CN100561250C - The clutter base-band analog signal production method of spaceborne bistatic radar - Google Patents

Abstract

The present invention relates to the production method of spaceborne bistatic radar clutter baseband signal, it comprises several steps: according to spaceborne bistatic radar system parameter setting starting condition, set up the equidistant ring model of spaceborne bistatic radar clutter, judge the upward validity of clutter unit of ring, calculate each effective clutter unit because the motion vector that earth rotation causes.Calculate satellite velocity vector according to satellite position and orbit parameter then, calculate effective clutter unit time corresponding frequency and spatial frequency.Further, with the space-time two-dimensional snap summation of all effective clutter unit, obtain clutter covariance matrix at last and produce the clutter data of obeying this statistical distribution.These data can be used for checking, selection or the improvement of the Clutter suppression algorithm of follow-up spaceborne radar signal processing system.

Description

The clutter base-band analog signal production method of spaceborne bistatic radar

Technical field

The present invention relates to the production method of Radar Clutter Signal, particularly relate to the production method of spaceborne bistatic radar noise signal.

Background technology

(bistatic space based radar BSBR) is a kind of new radar system notion that proposes on the recent international to spaceborne bistatic radar, and it is mainly used in ground or aerial military motion target detection.The transmitter and receiver of this radar system is placed on respectively on two different satellites, because satellite altitude is very high, the coverage of this radar system is very big, can not be subjected to the constraint on national boundaries to provide wider and early warning more timely, plays important effect in national defence.

Spaceborne radar shines earthward from satellite, the transmitter transmit burst, and receiver also will receive the echo that reflects from earth surface in a large number except receiving useful moving target echoed signal, be called land clutter.The difficult point that spaceborne bistatic radar carries out the moving-target detection is that the undesired signal when this radar system is carried out signal Processing is not only a noise, also has the very strong noise signal of big discharge amplitude, and making target to be submerged in the noise signal can't be detected.Usually, we must at first adopt rational algorithm to remove noise signal, just can carry out the detection of follow-up echo signal.And clutter environment changes with the change of radar system parameter and transceiver relative position relation usually, therefore also should adopt different Clutter suppression algorithm under different situations, the quality of moving-target testing result depends on the selection of Clutter suppression algorithm to a great extent.In the signal processing system of spaceborne radar, it is vital that the selection of rational Clutter suppression algorithm and the improvement of Clutter suppression algorithm finally detect performance to the raising radar.This paper proposes the production method of clutter baseband analog data at this problem, makes it to be used for checking, selection or the improvement of the Clutter suppression algorithm of follow-up spaceborne radar signal processing system.

The spaceborne radar system that is used for the moving-target detection is a new notion, and each state all just begins one's study now, does not therefore see the production method at the clutter simulation data of this radar system as yet on open source information.J.Ward is (referring to document [1]: J.Ward, " space-time adaptive processing for airborne radar ", London, 1994) narrated the production method of the clutter simulation signal under the onboard radar system (radar is placed aboard), but the production method of the noise signal under it and the spaceborne bistatic radar system has a great difference at some key place, and difference has 2 points.The first, under the airborne situation, ground can be similar to thinks the plane, and under spaceborne situation, and earth surface must be thought sphere.The second, under the spaceborne situation, the factor of earth rotation can not be ignored, and make floor surface produce a new movement velocity, and under airborne situation, ground can be thought static.Therefore, the production method of using the clutter simulation signal of existing onboard radar system can't obtain the noise performance of spaceborne radar system.

The main thought of clutter simulation signal generating method is to produce the clutter covariance battle array earlier, will multiply by white Gaussian noise behind this gust evolution then.The calculating key of covariance matrix is finding the solution of three parameters: the equidistant ring of clutter, the calculating of clutter unit temporal frequency and spatial frequency.The equidistant ring of clutter is meant that the clutter reflector element is at the track on ground in a bistatic range gate of radar, this ring can be divided into some little clutter unit, and each clutter unit equates apart from sum to transmitter and receiver, so receiver at a time receives noise signal goes up all clutter unit for this ring reflected signal sum.The shape of the equidistant ring of clutter is different under different radar system patterns.The equidistant ring of the clutter of airborne bistatic radar system is an ellipse in the plane, and airborne radar generally carries out remote detection, a lot of physical conditions can be similar to, and make oval focus can think directly that (referring to document [2]: the king becomes transmitter and receiver, Hu Weidong in the projection on ground, land clutter modeling of space base bistatic radar and specificity analysis: modern radar, Vol.26, No.9, PP.33-37,2004), simplified the complexity of asking for elliptic equation greatly.Earth surface under the spaceborne situation must be thought sphere and can not be similar to again to think the plane, this makes the equidistant ring of clutter just need find the solution on curved surface rather than planar, so the equidistant ring model of the clutter in the airborne radar clutter signal generating method is no longer suitable.Onboard radar system in the past all is that the echoed signal of supposing all clutter unit can both be received by radar simultaneously, and promptly noise signal is come (not considering that antenna modulation and back are to inhibition) from all directions.But under the spaceborne radar situation, some clutter unit on the clutter ring may exceed the coverage of transmitter and receiver and become invalidly, and the noise signal production method of therefore using existing airborne radar can't judge the validity of spaceborne radar clutter unit.

The temporal frequency of clutter unit is meant the normalization Doppler frequency that the clutter unit produces with respect to Texas tower, and it is by the relative motion generation of clutter unit and Texas tower.If change has taken place the speed of related movement of clutter unit and radar, temporal frequency also will change.Therefore, because the influence of earth rotation, the noise signal production method of application airborne radar can't calculate the clutter temporal frequency under the spaceborne situation.

In a word, in order to obtain the noise performance of spaceborne bistatic radar system, the clutter simulation signal that produces spaceborne bistatic radar system is very important.Noise signal production method under this radar system pattern has overcome the deficiency of existing onboard radar system noise signal production method, set up the equidistant ring model of clutter under the spaceborne situation, validity to the clutter unit under the spaceborne situation is judged, calculated the clutter temporal frequency under the spaceborne situation simultaneously, for checking, selection or the improvement of the Clutter suppression algorithm of follow-up spaceborne radar signal processing system provides the foundation.

Summary of the invention

The object of the invention is to propose the base band clutter simulation signal generating method under a kind of new radar system (spaceborne bistatic radar system), makes the signal of generation be used for checking, selection or the improvement of the Clutter suppression algorithm of follow-up spaceborne radar signal processing system.

In order to realize the foregoing invention purpose, the clutter baseband analog data creating method that the present invention proposes adopts the system platform shown in the accompanying drawing 1 to realize usually.This system platform is made up of computing machine and data transmitting equipment, wherein, computing machine provides hardware platform and operation system of software, method of the present invention is based on this environment, realize by software programming, the base band clutter simulation signal that produces sends to follow-up spaceborne radar signal processing system by data transmitting equipment.

For different radar system parameters, the statistical property of noise signal is different, and therefore the noise signal that produces is also with difference.The method that the present invention proposes will have an initial parameter setting, behind the different radar parameter of input, will produce the noise signal at this radar configuration.The method concrete steps are as follows:

The first step: import the starting condition of spaceborne bistatic radar parameter as this method:

The initial parameter of this method is set according to radar parameter.The parameter that needs to set mainly comprises three parts, i.e. the satellite platform parameter and the target component of radar installations parameter, placement radar.

The radar installations parameter: the wavelength X that transmits, transmitter antenna array element number Q, receiver antenna array element number G, receiver antenna array element distance and transmitter antenna array element distance equate, are designated as d, transmitter pulse repetition frequency f _r

Satellite platform parameter: radar transmitter place satellite platform height H _t, the orbit altitude H of receiver place satellite platform _r, transmitter inclination of satellite orbit θ _t, receiver inclination of satellite orbit θ _r, the longitude of transmitter ascending node of satellite orbit

, receiver ascending node of satellite orbit longitude

, transmitter sub-satellite point longitude ρ _t, receiver sub-satellite point longitude ρ _r

The substar latitude ξ of satellite platform _tAnd ξ _rNeed not provide, because it can be by θ _t,

, ρ _tAnd θ _r,

, ρ _rDirectly calculate, formula is as follows:

Target component: the longitude and latitude (ρ of measuring point D to be checked on the earth _d, ξ _d).

