CN113075635A - Method for reconstructing target information of frequency agile radar based on coherent accumulation - Google Patents

Method for reconstructing target information of frequency agile radar based on coherent accumulation Download PDF

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CN113075635A
CN113075635A CN202110342934.3A CN202110342934A CN113075635A CN 113075635 A CN113075635 A CN 113075635A CN 202110342934 A CN202110342934 A CN 202110342934A CN 113075635 A CN113075635 A CN 113075635A
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target
representing
phase
vector
distance
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CN113075635B (en
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张劲东
王娜
王玉莹
胡婉婉
赵家琛
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Nanjing University of Aeronautics and Astronautics
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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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/414—Discriminating targets with respect to background clutter

Abstract

The invention discloses a method for reconstructing frequency agile radar target information based on coherent accumulation. The method comprises the following steps: establishing a target echo signal model of the frequency agile radar based on coherent accumulation and an optimization model taking the phase error and the scene sparsity as optimization targets, and solving the optimization model through phase self-focusing algorithm reconstruction and an alternative direction multiplier method to further obtain the self-adaptive phase difference, speed and distance information of the targets and realize the reconstruction of target information. The method can be used for accurately estimating the target echo phase error and reconstructing an observation scene, effectively solves the problem of phase error caused by phase error that the coherent accumulation performance of the coherent frequency agile radar is reduced, provides good coherent accumulation performance, and realizes the accurate estimation of the target on the distance and the speed.

Description

Method for reconstructing target information of frequency agile radar based on coherent accumulation
Technical Field
The invention relates to the technical field of coherent agile frequency conversion radars.
Background
A coherent agile radar (FACR) combines two advantages of agile frequency and a coherent system, on one hand, the coherent system is used for providing signal phase information to improve the resolving capability of the radar on a target, and on the other hand, the working frequency of the radar is rapidly switched through the agile frequency technology so that the radar obtains advantages in electronic countermeasure. At present, the method for realizing coherent agile frequency conversion radar reception is generally through a direct digital frequency synthesis method, but because frequency hopping in a range of GHz cannot be realized, in order to realize large-range frequency modulation and avoid interference of a large broadband, the direct frequency synthesis method can be used instead, but the method cannot avoid generating random initial phase among pulses, so that coherent accumulation performance is influenced. How to realize the inter-pulse echo phase estimation caused by the random initial phase between pulses, the target distance and the speed and the good coherent accumulation performance become the key problems to be solved.
On the other hand, when the working carrier frequency of the frequency agile radar is in an inter-pulse frequency hopping state, the phase of a target echo is affected by the random change of the pulse carrier frequency and the change of the distance between the target radars, and the traditional delay cancellation or fast Fourier transform Doppler processing method is not compatible with the echo of the frequency agile radar, so that the Doppler information of the target cannot be extracted.
Disclosure of Invention
The invention aims to provide a new method for reconstructing target information of a frequency agile radar, which can perform accurate target echo phase error estimation and observation scene reconstruction, effectively solve the problem of phase error caused by phase error that coherent frequency agile radar has reduced coherent accumulation performance, provide good coherent accumulation performance, and realize accurate estimation of a target on distance and speed.
The invention also aims to propose an application of the method.
The invention firstly discloses the following technical scheme:
a method for reconstructing target information of a frequency agile radar based on coherent accumulation comprises the following steps:
establishing an echo signal model of the frequency agile radar based on the coherent accumulation, wherein the echo signal model comprises a phase error matrix and a scattering coefficient matrix;
s2: establishing an optimization model of the echo signal model, wherein the optimization model takes target estimation error precision and sparsity of the scattering coefficient matrix as optimization targets;
s3: and sparsely reconstructing the optimization model through a phase self-focusing algorithm, and iteratively solving the reconstructed optimization model through an alternating direction multiplier (ADMM) method to obtain an optimal phase error matrix and an optimal scattering coefficient matrix, so as to obtain the adaptive phase difference, speed and distance information of the target and realize the reconstruction of the target information.
In the scheme, the ADMM method is a calculation framework for solving the optimization problem, and the scale of the problem is reduced by dividing the original optimization problem into two subproblems to be alternately solved.
In the above scheme, the agile frequency radar operates by transmitting a group of pulse trains with randomly changing carrier frequencies, and synthesizing a larger bandwidth by performing coherent processing on pulses with different carrier frequencies to obtain a high range resolution.
According to some embodiments of the invention, the sparsity is determined by taking the matrix of scattering coefficients
Figure BDA0003000068800000021
And obtaining a norm.
