CN105467370A - Cross-range scaling method for precession object ISAR image of composite bistatic radar - Google Patents

Abstract

The invention discloses a cross-range scaling method for a precession object ISAR image of a composite bistatic radar, and the method comprises seven steps: 1, building a precession object bistatic ISAR imaging model, employing a T/R-R composite bistatic radar mode, and obtaining target one-dimensional range image sequences of monostatic/bistatic radars at the same time; 2, obtaining a monostatic/bistatic RID sequence through employing a combined time frequency distribution imaging method for the target echo sequences of the monostatic/bistatic radars; 3, extracting the positions of scattering centers in two monostatic/bistatic RID images through employing a peak detection method; 4, pairing the monostatic/bistatic scattering centers; 5, selecting the position parameters of two paired scattering centers for solving the initial values of a, b and theta delta; 6, building an optimal target function under the constraint conditions of the position parameters of the plurality of scattering center pairs, employing a Gauss-newton method to iteratively solve and obtain the optima values of a, b and theta delta; 7, respectively employing measuring scales (shown in the description) for achieving the cross-range scaling of the monostatic/bistatic RID images according to the obtained parameters a and b.

Description

The horizontal calibrating method of a kind of compound bistatic radar precession target ISAR image

Technical field

The present invention relates to the horizontal calibrating method of a kind of compound bistatic radar precession target ISAR image---it obtains the ISAR picture that can reflect precession target physical size based on fine motion theory, time frequency analysis, optimum theory.Belong to radar target signature technical field.

Background technology

Compound bistatic radar refers to increase a receiving station on existing monostatic radar basis, forms the radar system that two visual angles are observed simultaneously, i.e. T/R-R bistatic radar.The radar that the cost of a passive receiver is more complete than one is much lower, and the income obtained is very large, passive receiver itself has the potential advantages such as anti-stealthy, anti-interference, and pass through the information fusion of two visual angles observations, can more abundant, stable target information be obtained, thus promote the target recognition capability of existing radar.

Inverse synthetic aperture radar (ISAR) (ISAR) adopts Range compress, lateral coherence process can carry out two-dimentional high-resolution imaging to target, thus obtains object construction information, and wherein a gordian technique is horizontal calibration.For uniform rotation target, calibration realizes relatively easy; For the extraterrestrial target of high speed precession, targeted attitude is not uniform relative to the tarnsition velocity of radar line of sight, but time become, traditional ISAR formation method is no longer applicable, if adopt time frequency analysis imaging to obtain distance-instantaneous Doppler image, its lateral resolution is no longer determined by accumulation angle, but is decided by instantaneous rotational speed, adds difficulty to calibration.Golden light tiger waits people at document " based on the Ballistic Target ISAR image laterally calibration [J] of image registration, systems engineering and electronic technology, 2012, 32 (12): 2565-2569) the horizontal calibrating method of a kind of fine motion target ISAR based on image registration " is proposed, it is feasible for demonstrating and realizing laterally calibration according to two width ISAR image registrations, the two width images that the crucial precession targeted attitude transformed differences being to find monostatic radar to observe of the method is larger, but target angle of precession is usually less in reality, the attitudes vibration of target is less, greatly will reduce its calibration possibility and precision.

Summary of the invention

Elaborating of technical solution of the present invention

Goal of the invention: the object of the invention is to the deficiency for the horizontal calibrating method of existing precession target ISAR image, proposes the horizontal calibrating method of a kind of compound bistatic radar precession target ISAR image.Distance-the instantaneous Doppler (RID) at two visual angles that the method utilizes T/R-R compound bistatic radar to observe simultaneously as, both the ISAR image that acquisition attitude differs greatly had been easy to, calibration precision is improved by image registration, obtain again list/bistatic ISAR image simultaneously, make the information of acquisition abundanter, be conducive to target identification.