Second step: the foundation of the equidistant ring of spaceborne bistatic radar clutter:

Z very to the north of the earth latitude and longitude coordinates system ^uAxle, equatorial plane is X ^uOY ^uPlane, zero degree warp direction are X ^uAxle, receiver, transmitter and measuring point D to be checked are respectively in the position of earth longitude and latitude rectangular coordinate system

Subscript u represents that this coordinate is reference with latitude and longitude coordinates, symbol

The expression vector. $\stackrel{\→}{T^u}=(T_x^u,T_y^u,T_z^u),$ T wherein _x ^u, T _y ^u, T _z ^uBe respectively transmitter x under earth longitude and latitude rectangular coordinate system, y, the coordinate components of z axle; $\stackrel{\→}{R^u}=(R_x^u,R_y^u,R_z^u),$ R wherein _x ^u, R _y ^u, R _z ^uBe respectively receiver x under earth longitude and latitude rectangular coordinate system, y, the coordinate components of z axle; $\stackrel{\→}{D^u}=(D_x^u,D_y^u,D_z^u),$ (D wherein _x ^u, D _y ^u, D _z ^u) be respectively D point x under earth longitude and latitude rectangular coordinate system, y, the coordinate components of z axle;

Utilize transmitter longitude and latitude (ρ in the step 1 _t, ξ _t) and receiver longitude and latitude (ρ _r, ξ _r), the longitude and latitude (ρ of unit to be detected _d, ξ _d), calculate their position coordinateses respectively in earth latitude and longitude coordinates system.

$\left\{\begin{array}{c}{R}_x^u=(H_r+R_e)\cos {\mathrm{\ξ}}_r\cos {\mathrm{\ρ}}_r\\ R_y^u=(H_r+R_e)\cos {\mathrm{\ξ}}_r\sin {\mathrm{\ρ}}_r\\ R_z^u=(H_r+R_e)\sin {\mathrm{\ξ}}_r\end{array}\right.---\left(2\right)$

$\left\{\begin{array}{c}{T}_x^u=(H_t+R_e)\cos {\mathrm{\ξ}}_t\cos {\mathrm{\ρ}}_t\\ T_y^u=(H_t+R_e)\cos {\mathrm{\ξ}}_t\sin {\mathrm{\ρ}}_t\\ T_z^u=(H_t+R_e)\sin {\mathrm{\ξ}}_t\end{array}\right.---\left(3\right)$

$\left\{\begin{array}{c}{D}_x^u=R_e\cos {\mathrm{\ξ}}_d\cos {\mathrm{\ρ}}_d\\ D_y^u=R_e\cos {\mathrm{\ξ}}_d\sin {\mathrm{\ρ}}_d\\ D_z^u=R_e\sin {\mathrm{\ξ}}_d\end{array}\right.---\left(4\right)$

Wherein, R _eThe expression earth radius.

The track of the equidistant ring of clutter is made up of some little clutter unit, and the purpose of asking for the equidistant track of clutter is to try to achieve the position coordinates that this ring is gone up each little clutter unit.Can represent the coordinate of this clutter unit with the central point of each clutter unit.

For simpler this analytical solution of locus of trying to achieve, set up new coordinate system.As shown in Figure 3, set up rectangular coordinate system O-XYZ, establish Receiver And Transmitter and replace with R and T respectively, the position in the O-XYZ rectangular coordinate system is respectively

With,

, O is the earth centre of sphere,

Be the Z axle, plane vertical with the Z axle and the centre of sphere excessively is an XOY plane, and X-axis is

Projection on XOY plane,

With Angle be α.Definition $\stackrel{\→}{T}=(T_x,T_y,T_z)$ Be the position vector of transmitter in the O-XYZ rectangular coordinate system, wherein T _x,, T _y, T _zBe respectively transmitter x under the O-XYZ rectangular coordinate system, y, the coordinate components of z axle, $\stackrel{\→}{R}=(R_x,R_y,R_z)$ Be the position vector of receiver in the O-XYZ rectangular coordinate system, wherein R _x, R _y, R _zBe respectively receiver x under the O-XYZ rectangular coordinate system, y, the coordinate components of z axle, $\stackrel{\→}{D}=(D_x,D_y,D_z)$ Be the position vector of target to be measured in the O-XYZ rectangular coordinate system, wherein D _x, D _y, D _zBe respectively target to be measured x under the O-XYZ rectangular coordinate system, y, the component of z axle.

Therefore, under the O-XYZ coordinate system, the new coordinate of Receiver And Transmitter is as follows:

$\left\{\begin{array}{c}{R}_x=0\\ R_y=0\\ R_z=H_r+R_e\end{array}\right.---\left(5\right)$

$\left\{\begin{array}{c}{T}_x=(H_t+R_e)\sin \mathrm{\α}\\ T_y=0\\ T_z=(H_t+R_e)\cos \mathrm{\α}\end{array}\right.---\left(6\right)$

Wherein,

$\mathrm{\α}=\sqrt{{(R_e+H_r)}^2+{(R_e+H_t)}^2+{(R_x^u-T_x^u)}^2+{(R_y^u-T_y^u)}^2+{(R_y^u-T_y^u)}^2-2(R_e+H_r)(R_e+H_t)}$

In bistatic radar system, by measuring point D to be checked to R and T apart from sum be called bistatic distance and, be designated as g.

$g=\sqrt{{(T_x^u-D_x^u)}^2+{(T_y^u-D_y^u)}^2+{(T_z^u-D_z^u)}^2}+\sqrt{{(R_x^u-D_x^u)}^2+{(R_y^u-D_y^u)}^2+{(R_z^u-D_z^u)}^2}---\left(7\right)$

Because each the clutter unit on the equidistant ring of clutter equates apart from sum to Receiver And Transmitter, by solid geometry knowledge as can be known, it is focus with R and T that the position one of all the clutter unit on this rang ring fixes on one, and major axis is on the revolution ellipsoid of g/2.Simultaneously, every on the equidistant ring of clutter on earth sphere, it should satisfy spherical equation.Therefore, the equidistant ring of clutter should be the intersection of ellipsoid and earth sphere.We below will ask for revolution ellipsoid equation and earth spherical equation respectively, and with two formula simultaneous solutions, just can solve the track of equidistant ring.

The revolution ellipsoid equation is:

$\frac{{[(x-\frac{R_x+T_x}{2})\cos \mathrm{\β}+(z-\frac{R_z+T_z}{2})\sin \mathrm{\β}]}^2}{a^2}+\frac{y^2+{[-(x-\frac{R_x+T_x}{2})\sin \mathrm{\β}+(z-\frac{R_z+T_z}{2})\cos \mathrm{\β}]}^2}{b^2}=1---\left(8\right)$

Wherein, $\mathrm{\β}={\tan }^{-1}\left(\frac{T_z-R_z}{T_x-R_x}\right),$ $a=\frac{g}{2},$ $b=\sqrt{a^2-\frac{1}{2}\sqrt{{(R_x-T_x)}^2+{(R_y-T_y)}^2+{(R_z-T_z)}^2}}$

Dissolve and obtain:

b ²(xcosβ+zsinβ-ε _x) ²+a ²y ²+a ²(-xsinβ+zcosβ-ε _z) ²＝a ²b ² (9)

Wherein,

${\mathrm{\ϵ}}_x=\frac{R_x+T_x}{2}\cos \mathrm{\β}+\frac{R_z+T_z}{2}\sin \mathrm{\β},$ ${\mathrm{\ϵ}}_z=\frac{R_x+T_x}{2}\sin \mathrm{\β}+\frac{R_z+T_z}{2}\cos \mathrm{\β}$

Write out the sphere parametric equation in the O-XYZ rectangular coordinate system that the equidistant ring of clutter satisfies again:

$\left\{\begin{array}{c}x=R_e\sin \mathrm{\η}\cos \mathrm{\φ}\\ y=R_e\sin \mathrm{\η}\sin \mathrm{\φ}\\ z=R_e\mathrm{cso\η}\end{array}\right.---\left(10\right)$

φ wherein, η is respectively the position angle and the angle of pitch η ∈ [0, π] of spheric coordinate system, φ ∈ [0,2 π], as shown in Figure 3.