According to some embodiments of the invention, the echo signal model comprises the following phase factors: a phase factor due to a range factor of the target, a phase factor due to a velocity factor of the target, and a phase factor due to a random initial phase generated by non-digital frequency hopping of the radar.
According to some embodiments of the invention, the scattering coefficient matrix comprises scattering coefficient vectors for strong scattering points in the distance and velocity dimensions. .
According to some embodiments of the invention, the reconstructing in step S3 includes replacing the sparsity of the scattering coefficient matrix in the optimized model with a sparsity approximation of the scattering coefficient matrix.
According to some embodiments of the invention, the echo signal model is:
y＝EFa+w(8)，
wherein the content of the first and second substances,
y represents an observation data array of the range gate reference unit where the target is located, and is an N × 1-dimensional vector composed of N pulse echoes, as follows:
y＝[y0,y1,...yN-1]T (9)，
y＝[y0,y1,...yn，...yN-1]T (9)；
wherein, the nth dimension data ynObtained by the following formula:
Figure BDA0003000068800000031
and:
Figure BDA0003000068800000032
where N represents the total number of pulses within one coherent processing interval. w is anRepresenting noise, RlRepresenting the distance, v, of the ith target scatter point in the nth pulse echo signallIndicates its speed, fcRepresenting the initial carrier frequency of the pulse transmitted by the coherent frequency agile radar, where Δ f is the frequency hopping interval, dnA frequency modulated codeword representing a random integer, i.e. the nth pulse,
Figure BDA0003000068800000033
represents a fast time, wherein TrRepresenting the pulse repetition period, t represents the slow time,
Figure BDA0003000068800000034
representing a random initial phase of the nth pulse due to non-digital frequency hopping, R representing the distance of a target echo along the line of sight of the radar, v representing the velocity thereof, and C (R, v) representing the backscattering amplitude of the target in relation to the velocity and distance of the target;
f represents an N × PQ-dimensional sparse dictionary matrix formed after the target signal is discretized into P, Q scatteration grid points in the distance dimension and the velocity dimension, respectively, as follows:
Figure BDA0003000068800000035
wherein the guiding vector phi of the ith target scattering pointl∈CNThe nth element is as follows:
Figure BDA0003000068800000036
l and lp,lqThe relationship of (1) is: l ═ lp×Q+lq，
Figure BDA0003000068800000037
lq＝mod(l,Q)；
a represents PQ multiplied by 1 dimensional scattering coefficient vectors formed by target scattering points on distance and speed dimensional grid points;
w represents an additive noise vector;
e denotes an N × N dimensional phase error matrix as follows:
E＝diag(e) (11)，
wherein, diag (·) represents a diagonal matrix formed by taking elements in a vector e as diagonal elements, and the vector e is as follows:
Figure BDA0003000068800000041
according to some embodiments of the invention, the optimization model is:
Figure BDA0003000068800000042
s.t.||y-EFa||2＜ε (13)，
wherein | · | purple sweet1Representing an access vector
Figure BDA0003000068800000048
Norm operation, | ·| luminance2Representing an access vector
Figure BDA0003000068800000049
Norm operation, | | y-EFa | | non-conducting light2Representing the phase error equation, ε | | | w | | non-conducting phosphor2Representing the noise threshold.
According to some embodiments of the invention, the reconstructed optimization model is:
Figure BDA0003000068800000043
wherein, anRepresenting the nth element in the vector a,
Figure BDA0003000068800000044
denotes anRepresents the convergence threshold, and δ > 0.
According to some embodiments of the present invention, in the solving of the reconstructed optimization model in step S3, the iteration termination condition is: the iteration end conditions are set as:
||a(t+1)-a(t)||2/||a(t)||2+||E(t+1)-E(t)||F/||E(t)||F＜ζ (25)，
wherein E is(t)The t-th estimate, a, representing the phase error matrix(t)Represents the t-th estimate of the sparse vector, ζ represents a constant threshold value greater than zero.
According to some embodiments of the invention, the post-conversion optimization problem is:
Figure BDA0003000068800000045
wherein u ═ λr+jλi) Rho, wherein, omicron represents Hadamard product, rho is penalty coefficient, a, e, beta, u is value after ADMM iteration, (·)*Representing the conjugate of a matrix or vector.
