth array element are recorded as sm(t)，
sm(t)＝{sm,1(t),sm,2(t),…,sm,i(t),…,sm,J+1(t)}，m∈{1,2,…,M}，sm,i(t) represents the ith narrowband signal received by the mth array element; then, the M-dimensional signal received by the uniform linear array at the time t is x (t), and the expression thereof is:
Figure BDA0001370439230000031
Figure BDA0001370439230000041
n(t)＝[n1(t),n2(t),…,nm(t),…,nM(t)]T
wherein, i ∈ {1,2, …, J +1}, corresponds to the target signal when i is 1, and corresponds to the interference signal when i is not equal to 1, respectively, xm(t) represents a signal received by the mth array element in the uniform linear array at the time t, wherein the signal received by the mth array element in the uniform linear array at the time t is J +1 irrelevant narrow-band signals received by the mth array element; si(t) is the complex envelope of the ith incident signal at time t; a (theta)i) Is the guide vector of the ith incident signal, n (t) is Gaussian white noise of M array elements in the uniform linear array at the time of t, nm(T) Gaussian white noise of the m-th array element in the uniform linear array at the time T, superscript T represents transposition operation, d represents array element interval of the uniform linear array, and thetaiRepresenting the incoming wave direction of the ith incident signal, e representing an exponential function, superscript j representing an imaginary unit, and sin being a sine function; lambda [ alpha ]iIndicates the ith entryThe wavelength of the incident signal is equal to that of each incident signal; t represents a time variable, M represents the number of array elements contained in the uniform linear array, and M is a positive integer greater than 0.
Step 2, dividing the uniform linear array of M array elements into L sub-arrays, wherein the number of the array elements contained in each sub-array is g, g is a positive integer and is more than or equal to 1,
Figure BDA0001370439230000042
represents rounding up; and then calculating to obtain the guide vector of the ith incident signal after dividing L sub-arrays
Figure BDA0001370439230000043
Figure BDA0001370439230000044
Wherein, dividing the guide vector of the ith incident signal after L sub-arrays
Figure BDA0001370439230000045
The array comprises L elements, and the 1 st element in the L elements is 1 by taking the 1 st subarray as a reference unit, and the distance between the L elements is gd; g represents the number of array elements contained in each subarray, g is a positive integer, g is more than or equal to 1, d represents the array element spacing of the uniform linear array, and thetaiRepresenting the incoming wave direction of the ith incident signal, the superscript T representing transposition operation, e representing an exponential function, the superscript j representing an imaginary number unit, and sin being a sine function; lambda [ alpha ]iThe wavelength of the ith incident signal is represented, and the wavelength of each incident signal is equal.
The guide vector of each subarray takes the first array element in the corresponding subarray as a reference, so that the guide vector of the ith incident signal under the condition of the same incoming wave direction is obtained
Figure BDA0001370439230000046
The expression is as follows:
Figure BDA0001370439230000051
since the wavelength values of each incident signal are respectively equal, let λ represent the wavelength of each incident signal; and further calculating to obtain an L multiplied by M dimension reduction matrix T of L sub-arrays:
Figure BDA0001370439230000052
wherein the content of the first and second substances,
Figure BDA0001370439230000053
θ1indicating the incoming wave direction of the target signal, the incoming wave direction theta of the target signal1The method comprises the following steps of obtaining an L-dimensional reduced signal output M (T) of a uniform linear array at the time T, wherein the L-dimensional reduced signal output M (T) is obtained by reducing an M-dimensional signal x (T) received by the uniform linear array at the time T to L dimension according to an L × M-dimensional reduced matrix T of the L sub-arrays:
m(t)＝Tx(t)＝[m1(t),m2(t),…,ml'(t),…,mL(t)]T
wherein m isl'And (t) represents the output of the dimensionality reduction signal of the first sub-array of the uniform linear array at the time t, wherein L' is 1 and … L.