With (9) and (10) simultaneous solution, can obtain last every of the equidistant ring of clutter is the relation of clutter unit position angle φ and angle of pitch η:

[(b ²-a ²)R _e ²sin ²ηcos ²β]cos ²φ+(E ₁R _e ²sinηcosφ+E ₂R _esinη)cosφ

+(a ²R _e ²sin ²η+E ₃R _ecosη+E ₄+E ₅R _e ²cos ²η)＝0 (11)

Wherein:

E ₁＝2(b ²-a ²)cosβsinβ

E ₂＝2a ²ε _zsinβ-2b ²ε _xcosβ

E ₃＝-(2b ²ε _xsinβ+2a ²ε _zcosβ)

$E_4=b^2{\mathrm{\ϵ}}_x^2+a^2{\mathrm{\ϵ}}_z^2-a^2{b}^2$

E ₅＝b ²sin ²β+a ²cos ²β

A ₁＝(b ²-a ²)R _e ²sin ²ηcos ²β

Make A ₂=E ₁R _e ²Sin η cos η+E ₂R _eSin η

A ₃＝a ²R _e ²sin ²η+E ₃R _ecosη+E ₄+E ₅R _e ²cos ²η

Obtaining equidistant ring equation is:

A ₁cos ²φ+A ₂cosφ+A ₃＝0 (12)

Angle of pitch η and position angle cosine cos φ that this ring is gone up each clutter unit satisfy quadratic equation with one unknown, η ∈ [0, π], φ ∈ [0,2 π].

If the η of i clutter unit correspondence, φ are η _i, φ _iScanning η _i, η _i∈ [0, π] just can obtain corresponding cos φ _i, ${\cos \mathrm{\φ}}_i=\frac{-A_2\±\sqrt{{A_2}^2-4A_1{A}_3}}{2A_1},$ Try to achieve at last ${\mathrm{\φ}}_i={\cos }^{-1}\left(\frac{{-A}_2\±\sqrt{{A_2}^2-4A_1{A}_3}}{2A_1}\right),$ Obtain the coordinate C of i clutter unit in the O-XYZ coordinate system by formula (10) again _i

The 3rd step: spaceborne bistatic radar clutter unit validity is judged:

Because the earth is a sphere, satellite is limited to the coverage on ground.The echoed signal of the clutter unit outside coverage does not receive.As shown in Figure 4, A ' expression satellite, the frontier point of the reach of B ' this satellite of expression.Arrive the distance in the solstics in the coverage if the distance between A ' B ' is a satellite, use I _MaxExpression.

When the height of Receiver And Transmitter is H _rAnd H _tThe time, can obtain them respectively and be I to the solstics distance in the coverage _Rmax, I _Tmax:

$I_{R\max }=\sqrt{{H_r}^2+2*R_e*H_r}$

$I_{T\max }=\sqrt{{H_t}^2+2*R_e*H_t}---\left(13\right)$

Calculate the distance that all clutter unit branches are clipped to Receiver And Transmitter again

I represents i clutter unit.

$L_{{\mathrm{RC}}_i}=\sqrt{{(x_i-R_x)}^2+{(y_i-R_y)}^2+{(z_i-R_z)}^2}$

$L_{{\mathrm{TC}}_i}=\sqrt{{(x_i-T_x)}^2+{(y_i-T_y)}^2+{(z_i-T_z)}^2}---\left(14\right)$

Have only simultaneously and satisfy $L_{R{C}_i}<I_{R\max }$ With $L_{{\mathrm{TC}}_i}<I_{T\max }$ The clutter unit just in the common coverage of transmitter and receiver, be effective clutter unit, obtaining effective clutter number of unit is Na.

The 4th step: the temporal frequency of spaceborne bistatic radar clutter unit and the calculating of spatial frequency:

Under the spaceborne radar situation, the factor of earth rotation can not be ignored.Therefore the motion vector of the calculating of clutter unit temporal frequency and Receiver And Transmitter and each clutter unit are owing to the motion vector that earth rotation causes is all relevant.Following elder generation introduces the computing method of these several motion vectors in detail.

The calculating of each clutter unit speed vector of step 4.1:

Owing to will consider the influence of earth rotation, so need to calculate on the ground motion size and Orientation of each effective clutter unit on the equidistant ring of clutter, this just need know the longitude and the latitude of each unit correspondence.Above-mentioned O-XYZ coordinate method for building up can be relatively easy to obtain each position in the O-XYZ coordinate system, clutter unit on the equidistant ring, but can not ask longitude and latitude at every, therefore consider rotation of coordinate the O-XYZ coordinate system to be transformed into earth longitude and latitude rectangular coordinate system O-X ^uY ^uZ ^uGet on.

The coordinate conversion more complicated divided for three steps carried out, and as shown in Figure 5, the warp direction of establishing the R place is an X ' axle:

(1) plane ORT is rotated counterclockwise γ along the Z axle ₁Angle makes R and T on same coils to OX ' Z plane.

(2) at OX ' Z ^uIn the plane OZ axle is rotated counterclockwise γ ₂Angle is to OZ ^uAxle points to the positive north.

(3) with OX ' Z ^uThe plane is around Z ^uThe axle γ that turns clockwise ₃Angle is to zero degree meridianpiston OXZ ^u

Above-mentioned 3 steps, the anglec of rotation γ in two steps of back ₂And γ ₃The calculating ratio be easier to, respectively by the decision of the longitude and latitude at R place, ${\mathrm{\&gamma;}}_2=\frac{\mathrm{\&pi;}}{2}-{\mathrm{\&xi;}}_R,$ γ ₃＝ρ _R。Wherein, ρ _RAnd ξ _RBe respectively longitude and the latitude of R, the value of latitude is that the equator is zero, and north latitude is for just, and south latitude is for bearing.But γ ₁The calculating more complicated, tell about γ below ₁Calculating.

Cross the T point and make vertical line to the OZ axle, intersection point is some S, crosses some S to OZ ^uAxle is made vertical line, and intersection point is some J, then γ ' ₁Be ROT plane and ROZ ^uThe dihedral angle that the plane forms.γ ₁＝π-γ′ ₁.

Make B ₁=∠ ROZ, B ₂=∠ TOZ, B ₃=∠ TOR (0 to 180 degree), OT=r

Obtain $\left\{\begin{array}{c}\mathrm{OS}=r\cos B_3\\ \mathrm{TS}=r\sin B_3\\ \mathrm{OJ}=r{\cos B}_3\sec B_1\\ \mathrm{JS}=r\cos B_3\tan B_1\end{array}\right.$

Because ${\cos \mathrm{\&gamma;}}_1^{\&prime;}=\frac{{\mathrm{JS}}^2+{\mathrm{TS}}^2-{\mathrm{TJ}}^2}{2\mathrm{JS}\&CenterDot;\mathrm{TS}}$

JT is arranged again ²=OT ²+ OJ ²-2OTOJcosB ₂, substitution following formula abbreviation obtains

${\mathrm{\&gamma;}}_1^{\&prime;}={\cos }^{-1}\left(\frac{\sin {\mathrm{\&xi;}}_t-\cos \mathrm{\&alpha;}\sin {\mathrm{\&xi;}}_r}{\sin \mathrm{\&alpha;}\cos {\mathrm{\&xi;}}_r}\right)---\left(15\right)$

Then according to γ ₁=π-γ ' ₁Calculate γ ₁. here, γ ₁The rotation number of degrees be-180 to 180 the degree.In two kinds of situation, as the longitude of receiver Longitude In System, γ greater than transmitter ₁Be 0～180 degree, as the longitude of receiver Longitude In System, γ less than transmitter ₁Be-180～0 degree.Therefore, to need here to note judging, as the longitude of receiver Longitude In System, the γ that calculates less than transmitter ₁Get negative.

