CN113075635B - 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 PDFInfo
- Publication number
- CN113075635B CN113075635B CN202110342934.3A CN202110342934A CN113075635B CN 113075635 B CN113075635 B CN 113075635B CN 202110342934 A CN202110342934 A CN 202110342934A CN 113075635 B CN113075635 B CN 113075635B
- Authority
- CN
- China
- Prior art keywords
- target
- representing
- phase
- vector
- distance
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 57
- 230000001427 coherent effect Effects 0.000 title claims abstract description 38
- 238000009825 accumulation Methods 0.000 title claims abstract description 26
- 238000005457 optimization Methods 0.000 claims abstract description 46
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 17
- 239000011159 matrix material Substances 0.000 claims description 48
- 239000013598 vector Substances 0.000 claims description 46
- 230000008569 process Effects 0.000 claims description 8
- 238000012545 processing Methods 0.000 claims description 6
- 239000000654 additive Substances 0.000 claims description 3
- 230000000996 additive effect Effects 0.000 claims description 3
- 230000003044 adaptive effect Effects 0.000 claims description 2
- 230000003190 augmentative effect Effects 0.000 claims description 2
- 238000000605 extraction Methods 0.000 claims 1
- 238000004364 calculation method Methods 0.000 description 7
- 230000008901 benefit Effects 0.000 description 4
- 230000008859 change Effects 0.000 description 4
- 238000011084 recovery Methods 0.000 description 4
- 238000004088 simulation Methods 0.000 description 3
- 238000001308 synthesis method Methods 0.000 description 3
- 238000010586 diagram Methods 0.000 description 2
- 238000002592 echocardiography Methods 0.000 description 2
- 230000006978 adaptation Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000005540 biological transmission Effects 0.000 description 1
- 230000015572 biosynthetic process Effects 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 230000006835 compression Effects 0.000 description 1
- 238000007906 compression Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000010606 normalization Methods 0.000 description 1
- 238000001208 nuclear magnetic resonance pulse sequence Methods 0.000 description 1
- 238000003672 processing method Methods 0.000 description 1
- 238000003786 synthesis reaction Methods 0.000 description 1
- 230000009466 transformation Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/41—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 target information of a frequency agile radar based on coherent accumulation. The method comprises the following steps: and establishing a target echo signal model of the frequency agile radar based on coherent accumulation, taking a phase error and scene sparsity of the target echo signal model as an optimization model of an optimization target, and solving the optimization model through a phase self-focusing algorithm reconstruction and an alternate direction multiplier method to further obtain self-adaptive phase difference, speed and distance information of the target and reconstruct target information. The method can accurately estimate the phase error of the target echo and reconstruct the observation scene, effectively solves the problem of reduced phase-coherent accumulation performance of the coherent agile radar caused by the phase error, provides good coherent accumulation performance, and realizes accurate estimation of the target in distance and speed.
Description
Technical Field
The invention relates to the technical field of coherent agile radars.
Background
The coherent agile radar (frequency agile coherentradar, FACR) combines the advantages of agile and coherent systems, on one hand, the coherent systems are utilized to provide signal phase information to improve the resolution capability of the radar to a target, and on the other hand, the agile technology is utilized to rapidly switch the working frequency of the radar, so that the radar obtains advantages in electronic countermeasure. At present, the means for realizing the reception of the coherent agile radar generally adopts a direct digital frequency synthesis method, but the direct frequency synthesis method can be adopted to realize the wide-range frequency modulation and avoid the interference of a large broadband because the direct digital frequency synthesis method cannot realize the frequency hopping in a range of several GHz, however, the random initial phase can not be generated among the pulses by the method, so that the coherent accumulation performance is influenced. How to realize the inter-pulse echo phase estimation caused by the inter-pulse random initial phase, the target distance and the speed and the good phase-coherent accumulation performance become 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 target echo phase is influenced by the random change of the pulse carrier frequency and the distance change between the target radars, and the traditional Doppler processing method of delay cancellation or fast Fourier transformation is not compatible with the frequency agile radar echo, so that the Doppler information of the target cannot be extracted.
Disclosure of Invention
The invention aims to provide a novel method for reconstructing target information of a agile radar, which can be used for accurately estimating the phase error of a target echo and reconstructing an observation scene, effectively solves the problem of reduced phase error caused by the phase error of a phase-coherent agile radar, provides good phase-coherent accumulation performance, and realizes accurate estimation of the target in terms of distance and speed.
The invention also aims to provide an application of the method.
The invention firstly discloses the following technical scheme:
the method for reconstructing the target information of the frequency agile radar based on coherent accumulation comprises the following steps:
establishing an echo signal model of the frequency agile radar based on 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 the target estimation error precision and the sparsity of the scattering coefficient matrix as optimization targets;
s3: and performing sparse reconstruction on the optimization model through a phase self-focusing algorithm, and performing iterative solution on the reconstructed optimization model through an Alternating Direction Multiplication Method (ADMM) to obtain an optimal phase error matrix and an optimal scattering coefficient matrix, so as to obtain adaptive phase difference, speed and distance information of a target, and realize reconstruction on 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 sub-problems to be solved alternately.