And 3, processing the subarrays, and calculating sum beam weight by using a feature space-based adaptive beam forming method.
3a) Under finite times of snapshot, a target signal and J interference signals are calculated to obtain a covariance matrix R of J +1 incident signals received by L sub-arrays, and characteristic value decomposition is carried out on the covariance matrix R to obtain:
Figure BDA0001370439230000054
wherein, the covariance matrix R of J +1 incident signals received by L sub-arrays contains L eigenvalues, and λ1≥λ2≥…≥λJ+1>λJ+2＝…＝λL＝σn 2，
Figure BDA0001370439230000055
Denotes the Gaussian white noise power of each subarray receiving J +1 incident signals, and will be1,λ1,…,λi',…,λJ+！Record as J +1 large eigenvalues, let λJ+2,λJ+3,…,λi”,…,λLIs recorded as L-J-1 small characteristic value, vi'Indicates a feature vector corresponding to the i 'th feature value, i' 1, …, J +1, vi”Denotes a feature vector corresponding to the i-th "feature value, i ″, J +2, …, L, λi'Denotes the i' th characteristic value, i ═ J +2, J +3, …, L, λi”Denotes the ith "eigenvalue, and the superscript H denotes the conjugate transpose operation.
Let the diagonal matrix composed of J +1 large eigenvalues be DsLet the diagonal matrix composed of L-J-1 small eigenvalues be DnLet the matrix formed by the eigenvectors corresponding to J +1 large eigenvalues be VsLet the matrix formed by the eigenvectors corresponding to the L-J-1 small eigenvalues be VnThe expressions are respectively:
Ds＝diag(λ1,λ2,…,λi',…,λJ+1)，Dn＝diag(λJ+2,λJ+3,…,λi”,…,λL)
Vs＝[v1,v2,…,vi',…,vJ+1]，Vn＝[vJ+2,vJ+3,…,vi”,…,vL]
wherein λ isi"means the i-th" characteristic value, DsRepresenting a diagonal matrix of J +1 large eigenvalues, DnDenotes a diagonal matrix composed of L-J-1 small eigenvalues, diag denotes a diagonal matrix, VsRepresenting a matrix formed by eigenvectors corresponding to J +1 large eigenvalues, and recording the matrix as a signal subspace; vnAnd representing a matrix formed by eigenvectors corresponding to the L-J-1 small eigenvalue, and marking the matrix as a noise subspace.
3b) In the linear constraint minimum variance criterion, the adaptive weight vector of L sub-arrays for receiving J +1 incident signals is W0：
W0＝μR-1a(θ1)
Wherein mu is a set coefficient and takes any nonzero constant as a value; r represents the covariance matrix of J +1 incident signals received by L subarrays, and the inverse operation is denoted by superscript-1, a (theta)1) A steering vector representing a target signal; the adaptive weight vector W0Is composed of a signal subspace and a noise subspace.
In the ideal case, the target signal is located in the signal subspace and therefore has
Figure BDA0001370439230000061
Thus, L subarrays receive adaptive weight vectors W of J +1 incident signals0Only the component of the signal subspace, the component of the noise subspace is 0; thereby calculating the sum beam weight W of J +1 incident signals received by L sub-arrayssumThe expression is as follows:
Figure BDA0001370439230000062
step 4, recording the difference beam weight of J +1 incident signals received by L sub-arrays as WdiffAnd receiving the sum beam weight W of J +1 incident signals according to the L sub-arrayssumDetermining a monopulse ratio curve, wherein the expression is as follows:
Figure BDA0001370439230000071
wherein is the slope of the monopulse ratio curve, a (θ)1) A guide vector, theta, representing the target signal1Showing the incoming wave direction of the target signal, theta showing the actual incoming wave direction of the target signal, theta showing the incoming wave direction of the target signal1Is the expected incoming wave direction of the target signal; wdiffRepresents the difference beam weight, W, of J +1 incident signals received by L subarraysdiff∈Cm×1，WsumRepresenting L sub-array receptions J +1Sum beam weight, W, of individual incident signalssum∈Cm×1，Cm×1A complex matrix representing m × 1 dimensions, S (k) represents a complex envelope of L sub-arrays receiving J +1 incident signals at time k, n (k) represents Gaussian white noise of L sub-arrays receiving J +1 incident signals at time k, k represents a time variable, and1-theta) represents the single pulse ratio,
Figure BDA0001370439230000072
indicating that L sub-arrays receive the sum beam of J +1 incident signals,
Figure BDA0001370439230000073
indicating that L subarrays receive the difference beam of J +1 incident signals, Re indicates the real portion operation.