Obtaining at last from the O-XYZ coordinate system rotation to latitude and longitude coordinates is O-X ^uY ^uZ ^uThe coordinate transform formula be:

$\left\{\begin{array}{c}{x}^u=({\cos \mathrm{\&gamma;}}_1\sin {\mathrm{\&xi;}}_r\cos {\mathrm{\&rho;}}_r+\sin {\mathrm{\&gamma;}}_1{\sin \mathrm{\&rho;}}_r)x+({\sin \mathrm{\&gamma;}}_1\sin {\mathrm{\&xi;}}_r\cos {\mathrm{\&rho;}}_r-\cos {\mathrm{\&gamma;}}_1\sin {\mathrm{\&rho;}}_r)y+\cos {\mathrm{\&xi;}}_r\cos {\mathrm{\&rho;}}_{r}z\\ y^u=({\cos \mathrm{\&gamma;}}_1\sin {\mathrm{\&xi;}}_r\sin {\mathrm{\&rho;}}_r-\sin {\mathrm{\&gamma;}}_1\cos {\mathrm{\&rho;}}_r)x+({\sin \mathrm{\&gamma;}}_1\sin {\mathrm{\&xi;}}_r\sin {\mathrm{\&rho;}}_r+{\cos \mathrm{\&gamma;}}_1\cos {\mathrm{\&rho;}}_r)y+\cos {\mathrm{\&xi;}}_r\sin {\mathrm{\&rho;}}_{r}z\\ z^u=-\cos {\mathrm{\&gamma;}}_1\cos {\mathrm{\&xi;}}_{r}x-\sin {\mathrm{\&gamma;}}_1\cos {\mathrm{\&xi;}}_{r}y+\sin {\mathrm{\&xi;}}_{r}z\end{array}\right.---\left(16\right)$

(x ^u, y ^u, z ^u) in subscript u represent this point to be arranged in the new coordinate of latitude and longitude coordinates system.By rotation of coordinate, obtain the coordinate of i clutter unit at earth longitude and latitude coordinate system $\stackrel{\&RightArrow;}{C_i^u}=(x_i^u,y_i^u,z_i^u),$ I=1 ..., Na converts them to corresponding latitude ξ again _CiWith longitude ρ _Ci, ${\mathrm{\&xi;}}_{\mathrm{Ci}}={\sin }^{-1}(z_i^u/R_e),$ ${\mathrm{\&rho;}}_{\mathrm{Ci}}={\sin }^{-1}\left(\frac{y_i^u}{R_e\cos {\mathrm{\&xi;}}_{\mathrm{Ci}}}\right),$ ξ _CiScope is-pi/2 is to pi/2, ρ _CiScope is-π is to π.

So be positioned at (ρ _Ci, ξ _Ci) the clutter unit because the motion vector that causes of earth rotation is expressed as following formula in the longitude and latitude coordinate system, unit is m/s:

$\stackrel{\&RightArrow;}{V_{\mathrm{Ci}}}=\left\{\begin{array}{c}-459\sin {\mathrm{\&rho;}}_{\mathrm{Ci}}\cos {\mathrm{\&xi;}}_{\mathrm{Ci}}\\ 459\cos {\mathrm{\&rho;}}_{\mathrm{Ci}}\cos {\mathrm{\&xi;}}_{\mathrm{Ci}}\\ 0\end{array}\right.---\left(17\right)$

Wherein, 459m/s is that point on the terrestrial equator is because geostrophic velocity magnitude.

The calculating of step 4.2 radar transmitter and receiver velocity

Radar transmitter is identical with the computing method of receiver velocity, introduces the computing method of receiver velocity here earlier.Because radar receiver is placed on the satellite, the direction of motion of radar is consistent with satellite.As accompanying drawing 6, adopt the longitude and latitude rectangular coordinate system, suppose the inclination of satellite orbit θ at receiver place _r, the longitude of the ascending node N of this track

, the latitude and longitude coordinates (ρ of sub-satellite point _r, ξ _r) all known in step 1.

Suppose

Normal vector for orbit plane is designated as

, the satellite position vector is

, the unit vector behind the normalizing is designated as

, satellite velocity vector is

These vectors add bottom right mark x, and y, z represent them respectively at x, y, the component on the z axle.Because pairwise orthogonal between these three vectors, so utilize the cross product formula just can obtain

, be expressed as follows:

$\stackrel{\&RightArrow;}{V_R}=a_{V_R}(\stackrel{\&RightArrow;}{F_R}\&times;\stackrel{\&RightArrow;}{P_R})---\left(18\right)$

Wherein,

Being the velocity magnitude of receiver satellite, is a scalar, $a_{V_R}=629575/\sqrt{(H_r+R_e)/1000}.$

At x, y, three components on the z axle are:

$V_{\mathrm{Rx}}=a_{V_R}\left|\begin{array}{cc}{F}_{\mathrm{Ry}}& F_{\mathrm{Rz}}\\ P_{\mathrm{Ry}}& P_{\mathrm{Rz}}\end{array}\right|$ $V_{\mathrm{Ry}}=a_{V_R}\left|\begin{array}{cc}{F}_{\mathrm{Rz}}& F_{\mathrm{Rx}}\\ P_{\mathrm{Rz}}& P_{\mathrm{Rx}}\end{array}\right|$ $V_{\mathrm{Rz}}=a_{V_R}\left|\begin{array}{cc}{F}_{\mathrm{Rx}}& F_{\mathrm{Ry}}\\ P_{\mathrm{Rx}}& P_{\mathrm{Ry}}\end{array}\right|,$

Wherein, || the expression determinant.We go out a demand

With

Just can in the hope of Wherein, $\stackrel{\&RightArrow;}{P_R}=(\cos {\mathrm{\&xi;}}_r\cos {\mathrm{\&rho;}}_r,\cos {\mathrm{\&xi;}}_r\sin {\mathrm{\&rho;}}_r,\sin {\mathrm{\&xi;}}_r),$ Normal vector Be calculated as follows:

N is an ascending node, vector of unit length

, again because $\stackrel{\&RightArrow;}{F_R}\&perp;\stackrel{\&RightArrow;}{\mathrm{ON}},$ Can write out equation:

Solve normal vector

For:

Direct orbit:

Retrograde trajectory:

The feature of direct orbit be orbit inclination be orbit plane and earth equatorial plane angle less than 90 the degree.The feature of retrograde trajectory be orbit inclination be orbit plane and earth equatorial plane angle greater than 90 the degree less than 180 the degree.