In the above scheme, the working mode of the frequency agile radar is to transmit a group of pulse strings with carrier frequencies changed randomly, and the pulse strings with different carrier frequencies are subjected to coherent processing to synthesize a larger bandwidth so as to obtain a distance high resolution.
According to some embodiments of the invention, the sparsity is determined by taking the matrix of scattering coefficientsAnd obtaining norms.
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 speed 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 a scattering coefficient vector of strong scattering points in a distance and velocity dimension. .
According to some embodiments of the invention, the reconstructing in step S3 comprises replacing the sparsity of the scattering coefficient matrix in the optimization model with an approximate estimate of the sparsity of the scattering coefficient matrix.
According to some embodiments of the invention, the echo signal model is:
y＝EFa+w(8)，
wherein,
y represents an observation data array of a range gate reference unit where the target is located, and is an n×1-dimensional vector composed of N pulse echoes, as follows:
y＝[y 0 ,y 1 ,...y N-1 ] T (9)，
y＝[y 0 ,y 1 ,...y n ，...y N-1 ] T (9)；
wherein the nth dimensional data y n Obtained by the formula:
and:
where N represents the total number of pulses within a coherent processing interval. w (w) n Represents noise, R l Representing the distance, v, of the first target scattering point in the nth pulse echo signal l Indicating its speed, f c Representing initial carrier frequency of a coherent agile radar transmitting pulse, wherein deltaf is a frequency hopping interval d n A frequency modulated codeword representing a random integer, i.e. the nth pulse,representing a fast time, where T r Representing pulse repetition period, t representing slow time, < +.>Representing the random initial phase of the nth pulse due to non-digital frequency hopping, R representing the distance of the target echo along the radar line of sight, v representing its velocity, and C (R, v) representing the target backscatter amplitude as a function of the target velocity and distance;
f represents an N multiplied by PQ dimension sparse dictionary matrix formed after the target signal is respectively discretized into P and Q scattered grid points in the distance dimension and the speed dimension, and the N multiplied by PQ dimension sparse dictionary matrix is as follows:
wherein the steering vector phi of the first target scattering point l ∈C N The nth element is:
l and l p ,l q Is of (2)The method comprises the following steps: l=l p ×Q+l q ，l q ＝mod(l,Q)；
a represents PQ multiplied by 1 dimension scattering coefficient vectors formed by target scattering points on the distance and speed dimension grid points;
w represents an additive noise vector;
e represents an N-dimensional phase error matrix as follows:
E＝diag(e) (11)，
wherein diag (·) represents a diagonal matrix formed by diagonal elements of the elements in vector e, vector e being as follows:
according to some embodiments of the invention, the optimization model is:
s.t.||y-EFa|| 2 ＜ε (13)，
wherein I 1 Representing the vector of the extracted quantityThe norm operation is performed such that, I.I 2 Representing +.>Norm manipulation, ||y-EFa || 2 Representing the phase error equation, ε= |w|| 2 Representing a noise threshold.
According to some embodiments of the invention, the reconstructed optimization model is:
wherein a is n Representing the nth element in the vector a,representation a n Delta represents the convergence threshold and delta > 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 termination condition is 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) Representing the t-th estimate of the phase error matrix, a (t) Representing 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:
wherein u= (λ) r +jλ i ) Wherein, O represents Hadamard product, ρ is penalty term coefficient, a, e, beta, u is value after ADMM iteration, (. Cndot. * Representing the conjugate of the matrix or vector.
According to some embodiments of the invention, the above-mentioned transformed optimization problem is addressed according to the following steps
Row iteration update:
a1 will e (t) ,β (t) ,u (t) Regarding the known quantity, a is updated by:
a2 will be a (t+1) ,β (t) ,u (t) Regarding the known quantity, e is updated by:
wherein q (t) ＝β (t) -Fa (t+1) +u (t) ，(·) * Representing to take conjugate;
a3 a is a (t+1) ,e (t+1) ,u (t) Regarding the known quantity, beta is updated by:
wherein,
a4 will a (t+1) ,e (t+1) ,β (t+1) Regarding the known quantity, u is updated by:
repeating the steps A1-A4 until convergence;
wherein a is (t) ,e (t) ,β (t) ,u (t) The value after the t-th ADMM iteration 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 random initial phase is introduced into the echo signal model, the coherent accumulated phase error model is obtained according to the echo signal model, and the minimum is established through the sparse characteristic of the target in distance-speed two dimensionsThe norm optimizing model adopts the alternating direction multiplier method to carry out the phase error self-adaptive estimation, realizes the accurate estimation of the target distance-speed and good coherent accumulation performance, and simultaneouslyThe side lobe level of the restored scene is obviously reduced due to the sparse characteristic of the target scene.