Realizing technical scheme of the present invention is, first T/R-R compound bistatic radar precession target imaging model is set up, obtain list/bistatic distance-instantaneous Doppler image sequence by T/R-R compound bistatic radar simultaneously, and will laterally press vertical scale calibration, then two width images of synchronization are selected, extract the strong scattering center in two width images, and form scattering center to (be more than or equal to two to), optimal objective function under utilizing the mathematical principle of process of image registration to build constraint condition, obtained the horizontal calibration coefficient of list/bistatic ISAR picture by iterative simultaneously, calibrate while final realization list/bistatic ISAR picture.

The present invention is the horizontal calibrating method of a kind of compound bistatic radar precession target ISAR image, and the method concrete steps are as follows:

Step one: set up the bistatic ISAR imaging model of precession target, adopts T/R-R Composite Double base radar mode, obtains the target one-dimensional range profile sequence of list/bistatic radar simultaneously;

Single base one-dimensional range profile sequence can be expressed as

$S_M(r,\mathrm{\τ})=T_P{\mathrm{\Σ\σ}}_{M,i}\sin c\[\frac{B}{c}(r+{\mathrm{\ΔR}}_{M_i}(\mathrm{\τ}\left)\right)\]e^{-j\frac{2\mathrm{\π}}{\mathrm{\λ}}{\mathrm{\ΔR}}_{M_i}\left(\mathrm{\τ}\right)}---\left(1\right)$

Wherein, T _pfor pulsewidth, B is bandwidth, and c is the light velocity, and λ is wavelength, and r is distance, and τ is the slow time, σ _m,ifor single base RCS, represent that scattering center i departs from the distance at fixed phase center.

Bistatic one-dimensional range profile sequence can be expressed as

$S_B(r,\mathrm{\τ})=T_P{\mathrm{\Σ\σ}}_{B,i}\sin c\[\frac{B}{c}(r-{\mathrm{\ΔR}}_{S_i}(\mathrm{\τ}\left)\right)\]e^{-j\frac{2\mathrm{\π}}{\mathrm{\λ}}{\mathrm{\ΔR}}_{S_i}\left(\mathrm{\τ}\right)}---\left(2\right)$

Wherein, σ _b,ifor bistatic RCS, represent that scattering center i departs from the distance at fixed phase center.

Step 2: adopt joint time-frequency distribution formation method to obtain list/bistatic RID sequence to list/bistatic radar target echo sequence;

This list/bistatic RID sequence is expressed as follows respectively:

$\left\{\begin{array}{c}{S}_M(r,f,t)=SPWVD\left\{S_M\right(r,\mathrm{\τ}\left)\right\}\\ S_B(r,f,t)=SPWVD\left\{S_B(r,\mathrm{\τ})\right\}\end{array}\right.---\left(3\right)$

Symbol description in formula is as follows:

R, f, t represent distance, instantaneous Doppler, time respectively, S _m(r, f, t) represents single base RID image of t, S _b(r, f, τ) represents the bistatic RID image of t, and SPWVD{} represents and does the process of Smoothing Pseudo Wigner video distribution to the function in braces.

Step 3: extract the scattering center position in two width lists/bistatic RID image by peak-value detection method;

Select the two width lists/bistatic RID image of synchronization, require that image quality is more high better, namely select the image that picture contrast is higher as far as possible.Then by peak-value detection method, in RID image, selective scattering intensity crosses the point of thresholding, and obtains transverse and longitudinal coordinate.

Step 4: single/bistatic scattering center pairing

Extraction list/bistatic scattering center is carried out pairing association, also just adopt arest neighbors rule according to the Euclidean distance between targeted attitude and scattering center characteristic or calculating scattering center, thus judge that two scattering centers correspond to the same position in target;

Step 5: select two scattering center location parameters matched to solve a, b, θ _Δinitial value;

The equality condition utilizing the scattering center of having matched to meet, builds four equations, can solve a class value of three unknown numbers, as the initial value that successive iterations is optimized.

