CN110286375B - LS high-order fast motion compensation method and system for near real-time ISAR imaging - Google Patents

LS high-order fast motion compensation method and system for near real-time ISAR imaging Download PDF

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CN110286375B
CN110286375B CN201910404901.XA CN201910404901A CN110286375B CN 110286375 B CN110286375 B CN 110286375B CN 201910404901 A CN201910404901 A CN 201910404901A CN 110286375 B CN110286375 B CN 110286375B
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张钦宇
薛佳音
王野
顾术实
张引根
严熠彬
吕劭鹏
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Shenzhen Graduate School Harbin Institute of Technology
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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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/904—SAR modes
    • G01S13/9064—Inverse SAR [ISAR]
    • 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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/9094—Theoretical aspects
    • 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
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Abstract

The invention provides an LS high-order rapid motion compensation method and a system for near-real-time ISAR imaging, the invention provides a high-order symmetric cumulative cross-correlation method based on least square, which optimizes the cumulative mode of a classical cross-correlation method, and makes up the defect that the existing cross-correlation method can not estimate high-order parameters by using least square fitting; high order parameter estimation and motion compensation are achieved at very low computational cost and without a priori knowledge. The invention has the beneficial effects that: the invention realizes high-order parameter estimation and motion compensation, optimizes the computation complexity to meet the rapid processing requirement of near real-time imaging, can perform blind processing, does not need a priori estimation interval, and reduces the burden of a transmitting system.

Description

LS high-order fast motion compensation method and system for near real-time ISAR imaging
Technical Field
The invention relates to the field of communication technology and radar signal processing, in particular to a near real-time ISAR imaging-oriented LS high-order fast motion compensation method and system.
Background
ISAR imaging is mainly based on the classical Range-Doppler (RD) principle, namely, two-dimensional position information of each scattering point forming a target is obtained through two-dimensional compression processing by using frequency diversity of a distance dimension and angle diversity of an azimuth dimension. The one-dimensional range image of the echo can move along with the observation sequence due to the radial motion of the target, so that the scattering points of the same range unit cannot be aligned by the next azimuth compression.
The distance-Instantaneous-Doppler imaging method (RID) based on time-frequency two-dimensional joint processing can well solve the problem by using a time-frequency two-dimensional slicing mode, but the time-frequency two-dimensional joint processing method has very high computational complexity and cannot well meet the real-time requirements of rapid imaging, target identification and classification in a general imaging system processing environment.
The traditional RD imaging method is low in operation cost and fast in imaging, and generally motion compensation processing based on parameter estimation is performed before azimuth compression. After the echo data are subjected to translation compensation, the one-dimensional range profile envelopes of all observation sequences are accurately aligned, and then subsequent azimuth resolution is performed, so that a clear ISAR image (as shown in FIG. 1) is obtained. Therefore, the accuracy of the parameter estimation and the quality of the motion compensation directly affect the quality of the imaging. The currently commonly used parameter estimation algorithms can be roughly classified into the following three categories:
(1) one is an algorithm based on the scattering points of the target, but it is difficult to stably track the points of interest as a whole within the observed integration time based on analysis of actual test data. Therefore, such algorithms are not very extensive in practical applications.
(2) The second type is a method for implementing distance alignment based on the envelope similarity of adjacent echoes, and is also a type of algorithm which is simpler to implement and most widely applied, and classical methods include a global distance alignment algorithm, a cross-correlation method (CCM), a cumulative cross-correlation method (ACCM), and the like. The CCM method is the earliest basic algorithm in a class of algorithms of mutual class processing and has the advantages of simplicity, practicability and low calculation complexity. The CCM method is realized by selecting a certain range profile (generally the first one) as a reference range profile, performing cross-correlation processing on the reference range profile and other range profiles to obtain a group of cross-correlation functions, and then estimating the differential distance between echoes of each time by aligning the peak values of cross-correlation function curves to obtain the estimated value of the motion parameter of the target. The ACCM improves the mode of CCM obtaining the cross-correlation function, strengthens stable strong frequency components in each echo by an accumulation concept, inhibits irregular fast-changing disturbance, effectively reduces accidental errors of the CCM method at the cost of very small complexity, and improves the estimation performance to a great extent. In an implementation scheme, each accumulated cross-correlation function of the ACCM is obtained by performing cross-correlation processing on each reference range profile, taking a plurality of range profiles in front of the reference range profile, and accumulating the range profiles and the reference profile.
(3) The third type is an algorithm based on image entropy, typically a minimum entropy algorithm (MEM), by searching for a target motion parameter corresponding to when the image entropy is minimum within a certain parameter range with a fixed accuracy.
Some existing technologies and methods have respective advantages, but also have disadvantages, specifically:
(1) for the estimation method based on strong scattering point class: from the analysis of measured data, it is difficult to find and track a strong scattering point which is stable in the whole imaging accumulation time (CPI), even if the echo of the same target has a slightly changed posture, the strong scattering point in the echo may disappear, so that the distance alignment method based on the scattering point is difficult to be applied in the practical ISAR engineering practice.