The sum beam of J +1 incident signals received by the L sub-arrays is a beam formed by the J +1 incident signals received by the L sub-arrays in the direction of a target signal, and the difference beam of the J +1 incident signals received by the L sub-arrays is a beam formed by the J +1 incident signals received by the L sub-arrays after null steering in the direction of the target signal.
Under the condition of interference, the monopulse angle measurement performance is kept, and the optimal weight of the difference beam of J +1 incident signals received by the L sub-arrays is required to meet the monopulse ratio curve expression equation.
4a) Taking a monopulse ratio curve expression as a constraint condition for solving the difference beam of the L sub-arrays for receiving J +1 incident signals, taking the minimum power of the difference beam output signals of the L sub-arrays for receiving the J +1 incident signals as a target function, and constructing the following form to deduce the difference beam weight of the L sub-arrays for receiving the J +1 incident signals:
Figure BDA0001370439230000074
Figure BDA0001370439230000075
wherein, Re (W)diff HC) G' is a constraint conditionFunction, C in the expression of the single pulse ratio curve
Figure BDA0001370439230000081
Corresponding to a complex matrix of normalized form, C ∈ Cm×3，Cm×3A complex matrix representing m × 3 dimensions, g' representing the single pulse ratio curve expression (theta)1Theta), a (theta + △ theta) represents a steering vector deviating from the target actual direction △ theta in J +1 incident signals received by the L sub-arrays, a (theta) represents a steering vector deviating from the target actual direction △ theta in J +1 incident signals received by the L sub-arrays, a (theta- △ theta) represents a steering vector deviating from the target actual direction △ theta in J +1 incident signals received by the L sub-arrays, △ theta represents an angle of the target signal deviating from the beam center of J +1 incident signals received by the L sub-arrays, and a (theta)1) A guide vector, theta, representing the target signal1Indicating the incoming wave direction of the target signal, the incoming wave direction theta of the target signal1Is the expected incoming wave direction of the target signal; theta represents the actual incoming wave direction of the target signal, WdiffRepresents the difference beam weight, W, of J +1 incident signals received by L subarraysdiff∈Cm×1，WsumRepresents the sum beam weight, W, of J +1 incident signals received by L subarrayssum∈Cm×1，Cm×1A complex matrix representing m × 1 dimensions, S (k) represents a complex envelope of L sub-arrays receiving J +1 incident signals at time k, n (k) represents Gaussian white noise of L sub-arrays receiving J +1 incident signals at time k, k represents a time variable, and1-theta) represents the single pulse ratio,
Figure BDA0001370439230000082
sum beam representing J +1 incident signals received by L subarrays
Figure BDA0001370439230000083
It means that L sub-arrays receive the difference beam of J +1 incident signals, Re means the operation of the real part, min means the operation of taking the minimum value, and superscript H means the conjugate transpose operation.
And in the expression of the single pulse ratio curve (theta)1- θ) corresponds to a matrix of real numbers g' of:
g'＝[△θ 0 -△θ]
wherein R is1×3Representing a real number matrix of dimension 1 × 3.
4b) And solving the difference beam weight of J +1 incident signals received by the L sub-arrays.