Four equations built are

$\left(\begin{array}{c}{x}_{M_1}\\ y_{M_1}\\ x_{M_2}\\ y_{M_2}\end{array}\right)=\left(\begin{array}{cccc}{x}_{B_1}& y_{B_1}& 0& 0\\ 0& 0& x_{B_1}& y_{B_1}\\ x_{B_2}& y_{B_2}& 0& 0\\ 0& 0& x_{B_2}& y_{B_2}\end{array}\right)\left(\begin{array}{c}\frac{b}{a}{\mathrm{cos\θ}}_{\mathrm{\Δ}}\\ -\frac{1}{a}{\mathrm{sin\θ}}_{\mathrm{\Δ}}\\ {\mathrm{bsin\θ}}_{\mathrm{\Δ}}\\ {\mathrm{cos\θ}}_{\mathrm{\Δ}}\end{array}\right)---\left(4\right)$

Symbol description in formula is as follows:

A, b, θ _Δrepresent respectively, single base RID as the transversal stretching factor, bistatic RID as the transversal stretching Summing Factor anglec of rotation, coordinate corresponding to two scattering centers is obtained respectively in image A and B.

Step 6: set up the optimization objective function under the right location parameter constraint condition of multiple scattering center, adopts Gauss-Newton method iterative to obtain a, b, θ _Δoptimal value;

Utilize N to the scattering center location parameter matched, can obtain 2*N equation, thus can build the optimization objective function under constraint condition, the optimizing of recycling Gauss-Newton method iteration obtains a, b, θ _Δoptimal value.

Optimization objective function is

$f(a,b,\mathrm{\θ})=\underset{i}{\Σ}\left|\right|\left(\begin{array}{c}{x}_{M_i}\\ y_{M_i}\end{array}\right)-\left(\begin{array}{cc}\frac{b}{a}{\mathrm{cos\θ}}_{\mathrm{\Δ}}& -\frac{1}{a}{\mathrm{sin\θ}}_{\mathrm{\Δ}}\\ {\mathrm{bsin\θ}}_{\mathrm{\Δ}}& {\mathrm{cos\θ}}_{\mathrm{\Δ}}\end{array}\right)\left(\begin{array}{c}{x}_{B_i}\\ y_{B_i}\end{array}\right)|{|}^2---\left(5\right)$

Wherein, || || represent 2 norms, Σ represents summation, i=1,2,3....N.

Step 7: according to the parameter a solving acquisition, b, respectively adoption rate chi with the transverse direction realizing list/bistatic RID image is demarcated.

Adopt the beneficial effect that technical solution of the present invention is brought:

1, the present invention increases the receiver of a low cost on existing monostatic radar basis, can obtain the list/bistatic two-dimentional ISAR picture of reflection target full-size(d) simultaneously, obtain more abundant, stable target information, expanded the ability of existing radar;

2, instant invention overcomes the horizontal calibrating method of existing monostatic radar is difficult to the horizontal restriction of calibrating of the realization of goal that attitudes vibration amplitude is little;

3, instant invention overcomes the restriction that existing horizontal calibration technology is not suitable for non-uniform rotation target;

4, the present invention is applicable equally to other micromotion targets such as spin, swing, nutatings.

Accompanying drawing explanation

Fig. 1 is overview flow chart of the present invention.

Fig. 2 is the precession target ISAR imaging model that the present invention sets up.

Fig. 3 is that the present invention laterally calibrates principle schematic.

Fig. 4 a is that the present invention calibrates front single base ISAR as schematic diagram.

Fig. 4 b is that the present invention calibrates front bistatic ISAR as schematic diagram.

Fig. 5 a is that the present invention calibrates rear single base ISAR as schematic diagram.

Fig. 5 b is that the present invention calibrates rear bistatic ISAR as schematic diagram.

Fig. 6 is existing method list base ISAR the calibration results schematic diagram.