(2) Estimation methods based on entropy calculation (such as MEM): the method has the advantage that the high-order object motion parameters (such as acceleration) can be estimated, but an a priori estimation interval of the object motion parameters is generally required. On one hand, the radar transmitting system is required to alternately transmit wide and narrow band pulses to realize speed measurement and imaging, the system load is increased, or an estimation interval is obtained from echo data by an additional method, and the processing complexity is increased; on the other hand, the accuracy of the prior estimation interval has a great influence on the estimation performance of the algorithm — if the prior estimation interval does not contain the parameter true value, the estimation value obtained by the algorithm is completely invalid.
(3) The method based on the cross-correlation processing of the range profile comprises the following steps: the method has the advantages of simple implementation and capability of well meeting the requirement of near-real-time imaging processing. However, on the one hand, due to the fact that the echo of the actual flying target contains many varying factors, especially in some severe application environments, such as an aircraft observing internal disturbance components, such as a propeller aircraft, or in an imaging background with low signal-to-noise ratio, fluctuation variation of the scattering characteristics of the target can be very severe, and the fast-varying multi-peak envelope can influence the alignment accuracy of the cross-correlation, these factors can cause a large alignment error, and at this time, the existing algorithm cannot meet the imaging requirement in terms of accuracy or complexity, and specifically, the algorithm analysis is as follows:
a) CCM: the disadvantage is that alignment errors and incidental errors are large. On one hand, the wave adding distance image envelope under a complex condition is complex, so that the alignment error is very large; on the other hand, if a distance image has a large accidental error, the accidental error is continuously transmitted in the whole process of cross-correlation processing and alignment processing, so that the estimation performance of the algorithm is seriously reduced.
b) ACCM: although the concept of accumulation is utilized to effectively enhance the stable strong frequency components in the echo and greatly reduce the alignment error, and meanwhile, the accidental error caused by the individual distance image is also improved, the problem of the alignment error cannot be fundamentally solved from the perspective of the signal form, and in addition, a large phase accumulation error still exists in the accumulation process.
On the other hand, currently, such algorithms can only estimate the first-order motion parameters (i.e. speed) of the target, and when the target performs acceleration and deceleration motion within the observation dwell time, such algorithms cannot accurately perform high-quality estimation and compensation on the non-uniform motion.
Interpretation of terms:
ISAR: (Inverse Synthetic Aperture Radar).
RD: (Range-Doppler) distance-Doppler.
CCM: (Cross-Correlation Method) Cross-Correlation Method.
ACCM: (Accumulated Cross-Correlation Method).
MEM: (Minimun entrypy Method).
HSACM: (High-order Symmetric Accumulated Cross-Correlation Method).
Disclosure of Invention
The invention provides an LS high-order rapid motion compensation method facing near real-time ISAR imaging, which comprises the following steps:
step 1: construction of a discrete MxN echo matrix E from the baseband echo signals of an objectsM is the distance direction sampling number or the sub-pulse number, and N is the azimuth direction sampling number, namely the echo frequency;
step 2: for echo data EsOne-dimensional Fourier transform with the length of N is carried out according to the distance dimension to obtain one-dimensional range profile { RP) of each echon}；
And step 3: determining an optimal symmetric cumulative length Q;
and 4, step 4: calculating the expression of the cross-correlation function to obtain a set of U cumulative cross-correlation functions
Figure GDA0002916181250000031
Wherein U-N-2 (Q-1) represents the length of the symmetric accumulation region;
and 5: searching the peak value of each accumulated cross-correlation function, and calculating the corresponding difference distance { delta r according to each obtained correlation functionn1}；
Step 6: constructing a time matrix gamma, a distance difference matrix lambda and a corresponding least square relational expression, solving a least square problem, and calculating each order of motion parameters of a target;
and 7: for original echo data EsMultiplying by a compensation factor of the form
Figure GDA0002916181250000032
To achieve higher order motion compensation:
Figure GDA0002916181250000041
in the formula: f. oftThe instantaneous frequency of the transmitted carrier for the system; c is the speed of light in vacuum; v. ofiRepresenting the kinetic parameters of each order used to describe the radial motion of the target, and I-1, …, I being the highest description order that meets certain precision requirements, e.g. v1Representing the speed of radial movement of the first order, v2Radial acceleration representing the second order, etc.; t is a time variable.
As a further improvement of the present invention, in said step 3, an optimal symmetric cumulative length Q is determined according to equation 10, where equation 10 is:
Figure GDA0002916181250000042
wherein Q is the symmetric accumulation length, gamma is the accumulation factor, and N is the total number of echoes.
As a further improvement of the present invention, in step 6, the time matrix Γ and the distance difference matrix Λ in equation 19 and the corresponding least square relation are constructed, and the least square problem is solved according to equation 20 to calculate the motion parameters of each order of the target.
The invention also discloses an LS high-order rapid motion compensation system facing near real-time ISAR imaging, which comprises:
a construction unit: for constructing a discrete MxN echo matrix E from the baseband echo signals of an objectsM is the distance direction sampling number or the sub-pulse number, and N is the azimuth direction sampling number, namely the echo frequency;
a transformation unit: for echo data EsOne-dimensional Fourier transform with the length of N is carried out according to the distance dimension to obtain one-dimensional range profile { RP) of each echon}；
A processing unit: for determining an optimal symmetric cumulative length Q;
a calculation unit: an expression for calculating the cross-correlation function to obtain a set of U cumulative cross-correlation functions
Figure GDA0002916181250000045
Wherein U-N-2 (Q-1) represents the length of the symmetric accumulation region;
a search unit: for searching the peak value of each cumulative cross-correlation function, and calculating the corresponding difference distance { Δ r according to each obtained correlation functionn1}；
A construction unit: the method is used for constructing a time matrix gamma, a distance difference matrix lambda and a corresponding least square relational expression, solving a least square problem and calculating each order of motion parameters of a target;
an output unit: for the original echo data EsMultiplying by a compensation factor of the form
Figure GDA0002916181250000043
To achieve higher order motion compensation:
Figure GDA0002916181250000044
in the formula: f. oftThe instantaneous frequency of the transmitted carrier for the system; c is the speed of light in vacuum; v. ofiRepresenting the kinetic parameters of each order used to describe the radial motion of the target, and I-1, …, I being the highest description order that meets certain precision requirements, e.g. v1Representing the speed of radial movement of the first order, v2Radial acceleration representing the second order, etc.; t is a time variable.
The invention has the beneficial effects that: the invention realizes high-order parameter estimation and motion compensation, optimizes the computation complexity to meet the rapid processing requirement of near real-time imaging, can perform blind processing, does not need a priori estimation interval, and reduces the burden of a transmitting system.
Drawings
FIG. 1 is a range-Doppler schematic of ISAR imaging in the background art;
FIG. 2 is a schematic diagram of an ISAR imaging system;
FIG. 3 is a schematic diagram of the optimized symmetric cumulative cross-correlation function method;
FIG. 4a is a graph of the cross-correlation function in the CCM parameter estimation method;
FIG. 4b is a graph of a one-way cumulative cross-correlation function in the ACCM parameter estimation method;
FIG. 4c is a diagram of the symmetric cumulative cross-correlation function in the parameter estimation method HSACM of the present invention;
FIG. 4d is a graph of differential distance perturbation for different modes of cross-correlation function;
FIG. 5 is a schematic flow chart of the present invention for ISAR motion compensation and imaging;
FIG. 6a is a Normalized Mean Square Error (NMSE) plot of first order parameters;
FIG. 6b is a Normalized Mean Square Error (NMSE) plot of a second order parameter;
FIG. 7 is a graph of computational complexity for various types of estimation methods;
FIG. 8a is a distance alignment chart of the ACCM method (high order compensation deficiency);
FIG. 8b is a MEM method distance alignment chart (compensation accuracy is low);
FIG. 8c is a MEM method distance alignment chart (compensation accuracy is high);
FIG. 8d is a distance alignment chart for the high order compensation method of the present invention;
FIG. 9a is an ACCM high order compensation deficiency ISAR image map;
FIG. 9b is a low precision MEM compensated ISAR image map;
FIG. 9c is a high precision MEM compensated ISAR image map;
fig. 9d is an HSACM compensated ISAR image map.
Detailed Description
The invention aims at the application requirements of high-quality motion compensation and low-complexity rapid processing in a near-real-time Radar imaging application scene, and solves the defects and problems of the existing parameter estimation method in the motion compensation link of Inverse Synthetic Aperture Radar (ISAR) imaging.
Aiming at the defects in the background art, the invention aims to solve the following problems in the parameter estimation and motion compensation links in near-real-time ISAR imaging processing:
(1) and high-order parameter estimation and motion compensation are realized.
(2) And optimizing the computational complexity to meet the rapid processing requirement of near real-time imaging.
(3) Blind processing is carried out, a priori estimation interval is not needed, and the load of a transmitting system is reduced.
The invention discloses an LS high-order rapid motion compensation method facing near real-time ISAR imaging, and provides a high-order parameter estimation method (HSACM) based on Least Square (LS) fitting as a core algorithm of a motion compensation scheme in order to realize high-precision and low-complexity motion compensation of ISAR imaging. The invention relates to a cross-correlation parameter estimation method, which is derived from a widely used first-order parameter estimation method ACCM. The parameter estimation and motion compensation scheme proposed by the present invention is described in detail in the following from the aspects of signal model of application system, technical principle of proposed algorithm, specific implementation scheme, and technical application of scheme.
1. And (3) system signal model:
according to the RD principle, an ISAR image of an object is essentially a projection of the object onto a range-doppler plane, and fig. 2 is a schematic diagram of an ISAR imaging system. The X axis is the distance direction, namely the radar line of sight (RLOS) direction, the Y axis is the azimuth direction, namely the target rotation tangent direction, and O is the target phase center. For ease of discussion, regardless of initial phase and initial distance, for far-field small-angle observation targets, its fundamental radar echo may be expressed as
Figure GDA0002916181250000061
In the formula, Pk(xk，yk) Is the coordinate position of the kth scattering point relative to the phase center of the object, AkIs the backscatter intensity. f. oftInstantaneous frequency of carrier wave, theta, for system transmissionlIs the angular change caused by the target rotation during the observation. RtIs the instantaneous distance of the target phase center relative to the radar. Without loss of generality, the target radial motion can be described by the Taylor series as follows:
Figure GDA0002916181250000062
where Δ r is the instantaneous position offset caused by the radial motion of the target; v. ofiRepresenting the radial motion parameter of the ith order, i.e. v1Is radial velocity, v2Is the radial acceleration. For the cooperative observation target, the radial motion of the cooperative observation target is generally uniform motion and can be described by first-order parameters; for most non-cooperative observation targets, the radial component of the non-cooperative observation target can be accurately described by a second-order parameter。
In actual radar signal processing, continuous broadband signals are generally sampled in a fast time dimension and a slow time dimension to form range-azimuth two-dimensional echo data. Assume that during the observed integration time, the system transmits N sets of Step Frequency (SF) signals, each set of signals containing M sub-narrow pulses. Sub-pulse carrier frequency of ft＝f0+ m.DELTA.f, wherein f0At the center carrier frequency, Δ f is the step frequency. Let the pulse repetition time be TrAnd satisfy M.Tr≤TB. Then in the fast time dimension there is
Figure GDA0002916181250000075
The slow time dimension has t ═ mTr+nTB(M-0, 1, 2, …, M-1; N-0, 1, 2, …, N-1 are fast and slow time dimension indices, respectively). Two-dimensional echo data can thus be obtained as follows:
suppose that the object moves with a first order motion parameter v in the RLOS direction1Uniform rotation, based on the distance-Doppler principle, ISAR uses fast time dimension frequency diversity and slow time dimension angle diversity to realize two-dimensional compression, and the matrix form of echo signal is
Figure GDA0002916181250000071
It can be seen that at fm～xk，θn～ykOutside the formed transformation pair, there is a phase term caused by radial motion
Figure GDA0002916181250000072
Wherein
Figure GDA0002916181250000073
The existence of the phase term shown in equation (8) results in the distance envelope being parameterized by the orientation for compressionviA translation is generated such that scattering points within the same range bin cannot be aligned with a peak in the azimuth direction. Therefore, in ISAR imaging, parameter estimation needs to be performed on each order of translation, and then motion compensation processing is performed to compensate the phase term shown in (8), so that further imaging processing is facilitated, and a two-dimensional ISAR image in the following form is obtained
Figure GDA0002916181250000074
2. The technical principle of the invention is as follows:
2.1. symmetric accumulation and complexity optimization:
in order to solve the problem of phase error transmission and accumulation in the CCM method, the accumulated cross-correlation method ACCM uses the concept of accumulation, and performs cross-correlation between the current one-dimensional image and the first Z-1 one-dimensional images to complete the estimation and alignment of the distance offset, where Z is the cumulative number of pulses. Let each echo distance image obtained by distance compression be { RPn}，RPrefIs a reference range profile (typically with the first range profile as a reference).
Compared with CCM, although the method of accumulation in ACCM can strengthen stable components in spectrum components, suppress fast-varying disturbance and noise components, and improve the accuracy of distance alignment to a greater extent, the total correlation function obtained by such a unidirectional accumulation manner may accumulate phase errors in a single direction, thereby affecting the accuracy of distance alignment. The invention thus makes use of an improved symmetrical accumulation for generating the correlation function, i.e. a one-dimensional range profile of the current echo as a reference, for which the forward and backward one-dimensional range profiles are cross-correlated in a pair-wise fashion, as shown in fig. 3.
In actual discrete data processing, the correlation function between the range images can be quickly calculated by using the following formula by utilizing the relation between the cross-correlation and the convolution operation and the convolution theorem of the time-frequency domain
Cnr＝|IFFT(FFT(|RPref|)·FFT(|RPn|*)| (11)
In the formula, FFT (-) and IFFT (-) represent fast Fourier transform and fast inverse Fourier transform, respectively.
Correspondingly, in the symmetrical cumulative cross-correlation process of the present invention, the cumulative correlation function to be calculated is based on the distance image RP of the superimposed referencenThe cross-correlation function with the distance images of the symmetry numbers of the front and back directions is obtained, namely:
Figure GDA0002916181250000081
where Q is the symmetric cumulative length. For the sake of easy discussion of the performance of the algorithm, the symmetric accumulation length Q is generally taken as ceil { mod (Z, 2) }, i.e., Q is rounded up by half Z, so that the pulse accumulation number of the symmetric accumulation is equivalent to the one-way accumulation. To discuss the determination of the optimal accumulation length, we define an accumulation factor as follows:
Figure GDA0002916181250000082
where ρ ═ 2Q/N represents an accumulation ratio; l ═ L/deltacrNumber of sampling points, δ, required in azimuth direction to represent a target of length LcrIndicating the resolution of the azimuth direction. Without loss of generality, the target body length L is 24m and deltacrIota-64 is obtained when 0.375m is common.
On one hand, the larger the accumulation length is, the more stable components in the echo can be enhanced, and the better the estimation precision can meet the requirement of motion compensation; on the other hand, the more range images participate in the accumulation (especially those echoes that are further from the reference range image), the greater range walk and rotation angles are produced by the system, which can lead to the problem of the more unit range walk (MTRC) that is common in imaging. In view of the above, the accumulated length is preferably 0.5 to 1 times of the number of sampling points in one azimuth resolution unit. Therefore, the optimal range of the accumulation factor γ is 0.5-1, and the optimal symmetric accumulation length can be determined by the following formula:
Figure GDA0002916181250000091
compared with the traditional accumulation mode used by the ACCM, the symmetrical accumulation mode used by the invention can eliminate positive and negative phase errors generated when the current reference range profile is in cross correlation with the forward and backward range profiles, namely, the phase correction is realized at the same time in the range alignment link. Fig. 4(a, b, c) shows the cross-correlation function generated by different accumulation modes, and the curve of fig. 4d shows the error disturbance situation corresponding to various modes.
As can be seen from fig. 4a, 4b, and 4c, a set of cross-correlation function curves obtained by the CCM method is noisy and multimodal, and the intervals of the peak positions of the curves are not regular, which undoubtedly brings a very large error to the distance alignment; the ACCM method utilizes an accumulation concept, strengthens stable components in adjacent echo signals, has good regularity of peak value intervals and certain suppression of noise, but has larger errors in searching peak value positions because phase errors are accumulated continuously; the symmetric accumulation mode adopted by the invention eliminates the positive and negative phase errors generated in each pair of cross-correlation processing, so that the obtained group of cross-correlation curves has better performances in the aspects of noise suppression, peak value search, error reduction and the like. The perturbation curve shown in fig. 4d verifies that the cumulative method used in this scheme produces the smallest error perturbation.
The above verifies the effectiveness of the symmetric accumulation approach in reducing alignment errors, while on the other hand, we consider the computational complexity of the further optimization scheme in order to meet the real-time performance of the system imaging process. As can be seen from FIG. 3, the cross-correlation function C of region II in the figure is due to the cumulative symmetryijAnd CjiExhibits mirror symmetry with respect to the diagonal elements. From the commutative nature of the convolution operation, it is known
Cij＝Cji (15)
Therefore, when the cross-correlation processing is performed by using the symmetric accumulation scheme, the computational complexity of the algorithm can be further optimized. In FIG. 3, Q ═ is4 (i.e., Z ═ 8) for example, an optimizable structure for symmetric cumulative cross-correlation processing is shown. It can be seen that the cross-correlation function C is obtained in region II of the figureijAnd CjiSubscript symmetry exists. Therefore, the cross-correlation function required to be calculated in the area II only needs to calculate the upper triangular area or the lower triangular area. That is, the amount of convolution operations that need to be performed in the entire II region can be reduced by half.
We next performed a quantitative analysis of the optimization of computational complexity in the present invention. Table 1 lists the number of convolution calculations required for each sub-region in fig. 3, and the expression of the subscript of the cross-correlation function for each sub-region. In the table, U-N-2 (Q-1) indicates the length of the symmetric accumulation region, and U-7 corresponds to SACR4 to SACR10 in fig. 3. In Table IIuAnd IIdThe upper triangular zone and the lower triangular zone in region II of figure 3 are shown, respectively.
Table 1 table of cross-correlation functions corresponding to the regions of fig. 3
Figure GDA0002916181250000101
Then, according to fig. 3 and table 1, we can obtain that the number of cross-correlation functions that can be reduced in region II is calculated as
Figure GDA0002916181250000102
The total number of convolution operations which need to be calculated when optimization is not carried out is
NS＝(N-Z+2)(Z-2)＝2U(Q-1) (17)
Therefore, after the calculation complexity is optimized, the total number of the cross-correlation functions required to be calculated is obtained as
Ncon＝U2 (18)
Then the overall degree of optimization of the algorithm can be calculated as
Figure GDA0002916181250000103
Because the symmetric accumulation length Q is far less than the length N of the cross-correlation function, namely Q/(4U) is approximately equal to 0, the complexity optimization is carried out by utilizing a symmetric accumulation mode, and the following optimization degree can be approximately obtained
Odrg≈5％ (20)
Taking N-256, γ -0.5, and Q-4 as an example, to perform parameter estimation and calculate the cumulative cross-correlation function, the ACCM method needs to perform 62500 convolution operations to obtain the cross-correlation function participating in the accumulation, whereas the operation number can be reduced to 31384 times in the solution of the present invention. The computational complexity of the CCM, ACCM and the accumulation mode used in the scheme of the present invention is shown in table 2.
TABLE 2 computational complexity
Figure GDA0002916181250000111
2.2 least squares fit solution higher order parameter estimation:
the motion parameters of the target are contained in the cross-correlation function obtained in the symmetric accumulation processing mode, so in order to realize high-order parameter estimation on the target, distance difference information contained in the cross-correlation function is modeled into a least square problem, and an estimated value of the parameters is obtained by solving an LS problem.
Assume that the distance offset between the symmetric cumulative cross-correlation functions based on the nth and 1 st reference range profiles is Δ rn1Then, the mathematical relationship between the motion parameters and the distance offset of each order can be derived from equation (9):
Figure GDA0002916181250000112
briefly, the data matrix in the above formula
Figure GDA0002916181250000113
Representing time interval data; note the book
Figure GDA0002916181250000114
The parameter matrix of each order is obtained; and
Figure GDA0002916181250000115
is a distance offset matrix. Then the formula (21) can be abbreviated as
ΓV＝Λ (22)
Thus, the high order parameter estimation problem can be translated into a solution LS problem that solves the matrix V:
Figure GDA0002916181250000116
since in practical application scenarios the target radial motion can be accurately described by 2-order motion parameters, i.e. 1 < N, Γ is always column-full-rank, the above LS problem can be solved by computing the left pseudo-inverse of Γ:
Figure GDA0002916181250000117
in the formula (I), the compound is shown in the specification,
Figure GDA0002916181250000118
left pseudo-inverse matrix of the representation matrix, (-)HHermitian transpose of the representation matrix, (.)-1Representing the inverse of the invertible matrix. By solving the above LS problem, target high order motion parameter estimation and high order motion compensation can be achieved.
3. The implementation scheme of the invention is as follows:
in summary, the parameter estimation and motion compensation scheme provided by the invention utilizes a symmetric accumulation mode to generate a cross-correlation function, and then realizes parameter estimation by modeling as a least square problem, thereby realizing the distance alignment and phase correction links of motion compensation. As shown in fig. 5, the specific scheme of the present invention is as follows:
step 1: construction of a discrete MxN echo matrix E from the baseband echo signals of an objectsM is the distance direction sampling number or the sub-pulse number, and N is the azimuth direction sampling number, namely the echo frequency;
step 2: go back toWave data EsOne-dimensional Fourier transform with the length of N is carried out according to the distance dimension to obtain one-dimensional range profile { RP) of each echon}；
And step 3: determining an optimal symmetric cumulative length Q according to equation 10;
and 4, step 4: the expression of the cross-correlation function is calculated according to Table 1 to obtain a set of U cumulative cross-correlation functions
Figure GDA0002916181250000121
Wherein U-N-2 (Q-1) represents the length of the symmetric accumulation region;
and 5: searching the peak value of each accumulated cross-correlation function, and calculating the corresponding difference distance { delta r according to each obtained correlation functionn1}；
Step 6: constructing a time matrix gamma, a distance difference matrix lambda and a corresponding least square relational expression in a formula 19, and solving a matrix V according to a formula 20 to further calculate each order motion parameter of the target;
and 7: for original echo data EsMultiplying by a compensation factor of the form
Figure GDA0002916181250000122
To achieve higher order motion compensation:
Figure GDA0002916181250000123
in the formula: f. oftThe instantaneous frequency of the transmitted carrier for the system; c is the speed of light in vacuum; v. ofiRepresenting the kinetic parameters of each order used to describe the radial motion of the target, and I-1, …, I being the highest description order that meets certain precision requirements, e.g. v1Representing the speed of radial movement of the first order, v2Radial acceleration representing the second order, etc.; t is a time variable.
4. The technology of the invention is applied as follows:
the high-order parameter estimation method based on the least square can be used as a high-order motion compensation scheme for the near real-time imaging requirement, and high-quality pre-information is provided for the rapid identification and classification of non-cooperative targets. The higher-order parameter estimation method proposed by the scheme is first discussed in terms of performance of parameter estimation and operation cost of the scheme.
With the classical first-order methods CCM, ACCM and second-order MEM methods as representative comparison algorithms, fig. 6a and 6b give Normalized Mean Square Error (NMSE) curves for the first-order and second-order parameters, and fig. 7 gives the corresponding computational complexity curves. NMSE is defined as follows:
Figure GDA0002916181250000124
wherein N ismlMonte-Carlo number of times, X, representing the experimentest，iFor each estimated sample observation, XrealIs the true value of the estimated parameter. RMSE is the root mean square error. As can be seen from the figure, for the low-order parameter estimation, the proposed scheme performs the best estimation performance, especially compared to the MEM method, because it is not limited to the precision step set in advance, and the generated estimation error tends to decrease as the SNR increases; for higher order parameter estimation, the proposed method performs similarly to the MEM method, but in contrast, the proposed scheme is much less computationally complex than the MEM method. In summary, the parameter estimation method of the proposed scheme has the minimum estimation error and the minimum computation cost, and thus exhibits the best performance-cost balance.
Specifically applied to the ISAR imaging process, fig. 8 and 9 show the distance compression result and ISAR imaging result after motion compensation by the ACCM method, the low-precision and high-precision MEM method, and the HSACM method proposed by the present invention, respectively. The simulation parameter setting target has a second order motion parameter. Table 3 shows the operation time and the image entropy for each method. As can be seen from the figure, in the figure a), because the second-order parameters are not estimated and the high-order compensation is insufficient, the distance images are not well aligned, and the generated ISAR image presents obvious ghosts; although the high-order parameters are estimated by the MEM method in the diagram b), the compensation accuracy is low due to the low estimation accuracy of the setting when the low calculation complexity is pursued, and the obtained imaging result is also far from ideal. The graph c) improves the precision and obtains better distance alignment and imaging results, but the calculation complexity is rapidly increased, and the operation processing time of nearly ten seconds is consumed; graph d) presents quality alignment and imaging results with high precision MEM, but at computational cost in milliseconds. Therefore, the scheme provided by the invention can realize high-order parameter estimation and high-precision motion compensation with very small calculation cost, and is very beneficial to near-real-time ISAR imaging processing.
TABLE 3 image quality and computational cost
FIG. 9 Corresponding method Entropy of images Operation time (seconds)
a) ACCM 3.5334 0.0468
b) MEM (Low precision) 3.3529 0.4309
c) MEM (high precision) 2.6864 7.3808
d) HSACM 2.6668 0.0484
The invention also discloses an LS high-order rapid motion compensation system facing near real-time ISAR imaging, which comprises:
a construction unit: for constructing a discrete MxN echo matrix E from the baseband echo signals of an objectsM is the distance direction sampling number or the sub-pulse number, and N is the azimuth direction sampling number, namely the echo frequency;
a transformation unit: for echo data EsOne-dimensional Fourier transform with the length of N is carried out according to the distance dimension to obtain one-dimensional range profile { RP) of each echon}；
A processing unit: for determining an optimal symmetric cumulative length Q;
a calculation unit: an expression for calculating the cross-correlation function to obtain a set of U cumulative cross-correlation functions
Figure GDA0002916181250000144
Wherein U-N-2 (Q-1) represents the length of the symmetric accumulation region;
a search unit: for searching the peak value of each cumulative cross-correlation function, and calculating the corresponding difference distance { Δ r according to each obtained correlation functionn1}；
A construction unit: the method is used for constructing a time matrix gamma, a distance difference matrix lambda and a corresponding least square relational expression, solving a least square problem and calculating each order of motion parameters of a target;
an output unit: for the original echo data EsMultiplying by a compensation factor of the form
Figure GDA0002916181250000141
To achieve higher order motion compensation:
Figure GDA0002916181250000142
in the formula: f. oftThe instantaneous frequency of the transmitted carrier for the system; c is the speed of light in vacuum; upsilon isiRepresents each dynamic parameter of order for describing the radial movement of the target, and I is 1, …, I is the highest description order satisfying certain precision requirement, such as upsilon1Representing the velocity of radial movement of first order, u2Radial acceleration representing the second order, etc.; t is a time variable.
In the processing unit, an optimal symmetric cumulative length Q is determined according to equation 10, where equation 10 is:
Figure GDA0002916181250000143
wherein Q is the symmetric accumulation length, gamma is the accumulation factor, and N is the total number of echoes.
In the calculation unit, the expression of the cross-correlation function is calculated according to Table 1 to obtain a set of U cumulative cross-correlation functions
Figure GDA0002916181250000146
Subscript thereof
Figure GDA0002916181250000145
The range is Q to (N-Q + 1).
In the construction unit, a time matrix Γ and a distance difference matrix Λ in formula 19 and a corresponding least square relation are constructed, and a least square problem is solved according to formula 20 to calculate each order motion parameter of the target.
The high-order motion compensation scheme provided by the invention belongs to the second method of the background technology in principle, namely, the motion parameters of the target are estimated by utilizing the correlation and the difference distance of adjacent echoes, so that the motion compensation is realized. The most similar implementation scheme of the invention is the most widely applied cumulative cross-correlation method (ACCM), but the scheme of the invention improves the accumulation mode of the ACCM, optimizes the computational complexity and most importantly makes up the defect that the algorithm can not estimate high-order parameters.
Aiming at the problem that the existing parameter estimation algorithm can not carry out high-order motion parameter estimation quickly and efficiently, the invention aims to find a quick high-order motion compensation method, so that higher estimation precision can be obtained at lower calculation cost, and the ISAR imaging quality is improved. The High-order Symmetric Accumulated Cross-Correlation Method (HSACM, High-order Symmetric Accumulated Cross-Correlation Method) based on the least square optimizes the accumulation mode of the classical Cross-Correlation Method, and makes up the defect that the existing Cross-Correlation Method can not estimate High-order parameters by using least square fitting; high order parameter estimation and motion compensation are achieved at very low computational cost and without a priori knowledge. The invention better solves the balance problem between high-precision compensation and calculation complexity, and provides superior precondition for realizing rapid high-quality near real-time imaging processing.
The contributions and advantages of the invention are as follows:
(1) first, the proposed method uses symmetric accumulation instead of the traditional one-way accumulation to generate the cross-correlation function. This symmetry effectively cancels out positive and negative phase errors, which is very advantageous for range image alignment and phase correction.
(2) In addition, due to the convolution symmetry property of the cross-correlation function, the calculation cost of the proposed scheme is optimized by half compared with that of the ACCM, which is very beneficial for realizing near real-time imaging processing.
(3) Third, the method proposed by the present invention formulates the parameter estimation as solving a Least Squares (LS) problem, thereby achieving high order parameter estimation. The significance of the method is that the provided scheme makes up for the ubiquitous defect in estimating high-order parameters of an algorithm based on distance image correlation processing.
(4) The method of the present invention is a blind processing method compared to MEM. That is to say, the radar system is not required to alternately transmit broadband and narrowband waves to obtain the priori knowledge (namely the estimation range of the parameters), the calculation complexity of the method is different from that of the MEM method by 2-3 orders of magnitude and is far smaller than that of the MEM method, and the real-time requirement can be better met on the premise of achieving the same compensation precision.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (6)

1. A LS high-order fast motion compensation method facing near real-time ISAR imaging is characterized by comprising the following steps:
step 1: constructing a discrete MxN echo matrix Es by a baseband echo signal of a target, wherein M is a distance direction sampling number or a sub-pulse number, and N is an azimuth direction sampling number, namely an echo frequency;
step 2: one-dimensional Fourier transform with the length of N is carried out on the echo data Es according to the distance dimension to obtain one-dimensional range profile { RP (distance regression) of each echon}；
And step 3: determining an optimal symmetric cumulative length Q;
and 4, step 4: calculating the expression of the cross-correlation function to obtain a set of U cumulative cross-correlation functions
Figure FDA0002988931360000011
Wherein U-N-2 (Q-1) represents the length of the symmetric accumulation region;
and 5: searching the peak value of each accumulated cross-correlation function, and calculating the corresponding difference distance { delta r according to each obtained correlation functionn1}；
Step 6: constructing a time matrix gamma, a distance difference matrix lambda and a corresponding least square relational expression, solving a least square problem, and calculating each order of motion parameters of a target;
and 7: for original echo data EsMultiplying by a compensation factor of the form
Figure FDA0002988931360000012
To realize high orderAnd motion compensation:
Figure FDA0002988931360000013
in the formula: f. oftThe instantaneous frequency of the transmitted carrier for the system; c is the speed of light in vacuum; v. ofiRepresents each order of dynamic parameters for describing the target radial motion, I is 1, …, I is the highest description order meeting certain precision requirement, v1Representing the speed of radial movement of the first order, v2Radial acceleration representing the second order; t is a time variable.
2. The LS higher order fast motion compensation method according to claim 1, wherein in step 3, the optimal symmetric cumulative length Q is determined according to equation 10, where equation 10 is:
Figure FDA0002988931360000014
wherein Q is the symmetric accumulation length, gamma is the accumulation factor, and N is the total number of echoes.
3. The LS high-order fast motion compensation method according to claim 1, wherein in the step 6, a time matrix Γ and a distance difference matrix Λ in formula 19 and a corresponding least square relation are constructed, and a least square problem is solved according to formula 20 to calculate each order motion parameter of the target;
equation 19:
Figure FDA0002988931360000021
in the formula
Figure FDA0002988931360000022
Is a time interval matrix;
Figure FDA0002988931360000023
the parameter matrix of each order is obtained;
Figure FDA0002988931360000024
is a distance offset matrix;
equation 20:
Figure FDA0002988931360000025
in the formula (I), the compound is shown in the specification,
Figure FDA0002988931360000026
left pseudo-inverse matrix of the representation matrix, (-)HHermitian transpose of the representation matrix, (.)-1Representing the inverse of the invertible matrix.
4. A LS higher order fast motion compensation system oriented to near real time ISAR imaging, comprising:
a construction unit: the method comprises the steps that a discrete MxN echo matrix Es is constructed by a baseband echo signal of a target, M is a distance direction sampling number or the number of sub-pulses, and N is an azimuth direction sampling number, namely echo times;
a transformation unit: the method is used for performing one-dimensional Fourier transform with the length of N on echo data Es according to a distance dimension to obtain a one-dimensional range profile { RP (distance regression) of each echon}；
A processing unit: for determining an optimal symmetric cumulative length Q;
a calculation unit: an expression for calculating the cross-correlation function to obtain a set of U cumulative cross-correlation functions
Figure FDA0002988931360000027
Wherein U-N-2 (Q-1) represents the length of the symmetric accumulation region;
a search unit: for searching the peak value of each cumulative cross-correlation function, and calculating the corresponding difference distance { Δ r according to each obtained correlation functionn1}；
A construction unit: the method is used for constructing a time matrix gamma, a distance difference matrix lambda and a corresponding least square relational expression, solving a least square problem and calculating each order of motion parameters of a target;
an output unit: for original echo data EsCompensation by multiplying in the form of
Figure FDA0002988931360000031
To achieve higher order motion compensation:
Figure FDA0002988931360000032
in the formula: f. oftThe instantaneous frequency of the transmitted carrier for the system; c is the speed of light in vacuum; upsilon isiRepresents each dynamic parameter of order for describing the radial movement of the target, and I is 1, …, I is the highest description order satisfying a certain precision requirement, upsilon1Representing the velocity of radial movement of first order, u2Radial acceleration representing the second order; thus being a time variable.
5. The LS higher order fast motion compensation system of claim 4, wherein in the processing unit, the optimal symmetric cumulative length Q is determined according to equation 10, where equation 10 is:
Figure FDA0002988931360000033
wherein Q is the symmetric accumulation length, gamma is the accumulation factor, and N is the total number of echoes.
6. The LS high-order fast motion compensation system of claim 4, wherein in the constructing unit, the time matrix Γ and the distance difference matrix Λ in the formula 19 and the corresponding least square relation are constructed, and the least square problem is solved according to the formula 20 to calculate the motion parameters of each order of the target;
equation 19:
Figure FDA0002988931360000034
in the formula
Figure FDA0002988931360000035
Is a time interval matrix;
Figure FDA0002988931360000036
the parameter matrix of each order is obtained;
Figure FDA0002988931360000037
is a distance offset matrix;
equation 20:
Figure FDA0002988931360000038
in the formula (I), the compound is shown in the specification,
Figure FDA0002988931360000039
left pseudo-inverse matrix of the representation matrix, (-)HHermitian transpose of the representation matrix, (.)-1Representing the inverse of the invertible matrix.
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