According to some embodiments of the present invention, the above-described transformed optimization problem is solved according to the following steps
And (3) line iteration updating:
a1 mixing e(t),β(t),u(t)Considered a known quantity, a is updated by:
Figure BDA0003000068800000051
a2 reaction of a(t+1),β(t),u(t)As a known quantity, update e by:
Figure BDA0003000068800000052
wherein q is(t)＝β(t)-Fa(t+1)+u(t)，(·)*Representing taking conjugation;
a3 reaction of a(t+1),e(t+1),u(t)As a known quantity, β is updated by:
Figure BDA0003000068800000053
wherein the content of the first and second substances,
Figure BDA0003000068800000054
a4 reaction of a(t+1),e(t+1),β(t+1)As a known quantity, u is updated by:
Figure BDA0003000068800000056
repeating the steps A1-A4 until convergence;
wherein, a(t),e(t),β(t),u(t)The value after the t th iteration of ADMM is represented, and the superscript (t +1) correspondingly represents the value after the t +1 th iteration.
The invention has the following beneficial effects:
the invention introduces random initial phase into the echo signal model, obtains a coherent accumulation phase error model according to the echo signal model, and establishes minimum through the sparse characteristic of the target in distance-speed two dimensions
Figure BDA0003000068800000055
The norm optimization model adopts an alternative direction multiplier method to carry out phase error self-adaptive estimation, realizes accurate estimation of target distance-speed and good coherent accumulation performance, and obviously reduces the sidelobe level of a recovery scene due to the utilization of the sparse characteristic of a target scene.
The invention can carry out phase error estimation in a self-adaptive manner, so that the target amplitude basically does not fluctuate greatly along with the change of the phase error, and the invention has the advantages on the calculation efficiency, and according to the simulation result, the system phase error estimation error is 2 under the condition of the signal-to-noise ratio of 20dB°Compared with a direct phase autofocus sparse reconstruction algorithm, the mean square error of the reconstruction amplitude of the target can be improved by 10dB, and the operation time is reduced by half.
Drawings
Fig. 1 is a diagram illustrating direct coherent accumulation and target scene restoration contrast based on ADMM phase autofocus sparse reconstruction in an embodiment.
FIG. 2 is a graph comparing direct coherent accumulation with the method of the present invention in the presence of phase errors at different signal-to-noise ratios as described in the detailed description.
Fig. 3 is a comparison graph of the method of the present invention and the ISAR-based phase autofocus algorithm under different phase errors when the SNR is 20dB according to the embodiment.
FIG. 4 is a diagram illustrating the convergence of the ISAR phase autofocus method according to the present invention in an embodiment.
Detailed Description
The present invention is described in detail below with reference to the following embodiments and the attached drawings, but it should be understood that the embodiments and the attached drawings are only used for the illustrative description of the present invention and do not limit the protection scope of the present invention in any way. All reasonable variations and combinations that fall within the spirit of the invention are intended to be within the scope of the invention.
According to the technical scheme of the invention, a specific implementation mode comprises the following steps:
s1: establishing an echo signal model containing a target phase error matrix and a scattering coefficient vector of the frequency agile radar based on the coherent accumulation;
s2: establishing an optimization model of the echo signal model, wherein the optimization model takes estimation error precision and sparsity of the scattering coefficient vector as optimization targets;
s3: reconstructing the optimization model through a phase gradient self-focusing algorithm, iteratively solving the optimization model through an Alternating Direction Multiplier Method (ADMM), obtaining an optimal phase error matrix and a scattering coefficient vector, further obtaining self-adaptive phase difference, speed and distance information of the target, and realizing reconstruction of target information.
In a more specific implementation, the discrete model of the echo signal in step S1 is constructed as follows:
setting the nth pulse transmitted by the agile frequency conversion radar as follows:
Figure BDA0003000068800000071
wherein f isn＝fc+dnΔ f, N is 0, 1.. N-1 denotes the radar carrier frequency of the nth pulse, where N denotes the pulse sequence number, N denotes the total number of pulses in a Coherent Processing Interval (CPI), and f denotes the total number of pulses in the Coherent Processing Interval (CPI)cRepresenting the initial carrier frequency of the pulse transmitted by the coherent frequency agile radar, where Δ f is the frequency hopping interval, dnA frequency modulation code word which is a random integer, namely the nth pulse;
Figure BDA0003000068800000072
represents a fast time, wherein TrRepresenting a pulse repetition period; t represents a slow time; a (-) represents a baseband signal, which can be a square pulse and/or a chirp signal, etc.
Then the distance is R, and the target echo with the velocity v along the radar line-of-sight direction is:
Figure BDA0003000068800000073
the baseband signal is a rectangular pulse signal, the range expansion or compression caused by the target speed is ignored, the demodulated signal is directly sampled, and the echo signal of the target in the nth pulse is obtained as follows:
Figure BDA0003000068800000074
where C (R, v) represents the target backscatter amplitude in relation to target velocity and distance.