Constructing a function by using a Lagrange multiplier method:
Figure BDA0001370439230000084
wherein f represents the function Re (W) according to the constraint conditiondiff HC) G' and
Figure BDA0001370439230000085
the resulting function, ζ represents the Lagrangian multiplier, ζ ∈ R3×1，R3×1Representing a real number matrix of dimension 3 × 1, R representing a covariance matrix of J +1 incident signals received by L sub-arrays, WdiffRepresenting the difference beam weights for the L subarrays receiving J +1 incident signals.
To solve the above problem, L sub-arrays are introduced to receive the difference beam weight W of J +1 incident signalsdiffComplex gradient of
Figure BDA0001370439230000091
The expression is as follows:
Figure BDA0001370439230000092
wherein the content of the first and second substances,
Figure BDA0001370439230000093
the derivation is shown, Re is the real part operation, and Im is the imaginary part operation.
Thereby calculating and obtaining the difference beam weight W of J +1 incident signals received by L sub-arraysdiffThe calculation expression is as follows:
Wdiff＝R-1C[Re(CHR-1C)]-Tg'T
wherein, the superscript-1 is the inversion operation, and Re represents the operation of the real part.
Step 5, receiving the sum beam weight W of J +1 incident signals according to L sub-arrayssumAnd L sub-arrays receive the difference beam weight W of J +1 incident signalsdiffObtaining the difference beam signal output y of L sub-arrays receiving J +1 incident signals△And L sub-arrays receiving J +1 incident signals and outputting a sum beam signal y∑And taking the real part of the ratio to obtain the self-adaptive monopulse ratio of the L sub-arrays, and further obtaining an angle △ (theta) of the target signal deviating from the beam center of the J +1 incident signal received by the L sub-arrays:
Figure BDA0001370439230000094
Figure BDA0001370439230000095
the superscript H represents the conjugate transpose operation, m (t) represents J +1 incident signals received by L sub-arrays at time t, and represents the slope of the monopulse ratio curve, and t represents a time variable.
According to the incoming wave direction theta of the target signal1And an angle △ (theta) of the target signal deviating from the beam center of the J +1 incident signal received by the L sub-arrays, and calculating to obtain the actual incoming wave direction theta of the target signal, wherein theta is theta1△ theta, obtaining the actual incoming wave direction of the target signal and simultaneously suppressing the incoming wave directions of J interference signals.
The effect of the present invention is further verified and explained by the following simulation test.
Simulation conditions: the simulation adopts a 40-element uniform linear array with the array element spacing of 0.6 wavelength, and the directional diagram of the array element antenna is isotropic; the data received by the uniform linear array comprises additive white Gaussian noise, the direction of a target signal is 0 degrees, interference signals are irrelevant to the target signal, and the dimension of each subarray is 1 multiplied by 4.
The signal transmitted by the uniform linear array is a linear frequency modulation signal, and the bandwidth of a target signal is 50 MHZ; the baseband frequency of a signal transmitted by the uniform linear array is 10GHZ, the sampling frequency is 100MHZ, the signal-to-noise ratio is 0dB, 5 far-field interference signals which are not related and are not related to a target signal are respectively incident from-8 degrees, -10 degrees, -19 degrees and 36 degrees, the dry-to-noise ratio is 31.6dB, and the sampling fast-beat number is 4096.
(II) simulating contents:
the simulation result of the sum and difference beam pattern obtained by the method of the invention is shown in fig. 2, and fig. 2 is the sum and difference beam pattern obtained by the method of the invention; the simulation result of the single pulse ratio curve obtained by the method of the invention is shown in FIG. 3, and FIG. 3 is the single pulse ratio curve obtained by the method of the invention; under the condition of amplitude-phase errors, the sum-difference beam pattern obtained by the method is adopted, the simulation result is shown in figure 4, and figure 4 is the sum-difference beam pattern obtained under the condition of amplitude-phase errors; the simulation result of the single pulse ratio curve obtained by the method of the invention under the condition of amplitude-phase error is shown in fig. 5, and fig. 5 is the single pulse ratio curve obtained by the method of the invention under the condition of amplitude-phase error.