The invention can adaptively estimate the phase error, so that the target amplitude basically does not have large fluctuation along with the change of the phase error, and the invention has the advantage in calculation efficiency, and according to the simulation result, the system phase error estimation error is 2 under the condition of 20dB of signal-to-noise ratio ° In the method, compared with a direct phase self-focusing 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 comparison diagram of direct coherent accumulation and target scene restoration based on ADMM phase self-focusing sparse reconstruction in the specific 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 graph showing the comparison of the method of the present invention with reference to the ISAR phase self-focusing algorithm under different phase errors at snr=20 dB in the embodiment.
Fig. 4 is a diagram showing the convergence of the method of the present invention and the reference ISAR phase self-focusing method according to the embodiment.
Detailed Description
The present invention will be described in detail with reference to the following examples and drawings, but it should be understood that the examples and drawings are only for illustrative purposes and are not intended to limit the scope of the present invention in any way. All reasonable variations and combinations that are included within the scope of the inventive concept fall within the scope of the present 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 phase-coherent accumulation-based frequency agile radar;
s2: establishing an optimization model of the echo signal model, wherein the optimization model takes the estimated error precision and the sparsity of the scattering coefficient vector as optimization targets;
s3: reconstructing the optimization model through a phase gradient self-focusing algorithm, and iteratively solving the optimization model through an Alternate Direction Multiplication Method (ADMM) to obtain an optimal phase error matrix and a scattering coefficient vector, and further obtaining self-adaptive phase difference, speed and distance information of a target to reconstruct target information.
In a more specific implementation, the discrete model of the echo signal in step S1 is constructed as follows:
let the nth pulse of swift variable frequency radar transmission be:
wherein f n ＝f c +d n Δf, n=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 (Coherent Processing Interval, CPI), f c Representing initial carrier frequency of a coherent agile radar transmitting pulse, wherein deltaf is a frequency hopping interval d n A frequency modulated codeword that is a random integer, i.e., the nth pulse;representing a fast time, where T r Representing a pulse repetition period; t represents a slow time; a (·) represents a baseband signal, which may be a rectangular pulse and/or a chirp signal, etc.
The target echo with a velocity v in the radar line of sight direction, with a distance R, is:
the baseband signal is set as a rectangular pulse signal, the distance 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 can be obtained as follows:
where C (R, v) represents the target backscatter amplitude as a function of target speed and distance.
Further, consider that for a non-all-phase agile radar, there is a random initial phase due to non-digital frequency hopping in addition to the phase factor caused by the distance and speed of the target as described aboveSatisfying [0,2 pi), the echo signal of the target at the nth pulse can be expressed as:
wherein:
it can be seen that the first term of the phase in the index term in equation (4) is the phase due to the distance of the target, the second term is the phase due to the speed of the target, and the third term is the non-digital frequency hopping band to randomly phase.
Let the nth pulse echo signal contain L target scattering points, N c A clutter scattering point, wherein the distance of the first target scattering point is R l Speed v l Target scatter intensity C (R l ,v l ) The distance of the ith clutter scattering point is R i Speed v i Clutter scatter intensity C (R i ,v i ) The target echo can be expressed as:
wherein w is n Representing noise, typically Gaussian white noise。
In the above model, considering the tracking situation, that is, the target distance and speed can be obtained a priori, but a certain estimation error exists, the requirement of accurate compensation cannot be met, the target area and the clutter area can be separated, that is, the influence of the clutter can be ignored, and the following target echo model is obtained:
it can be further expressed in the following compact form:
y＝EFa+w (8)
wherein y represents observation data of a range gate reference unit where a target is located, the size of the range gate reference unit is an n×1-dimensional vector, and the range gate reference unit consists of N pulse echoes, and is expressed as:
y＝[y 0 ,y 1 ,...y n ，...y N-1 ] T (9)；
wherein the nth dimensional data y n Namely, the target echo obtained by the expression (7).
F represents an N multiplied by PQ dimension sparse dictionary matrix formed after the distance dimension and the speed dimension of the target observation scene are respectively discretized into P and Q scattered grid points, and the N multiplied by PQ dimension sparse dictionary matrix is expressed as:
wherein the steering vector phi of the first target scattering point l ∈C N The nth element is:
l and l p ,l q The relation of (2) is: l=l p ×Q+l q ，l q ＝mod(l,Q)；
a represents PQ multiplied by 1 dimension scattering coefficient vectors formed by target scattering points on the distance and speed dimension grid points;
w represents an additive noise vector;
e represents an N-dimensional phase error matrix as follows:
E＝diag(e) (11)，
wherein diag (·) represents a matrix operation with elements in vector e as diagonal elements, vector e being as follows:
wherein,representing the 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:
wherein I 1 Representing the vector of the extracted quantityThe norm operation is performed such that, I.I 2 Representing +.>Norm manipulation, ||y-EFa || 2 Representing an error equation for characterizing the accuracy of the estimated error of the reconstructed signal, wherein ε = i w i 2 Epsilon represents the noise threshold.