Further, consider that for a non-fully coherent agile radar, in addition to the above-mentioned phase factor due to range and velocity of the target, there is a random initial phase due to non-digital frequency hopping
Figure BDA0003000068800000075
Satisfying a uniform random distribution within [0,2 π), the echo signal of the target at the nth pulse can be represented as:
Figure BDA0003000068800000076
wherein:
Figure BDA0003000068800000081
it can be seen that the first term of the phase in the exponential term in equation (4) is the phase due to the distance of the target, the second term is the phase due to the velocity of the target, and the third term brings random phase for non-digital frequency hopping.
Let the nth pulse echo signal contain L scattering points of the target, NcA clutter scattering point, wherein the distance of the first target scattering point is RlVelocity vlScattering intensity of object C (R)l,vl) The distance of the ith clutter scattering point is RiVelocity viIntensity of clutter scattering C (R)i,vi) Then the target echo can be expressed as:
Figure BDA0003000068800000082
wherein, wnRepresenting noise, typically white gaussian noise.
In the above model, considering the tracking situation, that is, the target distance and speed can be obtained a priori, but there is a certain estimation error, which cannot meet the requirement of accurate compensation, the target region and the clutter region can be separated, that is, the influence of clutter can be ignored, and the following target echo model is obtained:
Figure BDA0003000068800000083
it can be further expressed in a compact form as follows:
y＝EFa+w (8)
wherein y represents observation data of a range gate reference unit where the target is located, the size of the observation data is an Nx 1-dimensional vector, the observation data is composed of N pulse echoes, and the observation data is represented as:
y＝[y0,y1,...yn，...yN-1]T (9)；
wherein, the nth dimension data ynNamely, the target echo obtained by equation (7).
F represents an N × PQ-dimensional sparse dictionary matrix formed after dispersing the distance dimension and the velocity dimension of the target observation scene into P and Q scattered grid points, and is represented as:
Figure BDA0003000068800000091
wherein the guiding vector phi of the ith target scattering pointl∈CNThe nth element is as follows:
Figure BDA0003000068800000092
l and lp,lqThe relationship of (1) is: l ═ lp×Q+lq，
Figure BDA0003000068800000093
lq＝mod(l,Q)；
a represents PQ multiplied by 1 dimensional scattering coefficient vectors formed by target scattering points on distance and speed dimensional grid points;
w represents an additive noise vector;
e denotes an N × N dimensional phase error matrix as follows:
E＝diag(e) (11)，
wherein, diag (·) represents the matrix operation formed by using the elements in the vector e as diagonal elements, and the vector e is as follows:
Figure BDA0003000068800000094
wherein the content of the first and second substances,
Figure BDA0003000068800000095
representing a random initial phase of the nth pulse due to non-digital frequency hopping.
In a more specific implementation, the optimization model in step S2 is:
Figure BDA0003000068800000096
wherein | · | purple sweet1Representing an access vector
Figure BDA00030000688000000910
Norm operation, | ·| luminance2Representing an access vector
Figure BDA00030000688000000911
Norm operation, | | y-EFa | | non-conducting light2Representing an error equation for characterizing an estimated error accuracy of the reconstructed signal, wherein ε | | | w | | luminance2And epsilon represents the noise threshold.
The optimization model is established by analyzing an observation equation of an equation (8) and utilizing the sparsity of a. Exploiting sparsity of signals based on compressive sensing theory by
Figure BDA00030000688000000912
The norm optimization problem can approximately perfectly reconstruct the characteristics of the original signal. In the invention, the number of strong scattering points of the target in a distance dimension-speed dimension is limited, so that the distance-speed distribution of the target can be approximately represented by the strong scattering points, and the self-adaptive phase error is solved by establishing an optimization problem by utilizing the sparsity of the target in a two-dimensional space, thereby obtaining the target distance-speed scene distribution based on sparse representation.
In the above optimization model, | | a1The expression a has only a few larger components, and the other most are smaller components, so as to characterize the sparsity of the target in the distance-velocity dimension.
In the optimization model, epsilon is related to the target scene recovery precision, namely different epsilon is set to obtain target distance-speed distribution with different sparsity. When epsilon takes a smaller value, the sparsity of the scene is weakened, and under the condition of low signal-to-noise ratio, the noise signal can be mistaken for the target signal to be recovered, so that the scene recovery precision is influenced. And conversely, when the epsilon takes a larger value, the sparsity of the scene to be recovered is enhanced, and the target at the weak scattering point is mistaken for a noise component, so that the scattering number of the recovered target is relatively reduced, but the noise can be effectively suppressed. Therefore, under a low signal-to-noise ratio, a larger epsilon value is preferred, and noise can be effectively suppressed to obtain a target distance-speed scene distribution with better coherent accumulation.