(III) simulation result analysis:
as can be seen from fig. 2 and 4, the deep null is formed in the interference direction by using the method of the present invention, which can effectively suppress interference, and the deep null is still formed in the interference direction under the condition of amplitude-phase error, thus the robustness is good.
It can be seen from fig. 3 and 5 that the obtained single pulse ratio curve directional diagram is consistent with the single pulse ratio curve of the normal sum and difference directional diagrams under the conditions of no amplitude phase error and amplitude phase error, which indicates that the performance of obtaining the actual direction of the target is good by using the new method to obtain the difference beam weight and measuring the angle of the target deviating from the beam center.
In conclusion, the simulation experiment verifies the correctness, the effectiveness and the reliability of the method.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention; thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (2)

1. A radar self-adaption sum and difference beam angle measurement method based on feature space is characterized by comprising the following steps:
step 1, determining an even linear array, wherein the even linear array comprises M array elements, J +1 signal sources exist in a detection range of the even linear array, the J +1 signal sources transmit J +1 incident signals to the even linear array, and the J +1 incident signals comprise target signals; further determining M-dimensional signals received by the uniform linear array at the time t;
wherein t represents a time variable, M represents the number of array elements included in the uniform linear array, and M, J are positive integers greater than 0 respectively;
the determination process of the M-dimensional signal received by the uniform linear array at the time t is as follows:
the J +1 incident signals comprise a target signal and J interference signals, the J +1 incident signals are respectively narrow-band signals, and the incoming wave direction of the ith incident signal is thetaiI ∈ {1,2, …, J +1}, where i is 1 for a target signal and i is not equal to 1 for an interference signal, respectively, and the incoming wave directions of the J +1 incident signals are different and are θ1,θ2,…,θi,…,θJ+1；
J +1 signal sources transmit J +1 incident signals to the uniform linear array, each array element receives J +1 irrelevant narrowband signals respectively, and the J +1 irrelevant narrowband signals received by the mth array element are recorded as sm(t)，
sm(t)＝{sm,1(t),sm,2(t),…,sm,i(t),…,sm,J+1(t)}，m∈{1,2,…,M}，sm,i(t) represents the ith narrowband signal received by the mth array element; then, the M-dimensional signal received by the uniform linear array at the time t is x (t), and the expression thereof is:
Figure FDA0002409027810000011
Figure FDA0002409027810000012
n(t)＝[n1(t),n2(t),…,nm(t),…,nM(t)]T
wherein x ism(t) represents a signal received by the mth array element in the uniform linear array at the time t, wherein the signal received by the mth array element in the uniform linear array at the time t is J +1 irrelevant narrow-band signals received by the mth array element; si(t) is the complex envelope of the ith incident signal at time t; a (theta)i) Is the guide vector of the ith incident signal, n (t) is Gaussian white noise of M array elements in the uniform linear array at the time of t, nm(T) Gaussian white noise of the m-th array element in the uniform linear array at the time T, superscript T represents transposition operation, d represents array element interval of the uniform linear array, and thetaiRepresenting the incoming wave direction of the ith incident signal, e representing an exponential function, superscript j representing an imaginary unit, and sin being a sine function; lambda [ alpha ]iThe wavelength of the ith incident signal is represented, and the wavelength value of each incident signal is respectively equal; t represents a time variable, M represents the number of array elements contained in the uniform linear array, and M is a positive integer greater than 0; step 2, dividing the uniform linear arrays of M array elements into L sub-arrays, and obtaining L-dimensional dimensionality reduction signal output of the uniform linear arrays at the time t according to M-dimensional signals received by the uniform linear arrays at the time t;