In like manner find the solution transmitter motor speed vector. Be the velocity of radar transmitter in earth longitude and latitude rectangular coordinate system, the normal vector of transmitter place orbit plane is

, be designated as , the position vector of transmitter is

, the vector of unit length after the normalization is designated as

Then

$\stackrel{\&RightArrow;}{V_T}=a_{V_T}(\stackrel{\&RightArrow;}{F_T}\&times;\stackrel{\&RightArrow;}{P_T})---\left(22\right)$

Wherein,

Being the velocity magnitude of transmitter satellite, is a scalar, $a_{V_T}=629575/\sqrt{(H_t+R_e)/1000}.$

At x, y, three components on the z axle are:

$V_{\mathrm{Tx}}=a_{V_T}\left|\begin{array}{cc}{F}_{\mathrm{Ty}}& F_{\mathrm{Tz}}\\ P_{\mathrm{Ty}}& P_{\mathrm{Tz}}\end{array}\right|$ $V_{\mathrm{Ty}}=a_{V_T}\left|\begin{array}{cc}{F}_{\mathrm{Tz}}& F_{\mathrm{Tx}}\\ P_{\mathrm{Tz}}& P_{\mathrm{Tx}}\end{array}\right|$ $V_{\mathrm{Tz}}=a_{V_T}\left|\begin{array}{cc}{F}_{\mathrm{Tx}}& F_{\mathrm{Ty}}\\ P_{\mathrm{Tx}}& P_{\mathrm{Ty}}\end{array}\right|,$

We go out a demand

With

Just can in the hope of

Wherein, $\stackrel{\&RightArrow;}{P_T}=(\cos {\mathrm{\&xi;}}_t\cos {\mathrm{\&rho;}}_t,\cos {\mathrm{\&xi;}}_t\sin {\mathrm{\&rho;}}_t,\sin {\mathrm{\&xi;}}_t),$ Normal vector

Be calculated as follows:

N is the ascending node of transmitter track, vector of unit length Again because $\stackrel{\&RightArrow;}{F_t}\&perp;\stackrel{\&RightArrow;}{\mathrm{ON}},$ Can write out equation:

Solve normal vector

For:

Direct orbit:

Retrograde trajectory:

The calculating of the temporal frequency of the spaceborne bistatic radar clutter of step 4.3 unit:

At last, the calculating of the temporal frequency of i clutter unit is formed by four:

Wherein,

Be respectively transmitter, the velocity of receiver in latitude and longitude coordinates system.

Be that i clutter unit is because the velocity that earth rotation causes.C _i ^uBe the coordinate of i clutter unit in earth longitude and latitude rectangular coordinate system, $C_i^u=(x_i^u,y_i^u,z_i^u),$ i＝1，…，Na。

Be respectively in the earth latitude and longitude coordinates system transmitter site and receiver location to the vector of i clutter unit.

Be respectively in the earth latitude and longitude coordinates system vector of i clutter unit, the following calculating of vector length to transmitter site and receiver location:

I clutter unit with respect to the Space Angle frequency of receiver is

Wherein, d is an array element distance.

The 5th step: the calculating of spaceborne bistatic radar clutter covariance matrix:

Radar receiver and transmitter are all adopted the normal linearity array, and adopt positive side formula to place, and promptly the antenna major axis is consistent with the satellite flight direction.Transmitter antenna array adopts even weighting, and array acceptor carries out omnidirectional and receives.I clutter unit is with respect to the cone angle cosine cos Φ of transmitter array placement direction _TiFor

Measuring point D to be checked is with respect to the cone angle cosine cos Φ of transmitter array placement direction _T0For

Φ _T0Main beam pointing for transmitter antenna.Wherein,

Be vector from transmitter site to point position to be checked.

Transmitter array has Q array element, and the transmitter antenna gain (dBi) on i clutter unit is:

$W_i=\underset{n=1}{\overset{Q}{\mathrm{\&Sigma;}}}\exp \left\{j\frac{2\mathrm{\&pi;d}}{\mathrm{\&lambda;}}(n-1)(\cos {\mathrm{\&Phi;}}_{\mathrm{Ti}}-\cos {\mathrm{\&Phi;}}_{T0})\right\}---\left(30\right)$

Equidistant ring is divided into N _cIndividual clutter unit judges that effective clutter unit number is N _a. then i clutter unit is ω with respect to the Space Angle frequency of receiver _Si=2 π f _Si, the time-angle frequency is ω _Ti=2 π f _Ti, f _Ti, f _SiCan get by formula (26) (27).

Define p respectively _i=[1, exp (j ω _Si), exp (j2 ω _Si) ... exp (j (G-1) ω _Si] ^TBe spatial domain Fourier guiding vector, q _i=[1, exp (j ω _Ti), exp (j2 ω _Ti) ..., exp (j (K-1) ω _Ti)] ^TBe time domain Fourier guiding vector, G wherein, K are respectively the array element number of receiver and coherent umber of pulse in handling at interval.The principle of work of radar is a plurality of pulses of emission in a period of time, and next section sends another series impulse again in the time interval.Coherent is handled at interval and is referred in this time interval, and the phase relation of these a plurality of pulse signals is fixed, and can carry out Combined Treatment.Two-dimension fourier guiding vector S _iPromptly be defined as vector p _iAnd q _iKronecker long-pending, promptly $k_i=p_i\&CircleTimes;q_i,$ k _iBe GK * 1 dimension.

The clutter space-time two-dimensional covariance matrix U of this rang ring _cFor

$U_c=\underset{i=1}{\overset{\mathrm{Na}}{\mathrm{\&Sigma;}}}{\mathrm{\&zeta;}}_i{k}_i{k}_i^H---\left(31\right)$

Wherein, subscript H represents conjugate transpose.U _cBe GK * GK dimension.ξ _iIt is the average power of i clutter cell signal.ξ _iTry to achieve by following formula, adopt the radar equation of simplifying here, mainly pay close attention to the influence that distance and antenna gain are brought:

The 6th step: produce the clutter simulation data w that obeys this covariance matrix statistical property.

The production method of clutter simulation data is to use U _c ^1/2Multiply each other with white Gaussian noise, promptly $w=U_c^{1/2}\&CenterDot;\mathrm{\&mu;},$ Wherein μ is the white Gaussian noise of GK * 1 dimension.

So far, the clutter base-band analog signal of spaceborne bistatic radar produces and finishes.

The present invention is directed to a kind of new radar system is the production method that spaceborne bistatic radar system has proposed the clutter simulation signal.By this method, we can be used for the clutter data that produce checking, selection or the improvement of the Clutter suppression algorithm of follow-up spaceborne radar signal processing system.

Description of drawings

The spaceborne bistatic radar clutter of Fig. 1 baseband signal produces system chart;

Fig. 2 clutter simulation baseband signal production method process flow diagram;

The equidistant ring establishing method model of Fig. 3 clutter: Cr represents the equidistant ring of clutter;

Fig. 4 satellite coverage synoptic diagram;

Fig. 5 O-XYZ is to earth longitude and latitude rectangular coordinate system rotation diagram;

The definition of Fig. 6 satellite velocities;

Clutter space-time two-dimensional spectrum under a kind of spaceborne bistatic radar configuration of Fig. 7;

Clutter space-time two-dimensional spectrum vertical view under a kind of spaceborne bistatic radar configuration of Fig. 8;

The multiple Clutter suppression algorithm performance of Fig. 9 compares:

FA, APD,

PSPD, JDL,

DBPD.

Embodiment

Below in conjunction with the drawings and specific embodiments the present invention is described in further detail.

Method of the present invention can be divided into 6 steps, and idiographic flow as shown in Figure 2.According to the spaceborne bistatic radar parameter of this process settings, adopt the system chart shown in the accompanying drawing 1 to realize.It is hardware platform that the system of accompanying drawing 1 adopts high performance server, the spaceborne bistatic radar clutter simulate signal software of exploitation under windows operating system, move corresponding flow process, baseband analog data according to the parameter generating spaceborne radar of setting, deposit in the server memory, then by standard pci bus output integrated circuit board according to host-host protocol, send the data to spaceborne basic Radar Signal Processing system.Because the noise signal characteristic difference under the different radar system parameter configuration, signal processing system will adopt different Clutter suppression algorithm at different radar system parameters.

Therefore, we need carry out the Clutter suppression algorithm selection according to concrete radar parameter, better curb noise signal, detect performance thereby improve follow-up moving-target.To provide clutter simulation signal that produces by emulation experiment and the performance map that adopts after multiple Clutter suppression algorithm is handled this signal below, so that its role when carrying out the Clutter suppression algorithm selection to be described, the radar system parameter that adopts during emulation is by shown in the table one.

Table one radar system parameter

Produce the simulation noise signal according to the radar parameter of setting, the space-time two-dimensional that provides this signal correspondence is composed as shown in Figure 7, and accompanying drawing 8 is the vertical view of this spectrum.Under the spaceborne radar situation, the doppler ambiguity of clutter is very serious as can be seen.

Next we consider to adopt multiple Clutter suppression algorithm that a kind of best algorithm is handled and selected to the clutter simulation signal that produces.Present Clutter suppression algorithm is generally considered dimensionality reduction STAP, and its kind is a lot, only enumerates wherein several below:

(1)Full?Adaptive(FA)

(2)Adjancent-bin-Post?Doppler(APD)

(3)PRI-Staggered-Post?Doppler(PSPD)

(4)Joint?DomainLocalized(JDL)

(5)Displaced-filter?Beamspace?Post-Doppler(DBPD)

Wherein, preceding 3 kinds of methods owing to adopted the degree of freedom of whole array elements and the degree of freedom of part time domain pulse, therefore are called the self-adaptive processing in array element territory.Then two kinds of algorithms have only adopted part array element and partial pulse to do self-adaptive processing, are called the self-adaptive processing in wave beam territory.In the array element territory, PSPD is bigger than the operand of APD.In the wave beam territory, DBPD is bigger than JDL operand.The AMP algorithm is an operand maximum in all algorithms.

Five kinds of dimensionality reduction STAP algorithms mentioning above adopting are handled the clutter data, and accompanying drawing 9 is to adopt the performance after five kinds of algorithms are handled the clutter simulation data to compare.Lsinr is SINR loss, generally we think Lsinr-notch width of 5dB place correspondence is the minimum detectable speed (MDV) of moving-target, if target velocity drops in this recess scope, then can't detect.Therefore, recess is narrow more, and the moving-target velocity range that can detect is big more, and performance is corresponding just good more.As can be seen, the DBPD in wave beam territory and JDL algorithm performance are better than the FA in array element territory, APD and PSPD, and the consideration of associative operation amount again should be selected the JDL algorithm under this bistatic configuration parameter.

As seen, the bistatic radar simulating signal of generation can be used for signal processing system Clutter suppression algorithm is selected.

Claims (1)

1. the production method of spaceborne bistatic radar clutter base-band analog signal is characterized in that, it contains following steps successively: step (1): import the starting condition of spaceborne bistatic radar system parameter as this method on computers:

The radar system parameter comprises three parts, i.e. the satellite platform parameter and the target component of radar installations parameter, placement radar;

The radar installations parameter: the wavelength X that transmits, transmitter antenna array element number Q, receiver antenna array element number G, receiver antenna array element distance and transmitter antenna array element distance equate, are designated as d, transmitter pulse repetition frequency f _r

Satellite platform parameter: radar transmitter place satellite platform height H _t, the orbit altitude H of receiver place satellite platform _r, transmitter inclination of satellite orbit θ _t, receiver inclination of satellite orbit θ _r, the longitude of transmitter ascending node of satellite orbit Receiver ascending node of satellite orbit longitude

Transmitter sub-satellite point longitude ρ _t, receiver sub-satellite point longitude ρ _r

By θ _t, ρ _tObtain transmitter substar latitude ξ _t,

By θ _r,

ρ _rObtain receiver substar latitude ξ _r,

Target component: the coordinate (ρ of cells D to be detected on the ground _d, ξ _d), ρ _dThe expression longitude, ξ _dThe expression latitude;

Step (2): set up the equidistant ring of spaceborne bistatic radar clutter on computers successively according to the following steps:

Z very to the north of step (2.1) earth longitude and latitude rectangular coordinate system ^uAxle, equatorial plane is X ^uOY ^uPlane, zero degree warp direction are X ^uAxle; Receiver, transmitter and measuring point D to be checked are respectively in the position of earth longitude and latitude rectangular coordinate system

Subscript u represents that this coordinate is reference with latitude and longitude coordinates, symbol

The expression vector; $\stackrel{\&RightArrow;}{T^u}=(T_x^u,T_y^u,T_z^u),$ T wherein _x ^u, T _y ^u, T _z ^uBe respectively transmitter x under earth longitude and latitude rectangular coordinate system, y, the coordinate components of z axle; $\stackrel{\&RightArrow;}{R^u}=(R_x^u,R_y^u,R_z^u),$ R wherein _x ^u, R _y ^u, R _z ^uBe respectively receiver x under earth longitude and latitude rectangular coordinate system, y, the coordinate components of z axle; $\stackrel{\&RightArrow;}{D^u}=(D_x^u,D_y^u,D_z^u),$ (D wherein _x ^u, D _y ^u, D _z ^u) be respectively D point x under earth longitude and latitude rectangular coordinate system, y, the coordinate components of z axle;

Step (2.2) is set up rectangular coordinate system O-XYZ, establishes the position of Receiver And Transmitter in the O-XYZ rectangular coordinate system and represents with R and T respectively, and the position of measuring point to be checked represents that with D O is the earth centre of sphere, then

Be the Z axle, plane vertical with the Z axle and the centre of sphere excessively is an XOY plane; Definition $\stackrel{\&RightArrow;}{T}=(T_x,T_y,T_z)$ Be the position vector of transmitter in the O-XYZ rectangular coordinate system, wherein T _x, T _y, T _zBe respectively transmitter x under the O-XYZ rectangular coordinate system, y, the coordinate components of z axle; Definition $\stackrel{\&RightArrow;}{R}=(R_x,R_y,R_z)$ Be the position vector of receiver in the O-XYZ rectangular coordinate system, wherein R _x, R _y, R _zBe respectively receiver x under the O-XYZ rectangular coordinate system, y, the coordinate components of z axle; Definition $\stackrel{\&RightArrow;}{D}=(D_x,D_y,D_z)$ Be the position vector of target to be measured in the O-XYZ rectangular coordinate system; G be bistatic distance and, equal tested point D to R and T apart from sum; If the point on the equidistant ring of clutter be the coordinate of clutter unit in the O-XYZ rectangular coordinate system for (x, y z), satisfy that the position with Receiver And Transmitter is the ellipsoid equation of focus in the O-XYZ rectangular coordinate system:

b ²(xcosβ+zsinβ-ε _x) ²+a ²y ²+a ²(-xsinβ+zcosβ-ε _z) ²＝a ²b ² (1)

Wherein, $a=\frac{g}{2},$ $b=\sqrt{a^2-\frac{1}{4}({(R_x-T_x)}^2+{(R_y-T_y)}^2+{(R_z-T_z)}^2)},$ $\mathrm{\&beta;}={\tan }^{-1}\left(\frac{T_z-R_z}{T_x-R_x}\right),$ ${\mathrm{\&epsiv;}}_x=\frac{R_x+T_x}{2}\cos \mathrm{\&beta;}+\frac{R_z+T_z}{2}\sin \mathrm{\&beta;},$ ${\mathrm{\&epsiv;}}_z=-\frac{R_x+T_x}{2}\sin \mathrm{\&beta;}+\frac{R_z+T_z}{2}\cos \mathrm{\&beta;};$

Step (2.3) clutter unit is gone up again simultaneously at the earth's surface, satisfies the sphere parametric equation:

$\left\{\begin{array}{c}x=R_e\sin \mathrm{\&eta;}\cos \mathrm{\&phi;}\\ y=R_e\sin \mathrm{\&eta;}\sin \mathrm{\&phi;}\\ z=R_e\cos \mathrm{\&eta;}\end{array}\right.---\left(2\right)$

φ wherein, η are respectively in the spheric coordinate system any the position angle and the angle of pitch arbitrarily, η ∈ [0, π], φ ∈ [0,2 π], R _eBe earth radius;

Step (2.4) obtains the angle of pitch and azimuthal relation of clutter unit with (1) and (2) simultaneous solution:

[(b ²-a ²)R _e ²?sin ²ηcos ²?β]cos ^2_φ+(E ₁R _e ²?sinηcosφ+E ₂R _e?sinη)cosφ

+(a ²R _e ²sin ²η+E ₃R ₃?cosη+E ₄+E ₅R _e ²cos ²η)＝0 (3)

Wherein, E ₁=2 (b ²-a ²) cos β sin β, E ₂=2a ²ε _zSin β-2b ²ε _xCos β

E ₃-＝-(2b ²ε _xsinβ+2a ²ε _zcosβ)， $E_4=b^2{\mathrm{\&epsiv;}}_x^2+a^2{\mathrm{\&epsiv;}}_z^2-a^2{b}^2,$ E ₅＝b ²sin ²β+a ²cos ²β；

Step (2.5) formula (3) is a quadratic equation with one unknown about η and cos φ, establishes the η of each clutter unit i correspondence, and φ is η _i, φ _i, by scanning η from Z axle positive dirction 0 to π _iObtain ${\mathrm{\&phi;}}_i={\cos }^{-1}\left(\frac{-A_2\&PlusMinus;\sqrt{{A_2}^2-4A_1{A}_3}}{2A_1}\right);$

A ₁＝(b ²-a ²)R _e ²sin ²ηcos ²β

A wherein ₂=E ₁R _e ²Sin η cos η+E ₂R _eSin η

A ₃＝a ²R _e ²sin ²η+E ₃R _ecosη+E ₄+E ₅R _e ²cos ²η

Step (2.6) is according to η _i, φ _i, utilize formula (2) to obtain each clutter unit coordinate under the O-XYZ rectangular coordinate system on the equidistant ring of clutter;

Step (3): in computing machine, carry out spaceborne bistatic radar clutter unit validity and judge:

Step (3.1), the distance of establishing two satellites being loaded with Receiver And Transmitter respectively solstics in the radar system coverage is I _Rmax, I _TmaxThen

$I_{R\max }=\sqrt{{H_r}^2+2*R_e*H_r}$

$I_{T\max }=\sqrt{{H_t}^2+2*R_e*H_t}$

Step (3.2) is calculated the distance that all clutter unit branches are clipped to Receiver And Transmitter in the O-XYZ rectangular coordinate system Subscript i represents i clutter unit:

$L_{{\mathrm{RC}}_i}=\sqrt{{(x_i-R_x)}^2+{(y_i-R_y)}^2+{(z_i-R_z)}^2}$

$L_{{\mathrm{TC}}_i}=\sqrt{{(x_i-T_x)}^2+{(y_i-T_y)}^2+{(z_i-T_z)}^2}$

Step (3.3) will

With I _Rmax, With I _TmaxCompare, have only simultaneously and satisfy $L_{{\mathrm{RC}}_i}<I_{R\max }$ With $L_{{\mathrm{TC}}_i}<I_{T\max }$ The clutter unit just in the common coverage of transmitter and receiver, be effective clutter unit, obtaining effective clutter number of unit is Na;

Step (4): in computing machine, carry out each clutter unit time corresponding frequency and spatial frequency and calculate:

Each clutter unit speed vector of step (4.1) Calculating:

The coordinate of Na clutter unit is rotated to earth longitude and latitude rectangular coordinate system O-X from the O-XYZ rectangular coordinate system ^uY ^uZ ^u, the rotation of coordinate formula is:

$\left\{\begin{array}{c}{x}^u=(\cos {\mathrm{\&gamma;}}_1\sin {\mathrm{\&xi;}}_r\cos {\mathrm{\&rho;}}_r+\sin {\mathrm{\&gamma;}}_1\sin {\mathrm{\&rho;}}_r)x+(\sin {\mathrm{\&gamma;}}_1\sin {\mathrm{\&xi;}}_r\cos {\mathrm{\&rho;}}_r-\cos {\mathrm{\&gamma;}}_1\sin {\mathrm{\&rho;}}_r)y+\cos {\mathrm{\&xi;}}_r\cos {\mathrm{\&rho;}}_{r}z\\ y^u=(\cos {\mathrm{\&gamma;}}_1\sin {\mathrm{\&xi;}}_r\sin {\mathrm{\&rho;}}_r-\sin {\mathrm{\&gamma;}}_1\cos {\mathrm{\&rho;}}_r)x+(\sin {\mathrm{\&gamma;}}_1\sin {\mathrm{\&xi;}}_r\sin {\mathrm{\&rho;}}_r+\cos {\mathrm{\&gamma;}}_1\cos {\mathrm{\&rho;}}_r)y+\cos {\mathrm{\&xi;}}_r\sin {\mathrm{\&rho;}}_{r}z\\ z^u=-\cos {\mathrm{\&gamma;}}_1\cos {\mathrm{\&xi;}}_{r}x-\sin {\mathrm{\&gamma;}}_1\cos {\mathrm{\&xi;}}_{r}y+\sin {\mathrm{\&xi;}}_{r}z\end{array}\right.$

Wherein, γ ₁The supplementary angle of the dihedral angle that forms for ROT plane and ROZ plane, (x ^u, y ^u, z ^u) be the coordinate figure of clutter unit in earth longitude and latitude rectangular coordinate system; γ ₁=π-γ ' ₁, γ ' ₁Be ROT plane and ROZ ^uThe dihedral angle that the plane forms,

${\mathrm{\&gamma;}}_1^{\&prime;}={\cos }^{-1}\left(\frac{\sin {\mathrm{\&xi;}}_t-\cos \mathrm{\&alpha;}\sin {\mathrm{\&xi;}}_r}{\sin \mathrm{\&alpha;}\cos {\mathrm{\&xi;}}_r}\right)$

Wherein, $\mathrm{\&alpha;}=\sqrt{{(R_e+H_r)}^2+{(R_e+H_r)}^2+{(R_x^u-T_x^u)}^2+{(R_y^u-T_y^u)}^2+{(R_y^u-T_y^u)}^2-2(R_e+H_r)(R_e+H_r)}$

By rotation of coordinate, obtain the coordinate of i clutter unit at earth longitude and latitude coordinate system $\stackrel{\&RightArrow;}{C_i^u}=(x_i^u,y_i^u,z_i^u),$ I=1 ..., Na will again

Be converted to corresponding latitude ξ _CiWith longitude ρ _Ci, ${\mathrm{\&xi;}}_{\mathrm{Ci}}={\sin }^{-1}(z_i^u/R_e),$ ${\mathrm{\&rho;}}_{\mathrm{Ci}}={\sin }^{-1}\left(\frac{y_i^u}{R_e\cos {\mathrm{\&xi;}}_{\mathrm{Ci}}}\right),$ ξ _CiScope is-pi/2 is to pi/2, ρ _CiScope is-π is to π;

Further obtain i clutter unit because the velocity that earth rotation causes

$\stackrel{\&RightArrow;}{V_{\mathrm{Ci}}}=(-459\sin {\mathrm{\&rho;}}_{\mathrm{Ci}}\cos {\mathrm{\&xi;}}_{\mathrm{Ci}},459\cos {\mathrm{\&rho;}}_{\mathrm{Ci}}\cos {\mathrm{\&xi;}}_{\mathrm{Ci}},0);$

Step (4.2), the radar receiver velocity

Calculate:

Be the velocity of radar receiver in earth longitude and latitude rectangular coordinate system, the normal vector of receiver place orbit plane is

Be designated as The unit vector of the position of receiver is

These vector titles add bottom right mark x, and y, z represent them respectively at x, y, and the component on the z axle, then

$\stackrel{\&RightArrow;}{V_R}=a_{V_R}(\stackrel{\&RightArrow;}{F_R}\&times;\stackrel{\&RightArrow;}{P_R})$

Wherein,

Be scalar, the velocity magnitude of expression receiver satellite, $a_{V_R}=629575/\sqrt{(H_r+R_e)/1000};$

Try to achieve the unit vector of the position of receiver by the latitude and longitude coordinates of receiver

$\stackrel{\&RightArrow;}{P_R}=(\cos {\mathrm{\&xi;}}_r\cos {\mathrm{\&rho;}}_r,\cos {\mathrm{\&xi;}}_r\sin {\mathrm{\&rho;}}_r,\sin {\mathrm{\&xi;}}_r);$

By receiver orbit inclination θ _rBe the corner dimension and the receiver ascending node of orbit longitude of orbit plane and earth equatorial plane

Determine:

Direct orbit is an orbit inclination during less than pi/2:

Retrograde trajectory is an orbit inclination greater than the pi/2 degree less than π:

Step (4.3), the velocity of radar transmitter Calculate:

Be the velocity of radar transmitter in earth longitude and latitude rectangular coordinate system, the normal vector of transmitter place orbit plane is

Be designated as

The position unit vector of transmitter

$\stackrel{\&RightArrow;}{V_T}=a_{V_T}(\stackrel{\&RightArrow;}{F_T}\&times;\stackrel{\&RightArrow;}{P_T}),$

Try to achieve the unit vector of the position of receiver by the latitude and longitude coordinates of transmitter,

$\stackrel{\&RightArrow;}{P_T}=(\cos {\mathrm{\&xi;}}_t\cos {\mathrm{\&rho;}}_t,\cos {\mathrm{\&xi;}}_t\sin {\mathrm{\&rho;}}_t,\sin {\mathrm{\&xi;}}_t);$

By transmitter orbit inclination size θ _tWith transmitter ascending node of orbit longitude

Determine,

Direct orbit:

Retrograde trajectory:

Step (4.4) is found the solution the temporal frequency f of i unit of the equidistant ring of spaceborne bistatic radar clutter _Ti:

$f_{\mathrm{ti}}=\frac{1}{\mathrm{\&lambda;}}(\frac{\stackrel{\&RightArrow;}{V_T}\&CenterDot;\stackrel{\&RightArrow;}{T^u{C}_i^u}}{\left|\right|\stackrel{\&RightArrow;}{T^u{C}_i^u}\left|\right|}+\frac{\stackrel{\&RightArrow;}{V_{\mathrm{Ci}}}\&CenterDot;\stackrel{\&RightArrow;}{C_i^u{T}^u}}{\left|\right|\stackrel{\&RightArrow;}{C_i^u{T}^u}\left|\right|}+\frac{\stackrel{\&RightArrow;}{V_R}\&CenterDot;\stackrel{\&RightArrow;}{R^u{C}_i^u}}{\left|\right|\stackrel{\&RightArrow;}{R^u{C}_i^u}\left|\right|}+\frac{\stackrel{\&RightArrow;}{V_{\mathrm{Ci}}}\&CenterDot;\stackrel{\&RightArrow;}{{C_i^{u}R}^u}}{\left|\right|\stackrel{\&RightArrow;}{C_i^u{R}^u}\left|\right|})$

Wherein,

Be respectively transmitter, the velocity of receiver in the longitude and latitude rectangular coordinate system,

Be the velocity that i clutter unit causes owing to earth rotation, C _i ^uBe the position of i clutter unit in earth longitude and latitude rectangular coordinate system,

Be respectively in the earth longitude and latitude rectangular coordinate system transmitter and receiver to the vector of i clutter cell position,

Be respectively in the earth longitude and latitude rectangular coordinate system vector of i clutter cell position to transmitter and receiver, vector length is calculated as follows:

$\left|\right|\stackrel{\&RightArrow;}{T^u{C}_i^u}\left|\right|=\left|\right|\stackrel{\&RightArrow;}{C_i^u{T}^u}\left|\right|=\sqrt{{(x_i^u-T_x^u)}^2+{(y_i^u-T_y^u)}^2+{(z_i^u-T_z^u)}^2},$

$\left|\right|\stackrel{\&RightArrow;}{R^u{C}_i^u}\left|\right|=\left|\right|\stackrel{\&RightArrow;}{C_i^u{R}^u}\left|\right|=\sqrt{{(x_i^u-R_x^u)}^2+{(y_i^u-R_y^u)}^2+{(z_i^u-R_z^u)}^2};$

Step (4.5) is found the solution the spatial frequency f of i unit of the equidistant ring of spaceborne bistatic radar clutter _Si:

$f_{\mathrm{si}}=\frac{d}{\mathrm{\&lambda;}}\frac{\stackrel{\&RightArrow;}{V_R}\&CenterDot;\stackrel{\&RightArrow;}{R^u{C}_i^u}}{\left|\right|\stackrel{\&RightArrow;}{V_R}\left|\right|\left|\right|\stackrel{\&RightArrow;}{R^u{C}_i^u}\left|\right|}$

Step (5) is carried out clutter covariance matrix U in computing machine _cCalculating:

Step (5.1), i clutter unit is ω with respect to the Space Angle frequency of receiver _Si=2 π f _Si, the time-angle frequency is ω _Ti=2 π f _Ti, define p respectively _i=[1, exp (j ω _Si), exp (j2 ω _Si) ... exp (j (G-1) ω _Si] ^TBe spatial domain Fourier guiding vector, q _i=[1, exp (j ω _Ti), exp (j2 ω _Ti) ..., exp (j (K-1) ω _Ti)] ^TBe time domain Fourier guiding vector, G wherein, K are respectively the array element number of receiver and coherent umber of pulse in handling at interval;

Two-dimension fourier guiding vector k _iPromptly be defined as vector p _iAnd q _iKronecker long-pending, promptly $k_i=p_i\&CircleTimes;q_i,$ k _iBe GK * 1 dimension;

I clutter unit is with respect to the cone angle cosine cos Φ of transmitter array placement direction _TiFor

$\cos {\mathrm{\&Phi;}}_{\mathrm{Ti}}=\frac{\stackrel{\&RightArrow;}{V_T}\&CenterDot;\stackrel{\&RightArrow;}{T^u{C}_i^u}}{\left|\right|\stackrel{\&RightArrow;}{V_T}\left|\right|\left|\right|\stackrel{\&RightArrow;}{T^u{C}_i^u}\left|\right|}$

Measuring point D to be checked is with respect to the cone angle cosine cos Φ of transmitter array placement direction _T0For

$\cos {\mathrm{\&Phi;}}_{T0}=\frac{\stackrel{\&RightArrow;}{V_T}\&CenterDot;\stackrel{\&RightArrow;}{T^u{D}^u}}{\left|\right|\stackrel{\&RightArrow;}{V_T}\left|\right|\left|\right|\stackrel{\&RightArrow;}{T^u{D}^u}\left|\right|}$

Φ _T0Main beam pointing for transmitter antenna; Wherein, wherein,

Be vector from transmitter site to point position to be checked; $\left|\right|\stackrel{\&RightArrow;}{T^u{D}^u}\left|\right|=\sqrt{{(D_x^u-R_x^u)}^2+{(D_y^u-R_y^u)}^2+{(D_z^u-R_z^u)}^2}$

Transmitter antenna gain (dBi) on i clutter unit is:

$W_i=\underset{n=1}{\overset{Q}{\mathrm{\&Sigma;}}}\exp \left\{j\frac{2\mathrm{\&pi;d}}{\mathrm{\&lambda;}}(n-1)(\cos {\mathrm{\&Phi;}}_{\mathrm{Ti}}-\cos {\mathrm{\&Phi;}}_{T0})\right\}$

Wherein Q is the transmitter array element number;

Step (5.2), the clutter space-time two-dimensional autocorrelation matrix of this rang ring is

$U_c=\underset{i=1}{\overset{\mathrm{Na}}{\mathrm{\&Sigma;}}}{\mathrm{\&zeta;}}_i{k}_i{k}_i^H$

Wherein, subscript H represents vectorial k _iConjugate transpose; ζ _iBe the average power of i clutter cell signal, try to achieve by following formula:

${\mathrm{\&zeta;}}_i=\frac{W_i}{{\left|\right|\stackrel{\&RightArrow;}{T^u{C}_i^u}\left|\right|}^2{\left|\right|\stackrel{\&RightArrow;}{R^u{C}_i^u}\left|\right|}^2}$

Step (6) produces in computing machine obeys U _cThe clutter baseband analog data w of statistical property:

The production method of clutter simulation data is to use U _c ^1/2Multiply each other with white Gaussian noise, promptly $w=U_c^{1/2}\&CenterDot;\mathrm{\&mu;},$ Wherein μ is the white Gaussian noise of GK * 1 dimension;

Step (7) sends to follow-up spaceborne radar signal processing system with this simulated data by data transmitting equipment.

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