In more specific implementations, step S3 may include:
according to Kuhn-Tucker theory, the optimization problem of formula (13) is transformed into:
Figure BDA0003000068800000101
the objective function comprises two kinds of constraint information of estimation error precision and scene sparsity. Wherein, the constant mu is more than 0, and the relationship between the sparsity and the estimation error precision can be balanced. When mu is larger, the sparsity of the scene to be reconstructed can be enhanced and the influence of noise can be effectively inhibited, so that when the signal-to-noise ratio of the echo to be processed is lower, a larger mu value can be reasonably optimized to ensure the sparsity and reduce the influence of noise.
To overcome
Figure BDA0003000068800000105
The norm is not a problem at zero, and the invention approximates by the following method:
Figure BDA0003000068800000102
wherein, anRepresenting the nth element in the vector a,
Figure BDA0003000068800000103
denotes anRepresents the convergence threshold, and δ > 0.
By substituting formula (15) into formula (14), the optimization problem can be converted into:
Figure BDA0003000068800000104
it can be seen from the above model that the phases between different pulses caused by random initial phase, velocity and distance are independent and uncoupled, i.e. the estimation of the sparse vector a and the phase error matrix E can be solved by alternating iteration.
The objective function in equation (16) is rewritten as:
Figure BDA0003000068800000111
the conjugate gradient function of a for the objective function is:
Figure BDA0003000068800000112
wherein:
Figure BDA0003000068800000113
the gradient of the conjugate gradient function is then the Hessian matrix of the objective function f (a):
Figure BDA0003000068800000114
wherein:
Figure BDA0003000068800000115
the first term in the formula (20) is a semi-positive definite matrix, the second term is Hessian matrix positive definite of a definite matrix-known target function, the target function is a convex function, and the stable point, the local minimum point and the global minimum point of the unconstrained convex function are equivalent.
And (3) making the conjugate gradient vector equal to the zero vector, and solving a recursion expression of a:
Figure BDA0003000068800000116
wherein E is(t)The t-th estimate, a, representing the phase error matrix(t)Representing the t-th estimate of the sparse vector. The formula (22) has the meaning: firstly, phase compensation is carried out on echo signal observation data by using an estimated phase error, then coherent accumulation is carried out by using a sparse dictionary matrix, and finally amplitude normalization processing is carried out to obtain self-focusing sparse reconstruction scene distribution.
Without phase error prior information, assume
Figure BDA0003000068800000117
The phase error recurrence expression can be expressed as:
Figure BDA0003000068800000118
and:
Figure BDA0003000068800000121
wherein [ ·]nRepresents the nth element operation of the vector, conj (-) represents the conjugate operation, and | represents the modulo operation.
A can be obtained by the formulae (22), (23) and (24)(t+1)And E(t+1)Is represented by an update of (c).
The iteration end conditions are set as:
||a(t+1)-a(t)||2/||a(t)||2+||E(t+1)-E(t)||F/||E(t)||F＜ζ (25)
where ζ represents a constant threshold value greater than zero.
When the adjacent two estimates of a and E satisfy equation (25) or satisfy a certain number of iterations, the iterative update is stopped.
The specific solving process can comprise the following steps:
step0, recording t as iteration number, initializing t to be 0 and initial value a(0)Randomly generated, initial value E(0)Setting as a unit matrix;
and Step1, solving the vector a by using a conjugate gradient algorithm:
Figure BDA0003000068800000122
step2, update E:
Figure BDA0003000068800000123
E(t+1)＝diag(e(t+1))
step3, if the iterative convergence condition | | | a is satisfied(t+1)-a(t) 2/||a(t)||2+||E(t+1)-E(t)||F/||E(t)||Fξ, ζ is a positive number small enough, the algorithm terminates, otherwise t is made t +1, and Step1 is returned.
In a more specific implementation, solving the reconstructed optimization model by the ADMM algorithm may include:
the following equivalence optimization problem is established:
Figure BDA0003000068800000131
wherein e isiRepresenting the ith element in the column vector e,
Figure BDA0003000068800000138
representing a Hadamard product, due to eiThe limitation of the constraint of the unit modulus,
Figure BDA0003000068800000132
representing the noise threshold.
The equivalent optimization problem is obtained by taking a phase error matrix E in the constraint condition of an equation (8) as an auxiliary variable and replacing the auxiliary variable by a vector E.