wherein, L represents the number of sub-arrays contained after the uniform linear array of M array elements is divided, and L is a positive integer greater than 0;
and outputting an L-dimensional dimensionality reduction signal of the uniform linear array at the time t, wherein the obtaining process is as follows:
dividing the uniform linear array of M array elements into L sub-arrays, wherein the number of the array elements contained in each sub-array is g, g is a positive integer and is more than or equal to 1,
Figure FDA0002409027810000021
Figure FDA0002409027810000022
represents rounding up; and then calculating to obtain the guide vector of the ith incident signal after dividing L sub-arrays
Figure FDA0002409027810000023
Figure FDA0002409027810000024
Wherein g represents the number of array elements contained in each subarray, d represents the array element spacing of the uniform linear array, and thetaiRepresenting the incoming wave direction of the ith incident signal, the superscript T representing transposition operation, e representing an exponential function, the superscript j representing an imaginary number unit, and sin being a sine function; lambda [ alpha ]iThe wavelength of the ith incident signal is represented, and the wavelength value of each incident signal is respectively equal;
further obtaining the guide vector of the ith incident signal under the condition of the same incoming wave direction
Figure FDA0002409027810000025
The expression is as follows:
Figure FDA0002409027810000026
and further calculating to obtain an L multiplied by M dimension reduction matrix T of L sub-arrays:
Figure FDA0002409027810000027
wherein the content of the first and second substances,
Figure FDA0002409027810000031
θ1indicating the incoming wave direction of the target signal, the incoming wave direction theta of the target signal1Is the expected incoming wave direction of the target signal; e represents an exponential function, the superscript j represents an imaginary number unit, sin is a sine function, lambda represents the wavelength of each incident signal, g represents the number of array elements contained in each subarray, g is a positive integer, and g is more than or equal to 1;
then, according to the L multiplied by M dimension reduction matrix T of L sub-arrays, reducing the M dimension signal x (T) received by the uniform linear array at the time T to L dimension, and obtaining L dimension reduction signal output M (T) of the uniform linear array at the time T:
m(t)＝Tx(t)＝[m1(t),m2(t),…,ml'(t),…,mL(t)]T
wherein m isl'(t) the output of the dimensionality reduction signal of the ith 'sub-array of the uniform linear array at the time t is shown, wherein L' is 1, … L, L represents the number of sub-arrays contained after the uniform linear array of M array elements is divided, and L is a positive integer greater than 0;
step 3, calculating to obtain the sum beam weight W of J +1 incident signals received by L sub-arrayssum；
The obtaining process comprises the following steps:
3a) and (3) calculating to obtain a covariance matrix R of J +1 incident signals received by L sub-arrays, and performing eigenvalue decomposition on the covariance matrix R to obtain:
Figure FDA0002409027810000032
wherein, the covariance matrix R of J +1 incident signals received by L sub-arrays contains L eigenvalues, and λ1≥λ2≥…≥λJ+1>λJ+2＝…＝λL＝σn 2，
Figure FDA0002409027810000033
Denotes the Gaussian white noise power of each subarray receiving J +1 incident signals, and will be1,λ2,…,λi',…,λJ+1Is recorded as J +1 large eigenvalues,
will be lambdaJ+2,λJ+3,…,λi”,…,λLIs recorded as L-J-1 small characteristic value, vi'Indicates a feature vector corresponding to the i 'th feature value, i' 1, …, J +1, vi”Denotes a feature vector corresponding to the i-th "feature value, i ″, J +2, …, L, λi'Denotes the i' th characteristic value, i ═ J +2, J +3, …, L, λi”The ith' characteristic value is represented, and the superscript H represents the conjugate transpose operation;