The optimization model is built by analyzing the observation equation of formula (8) and utilizing the sparsity of a. Based on compressed sensing theory, the sparsity of signals is utilized byThe norm optimization problem can be nearly perfectReconstructing the characteristics of the original signal. In the invention, the number of the strong scattering points of the target in the distance dimension-speed dimension is limited, so that the distance-speed distribution of the target can be approximately represented by the strong scattering points, the sparsity of the strong scattering points in the two-dimensional space is utilized, and the self-adaptive phase error is solved by establishing an optimization problem, so that the target distance-speed scene distribution based on sparse representation is obtained.
In the above optimization model, ||a 1 Representing a with only a few larger components, the other being mostly smaller components, to characterize the sparsity of the target in the distance-velocity dimension.
In the optimization model, epsilon is related to the recovery precision of the target scene, namely, different epsilon is set to obtain target distance-speed distribution with different sparsity. When epsilon takes a smaller value, the sparseness of the scene is weakened, and under the condition of low signal-to-noise ratio, the noise signal can be mistakenly considered as a target signal to be recovered, so that the scene recovery precision is affected. And conversely, when epsilon takes a larger value, the sparsity of the scene to be restored is enhanced, and the weak scattering point target is mistaken for a noise component, so that the scattering number of the restored target is relatively reduced, but the noise can be effectively inhibited. Therefore, under the condition of low signal-to-noise ratio, a larger epsilon value is preferable, so that noise can be effectively suppressed, and the target distance-speed scene distribution with better coherent accumulation can be obtained.
In a more specific implementation, step S3 may include:
the optimization problem of equation (13) is translated into one according to Kuhn-Tucker theory:
the objective function contains two constraint information of estimation error precision and scene sparsity. Wherein the constant mu > 0, the relationship between sparsity and estimation error accuracy 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 restrained, so that when the signal-to-noise ratio of the echo to be processed is lower, a larger mu value can be reasonably optimized, the sparsity is ensured, and the influence of noise is reduced.
To overcome the following problemsThe norm is not conductive at the zero point, and the invention approximates the problem by the following method:
wherein a is n Representing the nth element in the vector a,representation a n Delta represents the convergence threshold and delta > 0.
Substituting equation (15) into equation (14) can translate the optimization problem into:
it can be seen from the above model that the phases between the different pulses caused by random initial phases, velocities and distances are independent of each other and decoupled, i.e. the estimation of the sparse vector a and the phase error matrix E can be solved using alternating iterations.
The objective function in equation (16) is rewritten as:
the conjugate gradient function of a is obtained for the objective function as:
wherein:
the gradient of the conjugate gradient function is then the Hessian matrix of the objective function f (a):
wherein:
the Hessian matrix of the objective function is determined positively by the first term in the formula (20) being a semi-positive definite matrix, the second term being a positive definite matrix, the objective function being a convex function, and for an unconstrained convex function, the stable point, the local minimum point and the global minimum point are equivalent.
Let the conjugate gradient vector equal to zero vector, find the recurrence expression of a:
wherein E is (t) Representing the t-th estimate of the phase error matrix, a (t) Representing the t-th estimate of the sparse vector. The meaning of formula (22) is: firstly, carrying out phase compensation on echo signal observation data by using estimated phase errors, then carrying out coherent accumulation by using a sparse dictionary matrix, and finally carrying out amplitude normalization processing to obtain self-focusing sparse reconstruction scene distribution.
Without phase error a priori information, assume thatThe phase error recurrence expression can be expressed as:
and:
wherein [ (S)] n An nth element operation representing a fetch vector, conj (·) represents a conjugate operation, and |·| represents a modulo operation.
A can be obtained by the formulae (22), (23) and (24) (t+1) And E is (t+1) Is updated with the updated representation of (c).
The iteration termination condition is set as:
||a (t+1) -a (t) || 2 /||a (t) || 2 +||E (t+1) -E (t) || F /||E (t) || F ＜ζ (25)
wherein ζ represents a constant threshold value greater than zero.
When the two adjacent estimates of a and E satisfy equation (25) or satisfy a certain number of iterations, the iterative update is stopped.
The specific solution process may include:
step0, recording t as iteration times, initializing t=0, and starting the value a (0) Randomly generate, initial value E (0) Setting the matrix as an identity matrix;
step1, solving a vector a by using a conjugate gradient algorithm:
step2, updating E:
E (t+1) ＝diag(e (t+1) )
step3, if the iteration convergence condition is satisfied (t+1) -a (t) 2 /||a (t) || 2 +||E (t+1) -E (t) || F /||E (t) || F < ζ, ζ is a sufficiently small positive number, the algorithm terminates, otherwise let t=t+1, back to Step1.