According to the ADMM framework, the equivalence optimization problem is transformed into:
Figure BDA0003000068800000133
it is transformed into the form of an augmented lagrange function as follows:
Figure BDA0003000068800000134
remember u ═ λr+jλi) /, then equation (31) can be transformed into:
Figure BDA0003000068800000135
let a(t),e(t),β(t),u(t)For the value after the t-th ADMM iteration, the updating process is carried out as follows:
a1 mixing e(t),β(t),u(t)As a known quantity, update a:
wherein:
Figure BDA0003000068800000136
through formula (15) | | a | | non-woven phosphor1To convert it into:
Figure BDA0003000068800000137
the gradient function is found to be:
Figure BDA0003000068800000141
let the gradient equal zero, the solution for a can be found by the conjugate gradient algorithm as follows:
Figure BDA0003000068800000142
a2 reaction of a(t+1),β(t),u(t)As a known quantity, update e:
wherein:
Figure BDA0003000068800000143
ignoring the constant part, it is converted into:
Figure BDA0003000068800000144
the N elements in the above formula e are variables to be solved, and are independent of each other, and can be decomposed into N subproblems, and q is written(t)＝β(t)-Fa(t+1)+u(t)Then, the ith sub-question is:
Figure BDA0003000068800000145
a reaction product of [ q ](t)]i,
Figure BDA0003000068800000146
Looking as a vector on the complex plane, then:
Figure BDA0003000068800000147
wherein cos <, > represents the cosine of the vector angle.
By ignoring the constant part, the ith sub-problem can be converted into:
Figure BDA0003000068800000151
the geometric meaning of the problem is to solve k (i) which satisfies k (i) is more than or equal to 0 and less than 1, so that the included angle between two vectors of the complex plane is minimum.
Order:
Figure BDA0003000068800000152
wherein arg (·) represents a phase taking operation.
The solution of k (i) is:
Figure BDA0003000068800000153
further can obtain
Figure BDA0003000068800000154
As follows:
Figure BDA0003000068800000155
a3 reaction of a(t+1),e(t+1),u(t)As a known quantity, update β:
wherein:
Figure BDA0003000068800000156
note the book
Figure BDA0003000068800000157
Then the beta optimization solution is:
Figure BDA0003000068800000158
a4 reaction of a(t+1),e(t+1),β(t+1)As a known quantity, update u:
wherein:
Figure BDA0003000068800000165
repeating the steps A1-A4 until the algorithm is converged, and judging that the convergence condition is | | beta(t+1)-β(t)||2ζ or up to a certain number of iterations.
According to the above steps, the specific solving process may include:
step0, recording t as iteration number, initializing t to 0, and giving an initial value a generated randomly(0),e(0),β(0),u(0)
Step1 solving for vector a using conjugate gradients:
Figure BDA0003000068800000161
step2, update e:
Figure BDA0003000068800000162
wherein:
Figure BDA0003000068800000163
step3, updating the beta:
Figure BDA0003000068800000164
step4, update u:
Figure BDA0003000068800000166
step5, if the iterative convergence condition is satisfied, beta(t+1)-β(t)||2ζ, which is a sufficiently small positive number, the algorithm terminates, otherwise t +1 is returned to Step 1.
The following simulation experiment is performed through the recognition process and the recognition model described in the above embodiment:
simulation conditions are as follows:
in one CPI, parameters of coherent agile frequency conversion radar signals are set as follows: the number of pulses M is 64, and the pulse repetition period Tr100us, pulse width Tp20us, carrier frequency reference f0The method comprises the steps of (10 GHz), hopping number 64, inter-pulse hopping mode adopting pseudo-random traversal, hopping interval delta f being 16MHz, synthetic bandwidth B being 1GHz, assuming that a moving target exists in an observation scene of distance-speed dimension, distance parameter R being 118m, speed parameter v being 10m/s, and the targetThe backscatter amplitude a of 10. The phase error takes the form of a random phase error.
In the reconstruction method of the invention, the ADMM algorithm parameters are set as follows: convergence threshold ζ 10-3And the quadratic term punishment coefficient rho is reasonably set correspondingly according to different signal-to-noise ratios. The initial value of the phase error matrix E is set as a unit matrix, the initial values of beta, a and u are randomly generated,
the specific calculation process of direct coherent accumulation in comparison with the ADMM algorithm comprises the following steps:
the target echo model is
Figure BDA0003000068800000171
For agile coherent radar target distance-speed (R)l,vl) The problem of measuring the values is ascribed to the problem of matching the echoes on the (R ', v') plane, making their compensation phases;
Figure BDA0003000068800000172
the matching of the echoes in the (R ', v') plane results in
Figure BDA0003000068800000173
At the matching point (R ', v '), AF (R ', v ', R, v) ═ NC ' (R ', v '), is presentl,vl) The peak point is obtained.
Let Δ R ═ R ', Δ v ═ v-v', then there are side lobes
Figure BDA0003000068800000174
Figure BDA0003000068800000175
The process of calculating the phase self-focusing of ISAR for comparison with ADMM comprises the following steps:
step one, recording t as iteration times, initializing t to be 0 and obtaining an initial value a(0)Randomly generated, initial value E(0)Set as the identity matrix.
Step two, updating the vector a by the following formula:
Figure BDA0003000068800000181
step three, updating E through the following formula:
Figure BDA0003000068800000182
E(t+1)＝diag(e(t+1))
and step four, if the iterative convergence condition (25) is met, the algorithm is terminated, otherwise, the step t is made to be t +1, the operation returns to the step two, and the loop is continued.
The comparison of the figures 1-4 is obtained according to the above simulation conditions and procedures, wherein:
fig. 1 shows the direct coherent accumulation and target scene recovery contrast diagram based on ADMM phase autofocus sparse reconstruction when the SNR is 10dB and the phase error is randomly present. The method realizes the accurate estimation of the target distance-speed and improves the coherent accumulation performance by the self-adaptive estimation of the phase error, and simultaneously obviously reduces the side lobe level of a recovery scene by utilizing the sparse characteristic of a target scene.
Figure 2 shows a comparison of direct coherent accumulation in the presence of phase error at different signal-to-noise ratios with the method of the present invention. It can be seen that the method of the present invention can obtain good coherent accumulation results under different signal-to-noise ratios, because the method of the present invention can effectively suppress noise and ensure the balance between sparsity and estimation error accuracy. Meanwhile, under different phase errors, the target amplitude is continuously reduced along with the increase of the phase errors due to direct coherent accumulation, and the target amplitude basically does not fluctuate greatly along with the change of the phase errors due to the fact that the method can carry out self-adaptive phase error estimation.
Fig. 3 shows a comparison graph of the method of the present invention and the reference ISAR phase self-focusing algorithm under different phase errors when SNR is 20 dB. It can be seen that the method of the present invention is superior to the ISAR phase self-focusing algorithm for reference in the coherent accumulation performance.
Fig. 4 shows the convergence of the method of the present invention and the ISAR-based phase self-focusing method, and it can be seen that the method of the present invention gradually converges after about 10 iterations, whereas the convergence tends to only about 15 iterations after the ISAR-based phase self-focusing method. Compared with the method of using ISAR phase self-focusing for reference, the method of the invention improves the target reconstruction amplitude error by about 10 dB. Table 3 shows the computation time of the two methods, and it can be seen that the method of the present invention is also advantageous in terms of computational efficiency.
TABLE 3 calculation time of the method of the present invention and the method of self-focusing by using ISAR phase
Figure BDA0003000068800000191
The above examples are merely preferred embodiments of the present invention, and the scope of the present invention is not limited to the above examples. All technical schemes belonging to the idea of the invention belong to the protection scope of the invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention, and such modifications and embellishments should also be considered as within the scope of the invention.

Claims (10)

1. The method for reconstructing the target information of the frequency agile radar based on the coherent accumulation is characterized by comprising the following steps: the method comprises the following steps:
s1: establishing an echo signal model of the frequency agile radar based on the coherent accumulation, wherein the echo signal model comprises a phase error matrix and a scattering coefficient matrix;
s2: establishing an optimization model of the echo signal model, wherein the optimization model takes target estimation error precision and sparsity of the scattering coefficient matrix as optimization targets;
s3: and sparsely reconstructing the optimization model through a phase self-focusing algorithm, and iteratively solving the reconstructed optimization model through an alternating direction multiplier method to obtain an optimal phase error matrix and an optimal scattering coefficient matrix, so as to obtain the self-adaptive phase difference, speed and distance information of the target and realize the reconstruction of the target information.
2. The reconstruction method according to claim 1, characterized in that: the sparsity is calculated by taking l from the scattering coefficient matrix1And obtaining a norm.
3. The reconstruction method according to claim 1, characterized in that: the echo signal model includes the following phase factors: a phase factor due to a range factor of the target, a phase factor due to a velocity factor of the target, and a phase factor due to a random initial phase generated by non-digital frequency hopping of the radar.
4. The reconstruction method according to claim 3, characterized in that: the scattering coefficient matrix comprises scattering coefficient vectors of strong scattering points in the distance and velocity dimensions.
5. The reconstruction method according to claim 1, characterized in that: the reconstructing in step S3 includes replacing the sparsity of the scattering coefficient matrix in the optimized model with an approximate estimate of the sparsity of the scattering coefficient matrix.