let the diagonal matrix composed of J +1 large eigenvalues be DsLet passL-J-1 small eigenvalues form a diagonal matrix DnLet the matrix formed by the eigenvectors corresponding to J +1 large eigenvalues be VsLet the matrix formed by the eigenvectors corresponding to the L-J-1 small eigenvalues be VnThe expressions are respectively:
Ds＝diag(λ1,λ2,…,λi',…,λJ+1)，Dn＝diag(λJ+2,λJ+3,…,λi”,…,λL)
Vs＝[v1,v2,…,vi',…,vJ+1]，Vn＝[vJ+2,vJ+3,…,vi”,…,vL]
wherein λ isi”Denotes the i-th "characteristic value, DsRepresenting a diagonal matrix of J +1 large eigenvalues, DnDenotes a diagonal matrix composed of L-J-1 small eigenvalues, diag denotes a diagonal matrix, VsRepresenting a matrix formed by eigenvectors corresponding to J +1 large eigenvalues, and recording the matrix as a signal subspace; vnRepresenting a matrix formed by eigenvectors corresponding to the L-J-1 small eigenvalue, and recording the matrix as a noise subspace;
3b) calculating the self-adaptive weight vector of J +1 incident signals received by L sub-arrays to be W0：
W0＝μR-1a(θ1)
Wherein mu is a set coefficient, and mu is not equal to 0; r represents the covariance matrix of J +1 incident signals received by L subarrays, and the inverse operation is denoted by superscript-1, a (theta)1) A steering vector representing a target signal;
thereby calculating the sum beam weight W of J +1 incident signals received by L sub-arrayssumThe expression is as follows:
Wsum＝VsVs HW0
＝μVsVs HR-1a(θ1)；
step 4, calculating to obtain the difference beam weight W of J +1 incident signals received by L sub-arraysdiff；
The obtaining process comprises the following steps:
recording the weight of the difference beam of J +1 incident signals received by L subarrays as WdiffAnd receiving the sum beam weight W of J +1 incident signals according to the L sub-arrayssumDetermining a monopulse ratio curve, wherein the expression is as follows:
Figure FDA0002409027810000041
wherein is the slope of the monopulse ratio curve, a (θ)1) A guide vector, theta, representing the target signal1Showing the incoming wave direction of the target signal, theta showing the actual incoming wave direction of the target signal, theta showing the incoming wave direction of the target signal1Is the expected incoming wave direction of the target signal; wdiffRepresents the difference beam weight, W, of J +1 incident signals received by L subarraysdiff∈Cm×1，WsumRepresents the sum beam weight, W, of J +1 incident signals received by L subarrayssum∈Cm×1，Cm×1A complex matrix representing m × 1 dimensions, S (k) represents a complex envelope of L sub-arrays receiving J +1 incident signals at time k, n (k) represents Gaussian white noise of L sub-arrays receiving J +1 incident signals at time k, k represents a time variable, and1-theta) represents the single pulse ratio,
Figure FDA0002409027810000051
indicating that L sub-arrays receive the sum beam of J +1 incident signals,
Figure FDA0002409027810000052
indicating that L subarrays receive the difference beam of J +1 incident signals, Re indicates the real part operation;
4a) taking a monopulse ratio curve expression as a constraint condition for solving the difference beam of the L sub-arrays for receiving J +1 incident signals, taking the minimum power of the difference beam output signals of the L sub-arrays for receiving the J +1 incident signals as a target function, and constructing the following form to deduce the difference beam weight of the L sub-arrays for receiving the J +1 incident signals:
Figure FDA0002409027810000053
Figure FDA0002409027810000054
wherein, Re (W)diff HC) G' is a constraint function, and C is expressed in a single pulse ratio curve expression
Figure FDA0002409027810000055