In a more specific implementation, the solving of the reconstructed optimization model by the ADMM algorithm may include:
the following equivalent optimization problem is established:
wherein e i Representing the i-th element in the column vector e,representing Hadamard product due to e i Restriction of unit mode constraint, +.>Representing a noise threshold.
The equivalent optimization problem is obtained by considering the phase error matrix E in the equation constraint of equation (8) as an auxiliary variable and replacing it by the vector E.
According to the ADMM framework, the equivalent optimization problem is deformed into:
transform it into the form of an augmented lagrangian function as follows:
note u= (λ) r +jλ i ) And/ρ, the equation (31) can be transformed into:
let a be (t) ,e (t) ,β (t) ,u (t) For the value after the t-th ADMM iteration, the updating process is performed as follows:
a1 will e (t) ,β (t) ,u (t) Regarding the known quantity, update a:
wherein:
through (15) a 1 Is transformed into an approximation of:
the gradient function is obtained as follows:
let the gradient equal zero, the solution of a can be obtained by conjugate gradient algorithm as follows:
a2 will be a (t+1) ,β (t) ,u (t) Regarding the known quantity, update e:
wherein:
ignoring the constant part, converting it into:
n elements in the above formula e are required variables and are independent of each other, and can be decomposed into N sub-problems, and q is recorded (t) ＝β (t) -Fa (t+1) +u (t) The i-th sub-problem is:
will [ q ] (t) ] i ,Seen as a complex in-plane vector, then:
/>
where cos <.cndot >,.cndot > represents the cosine of the vector angle.
By ignoring the constant portion, the ith sub-problem can be translated into:
the geometric meaning of the problem is that k (i) which is more than or equal to 0 and less than or equal to k (i) < 1 is obtained, so that the included angle between two vectors of the complex plane is minimum.
And (3) making:
wherein arg (. Cndot.) represents a phase-taking operation.
The solution for k (i) is:
further can obtainIs as follows:
a3 a is a (t+1) ,e (t+1) ,u (t) Regarding the known quantity, update β:
wherein:
recording deviceThen the beta optimization solution is:
a4 will a (t+1) ,e (t+1) ,β (t+1) Regarding the known quantity, update u:
wherein:
repeating the steps A1-A4 until the algorithm converges, and judging the convergence condition as beta (t+1) -β (t) || 2 < ζ or a certain number of iterations is reached.
According to the above steps, a specific solving process may include:
step0, recording t as iteration times, initializing t=0, and giving a randomly generated initial value a (0) ,e (0) ,β (0) ,u (0)
Step1, solving a vector a by using a conjugate gradient:
step2, updating e:
wherein:
step3, updating beta:
step4, updating u:
step5, if the iteration convergence condition is satisfied (t+1) -β (t) || 2 < ζ, ζ is a sufficiently small positive number, the algorithm terminates, otherwise let t=t+1, back to Step1.
The following simulation experiment is performed through the identification process and the identification model described in the above specific embodiments:
simulation conditions:
in one CPI, the parameters of the coherent agile radar signal are set as: pulse number m=64, pulse repetition period T r Pulse width T =100 us p =20us, carrier frequency reference f 0 The frequency hopping method adopts pseudo-random traversal, the frequency hopping interval deltaf=16 MHz and the synthesis bandwidth B=1 GHz in the frequency hopping mode with the frequency hopping number of 64 in 10GHz, and the distance parameter R=118 m, the speed parameter v=10 m/s and the backscattering amplitude A=10 of a target are assumed to exist in an observation scene of a distance-speed dimension. The phase error takes the form of a random phase error.
In the reconstruction method of the invention, ADMM algorithm parameters are set as follows: convergence threshold ζ=10 -3 And the quadratic term penalty coefficient rho is correspondingly and reasonably set according to different signal-to-noise ratios. The initial value of the phase error matrix E is set as an identity matrix, the initial values of beta, a and u are randomly generated,
the direct coherent accumulation concrete calculation process in contrast to the ADMM algorithm includes:
the target echo model is
For agile coherent radar target distance-speed (R l ,v l ) The measurement problem of the value is classified into the matching problem of the echo on the (R ', v') plane, and the compensation phase is set as follows;
/>
the matching output result of the echo on the (R ', v') plane is that
At the matching point (R ', v '), there is AF (R ', v ', R, v) =nc ' (R) l ,v l ) Is the peak point.
Let Δr=r-R ', Δv=v-v', there are side lobes
Reference ISAR phase self-focusing calculation process in contrast to ADMM includes:
step one, recording t as iteration times, initializing t=0 and an initial value a (0) Randomly generate, initial value E (0) Set as an identity matrix.
Step two, updating the vector a by the following formula:
step three, updating E through the following formula:
E (t+1) ＝diag(e t(+1) )
and step four, if the iteration convergence condition (25) is met, the algorithm is terminated, otherwise, t=t+1 is returned to the step two, and the loop is continued.