6. The reconstruction method according to claim 1, characterized in that: the model of the echo signal model is as follows:
y＝EFa+w (8)，
wherein y represents an observation data array of the range gate reference unit where the target is located, and is an N × 1 dimensional vector composed of N pulse echoes, as follows:
y＝[y0,y1,...yn，...yN-1]T (9)；
wherein, the nth dimension data ynObtained by the following formula:
Figure FDA0003000068790000011
and:
Figure FDA0003000068790000021
where N represents the total number of pulses within one coherent processing interval. w is anRepresenting noise, RlRepresenting the distance, v, of the ith target scatter point in the nth pulse echo signallIndicates its speed, fcRepresenting the initial carrier frequency of the pulse transmitted by the coherent frequency agile radar, where Δ f is the frequency hopping interval, dnA frequency modulated codeword representing a random integer, i.e. the nth pulse,
Figure FDA0003000068790000022
represents a fast time, wherein TrRepresenting the pulse repetition period, t represents the slow time,
Figure FDA0003000068790000023
representing a random initial phase of the nth pulse due to non-digital frequency hopping, R representing the distance of a target echo along the line of sight of the radar, v representing the velocity thereof, and C (R, v) representing the backscattering amplitude of the target in relation to the velocity and distance of the target;
f represents an N × PQ-dimensional sparse dictionary matrix formed after the target signal is discretized into P, Q scatteration grid points in the distance dimension and the velocity dimension, respectively, as follows:
Figure FDA0003000068790000024
wherein the guiding vector phi of the ith target scattering pointl∈CNThe nth element is as follows:
Figure FDA0003000068790000025
l and lp,lqThe relationship of (1) is: l ═ lp×Q+lq，
Figure FDA0003000068790000026
lq＝mod(l,Q)；
a represents PQ multiplied by 1 dimensional scattering coefficient vectors formed by target scattering points on distance and speed dimensional grid points;
w represents an additive noise vector;
e denotes an N × N dimensional phase error matrix as follows:
E＝diag(e) (11)，
wherein, diag (·) represents a diagonal matrix formed by taking elements in a vector e as diagonal elements, and the vector e is as follows:
Figure FDA0003000068790000027
7. the reconstruction method according to claim 6, characterized in that: the optimization model is as follows:
Figure FDA0003000068790000031
wherein | · | purple sweet1Representing a vector of choices l1Norm operation, | ·| luminance2Representing a vector of choices l2Norm operation, | | y-EFa | | non-conducting light2Representing the phase error equation, ε | | | w | | non-conducting phosphor2Representing the noise threshold.
8. The reconstruction method according to claim 7, characterized in that: the reconstructed optimization model is as follows:
Figure FDA0003000068790000032
wherein, anRepresenting the nth element in the vector a,
Figure FDA0003000068790000033
denotes anRepresents the convergence threshold, and δ > 0.
9. The reconstruction method according to claim 8, characterized in that: in the step S3, in the solution of the reconstructed optimization model, the iteration termination condition is:
||a(t+1)-a(t)||2/||a(t)||2+||E(t+1)-E(t)||F/||E(t)||F＜ζ (25)，
wherein E is(t)The t-th estimate, a, representing the phase error matrix(t)Represents the t-th estimate of the sparse vector, ζ represents a constant threshold value greater than zero.
10. The reconstruction method according to claim 8, characterized in that: solving the reconstructed optimization model by:
establishing an equivalent optimization problem in the form of an augmented Lagrange function as follows:
Figure FDA0003000068790000034
wherein L isρDenotes the Lagrange function, u ═ λr+jλi) Where/, e denotes the conjugate of the e-vector,
Figure FDA0003000068790000035
expressing Hadamard product, rho expressing punishment coefficient, a, e, beta and u being values after ADMM iteration,
iteratively updating the equivalence optimization problem according to the following steps:
a1 mixing e(t),β(t),u(t)Considered a known quantity, a is updated by:
Figure FDA0003000068790000041
a2 reaction of a(t+1),β(t),u(t)As a known quantity, update e by:
Figure FDA0003000068790000042
wherein q is(t)＝β(t)-Fa(t+1)+u(t)，(·)*Representing taking conjugation;
a3 reaction of a(t+1),e(t+1),u(t)As a known quantity, β is updated by:
Figure FDA0003000068790000043
wherein the content of the first and second substances,
Figure FDA0003000068790000044
a4 reaction of a(t+1),e(t+1),β(t+1)As a known quantity, u is updated by:
Figure FDA0003000068790000045
repeating the steps A1-A4 until convergence;
wherein, a(t),e(t),β(t),u(t)The value after the t th iteration of ADMM is represented, and the superscript (t +1) correspondingly represents the value after the t +1 th iteration.
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