G' represents the single pulse ratio curve expression (theta)1- θ), g' ═ △ θ 0- △ θ]The slope of the monopulse ratio curve is shown, theta represents the actual incoming wave direction of the target signal, a (theta + △ theta) represents a guide vector deviating from the target actual direction △ theta in J +1 incident signals received by L sub-arrays, a (theta) represents a guide vector deviating from the target actual direction- △ theta in the actual incoming wave direction theta of the target signal, a (theta- △ theta) represents a guide vector deviating from the target actual direction- △ theta in J +1 incident signals received by L sub-arrays, △ theta represents the angle of the target signal deviating from the beam center of J +1 incident signals received by L sub-arrays, and a (theta)1) A guide vector, theta, representing the target signal1Indicating the incoming wave direction of the target signal, the incoming wave direction theta of the target signal1Is the expected incoming wave direction of the target signal; theta represents the actual incoming wave direction of the target signal, WdiffRepresents the difference beam weight, W, of J +1 incident signals received by L subarrayssumRepresenting the sum beam weight of J +1 incident signals received by L subarrays, S (k) representing the complex envelope of J +1 incident signals received by the L subarrays at the k moment, n (k) representing Gaussian white noise of J +1 incident signals received by the L subarrays at the k moment, and k representing a time variable; (theta)1-theta) represents the single pulse ratio,
Figure FDA0002409027810000056
indicating that L sub-arrays receive the sum beam of J +1 incident signals,
Figure FDA0002409027810000057
indicating that L sub-arrays receive difference beams of J +1 incident signals, Re indicating real part operation, min indicating minimum value operation, and superscript H indicating conjugate transpose operation;
4b) constructing a function by using a Lagrange multiplier method:
Figure FDA0002409027810000061
wherein f represents the function Re (W) according to the constraint conditiondiff HC) G' and
Figure FDA0002409027810000062
the resulting function, ζ represents the lagrange multiplier, R represents the covariance matrix of the L subarrays receiving J +1 incident signals, WdiffRepresenting the difference beam weight of J +1 incident signals received by L subarrays;
calculating the difference beam weight W of J +1 incident signals received by L subarraysdiffComplex gradient of
Figure FDA0002409027810000063
The expression is as follows:
Figure FDA0002409027810000064
wherein the content of the first and second substances,
Figure FDA0002409027810000065
representing partial derivation, Re representing real part operation, and Im representing imaginary part operation;
thereby calculating and obtaining the difference beam weight W of J +1 incident signals received by L sub-arraysdiffThe calculation expression is as follows:
Wdiff＝R-1C[Re(CHR-1C)]-Tg'T(ii) a Wherein, the superscript-1 is the inversion operation, and Re represents the operation of the real part;
step 5, receiving the sum beam weight W of J +1 incident signals according to L sub-arrayssumL subarrays receive difference beam weight W of J +1 incident signalsdiffAnd outputting the L-dimensional dimensionality reduction signal of the uniform linear array at the time t, and calculating to obtain the actual incoming wave direction of the target signal.
2. The eigenspace-based radar adaptive sum and difference beam angle measurement method according to claim 1, wherein in step 5, the actual incoming wave direction of the target signal is obtained by:
receiving the sum beam weight W of J +1 incident signals according to L sub-arrayssumAnd L sub-arrays receive the difference beam weight W of J +1 incident signalsdiffObtaining the difference beam signal output y of L sub-arrays receiving J +1 incident signals△And L sub-arrays receiving J +1 incident signals and outputting a sum beam signal y∑And taking the real part of the ratio to obtain the self-adaptive monopulse ratio of the L sub-arrays, and further obtaining an angle △ (theta) of the target signal deviating from the beam center of the J +1 incident signal received by the L sub-arrays:
Figure FDA0002409027810000066
the superscript H represents conjugate transpose operation, m (t) represents J +1 incident signals received by L sub-arrays at t moment, represents the slope of a monopulse ratio curve, and t represents a time variable;
according to the incoming wave direction theta of the target signal1And an angle △ (theta) of the target signal deviating from the beam center of the J +1 incident signal received by the L sub-arrays, and calculating to obtain the actual incoming wave direction theta of the target signal, wherein theta is theta1-△θ。
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