The comparison of the conditions and processes described above with respect to figures 1-4 is obtained, wherein:
fig. 1 shows a comparison of direct coherent accumulation and target scene recovery based on ADMM phase self-focusing sparse reconstruction when the signal-to-noise ratio snr=10 dB and the phase error is randomly present. It can be seen that the method of the invention realizes accurate estimation of the target distance-speed and improves the coherent accumulation performance by self-adaptive estimation of the phase error, and simultaneously, the side lobe level of the recovery scene is obviously reduced by utilizing the sparse characteristic of the target scene.
Figure 2 shows a comparison of the direct coherent accumulation and the method of the present invention in the presence of phase errors at different signal-to-noise ratios. The method can obtain good coherent accumulation results under different signal to noise ratios, and the reason is that the method can effectively inhibit noise and ensure the balance between sparsity and estimation error precision. Meanwhile, under different phase errors, the direct phase-coherent accumulation is enabled to continuously reduce the target amplitude along with the increase of the phase errors, and the method can adaptively estimate the phase errors, so that the target amplitude basically does not have large fluctuation along with the change of the phase errors.
Fig. 3 shows a comparison of the method of the present invention with reference to the ISAR phase self-focusing algorithm at snr=20 dB for different phase errors. The method is superior to reference ISAR phase self-focusing algorithm in the aspect of coherent accumulation performance.
Fig. 4 shows the convergence of the method of the present invention and the reference ISAR phase self-focusing method, and it can be seen that after about 10 iterations, the method of the present invention gradually tends to converge, whereas the reference ISAR phase self-focusing tends to converge only about 15 iterations. Compared with the reference ISAR phase self-focusing method, the method of the invention improves the target reconstruction amplitude error by about 10 dB. Table 3 shows the calculation time of the two methods, and it can be seen that the method of the invention also has an advantage in terms of calculation efficiency.
TABLE 3 calculation time of the method of the present invention and reference ISAR phase self-focusing method
The above examples are only 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 concept of the invention belong to the protection scope of the invention. It should be noted that modifications and adaptations to the present invention may occur to one skilled in the art without departing from the principles of the present invention and are intended to be within the scope of the present invention.
Claims (8)
1. The method for reconstructing the target information of the frequency agile radar based on coherent accumulation is characterized by comprising the following steps of: comprising the following steps:
s1: establishing an echo signal model of the frequency agile radar based on 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 the target estimation error precision and the sparsity of the scattering coefficient matrix as optimization targets;
s3: sparse reconstruction is carried out on the optimization model through a phase self-focusing algorithm, iterative solution is carried out on the reconstructed optimization model through an alternating direction multiplier method, an optimal phase error matrix and an optimal scattering coefficient matrix are obtained, and then adaptive phase difference, speed and distance information of a target are obtained, so that reconstruction of the target information is realized;
wherein, the echo signal model is:
y＝EFa+w (8)，
wherein y represents an observation data array of a range gate reference unit where a target is located, and is an N-pulse echo composed vector with a size of n×1 dimensions, as follows:
y＝[y 0 ,y 1 ,...y n ，...y N-1 ] T (9)；
wherein the nth dimensional data y n Obtained by the formula:
and:
wherein N represents the total number of pulses in a coherent processing interval, w n Represents noise, R l Representing the distance, v, of the first target scattering point in the nth pulse echo signal l Indicating its speed, f c Representing initial carrier frequency of a coherent agile radar transmitting pulse, wherein deltaf is a frequency hopping interval d n A frequency modulated codeword representing a random integer, i.e. the nth pulse,representing a fast time, where T r Representing pulse repetition period, t representing slow time, < +.>Representing the random initial phase of the nth pulse due to non-digital frequency hopping, R representing the distance of the target echo along the radar line of sight, v representing its velocity, and C (R, v) representing the target backscatter amplitude as a function of the target velocity and distance;
f represents an N multiplied by PQ dimension sparse dictionary matrix formed after the target signal is respectively discretized into P and Q scattered grid points in the distance dimension and the speed dimension, and the N multiplied by PQ dimension sparse dictionary matrix is as follows:
wherein the steering vector phi of the first target scattering point l ∈C N Which is provided withThe nth element is:
l and l p ,l q The relation of (2) is: l=l p ×Q+l q ，
a represents PQ multiplied by 1 dimension scattering coefficient vectors formed by target scattering points on the distance and speed dimension grid points;
w represents an additive noise vector;
e represents an N-dimensional phase error matrix as follows:
E＝diag(e) (11)，
wherein diag (·) represents a diagonal matrix formed by diagonal elements of the elements in vector e, vector e being as follows:
the optimization model in the step2 is as follows:
wherein I 1 Representing the vector of the extracted quantityThe norm operation is performed such that, I.I 2 Representing +.>Norm manipulation, ||y-EFa || 2 Representing the phase error equation, ε= |w|| 2 Representing a noise threshold.