In figure, symbol description is as follows:

In Fig. 2, reference coordinate is O-XYZ, and true origin O is positioned at target centroid, and target local coordinate system is that O '-xyz, O ' are positioned at the facies basialis pyramidis center of circle.γ _tfor the T/R station sight line angle of pitch, R _tfor T/R station and the distance of barycenter, φ _rand γ _rbe respectively R sight line position angle, station and the angle of pitch, R _rfor R stands the distance of barycenter, β is that stand sight line and R of T/R stands the angle (i.e. double-basis ditch) of sight line, φ ₀be respectively initial orientation angle corresponding to object axis and the angle of pitch with θ (i.e. angle of precession), h is target length, and r is bottom surface radius, and b is the length between OO ', θ _tfor T/R station sight line and target axle clamp angle, θ _rfor R station sight line and target axle clamp angle, ω is angular velocity of precession.A, B, C are the scattering center of T/R station observation, and A, D, E are the scattering center of R station observation.

In Fig. 3, (x _m, y _m) and (x _b, y _b) scattering center is corresponding in single base RID picture and bistatic RID picture respectively coordinate, (x, y) is (x _m, y _m) and (x _b, y _b) carry out coordinate corresponding in image after calibration after stretching and rotating respectively.

5, specific embodiments

Fig. 1 is overview flow chart of the present invention.In order to understand technical scheme of the present invention better, below in conjunction with accompanying drawing, embodiments of the present invention are further described.

Step one: set up the bistatic ISAR imaging model of precession target, adopts T/R-R Composite Double base radar mode, obtains the target one-dimensional range profile sequence of list/bistatic radar simultaneously

As shown in Figure 2, monostatic radar T/R erect-position is in T _x, bistatic receiving station R is positioned at R _xrotational Symmetry cone target backscattering characteristic is primarily of three scattering center (A, B, C) contribution, B, C is that T/R stands the intersection point of plane that sight line and target axle form and circular cone bottom edge, and the bistatic scattering properties of circular cone target is contributed primarily of three scattering centers (A, D, E), D, E are the intersection point of the plane that forms of bistatic angular bisector and target axle and circular cone bottom edge.T/R station is different with the scattering center position that bistatic receiving station R observes under normal circumstances.Set up rectangular coordinate system as shown in Figure 2, wherein reference coordinate is O-XYZ, and true origin O is positioned at target centroid, and OZ overlaps with the precession axis of target, and OX axle is positioned at the plane of radar line of sight and precession axis formation, and OY and OX, OZ form right hand rectangular coordinate system; Target local coordinate system is that O '-xyz, O ' are positioned at the facies basialis pyramidis center of circle, and O ' z-axis overlaps with target axis of symmetry, and O ' x-axis is along O ' B direction, and O ' y and O ' x, O ' z form right hand rectangular coordinate system.The T/R station sight line angle of pitch is γ _t(approximate constant in short observation time), the distance of T/R station radar and barycenter is R _t, R sight line position angle, station and the angle of pitch are respectively φ _rand γ _r(short observation time in approximate constant), the stand distance of barycenter of R is R _r, T/R the stand angle of sight line of sight line and R of standing is β (i.e. double-basis ditch), and the initial orientation angle that object axis is corresponding and the angle of pitch are respectively φ ₀with θ (i.e. angle of precession), target length is h, and bottom surface radius is r, | OO ' |=b.

T/R station sight line and target axle clamp angle meet:

cosθ _T＝cosθcosγ _T+sinθsinγ _Tcos(ωt+φ ₀)(6)

R station sight line and target axle clamp angle meet:

cosθ _R＝cosθcosγ _R+sinθsinγ _Rcos(ωt+φ ₀-φ _R)(7)

Double-basis ditch β meets

cosβ＝cosγ _Tcosγ _R+sinγ _Tsinγ _Rcosφ _R(8)

$cos\mathrm{\β}/2=\sqrt{\frac{1+{\mathrm{cos\γ}}_T{\mathrm{cos\γ}}_R+{\mathrm{sin\γ}}_T{\mathrm{sin\γ}}_R{\mathrm{cos\φ}}_R}{2}}---\left(9\right)$

The angle of bistatic angular bisector and target axle is

${\mathrm{cos\θ}}_{Bi}=\frac{({\mathrm{cos\θ}}_R+{\mathrm{cos\θ}}_T)}{2cos\mathrm{\β}/2}---\left(10\right)$

The scattering center of bistatic receiving station observation is A, D, E, then the distance that its scattering center observed departs from reference center can be expressed as

$\left\{\begin{array}{c}{\mathrm{\ΔR}}_{S_A}\≈-2\cos (\mathrm{\β}/2)(b+h){\mathrm{cos\θ}}_{Bi}\\ {\mathrm{\ΔR}}_{S_D}\≈-2\cos (\mathrm{\β}/2)({\mathrm{bcos\θ}}_{Bi}+{\mathrm{rsin\θ}}_{Bi})\\ {\mathrm{\ΔR}}_{S_E}\≈-2\cos (\mathrm{\β}/2)({\mathrm{bcos\θ}}_{Bi}-{\mathrm{rsin\θ}}_{Bi})\end{array}\right.---\left(11\right)$

Work as θ _r=θ _t, above formula deteriorates to single base situation,

$\left\{\begin{array}{c}{\mathrm{\ΔR}}_{M_A}\≈-2(b+h){\mathrm{cos\θ}}_T\\ {\mathrm{\ΔR}}_{M_B}\≈-2({\mathrm{bcos\θ}}_T+{\mathrm{rsin\θ}}_T)\\ {\mathrm{\ΔR}}_{M_C}\≈-2({\mathrm{bcos\θ}}_T-{\mathrm{rsin\θ}}_T)\end{array}\right.---\left(12\right)$

Suppose that radar adopts linear FM signal, by stretch process and motion compensation, bistatic one-dimensional range profile sequence can be expressed as

$S_B(r,\mathrm{\τ})=T_P{\mathrm{\Σ\σ}}_{B,i}\sin c\[\frac{B}{c}(r-{\mathrm{\ΔR}}_{S_i}(\mathrm{\τ}\left)\right)\]e^{-j\frac{2\mathrm{\π}}{\mathrm{\λ}}{\mathrm{\ΔR}}_{S_i}\left(\mathrm{\τ}\right)}---\left(13\right)$

Wherein, T _p, B, is respectively pulsewidth and bandwidth, and c is the light velocity, and λ is wavelength, σ _b,ifor bistatic RCS, represent that scattering center i departs from the distance at fixed phase center, i=A, D, E.

Single base one-dimensional range profile sequence can be expressed as

$S_M(r,\mathrm{\τ})=T_P{\mathrm{\Σ\σ}}_{M,i}\sin c\[\frac{B}{c}(r+{\mathrm{\ΔR}}_{M_i}(\mathrm{\τ}\left)\right)\]e^{-j\frac{2\mathrm{\π}}{\mathrm{\λ}}{\mathrm{\ΔR}}_{M_i}\left(\mathrm{\τ}\right)}---\left(14\right)$

Wherein, σ _m,ifor single base RCS, represent that scattering center i departs from the distance at fixed phase center, i=A, B, C.

Step 2: adopt joint time-frequency distribution formation method to obtain single base/bistatic RID sequence to list/bistatic radar target echo sequence

Respectively to the list in formula (13) (14)/bistatic one-dimensional range profile sequence smoothing pseudo derivative feedback (SPWVD) time frequency analysis process, obtain list/bistatic RID image sequence.Then, select the two width lists/bistatic RID image of synchronization, wherein single base RID image lateral separation and fore-and-aft distance all adopt resolution calibration, bistatic RID image lateral separation and fore-and-aft distance all adopt resolution calibration.

Step 3: extract the scattering center position in two width lists/bistatic RID image by peak-value detection method

Select the two width lists/bistatic RID image of synchronization, extract scattering center position wherein respectively.Due to the restriction by resolution, each scattering center is not often a point at RID image, but certain peak region, therefore need first by Threshold detection, and carry out cluster, extract scattering center position more accurately.

Step 4: single/bistatic scattering center pairing

In bistatic joint observation, scattering center pairing is a difficult problem, do not having under prior imformation condition, the association pairing realizing scattering center is very difficult, but extracted by tracking and narrow-band feature and can have certain understanding to the attitude of target, and the corner of two width image differences can be judged roughly according to the size in double-basis ditch, thus manually can select the association realizing list/bistatic scattering center.Also first can calculate the Euclidean distance between scattering center, then adopt the methods such as arest neighbors to realize auto-associating.

Step 5: select two scattering center location parameters matched, utilizes two scattering centers to solving a, b, θ _Δinitial value

As shown in Figure 3, suppose that T/R-R bistatic radar has obtained two width ISAR image A and B of incorrect calibration, C is actual ratio chi image.(contraction-expansion factor is set to a), namely realizes the conversion of image A to actual ratio chi image C to carry out transversal stretching to image A; And for image B, (contraction-expansion factor is set to b), then carries out rotational transform, and rotational angle is θ, realizes the corresponding attitude of image B and rotates to the corresponding attitude of figure C equally first to carry out transversal stretching.For rotational symmetric target, two width images after the correct calibration that list/bistatic radar obtains should be identical (scattering centers of public observation), a bit (x in image A _m, y _m) with a bit (x in image B _b, y _b), in image C, correspond to same position, then can obtain following equation:

$\left(\begin{array}{cc}a& 0\\ 0& 1\end{array}\right)\left(\begin{array}{c}{x}_M\\ y_M\end{array}\right)=\left(\begin{array}{cc}cos\mathrm{\θ}& -sin\mathrm{\θ}\\ sin\mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right)\left(\begin{array}{cc}b& 0\\ 0& 1\end{array}\right)\left(\begin{array}{c}{x}_B\\ y_B\end{array}\right)---\left(15\right)$

So two equations just can be obtained, and need to ask three unknown numbers, if there are two scattering centers of having matched again, then can obtain again two equations, obtain one group of estimated value so can solve

Step 6: set up multiple scattering center to the optimization objective function under the parameter constraints of position, adopts Gauss-Newton method iterative to obtain a, b, θ _Δoptimal value

Suppose that the list/bistatic scattering center position of extracting is respectively (i=1,2 ... ..N, N > 2), then can build following cost function

$f(a,b,\mathrm{\θ})=\underset{i}{\Σ}\left|\right|\left(\begin{array}{c}{x}_{M_i}\\ y_{M_i}\end{array}\right)-\left(\begin{array}{cc}\frac{b}{a}{\mathrm{cos\θ}}_{\mathrm{\Δ}}& -\frac{1}{a}{\mathrm{sin\θ}}_{\mathrm{\Δ}}\\ {\mathrm{bsin\θ}}_{\mathrm{\Δ}}& {\mathrm{cos\θ}}_{\mathrm{\Δ}}\end{array}\right)\left(\begin{array}{c}{x}_{B_i}\\ y_{B_i}\end{array}\right)|{|}^2---\left(16\right)$

The estimation problem of 3 parameters is converted to the optimization problem under constraint condition, when this function arrives minimum value, just obtains the optimal value of above-mentioned 3 parameters.Due to very difficult acquisition analytic solution, therefore adopt Gauss-Newton method, optimize this estimated value by successive ignition, thus obtain the optimum solution of equation.And adopt and to solve in step 5 to make iterative process Fast Convergent.

Step 7: single/bistatic RID image is laterally demarcated

Utilize the parameter a obtained, b, respectively adoption rate chi with the transverse direction realizing list/bistatic RID image is demarcated.In order to obtain more laterally calibration, for same width list base ISAR picture, multiple image in itself and bistatic ISAR sequence can be carried out registration, then the engineer's scale of gained is averaging and obtains final transverse direction calibration yardstick, in like manner same bistatic ISAR image can carry out registration with the multiple image in the ISAR sequence of single base, is then averaging by the engineer's scale of gained and obtains final transverse direction calibration yardstick.

Effect of the present invention is illustrated by following emulation experiment.Parameters is as follows: cone height 3m, bottom surface radius 0.5m, and set three equivalent scattering centers, each scattering coefficient is 0.15m ², target precession period is 2s, and angle of precession is 10 °, T/R station angle of pitch γ _t=40 °, R orientation, station and the angle of pitch are respectively γ _r=100 °, φ _r=0 °, double-basis ditch is 60 °, signal carrier frequency 10GHz, bandwidth 1GHz, pulsewidth 100 μ s, and pulse repetition rate is 500Hz, and umber of pulse is 1024.

Fig. 4 a, Fig. 4 b are respectively certain moment list/bistatic RID image, by extracting three scattering centers in figure, form scattering center pair, coefficient of dilatation b=0.098 is obtained by optimum iteration, a=0.096, then the engineer's scale estimated value obtaining list/bistatic ISAR is 0.0072 and 0.0085, finally image is calibrated again, result is respectively as shown in Fig. 5 a, Fig. 5 b, in figure, solid line represents the profile of current target section, can find out that scattering center is almost positioned on objective contour, illustrate that the image of calibration truly can reflect the full-size(d) of target.Adopt two width list base RID image calibration results, as shown in Figure 6, in figure, solid line represents the profile of current target section, can see that calibrated ISAR picture and objective contour are misfitted, can not reflect the full-size(d) of target.Reason is that target is too little relative to the angle change of sight line, causes monostatic radar correctly not calibrate; And bistatic radar is when observing simultaneously, due to the existence in double-basis ditch, the object attitude angle difference of Liang Ge receiving station observation is comparatively large, thus can correctly calibrate, and embodies advantage of the present invention.

Claims (1)

1. the horizontal calibrating method of compound bistatic radar precession target ISAR image, is characterized in that: the method concrete steps are as follows:

Step one: set up the bistatic ISAR imaging model of precession target, adopts T/R-R Composite Double base radar mode, obtains the target one-dimensional range profile sequence of list/bistatic radar simultaneously;

Single base one-dimensional range profile sequence is expressed as

$S_M(r,\mathrm{\τ})=T_P{\mathrm{\Σ\σ}}_{M,i}\sin c\[\frac{B}{c}(r+{\mathrm{\ΔR}}_{M_i}(\mathrm{\τ}\left)\right)\]e^{-j\frac{2\mathrm{\π}}{\mathrm{\λ}}{\mathrm{\ΔR}}_{M_i}\left(\mathrm{\τ}\right)}---\left(1\right)$

Wherein, T _pfor pulsewidth, B is bandwidth, and c is the light velocity, and λ is wavelength, and r is distance, and τ is the slow time, σ _m,ifor single base RCS, represent that scattering center i departs from the distance at fixed phase center;

Bistatic one-dimensional range profile sequence is expressed as

$S_B(r,\mathrm{\τ})=T_P{\mathrm{\Σ\σ}}_{B,i}\sin c\[\frac{B}{c}(r-{\mathrm{\ΔR}}_{S_i}(\mathrm{\τ}\left)\right)\]e^{-j\frac{2\mathrm{\π}}{\mathrm{\λ}}{\mathrm{\ΔR}}_{S_i}\left(\mathrm{\τ}\right)}---\left(2\right)$

Wherein, σ _b,ifor bistatic RCS, represent that scattering center i departs from the distance at fixed phase center;

Step 2: adopt joint time-frequency distribution formation method to obtain list/bistatic RID sequence to list/bistatic radar target echo sequence;

This list/bistatic RID sequence is expressed as follows respectively:

$\left\{\begin{array}{c}{S}_M(r,f,t)=SPWVD\left\{S_M(r,\mathrm{\τ})\right\}\\ S_B(r,f,t)=SPWVD\left\{S_B(r,\mathrm{\τ})\right\}\end{array}\right.---\left(3\right)$

Symbol description in formula is as follows:

R, f, t represent distance, instantaneous Doppler, time respectively, S _m(r, f, t) represents single base RID image of t, S _b(r, f, τ) represents the bistatic RID image of t, and SPWVD{} represents and does the process of Smoothing Pseudo Wigner video distribution to the function in braces;

Step 3: extract the scattering center position in two width lists/bistatic RID image by peak-value detection method;

Select the two width lists/bistatic RID image of synchronization, require that image quality is more high better, namely select the image that picture contrast is higher as far as possible, then pass through peak-value detection method, in RID image, selective scattering intensity crosses the point of thresholding, and obtains transverse and longitudinal coordinate;

Step 4: single/bistatic scattering center pairing

Extraction list/bistatic scattering center is carried out pairing association, also just adopt arest neighbors rule according to the Euclidean distance between targeted attitude and scattering center characteristic or calculating scattering center, thus judge that two scattering centers correspond to the same position in target;

Step 5: select two scattering center location parameters matched to solve a, b, θ _Δinitial value;

The equality condition utilizing the scattering center of having matched to meet, builds four equations, solves a class value of three unknown numbers, as the initial value that successive iterations is optimized;

Four equations built are

$\left(\begin{array}{c}{x}_{M_1}\\ y_{M_1}\\ x_{M_2}\\ y_{M_2}\end{array}\right)=\left(\begin{array}{cccc}{x}_{B_1}& y_{B_1}& 0& 0\\ 0& 0& x_{B_1}& y_{B_1}\\ x_{B_2}& y_{B_2}& 0& 0\\ 0& 0& x_{B_2}& y_{B_2}\end{array}\right)\left(\begin{array}{c}\frac{b}{a}{\mathrm{cos\θ}}_{\mathrm{\Δ}}\\ -\frac{1}{a}{\mathrm{sin\θ}}_{\mathrm{\Δ}}\\ {\mathrm{bsin\θ}}_{\mathrm{\Δ}}\\ {\mathrm{cos\θ}}_{\mathrm{\Δ}}\end{array}\right)---\left(4\right)$

Symbol description in formula is as follows:

A, b, θ _Δrepresent respectively, single base RID as the transversal stretching factor, bistatic RID as the transversal stretching Summing Factor anglec of rotation, coordinate corresponding to two scattering centers is obtained respectively in image A and B;

Step 6: set up the optimization objective function under the right location parameter constraint condition of multiple scattering center, adopts Gauss-Newton method iterative to obtain a, b, θ _Δoptimal value;

Utilize N to the scattering center location parameter matched, obtain 2*N equation, thus build the optimization objective function under constraint condition, the optimizing of recycling Gauss-Newton method iteration obtains a, b, θ _Δoptimal value;

Optimization objective function is

$f(a,b,\mathrm{\θ})=\underset{i}{\mathrm{\Σ}}\left|\right|\left(\begin{array}{c}{x}_{M_i}\\ y_{M_i}\end{array}\right)-\left(\begin{array}{cc}\frac{b}{a}{\mathrm{cos\θ}}_{\mathrm{\Δ}}& -\frac{1}{a}{\mathrm{sin\θ}}_{\mathrm{\Δ}}\\ {\mathrm{bsin\θ}}_{\mathrm{\Δ}}& {\mathrm{cos\θ}}_{\mathrm{\Δ}}\end{array}\right)\left(\begin{array}{c}{x}_{B_i}\\ y_{B_i}\end{array}\right)|{|}^2---\left(5\right)$

Wherein, || || represent 2 norms, Σ represents summation, i=1,2,3 ... .N;

Step 7: according to the parameter a solving acquisition, b, respectively adoption rate chi with the transverse direction realizing list/bistatic RID image is demarcated.