2. The reconstruction method according to claim 1, wherein: the sparsity is obtained by applying the method to theScattering coefficient matrix extractionAnd obtaining norms.
3. The reconstruction method according to claim 1, wherein: 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 speed factor of the target, and a phase factor due to a random initial phase generated by non-digital frequency hopping of the radar.
4. A reconstruction method according to claim 3, wherein: the scattering coefficient matrix comprises a vector of scattering coefficients of strong scattering points in the distance and velocity dimensions.
5. The reconstruction method according to claim 1, wherein: the reconstructing in step S3 includes estimating the sparsity of the scattering coefficient matrix in the surrogate optimization model with an approximation of the sparsity of the scattering coefficient matrix.
6. The reconstruction method according to claim 1, wherein: the reconstructed optimization model is as follows:
wherein a is n Representing the nth element in the vector a,representation a n Delta represents the convergence threshold and delta > 0.
7. The reconstruction method according to claim 6, wherein: in the step S3, in the solving of the reconstructed optimization model, the iteration termination condition is as follows:
||a (t+1) -a (t) || 2 /||a (t) || 2 +||E (t+1) -E (t) || F /||E (t) || F ＜ζ (25)，
wherein E is (t) Representing the t-th estimate of the phase error matrix, a (t) Representing the t-th estimate of the sparse vector, ζ represents a constant threshold value greater than zero.
8. The reconstruction method according to claim 6, wherein: solving the reconstructed optimization model by the following process:
establishing an equivalent optimization problem in the form of an augmented lagrangian function as follows:
wherein L is ρ Represents a lagrangian function, u= (λ) r +jλ i ) And/ρ, e represents the conjugate of the e vector,representing Hadamard product, ρ representing penalty term coefficients, a, e, β, u being the value of ADMM after iteration,
iteratively updating the equivalent optimization problem according to the following steps:
a1 will e (t) ,β (t) ,u (t) Regarding the known quantity, a is updated by:
a2 will be a (t+1) ,β (t) ,u (t) Regarding the known quantity, e is updated by:
wherein q (t) ＝β (t) -Fa (t+1) +u (t) ，(·) * Representing the conjugate；
A3 a is a (t+1) ,e (t+1) ,u (t) Regarding the known quantity, beta is updated by:
wherein,
a4 will a (t+1) ,e (t+1) ,β (t+1) Regarding the known quantity, u is updated by:
repeating the steps A1-A4 until convergence;
wherein a is (t) ,e (t) ,β (t) ,u (t) The value after the t-th ADMM iteration is represented, and the superscript t+1 correspondingly represents the value after the t+1-th iteration.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110342934.3A CN113075635B (en) | 2021-03-30 | 2021-03-30 | Method for reconstructing target information of frequency agile radar based on coherent accumulation |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110342934.3A CN113075635B (en) | 2021-03-30 | 2021-03-30 | Method for reconstructing target information of frequency agile radar based on coherent accumulation |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN113075635A CN113075635A (en) | 2021-07-06 |
| CN113075635B true CN113075635B (en) | 2024-04-12 |
Family
ID=76612008
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110342934.3A Active CN113075635B (en) | 2021-03-30 | 2021-03-30 | Method for reconstructing target information of frequency agile radar based on coherent accumulation |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN113075635B (en) |
Families Citing this family (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113589250B (en) * | 2021-07-29 | 2024-02-23 | 上海无线电设备研究所 | Sparse learning coherent agile radar distance high-resolution processing method |
| CN113721216A (en) * | 2021-08-30 | 2021-11-30 | 西安电子科技大学 | Target detection waveform optimization and processing method of agile coherent radar |
| CN114488132B (en) * | 2022-02-22 | 2023-01-20 | 北京卫星信息工程研究所 | Target detection method of satellite-borne GNSS-S radar |
| CN115436908B (en) * | 2022-11-10 | 2023-03-24 | 艾索信息股份有限公司 | Target detection method, device and medium based on radar frequency agile signal |
| CN115453490B (en) * | 2022-11-10 | 2023-03-24 | 艾索信息股份有限公司 | Coherent accumulation method, device and equipment based on radar signals and storage medium |
| CN116027280B (en) * | 2023-03-30 | 2023-06-09 | 西安电子科技大学 | Low peak sidelobe frequency coding radar waveform design method |
| CN116626646B (en) * | 2023-07-21 | 2023-09-22 | 西安电子科技大学 | Radar target gridding-free loss coherent accumulation method based on time-frequency non-uniform sampling |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110275166A (en) * | 2019-07-12 | 2019-09-24 | 中国人民解放军国防科技大学 | ADMM-based rapid sparse aperture ISAR self-focusing and imaging method |
| CN110703249A (en) * | 2019-11-05 | 2020-01-17 | 中国民航大学 | Robust and efficient synthetic aperture radar multi-feature enhanced imaging method |
| CN110703211A (en) * | 2019-08-29 | 2020-01-17 | 西安电子科技大学 | Distributed coherent radar phase error estimation method and system based on polynomial iteration |
| CN110954885A (en) * | 2019-11-26 | 2020-04-03 | 西安电子科技大学 | Adaptive target reconstruction method for frequency agile radar based on SBL |
| CN110954883A (en) * | 2019-11-12 | 2020-04-03 | 西安电子科技大学 | Non-parameter iteration self-adaption based frequency agile radar target reconstruction method |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7535408B2 (en) * | 2007-08-31 | 2009-05-19 | Lockheed Martin Corporation | Apparatus and methods for detection of multiple targets within radar resolution cell |
-
2021
- 2021-03-30 CN CN202110342934.3A patent/CN113075635B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110275166A (en) * | 2019-07-12 | 2019-09-24 | 中国人民解放军国防科技大学 | ADMM-based rapid sparse aperture ISAR self-focusing and imaging method |
| CN110703211A (en) * | 2019-08-29 | 2020-01-17 | 西安电子科技大学 | Distributed coherent radar phase error estimation method and system based on polynomial iteration |
| CN110703249A (en) * | 2019-11-05 | 2020-01-17 | 中国民航大学 | Robust and efficient synthetic aperture radar multi-feature enhanced imaging method |
| CN110954883A (en) * | 2019-11-12 | 2020-04-03 | 西安电子科技大学 | Non-parameter iteration self-adaption based frequency agile radar target reconstruction method |
| CN110954885A (en) * | 2019-11-26 | 2020-04-03 | 西安电子科技大学 | Adaptive target reconstruction method for frequency agile radar based on SBL |
Non-Patent Citations (3)
| Title |
|---|
| SAR imagery using chaotic carrier frequency agility pulses;Xiaojian Xu等;《 RADAR SENSOR TECHNOLOGY XV》;80211B-0-80211B-12 * |
| 捷变频信号相参积累方法;苏军海;《现代工业经济和信息化》;第66-69页 * |
| 频谱拥堵环境下的自适应雷达波形设计研究;赵德华;《中国博士学位论文全文数据库信息科技辑》;第86-103页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN113075635A (en) | 2021-07-06 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN113075635B (en) | Method for reconstructing target information of frequency agile radar based on coherent accumulation | |
| Xu et al. | Enhanced ISAR imaging and motion estimation with parametric and dynamic sparse Bayesian learning | |
| Zhang et al. | High-resolution ISAR imaging by exploiting sparse apertures | |
| Wu et al. | ISAR imaging of targets with complex motion based on discrete chirp Fourier transform for cubic chirps | |
| CN104898113B (en) | A kind of multi-input multi-output radar waveform design method | |
| Wang et al. | Enhanced ISAR imaging by exploiting the continuity of the target scene | |
| Zhang et al. | High-resolution ISAR imaging with sparse stepped-frequency waveforms | |
| Zhang et al. | Fast inverse-scattering reconstruction for airborne high-squint radar imagery based on Doppler centroid compensation | |
| CN110954884B (en) | StOMP-based frequency agile radar sparse scene target reconstruction method | |
| Kang et al. | Bistatic ISAR imaging and scaling of highly maneuvering target with complex motion via compressive sensing | |
| CN110275158A (en) | Wideband radar echo-signal method for parameter estimation based on Bayes's compressed sensing | |
| Zheng et al. | Fast parameter estimation algorithm for cubic phase signal based on quantifying effects of Doppler frequency shift | |
| Lin et al. | Long-time coherent integration for maneuvering target detection based on ITRT-MRFT | |
| Zheng et al. | Radar detection and motion parameters estimation of maneuvering target based on the extended keystone transform (July 2018) | |
| Rao et al. | Comparison of parametric sparse recovery methods for ISAR image formation | |
| Sun et al. | Airborne radar STAP using sparse recovery of clutter spectrum | |
| CN112014807A (en) | Self-adaptive clutter suppression method for frequency agile radar | |
| CN111044996A (en) | LFMCW radar target detection method based on dimension reduction approximate message transfer | |
| CN115877380A (en) | SAR multi-moving-target imaging method and device and storage medium | |
| CN114280594A (en) | Object level radar ranging method based on orthogonal matching pursuit | |
| Albaba et al. | Low-complexity forward-looking volumetric SAR for high resolution 3-D radar imaging | |
| Gu et al. | An impoved parameter estimation of LFM signal based on MCKF | |
| Zhang et al. | Multiband passive ISAR processing based on Bayesian compressive sensing | |
| Liu et al. | High resolution wideband imaging of fast rotating targets based on random PRI radar | |
| Zhang et al. | Tensor RPCA for downward-looking 3-D SAR imaging with sparse linear array |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant |