CN103363959B - Stereo surveying and mapping imaging system and method based on separation load satellite formation - Google Patents

Abstract

The invention relates to a stereo surveying and mapping imaging system based on a separation load satellite formation. The imaging system comprises the separation load satellite formation, a satellite antenna and a ground observation station, wherein the separation load satellite formation comprises at least two satellites; each satellite comprises a satellite borne point detector; one satellite comprises an area array detector; the satellite antenna is installed on the ground observation station; sunlight comes to the surface of the globe and is reflected through the ground, the satellite borne point detectors on the various satellites receive the total light intensity in various detection directions, and a detection result is taken as a detection signal of an object arm; the area array detector detects the optical field distribution of sunlight, and a detection result is taken as a detection signal of a reference arm; the detection signals of the object arm and the reference arm are wirelessly transmitted to the ground and received by the satellite antenna; the ground observation station reconstructs a two-dimensional image observed by the various formation satellites by virtue of a compression sensing algorithm according to the received data, and then a stereo surveying and mapping image is constructed by comparing shaded area information of the images.

Description

A kind of stereo mapping imaging system and method based on being separated load satellites formation

Technical field

The present invention relates to sunshine ghost imaging technique, be separated load satellites formation technology and compressive sensing theory field, particularly a kind of stereo mapping imaging system and method based on being separated load satellites formation.

Background technology

Relevance imaging, or be called terrible imaging (Ghost Imaging, GI), be one of the forward position and focus in quantum optics field in the last few years.Relevance imaging can generate the picture of object in the light path not comprising object, receives at present pay close attention to widely as the novel imaging technique of one.First the concept of ghost imaging is verified with producing space entangled photon pairs by parametric down conversion.The principle of common terrible imaging is: be placed with object in thing arm light path, but do not have the bucket of spatial resolving power (single pixel) detector to detect with one, object is not had in reference arm light path, but there is with one at light path place identical with object the field information of the detector Detect change of spatial resolving power, by the association of two-arm detectable signal, just image can be obtained.Current research shows, the light source of terrible imaging can be not only entangled light source, can also be thermo-optical or counterfeit thermo-optical, thus create Quantum Explanation and classic explanation, provides possibility for opening up new optical information technology.

Existing relevance imaging is also mainly limited to small-scale two-dimensional imaging, the object adopted also is simple two-dimensional bodies, even if be used as three-dimensional imaging, also the general profile of simple three-dimensional body can only be gone out by chromatography, and arrived the outer space, want association imaging, active probe and modulation light intensity are no longer real, the mode of traditional beam splitter light splitting or spatial light modulator modulation speckle must be discarded, this proposes new challenge to imaging.

It is one of the most basic theme of computer vision research that 3D rebuilds, the mode of rebuilding according to obtaining data based on the 3D of image can be divided into active light, passive light two kinds of modes, active light 3D rebuilds general structured light or the monumented point of adopting and marks target surface, and by asking for the three-dimensional geometry positional information of these marks, finally reconstruct three-D profile or the three-dimensional motion of target; It is the mode utilizing the relevant information of multiple image to carry out Object reconstruction that passive smooth 3D rebuilds, and usually utilizes multi-view image information at present.More common several method has: shading value method (Shape From Shading, SFS), photometric stereo (photometric stereo), texturing method, consistency profiles, focusing method, the method for movement, stereo vision method, trinocular vision method etc.At present, the three-dimensional reconstruction research of view-based access control model is still for the exploratory stage, and the practical application of various method distance also exists certain gap, needs further further investigation badly.

Being separated load formation flight is a kind of brand-new Spacecraft guidance and control theory, from concept to engineering construction, also have a lot of technological difficulties.The impact of the perturbative force such as earth aspherical gravitation, atmospherical drag, lunisolar attraction, optical pressure that low orbit satellite is subject to, the perturbation factors had the greatest impact is called that J2 perturbs.Under J2 Perturbation Effect, form into columns along mark to there is long term drift, Z item motion amplitude and phase place all change, and three-axis moving is no longer synchronous, finally causes flight pattern to keep.J2 perturbation and atmospherical drag are also the perturbation factors that the low rail of impact is separated load flight pattern stability.In order to suppress J2 to perturb the formation long term drift caused, urgently study the modification method of the lower formation of J2 perturbation, for effective control separation load form into columns along mark to long term drift.There is the defect of intrinsic and cannot maintain in traditional pearl necklace formation under J2 perturbation, and thus studying new satellites formation configuration has extremely important status to the development being separated load field.

Summary of the invention

The object of the invention is to overcome prior art Satellite stereo mapping and there is sampling redundancy, waste detector resource, low rail is separated the impact that load flight pattern stability is subject to again J2 perturbation and atmospherical drag, direct problem and indirect problem is there is in configuration design, how the imaging of sunshine ghost keeps the problems such as its validity in space, thus provides a kind of stereo mapping imaging system and method based on being separated load satellites formation.

To achieve these goals, the invention provides a kind of stereo mapping imaging system based on being separated load satellites formation, comprising: be separated load satellites formation, satellite antenna 2, surface-based observing station 3; Described separation load satellites formation comprises at least two satellites, and each satellite all includes a spaceborne point probe, a satellite includes a planar array detector wherein; Described satellite antenna 2 is arranged on described surface-based observing station 3;

Sunshine incides earth surface, through earth reflection, the total light intensity on each detection direction is received by the spaceborne point probe on each satellite in described separation load satellites formation, using the detectable signal of result of detection as thing arm, the optical field distribution of the planar array detector detection sunshine comprised in described separation load satellites formation, using result of detection as the detectable signal with reference to arm; By the detectable signal of described thing arm and reference arm by being wirelessly transmitted to ground, received by described satellite antenna 2, described surface-based observing station 3 is according to received data, utilize compressed sensing algorithm to rebuild the two dimensional image that each Satellite Formation Flying observes, then compare the dash area information of these images to build stereo mapping image.

In technique scheme, also comprise optical filter, described optical filter is before described spaceborne point probe.

In technique scheme, described optical filter is red, green, blue three-colour filter, or has the optical filter of different wave length.

In technique scheme, also comprise camera lens or optical lens, described camera lens or optical lens are before described spaceborne point probe.

In technique scheme, the spaceborne point probe in described separation load satellites formation on each satellite keeps synchronous with unique planar array detector.

In technique scheme, the spaceborne point probe in described separation load satellites formation on each satellite adopt in opto-electronic conversion point probe or bucket detector or single pixel detector or avalanche diode or photomultiplier any one realize.

In technique scheme, described separation load satellites formation adopts space circle pearl necklace to form into columns or wheel is formed into columns or hybrid wheel is formed into columns; Wherein, described space circle pearl necklace is formed into columns at the ellipse being projected as 1:2 of virtual primary orbital coordinate system xy plane, being projected as of yz plane ellipse, be projected as straight line in xz plane;

If space circle pearl necklace Satellite Formation Flying number is N, adjacent interstellar distance is L, and space circle radius is that R, N decimetre star is uniformly distributed in space circle, then the subtended angle of adjacent star is:

$\mathrm{\θ}=\frac{2\mathrm{\π}}{N}$

If known N and R, then have:

$L=R\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})};$

If known N and L, then have:

$R=\frac{L}{\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})}};$

If known L and R, then have:

$N=\frac{2\mathrm{\π}}{{\cos }^{-1}(1-\frac{1}{2}{\left(\frac{L}{R}\right)}^2)};$

Described wheel is formed into columns: cancel normal component, and making z direction amplitude be zero, xy plane configuration is that 1:2 is oval, and all satellites of formation are all in an orbit plane;

Suppose that R is major axis radius, at phasing degree be 0 ° and 180 ° time, intersatellite spacing is maximum,

$L_{\max }=R\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})}$

$R=\frac{L_{\max }}{\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})}}$

At phasing degree be 90 ° and 270 ° time, intersatellite spacing is minimum,

$L_{\min }=\frac{R}{2}\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})}$

$R=\frac{2L_{\min }}{\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})}};$

Described hybrid wheel formation is divided into two-layer, odd-level and even level, and odd number satellite still keeps wheel to form into columns, and even number satellite increases longitude of ascending node difference on the basis that wheel is formed into columns; The distance that hybrid wheel is formed into columns is uneven, and adjacent interstellar distance is maximum in X-axis, minimum in Y-axis; Hybrid wheel is formed into columns and be there is normal direction component motion.

In technique scheme, the compressed sensing algorithm that described surface-based observing station 3 adopts adopts any one algorithm realization following: greedy reconstruction algorithm, Matching pursuitalgorithm MP, orthogonal Matching pursuitalgorithm OMP, base track algorithm BP, LASSO, LARS, GPSR, Bayesian Estimation algorithm, magic, IST, TV, StOMP, CoSaMP, LBI, SP, l1_ls, smp algorithm, SpaRSA algorithm, TwIST algorithm, l ₀reconstruction algorithm, l ₁reconstruction algorithm, l ₂reconstruction algorithm; Sparse base adopts any one realization in dct basis, wavelet basis, Fourier transform base, gradient base, gabor transform-based.

Present invention also offers a kind of based on the described stereo mapping formation method realized based on the stereo mapping imaging system being separated load satellites formation, comprising:

Step 1), setting are separated the step of load satellites formation;

In this step, according to satellite orbit kinetic model, EVOLUTION ANALYSIS is carried out to flight pattern, according to analysis result, separation load Satellite formation flying is set as that space circle pearl necklace is formed into columns or wheel is formed into columns or hybrid wheel is formed into columns, make under J2 Perturbation Effect, be separated the stability that load satellites formation can keep rank;

Step 2), compression sampling step;

On N number of reflected light direction, each spaceborne point probe collects the party upwards from total light intensity m time of the solar reflection optical on earth's surface, and N number of spaceborne point probe detects the measurement result of m time as measured value y _{m × N}, meanwhile, face battle array detects the optical field distribution of m sunshine, is denoted as calculation matrix A _{m × n};

Step 3), star ground data communication step;

Satellite Formation Flying is by step 2) fructufy after compression sampling time be wirelessly transmitted to ground, by satellite antenna 2 receiving communication signal;

Step 4), sparse reconstruction procedures, generate the two dimensional image in each spaceborne point probe direction corresponding;

Surface-based observing station 3 utilizes natural image compressible or can the priori of rarefaction representation, chooses suitable sparse base Ψ, makes subject image x _{n × N}coefficient x ' is obtained after Ψ conversion _{n × N}the most sparse; At known measurements y _{m × N}, calculation matrix A _{m × n}with under the condition of sparse base Ψ, founding mathematical models y _{m × N}=A _{m × n}Ψ _{n × n}x' _{n × N}+ e _{n × N}, wherein N is detector number, and n is the signal total length of single width two dimensional image; Convex optimization is carried out, after obtaining x ', then by x by compressed sensing algorithm _{n × N}=Ψ _{n × n}x' _{n × N}be finally inversed by x _{n × N}, each row wherein are all lined up matrix image by column weight, and its image pixel dimensions is the optical field distribution a of the single frames sunshine photographed _isize, namely in x i-th row corresponding I _i;

Step 5), stereo mapping image-forming step;

If the luminance equation of the pixel image on i-th detector is the i.e. two dimensional image in each spaceborne point probe direction that obtains of step 4), wherein i=1,2,3 ..., N, I _sfor the intensity of light source, α is surface reflectivity, for pointing to the unit direction vector of i-th detector from object, for body surface unit normal vector, p, q are image pixel row-coordinate and row coordinate, open two dimensional image for N, are rewritten as by above-mentioned formula wherein D is the matrix comprising all units direction vector, and I is the matrix comprising respective image intensity signal, and for any pixel (p, q), unit normal vector is surface reflectivity α=D ^-1, the gradient between neighbor can be determined according to the normal vector of each pixel calculating gained, thus by integrating the 3D geometric configuration obtaining body surface; Specifically comprise:

First extract minutiae, and start to calculate using these unique points as center radiation to surrounding respectively, certain a bit on surface elevation by utilizing the height of the point of arest neighbors and surface gradedly estimating; Then be optimized, often walk iterative computation pixel, the averaged power spectrum of the height of this pixel and its all nearest neighbor point is matched, the pixel of non-object edge part, it estimates that the Laplace transform of height is equivalent to the Laplace transform of measuring gradient, the pixel of object edge part, its gradient vertical is in body surface; Final iteration terminates to obtain earth's surface stereo mapping image.

In technique scheme, in described step 1), the foundation of described satellite orbit kinetic model comprises the following steps:

Step 1-1), first determine describe be separated load form into columns motion orbital coordinate system:

Coordinate origin is at aircraft barycenter, and Z axis is perpendicular to satellite orbit plane; XY axle is in satellite orbit plane, and X-axis points to aircraft barycenter direction from the earth's core; Y-axis meets right-hand screw rule;

Step 1-2), then derive from dynamic (dynamical) angle and be separated load formation relative motion mechanics equation and approximate analytic solution thereof:

Step 1-3), then from kinematic angle, derive and be separated load formation Relative Kinematics:

R _ref＝a _ref(1-e _refcosE _ref)

R _sat＝a _sat(1-e _satcosE _sat)

R in formula _ref, R _satbe respectively the geocentric distance of principal and subordinate's spacecraft, e _ref, e _satbe respectively the excentricity of principal and subordinate's spacecraft, E _ref, E _satbe respectively the eccentric anomaly of principal and subordinate's spacecraft;

Step 1-4), except earth center gravitation, also must consider the impact of various perturbation factors:

Concerning below 1000km height low orbit satellite, affecting larger has perturbation of earths gravitational field power, atmospherical drag perturbation, in addition, and the 3rd body Gravitational perturbation such as the sun, the moon, the motion of solar radiation pressure perturbation to low orbit satellite also has a certain impact, and need carry out Modifying model for these perturbations.

The invention has the advantages that

The stereo mapping imaging on earth's surface is obtained in order to overcome these limitation, the present invention proposes sunshine ghost imaging skill first, separation load satellites formation technology and compressive sensing theory combine, from the angle research configuration design of direct problem and indirect problem, set up accurate satellite orbit kinetic model, have studied the modification method of the lower formation of J2 perturbation, effectively inhibit be separated load form into columns along mark to long term drift, and with pearl necklace formation for background, devise three kinds of pearl necklace Formation Configurations, wherein hybrid wheel is formed into columns and stability can be kept to provide normal direction baseline again, every Satellite Formation Flying carries point probe, wherein also have one and carried planar array detector for taking sunshine light field, and for each spaceborne point probe, lighting angle is different, each detection direction can utilize compression sunshine ghost Scattering data go out a width two dimensional image, relatively to build 3D surface graded for the dash area information of these images, finally reconstruct 3D body form.The present invention also provides new effective solution route by for remotely sensed image, 3D imaging, multispectral imaging.

Accompanying drawing explanation

Fig. 1 is the structural representation of a kind of stereo mapping imaging system based on separation load satellites formation of the present invention;

Fig. 2 is that satellite covers geometrical property schematic diagram;

Fig. 3 is union observation schematic diagram;

Fig. 4 is the observation schematic diagram that occurs simultaneously;

Fig. 5 is separated load to cover schematic diagram;

Fig. 6 is separated load overlay area;

Fig. 7 is that space circle formation pearl necklace is formed into columns;

Fig. 8 is space circle formation pearl necklace formation analogous diagram;

Fig. 9 is that wheel formation pearl necklace is formed into columns;

Figure 10 is wheel formation pearl necklace formation analogous diagram (XY plane);

Figure 11 is hybrid wheel formation pearl necklace formation analogous diagram (XY plane);

Figure 12 is hybrid wheel formation pearl necklace formation analogous diagram (YZ plane).

Drawing explanation

1-1 first satellite 1-2 second satellite 1-3 the 3rd satellite

1-4 the 4th satellite 1-i i-th satellite 1-N N satellite

2 satellite antenna 3 surface-based observing stations

Embodiment

Now the invention will be further described by reference to the accompanying drawings.

Before System and method for of the present invention is elaborated, first concept involved in the present invention is described.

1, load satellites formation is separated

Due to Satellite Formation Flying dense distribution, it is still equivalent to a satellite on allomeric function, or " virtual satellite " that composition one is large, and coverage property is substantially identical with the coverage property of single satellite over the ground for it.Therefore first do single star covering analyzing at this, on the basis that single star covers, research is separated the covering analyzing that load is formed into columns.

For single satellite, satellite area coverage just refers to that the radio signal that satellite sends can be propagated and not need through reflection, relays and the scope that is received in air line distance, if can, directly from the place of Received signal strength satellite, be exactly that is within the quorum sensing inhibitor area of this satellite on ground.

Fig. 2 is that satellite covers geometrical property schematic diagram, wherein, and φ _ethe elevation angle of ground observation point to satellite; α is the geocentric angle between satellite and observation point; β is the half angle of view (or half angle of depression) of satellite, and its span is [0 °, 90 °]; D is the distance of satellite to observation point; X is the radius of footprint; r _ebe earth mean radius, conventional value is 6378km; H is satellite orbital altitude.

According to plane geometry formula, the correlation computations formula of above-mentioned parameter is as follows,

Geocentric angle between satellite and observation point:

$\mathrm{\α}=\arccos \[\frac{r_E}{h+r_E}\·\cos {\mathrm{\φ}}_e\]-{\mathrm{\φ}}_e=\arcsin \[\frac{h+r_E}{r_E}\·\sin \mathrm{\β}\]-\mathrm{\β}---\left(1.1\right)$

The half angle of view of satellite:

$\mathrm{\β}=\arcsin \[\frac{r_E}{h+r_E}\·\cos {\mathrm{\φ}}_e\]=\arctan \[\frac{r_E\·\sin \mathrm{\α}}{(h+r_E)-r_E\·\cos \mathrm{\α}}\]---\left(1.2\right)$

The elevation angle of observation point:

${\mathrm{\φ}}_e=\arctan \[\frac{(h+r_E)\·\cos \mathrm{\α}-r_E}{(h+r_E)\·\sin \mathrm{\α}}\]=\arccos \[\frac{h+r_E}{r_E}\·\sin \mathrm{\β}\]---\left(1.3\right)$

Observation point and intersatellite distance:

$\begin{array}{c}d=\sqrt{{r_E}^2+{(h+r_E)}^2-2\·r_E\·(h+r_E)\·\cos \mathrm{\α}}\\ =\sqrt{{r_E}^2{\sin }^2{\mathrm{\φ}}_e+2\·h\·r_E+h^2}-r_E\·\sin {\mathrm{\φ}}_e\end{array}--\left(1.4\right)$

Areal coverage radius:

X＝r _E·sinα （1.5）

Areal coverage area:

A＝2π·r _E ²·(1-cosα) （1.6）

In theory, φ _espan be [0 °, 90 °], in fact, when earth station antenna (i.e. observation point) to the elevation angle of satellite close to 0 ° time because the elevation angle is too low, by the impact of landform, atural object and surface noise, can not effectively communicate.Therefore, for satellite communication system, there is a minimum angle of elevation φ _egiven index, can not communicate lower than this elevation angle region.Such as, INTELSAT specifies that the work elevation angle of earth station antenna must not be less than 5 °.

Minimum angle of elevation φ _eit is a given index of system.According to minimum angle of elevation φ _ethe coverage of satellite can be calculated with satellite orbital altitude h.After obtaining the coverage of satellite, if provide the longitude and latitude of certain point on the earth, so just can forecast the moment of this some turnover satellite borne equipment coverage, namely along the direction of satellite motion, cover edge and pass through the moment of this point first for entering the moment, the moment that covering continuous edge passes through this point is again the departure time.

The coverage property of Satellite Formation Flying and the coverage property of single satellite do not have essential distinction, specifically have two kinds of situations:

1) if in order to detect space difference at synchronization, expand scope of investigation, extending the aspects such as call duration time as being applied in, so forming into columns can extended coverage range or prolongation observation time.At this moment, the coverage property of Satellite Formation Flying can get union to the coverage property of every satellite, dash area as shown in Figure 3.

2) observe if will carry out multi-angle to same target, as stereo mapping, then the coverage property of Satellite Formation Flying is that the coverage property of every satellite gets common factor, as the dash area in Fig. 4 simultaneously.At present, be loaded with multiple measuring equipment with a satellite and also can realize stereo mapping, but limit size and the precision of measuring equipment, and Satellite Formation Flying can improve this situation.

Form into columns for the pearl necklace of 800km height below, research is separated load to the covering on ground.Because each star in pearl necklace formation is apart from closely, in the pearl necklace shown in Fig. 5 is formed into columns, 3 equally distributed separation load are selected to carry out coverage emulation, as the 1st, the 11st and the 21st star.

In Figure 5, trigonum, the right represents the covering of the 1st star, and trigonum, the left side represents the covering of the 11st star, and middle triangle district represents the covering of the 21st star.

Fig. 6 provides the result of emulation of coverage capability over the ground of the 1st, 11,21 star.As can be seen from the figure, the substar of three satellites overlaps substantially, and overlay area also overlaps substantially, and be applicable to three satellites and observe the same target in ground simultaneously, this is consistent with analysis before.

Due to pearl necklace form into columns in each satellite distance closely, being separated covering result and virtual primary that load forms into columns, to cover result consistent, when carrying out task analysis, can be similar to by the covering result of the covering result of virtual primary to separation load.

Orbital tracking refers to the general designation of the basic parameter of spacecraft orbit, as major semi-axis, excentricity, orbit inclination, right ascension of ascending node, argument of perigee, true anomaly, eccentric anomaly, mean anomaly and orbit angular velocity etc., the orbital motion describing single spacecraft by orbital tracking has directly perceived, distinct and easy feature, and be parameter with orbital tracking, the relative motion of setting up the kinematical equation expression spacecraft of relative motion according to Keplerian orbit theory is kinematic method.

The direct problem of configuration design is the relative light intensity providing each satellite in formation according to the characteristic parameter of formation.Direct problem is used for the configuration design stage.According to the application demand of task, combing goes out the characteristic parameter of formation, utilizes configuration design direct problem to provide the orbit parameter of each satellite in formation.

The indirect problem of configuration design is then identify the characteristic parameter of formation according to the relative light intensity of each satellite in forming into columns, and can be used for analyzing the Evolution of formation.If we obtain certain relative light intensity of forming into columns by technological means, just can identify the characteristic parameter of formation, application scenarios and the technical indicator of formation can be finally inversed by further, the long-term evolution of prediction formation.

When configuration design, formation characteristic parameter can be summed up according to mission requirements, by configuration design direct problem, obtain the orbital tracking of each satellite in forming into columns.

In desirable two-body problem model, semi-major axis of orbit, excentricity, orbit inclination, longitude of ascending node, argument of perigee five parameters are constants, and mean anomaly is even variation.Under the impact of perturbative force, orbital tracking is no longer constant and even variation amount, but there is secular term, long period term and short-period term.

Concerning low orbit satellite, the perturbation factors had the greatest impact is J2 perturbation.Due to the existence of compression of the earth, the earth off-gauge desirable spheroid, but major axis under the line, the approximate spheroid of minor axis at the two poles of the earth.J2 perturbation can image be described as the very large waistband of earth bundle one.Under J2 Perturbation Effect, form into columns along mark to there is long term drift, Z item motion amplitude and phase place all change, and three-axis moving is no longer synchronous, finally causes flight pattern to keep.Therefore must revise the long term drift of J2 perturbation.Generally, in order to ensure around the movement, around ensureing relative eccentric rate variance δ e between star/reference star.

In order to the drift that the formation revising Satellite Formation Flying produces by Perturbation Effect, formation is tended towards stability, needs to set up accurate satellite orbit kinetic model.The process of establishing of this model comprises the following steps:

Step 1), first determine describe be separated load form into columns motion orbital coordinate system:

Coordinate origin is at aircraft barycenter, and Z axis is perpendicular to satellite orbit plane; XY axle is in satellite orbit plane, and X-axis points to aircraft barycenter direction from the earth's core; Y-axis meets right-hand screw rule.

Step 2), then to have derived separation load formation relative motion mechanics equation and approximate analytic solution thereof from dynamic (dynamical) angle:

According to Newton interpolation algorithm, have at inertial coordinates system:

${\stackrel{\stackrel{\·\·}{\→}}{r}}_{\mathrm{ref}}=-\frac{\mathrm{\μ}}{{r_{\mathrm{ref}}}^3}{\stackrel{\→}{r}}_{\mathrm{ref}}+{\stackrel{\→}{f}}_{\mathrm{ref}}$

${\stackrel{\stackrel{\·\·}{\→}}{r}}_{\mathrm{sat}}=-\frac{\mathrm{\μ}}{{r_{\mathrm{sat}}}^3}{\stackrel{\→}{r}}_{\mathrm{ast}}+{\stackrel{\→}{f}}_{\mathrm{sat}}---\left(1.7\right)$

Wherein, μ is geocentric gravitational constant, for satellite is subject to making a concerted effort of all perturbative forces outside earth center gravitation, comprise earth aspherical gravitation, atmospherical drag, solar light pressure, the 3rd body Gravitational perturbation etc., be respectively actual the earth's core displacement vector of principal and subordinate's spacecraft, be respectively all perturbative force vectors except terrestrial attraction of principal and subordinate's spacecraft, what be respectively that principal and subordinate's spacecraft is subject to comprises gravitation, the making a concerted effort of perturbative force.

To (1.7) formula integration, the position under principal and subordinate's star any time inertial system and speed can be obtained; Utilize coordinate conversion matrix, principal and subordinate's star any time position under primary orbital coordinate system and speed can be obtained; Finally, utilize the relation of absolute motion and relative motion, the relative position under any time primary orbital coordinate system system and speed can be obtained.

Numerical integrating can not provide the analytical expression of relative motion, can not be used for flight pattern design.But it is not through any simplification, so it may be used for EVOLUTION ANALYSIS and the formation control of formation, can obtain very high control accuracy, precision depends on the precision of Computer Precision and algorithm.

Approximate relative dynamics equation is based upon in primary orbital coordinate system, is usually also referred to as C-W equation, when primary track is oval, is also referred to as Lawden equation.

When setting up C-W equation, two hypothesis first to be carried out: 1, suppose that each satellite moves in earth center gravitational field; 2, primary is circuit orbit or near-circular orbit (excentricity is close to zero), and two intersatellite distance are much smaller than orbit radius.

If x ₀, y ₀, z ₀the initial displacement component in x direction, y direction, z direction respectively, the initial velocity components in x direction, y direction, z direction respectively, be the initial acceleration component in x direction, y direction, z direction respectively, the point in letter top represents first order derivative, and two points in letter top represent second derivative.

According to supposing that primary is circular orbit, then the mean angular velocity of primary, angular acceleration is respectively:

$n=\sqrt{\mathrm{\μ}/{r_c}^3},\stackrel{\·}{n}=0---\left(1.8\right)$

The C-W equation of satellite formation flying is:

$\left\{\begin{array}{c}\stackrel{\·\·}{x}-2n\stackrel{\·}{y}-3n^{2}x=0\\ \stackrel{\·\·}{y}+2n\stackrel{\·}{x}=0\\ \stackrel{\·\·}{z}+n^{2}z=0\end{array}\right.---\left(1.9\right)$

Do not consider perturbation and control, to above formula integration, following analytic solution can be obtained:

$\left\{\begin{array}{c}x=2(2x_0+\frac{{\stackrel{\·}{y}}_0}{n})-(2\frac{{\stackrel{\·}{y}}_0}{n}+3x_0)\cos \left(\mathrm{nt}\right)+\frac{{\stackrel{\·}{x}}_0}{n}\sin \left(\mathrm{nt}\right)\\ y=(y_0-2\frac{{\stackrel{\·}{x}}_0}{n})+2(2\frac{{\stackrel{\·}{y}}_0}{n}+3x_0)\sin \left(\mathrm{nt}\right)+2\left(\frac{{\stackrel{\·}{x}}_0}{n}\right)\cos \left(\mathrm{nt}\right)-3({\stackrel{\·}{y}}_0+2n{x}_0)t\\ z=\left(\frac{{\stackrel{\·}{z}}_0}{n}\right)\sin \left(\mathrm{nt}\right)+z_0\cos \left(\mathrm{nt}\right)\end{array}\right.---\left(1.10\right)$

Can find out, in x direction and z direction, the relative motion of principal and subordinate's star periodically changes in time, and in the impact of the existing periodic term in y direction, also has the impact of secular term.In order to ensure the long-time stability of Satellite formation flying, the impact of secular term must be eliminated, is namely required to meet:

${\stackrel{\·}{y}}_0=-2n{x}_0---\left(1.11\right)$

Now, can be reduced to:

$\left\{\begin{array}{c}x=x_0\cos \left(\mathrm{nt}\right)+\frac{{\stackrel{\·}{x}}_0}{n}\sin \left(\mathrm{nt}\right)\\ y=(y_0-2\frac{{\stackrel{\·}{x}}_0}{n})-2x_0\sin \left(\mathrm{nt}\right)+2\left(\frac{{\stackrel{\·}{x}}_0}{n}\right)\cos \left(\mathrm{nt}\right)\\ z=\left(\frac{{\stackrel{\·}{z}}_0}{n}\right)\sin \left(\mathrm{nt}\right)+z_0\cos \left(\mathrm{nt}\right)\end{array}\right.---\left(1.12\right)$

This formula can be reduced to further

x(t)＝-0.5r _xycos(nt+θ _xy)

y(t)＝r _xysin(nt+θ _xy)+y _off

z(t)＝-r _zcos(nt+θ _z) （1.13）

$\begin{array}{cc}{r}_{\mathrm{xy}}=2\sqrt{{x_0}^2+{({\stackrel{\·}{x}}_0/n)}^2}& r_z=\sqrt{{z_0}^2+{({\stackrel{\·}{z}}_0/n)}^2}\end{array}$

$\begin{array}{cc}\cos {\mathrm{\θ}}_{\mathrm{xy}}=\frac{-x_0}{\sqrt{{x_0}^2+{({\stackrel{\·}{x}}_0/n)}^2}}& \sin {\mathrm{\θ}}_{\mathrm{xy}}=\frac{{\stackrel{\·}{x}}_0/n}{\sqrt{{x_0}^2+{({\stackrel{\·}{x}}_0/n)}^2}}\end{array}$

$\begin{array}{cc}\cos {\mathrm{\θ}}_z=\frac{-z_0}{\sqrt{{z_0}^2+{({\stackrel{\·}{z}}_0/n)}^2}}& \sin {\mathrm{\θ}}_z=\frac{{\stackrel{\·}{z}}_0/n}{\sqrt{{z_0}^2+{({\stackrel{\·}{z}}_0/n)}^2}}\end{array}$

$y_{\mathrm{off}}=y_0-2\frac{{\stackrel{\·}{x}}_0}{n}---\left(1.14\right)$

Step 3), then from kinematic angle, separation load of having derived formation Relative Kinematics:

R _ref＝a _ref(1-e _refcosE _ref)

R _sat＝a _sat(1-e _satcosE _sat) (1.15)

R in formula _ref, R _satbe respectively the geocentric distance of principal and subordinate's spacecraft, e _ref, e _satbe respectively the excentricity of principal and subordinate's spacecraft, E _ref, E _satbe respectively the eccentric anomaly of principal and subordinate's spacecraft.

Step 4), except earth center gravitation, also must consider the impact of various perturbation factors:

Concerning the low orbit satellite of below 1000km height, affecting larger has perturbation of earths gravitational field power, atmospherical drag perturbation.In addition, the 3rd body Gravitational perturbation such as the sun, the moon, the motion of solar radiation pressure perturbation to low orbit satellite also has a certain impact.

2, satellites formation configuration

This sentences and is separated the formation of load pearl necklace is application background, gives the method for designing of pearl necklace formation.The method, on the basis that classical wheel is formed into columns, provides a kind of stable hybrid wheel and forms into columns, and can overcome the shortcoming that wheel formation does not have normal direction baseline.

Pearl necklace is formed into columns and is referred to the formation flight on closed (ellipse) circular orbit centered by a virtual satellite of some separation load.

Defining virtual primary orbital coordinate system, true origin is on virtual primary, and x-axis is along the earth-virtual primary barycenter direction, vertical with x-axis in y-axis virtual primary orbit plane, point to working direction, z-axis points to virtual primary tracks face normal direction, forms right hand orthogonal coordinate system with x, y-axis.

2.1, space circle pearl necklace is formed into columns

Space circle is formed into columns at the ellipse being projected as 1:2 of virtual primary orbital coordinate system xy plane, being projected as of yz plane ellipse, be projected as straight line in xz plane.

Study space circle pearl necklace Satellite Formation Flying number N, relation between adjacent interstellar distance L and space circle radius R below.

As shown in Figure 7, suppose that N decimetre star is uniformly distributed in space circle, then the subtended angle of adjacent star is:

$\mathrm{\θ}=\frac{2\mathrm{\π}}{N}---\left(2.1\right)$

If known N and R, has according to the cosine law

$\begin{array}{c}L=\sqrt{R^2+R^2-2R^2\cos \mathrm{\θ}}\\ =R\sqrt{2-2\cos \mathrm{\θ}}\\ =R\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})}\end{array}---\left(2.2\right)$

If known N and L, then have

$R=\frac{L}{\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})}}---\left(2.3\right)$

If known L and R, then have

$N=\frac{2\mathrm{\π}}{{\cos }^{-1}(1-\frac{1}{2}{\left(\frac{L}{R}\right)}^2)}---\left(2.4\right)$

Such as, if space circle radius is 1 kilometer, space circle distributes 30 decimetre stars, then adjacent interstellar distance is 0.209km.

Fig. 8 gives the analogous diagram that space circle pearl necklace is formed into columns.Can find out, 30 stars are evenly distributed in a space circle, form pearl necklace and form into columns.

2.2, wheel is formed into columns

Under J2 perturbation, the configuration of space circle track is unstable, cannot keep for a long time.If cancellation normal component, even z direction amplitude is zero, then xy plane configuration is that 1:2 is oval.All satellites of forming into columns, all in an orbit plane, form in orbit plane and form into columns.This kind of formation is formed into columns also referred to as wheel (cartwheel).The advantage of forming into columns in plane to keep rank stable under J2 perturbation, and shortcoming lacks normal direction baseline.

Form into columns for wheel, as shown in Figure 9, if formed into columns according to equiphase angle, the distance between satellite changes along with phase place.Maximum spacing is about 2 times of minimum spacing.

Suppose that R is major axis radius.At phasing degree be 0 ° and 180 ° time, intersatellite spacing is maximum.

$L_{\max }=R\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})}---\left(2.5\right)$

$R=\frac{L_{\max }}{\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})}}---\left(2.6\right)$

At phasing degree be 90 ° and 270 ° time, intersatellite spacing is minimum.

$L_{\min }=\frac{R}{2}\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})}---\left(2.7\right)$

$R=\frac{2L_{\min }}{\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})}}---\left(2.8\right)$

Such as, if major axis radius is 1km, dispose 30 decimetre stars, then the adjacent spacing of satellite is 0.209km to the maximum, and minimum is 0.104km.

Figure 10 provides wheel pearl necklace formation XY plane analogous diagram.As can be seen from the figure, the distance that wheel is formed into columns is uneven.Adjacent interstellar distance is maximum in X-axis, minimum in Y-axis.Wheel forms into columns all satellites all in orbit plane in addition, and namely Z-direction component is zero.

2.3, hybrid wheel is formed into columns

Can maintain a long-term stability under J2 perturbation although wheel is formed into columns, Satellite Formation Flying, all in the orbit plane of virtual primary, lacks normal direction baseline, limits its application.

From formation indirect problem, formation normal component mainly from orbit inclination difference and longitude of ascending node poor.The relative size of orbit inclination difference and longitude of ascending node difference and argument of perigee determine the phase place that normal direction is moved.

$r_z=a{e}_B=a\sqrt{{\left(\mathrm{\δ\Ω}\sin \left(i\right)\right)}^2+{\left(\mathrm{\δi}\right)}^2}---\left(2.9\right)$

Wherein, r _zrepresent Z-direction amplitude, represent Z-direction phase place, a is major semi-axis, e _bfor excentricity, Ω is right ascension of ascending node, and i is orbit inclination, and ω is argument of perigee.

Orbit inclination missionary society causes Satellite Formation Flying generation long term drift, and this is that space circle is formed into columns the reason that cannot keep for a long time.In fact, change separately longitude of ascending node and can reach the effect changing normal direction amplitude too, and relative motion can not be caused to disperse for a long time.But now, the phase place of normal direction motion is equal to argument of perigee, cannot design separately again.

In the formation of 30 decimetre stars, odd number satellite still keeps wheel to form into columns, and even number satellite increases longitude of ascending node difference on the basis that wheel is formed into columns.Under the prerequisite that so just in orbit plane, baseline is constant between maintenance adjacent star, increase normal direction baseline, the monolithic stability that can also keep rank under J2 perturbation.

Hybrid wheel Satellite Formation Flying number N, relation between adjacent interstellar distance L and space circle radius R and wheel are formed into columns similar.

Figure 11, Figure 12 provide hybrid wheel pearl necklace formation XY plane and YZ plane analogous diagram respectively, and as can be seen from the figure, hybrid wheel formation is divided into two-layer, odd-level and even level.The distance that hybrid wheel is formed into columns also is uneven.Adjacent interstellar distance is maximum in X-axis, minimum in Y-axis.Poor owing to having introduced relative longitude of ascending node in addition, hybrid wheel form into columns there is normal direction component motion, not only can realize between adjacent star mark to radial baseline, also can realize normal direction baseline, this be also hybrid wheel form into columns advantage.

Formation EVOLUTION ANALYSIS under high-precision orbital kinetic model shows, in certain orbit altitude, atmospherical drag is the reason causing satellite to bump against, if need to overcome the impact that atmospherical drag perturbation is formed into columns on pearl necklace, needing by pearl necklace form into columns is deployed in the safety track of certain altitude, and orbit altitude and solar active index closely related.

3, the imaging of sunshine ghost is compressed

Be described for the principle of beam splitter both arms intensity correlation to relevance imaging of classics, laser is beaten on beam splitter after frosted glass, be evenly distributed to two angles, namely on thing arm and reference arm, the light beam of thing arm is imaged onto on object, then collects its total light intensity by a bucket (single pixel) detector; Another road reference arm light beam does not interact with object, the information of the Two dimensional Distribution of distribution of light intensity is directly recorded with the CCD of a resolution characteristic of having living space.Because the light field on CCD face is consistent with the light field of beating on object, the image that CCD records is multiplied by total light intensity signal of point probe, obtains the image of a secondary weighting with this.Then rotated to an angle by frosted glass, repeat aforesaid operations, frosted glass rotates repeatedly angle, just can obtain the image of several weightings, these weighted images is added together the sharp picture that just can obtain actual object.

Compressed sensing (Compressive Sensing, CS) can recover original signal with the mode of stochastic sampling, a small amount of data sampling number (limit far below Nyquist/Shannon's sampling theorem) perfection.Its basic operation is: first utilize priori, chooses suitable sparse base Ψ, and it is the most sparse for making subject image x obtain coefficient x ' after Ψ conversion; Under the condition of known measurements y, calculation matrix A and sparse base Ψ, set up mathematical model y=A Ψ x '+e, carry out convex optimization by compressed sensing algorithm, after obtaining x ', then by be finally inversed by x.

Utilize natural image can the priori of rarefaction representation under certain base, but the process of its weighted image is become the process solving y=A Ψ x '+e, A is calculation matrix, the optical field distribution that reference arm takes each frame is stretched as a line, as a line in A, Ψ is sparse base, x ' is sparse coefficient, e is noise, y is measured value, i.e. total light intensity from reflections off objects of point probe record, and ranking operation linear has like this changed nonlinear optimization algorithm, thought mainly based on convex optimization solves, and this is the terrible imaging of compression.

The imaging of described compression sunshine ghost, namely sunshine incides earth surface, through earth reflection, the total light intensity on each detection direction is received by the spaceborne point probe on Satellite Formation Flying, as the detection of thing arm, a satellite simultaneously in Satellite Formation Flying is also equipped with planar array detector, for detecting the optical field distribution of sunshine, as the detection with reference to arm, by two-arm detectable signal by being wirelessly transmitted to ground, received by satellite antenna, surface-based observing station is according to received data, compressed sensing algorithm is utilized to rebuild the two dimensional image that each Satellite Formation Flying observes.

4, three-dimensional reconstruction

Binocular vision normally has the two dimensional image of slight shift to judge the distance of object, shape and change in time by obtaining.The present invention is based on this principle, utilize and be separated load satellites formation, every satellite carries point probe, observes earth surface from different perspectives, gone out the two dimensional image in all directions by sunshine ghost imaging reconstruction, then reconstruct stereo mapping image according to the dash area of every width image.And each spaceborne point probe does not have spatial resolving power, be only collect the total light intensity arrived on it, thus they directly cannot obtain image.And only have detectable signal can go out three-dimensional body information by accurate reconstruction in conjunction with the priori of the geometric relationship of lighting angle.

The depth information of a scene is often lost in two dimensional image, but can reconstruct 3-dimensional image in conjunction with the shade geometric relationship in the image of several different angles shooting.Technically, shading value (Shape From Shading, SFS) method can recover more accurate three-dimensional model from single image, but in single image, retrievable information is less after all, actual reconstruction effect is general, and the photometric stereo improved by shading value method needs the multiple image being obtained object by the light source of multiple not conllinear usually, again by the luminance equation simultaneous of different images, solve the direction of body surface normal vector, finally realize the recovery of body form, use multiple light source that data redundancy can be utilized to solve the problem that cannot solve caused by the factor such as shade and mirror-reflection, robustness is better, rebuild effect also better, but multiple light source is more difficult enforcement in satellite surveying and mapping, sun single light source is only there is at the solar system, the light that fixed star in other galaxy is irradiated to earth surface is almost negligible, thus this obtaining three-dimensional model mode need further improvement.

The present invention is for solving the above problem, the basis of original photometric stereo vision is improved, adopt sun light lighting, multiple Satellite-borne Detector carries out the mode detected, system complexity reduces greatly, algorithm complex also reduces greatly, can obtain higher-quality stereo mapping, also a saving cost.If the luminance equation of the pixel image in i-th Satellite-borne Detector is wherein i=1,2,3 ..., N, I _sfor the intensity of light source, α is surface reflectivity, for pointing to the unit direction vector of i-th detector from object, for body surface unit normal vector, two dimensional image is opened for N, above-mentioned formula can be rewritten as wherein D is the matrix comprising all units direction vector, and I is the matrix comprising respective image intensity signal.For any pixel (p, q), unit normal vector is surface reflectivity α=D ^-1.The gradient between neighbor can be determined according to the normal vector of each pixel calculating gained, thus by integrating the 3D geometric configuration obtaining body surface.First extract minutiae, and start to calculate using these unique points as center radiation to surrounding respectively, certain a bit on surface elevation can utilize the height of the point of arest neighbors and surface gradedly to estimate, namely the height of all nearest neighbor points and surface graded average is calculated to obtain estimated value, then be optimized, often walk iterative computation pixel, the averaged power spectrum of the height of this pixel and its all nearest neighbor point is matched, the pixel of non-object edge part, it estimates that the Laplace transform of height is equivalent to the Laplace transform of measuring gradient; The pixel of object edge part, its gradient vertical is in body surface, and final iteration terminates to obtain earth's surface stereo mapping image.

On the basis of the above description, below a kind of stereo mapping imaging system and method based on being separated load satellites formation of the present invention is introduced.

Fig. 1 is the stereo mapping imaging system optical principle schematic diagram in one embodiment based on being separated load satellites formation of the present invention, and this system comprises: be separated load satellites formation, satellite antenna 2, surface-based observing station 3; Described separation load satellites formation has N number of satellite, use the first satellite 1-1, the second satellite 1-2, the 3rd satellite 1-3, the 4th satellite 1-4, the i-th satellite 1-i, N satellite 1-N(i=1 respectively, 2,3, ..., N, N >=2) represent, each satellite all includes a spaceborne point probe, a satellite includes a planar array detector wherein;

Sunshine incides earth surface, through earth reflection, the total light intensity on each detection direction is received by the spaceborne point probe on each satellite in described separation load satellites formation, using the detectable signal of result of detection as thing arm, the optical field distribution of the planar array detector detection sunshine comprised in described separation load satellites formation, using result of detection as the detectable signal with reference to arm; By the detectable signal of described thing arm and reference arm by being wirelessly transmitted to ground, received by the satellite antenna 2 on ground, surface-based observing station 3 is according to received data, utilize compressed sensing algorithm to rebuild the two dimensional image that each Satellite Formation Flying observes, then compare the dash area information of these images to build stereo mapping image.

Below the various piece in present system is further described.

Spaceborne point probe in described separation load satellites formation on each satellite adopt in opto-electronic conversion point probe or bucket detector or single pixel detector or avalanche diode or photomultiplier any one realize.

Spaceborne point probe in described separation load satellites formation on each satellite keeps synchronous with unique planar array detector.

Described separation load satellites formation adopts space circle pearl necklace to form into columns or wheel is formed into columns or hybrid wheel is formed into columns.Wherein, space circle pearl necklace is formed into columns in virtual primary orbital coordinate system (in this coordinate system, true origin is on virtual primary, x-axis is along the earth-virtual primary barycenter direction, vertical with x-axis in y-axis virtual primary orbit plane, point to working direction, z-axis points to virtual primary tracks face normal direction, right hand orthogonal coordinate system is formed with x, y-axis) ellipse being projected as 1:2 of xy plane, being projected as of yz plane ellipse, be projected as straight line in xz plane;

If space circle pearl necklace Satellite Formation Flying number is N, adjacent interstellar distance is L, and space circle radius is that R, N decimetre star is uniformly distributed in space circle, then the subtended angle of adjacent star

$\mathrm{\θ}=\frac{2\mathrm{\π}}{N}$

If known N and R, then have

$L=R\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})}$

If known N and L, then have

$R=\frac{L}{\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})}}$

If known L and R, then have

$N=\frac{2\mathrm{\π}}{{\cos }^{-1}(1-\frac{1}{2}{\left(\frac{L}{R}\right)}^2)}.$

Described wheel is formed into columns: cancel normal component, and making z direction amplitude be zero, xy plane configuration is that 1:2 is oval, and all satellites of formation are all in an orbit plane; Form into columns for wheel, if formed into columns according to equiphase angle, the distance between satellite changes along with phase place, and maximum spacing is about 2 times of minimum spacing.

Suppose that R is major axis radius, at phasing degree be 0 ° and 180 ° time, intersatellite spacing is maximum,

$L_{\max }=R\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})}$

$R=\frac{L_{\max }}{\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})}}$

At phasing degree be 90 ° and 270 ° time, intersatellite spacing is minimum,

$L_{\min }=\frac{R}{2}\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})}$

$R=\frac{2L_{\min }}{\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})}}.$

Described hybrid wheel formation is divided into two-layer, odd-level and even level, and odd number satellite still keeps wheel to form into columns, and even number satellite increases longitude of ascending node difference on the basis that wheel is formed into columns; The distance that hybrid wheel is formed into columns is uneven, and adjacent interstellar distance is maximum in X-axis, minimum in Y-axis; Hybrid wheel is formed into columns and be there is normal direction component motion.

The compressed sensing algorithm that described surface-based observing station 3 adopts adopts any one algorithm realization following: greedy reconstruction algorithm, Matching pursuitalgorithm MP, orthogonal Matching pursuitalgorithm OMP, base track algorithm BP, LASSO, LARS, GPSR, Bayesian Estimation algorithm, magic, IST, TV, StOMP, CoSaMP, LBI, SP, l1_ls, smp algorithm, SpaRSA algorithm, TwIST algorithm, l ₀reconstruction algorithm, l ₁reconstruction algorithm, l ₂reconstruction algorithm; Sparse base adopts any one realization in dct basis, wavelet basis, Fourier transform base, gradient base, gabor transform-based.

Be more than describe stereo mapping imaging system of the present invention structure in one embodiment, in other embodiments, the structure of this system also allows certain distortion.In one embodiment, also comprised in optical filter, camera lens and optical lens before the spaceborne point probe of each satellite one or more, if having multiple, then the front and back position relation between described optical filter or camera lens or optical lens is any.In another embodiment, red, green, blue three-colour filter is added respectively before the spaceborne point probe of each satellite, the light distribution situation of the object respectively light of reflect red, green, blue three-color can be obtained thus, just can recover the cromogram on each detection angle according to RGB three primary color theory, thus reconstruct colored 3D rendering.In yet another embodiment, before the spaceborne point probe of each satellite, add the optical filter of different wave length, thus can multispectral imaging be realized, obtain the three-dimensional imaging of multi-wavelength.

Based on the above-mentioned stereo mapping imaging system based on separation load satellites formation, stereo mapping formation method of the present invention comprises the following steps:

Step 1), setting are separated the step of load satellites formation;

In this step, according to satellite orbit kinetic model, EVOLUTION ANALYSIS is carried out to flight pattern, according to analysis result, separation load Satellite formation flying is set as that space circle pearl necklace is formed into columns or wheel is formed into columns or hybrid wheel is formed into columns, make under J2 Perturbation Effect, be separated the stability that load satellites formation can keep rank;

The foundation of described satellite orbit kinetic model comprises the following steps:

Step 1-1), first determine describe be separated load form into columns motion orbital coordinate system:

Coordinate origin is at aircraft barycenter, and Z axis is perpendicular to satellite orbit plane; XY axle is in satellite orbit plane, and X-axis points to aircraft barycenter direction from the earth's core; Y-axis meets right-hand screw rule;

Step 1-2), then derive from dynamic (dynamical) angle and be separated load formation relative motion mechanics equation and approximate analytic solution thereof:

Step 1-3), then from kinematic angle, derive and be separated load formation Relative Kinematics:

R _ref＝a _ref(1-e _refcosE _ref)

R _sat＝a _sat(1-e _satcosE _sat)

R in formula _ref, R _satbe respectively the geocentric distance of principal and subordinate's spacecraft, e _ref, e _satbe respectively the excentricity of principal and subordinate's spacecraft, E _ref, E _satbe respectively the eccentric anomaly of principal and subordinate's spacecraft;

Step 1-4), except earth center gravitation, also must consider the impact of various perturbation factors:

Concerning below 1000km height low orbit satellite, affecting larger has perturbation of earths gravitational field power, atmospherical drag perturbation, in addition, and the 3rd body Gravitational perturbation such as the sun, the moon, the motion of solar radiation pressure perturbation to low orbit satellite also has a certain impact, and need carry out Modifying model for these perturbations.

Known by the formation EVOLUTION ANALYSIS under dynamics of orbits model: in certain orbit altitude, atmospherical drag is the reason causing satellite to bump against, if need to overcome the impact that atmospherical drag perturbation is formed into columns on pearl necklace, need load satellites formation to be deployed in the safety track of certain altitude, orbit altitude and solar active index closely related.

Step 2), compression sampling step;

On N number of reflected light direction, each spaceborne point probe collects the party upwards from total light intensity m time of the solar reflection optical on earth's surface, and N number of spaceborne point probe detects the measurement result of m time as measured value y _{m × N}, meanwhile, face battle array detects the optical field distribution of m sunshine, is denoted as calculation matrix A _{m × n};

Step 3), star ground data communication step;

Satellite Formation Flying is by step 2) fructufy after compression sampling time be wirelessly transmitted to ground, by satellite antenna 2 receiving communication signal;

Step 4), sparse reconstruction procedures, generate the two dimensional image in each spaceborne point probe direction corresponding;

Surface-based observing station 3 utilizes natural image compressible or can the priori of rarefaction representation, chooses suitable sparse base Ψ, makes subject image x _{n × N}coefficient x ' is obtained after Ψ conversion _{n × N}the most sparse; At known measurements y _{m × N}, calculation matrix A _{m × n}with under the condition of sparse base Ψ, founding mathematical models y _{m × N}=A _{m × n}Ψ _{n × n}x' _{n × N}+ e _{n × N}, wherein N is detector number, and n is the signal total length of single width two dimensional image; Convex optimization is carried out, after obtaining x ', then by x by compressed sensing algorithm _{n × N}=Ψ _{n × n}x' _{n × N}be finally inversed by x _{n × N}, each row wherein are all lined up matrix image by column weight, and its image pixel dimensions is the optical field distribution a of the single frames sunshine photographed _isize, namely in x i-th row corresponding I _i;

Step 5), stereo mapping image-forming step;

If the luminance equation of the pixel image on i-th detector is the i.e. two dimensional image in each spaceborne point probe direction that obtains of step 4), wherein i=1,2,3 ..., N, I _sfor the intensity of light source, α is surface reflectivity, for pointing to the unit direction vector of i-th detector from object, for body surface unit normal vector, p, q are image pixel row-coordinate and row coordinate, open two dimensional image for N, are rewritten as by above-mentioned formula wherein D is the matrix comprising all units direction vector, and I is the matrix comprising respective image intensity signal, and for any pixel (p, q), unit normal vector is surface reflectivity α=D ^-1the gradient between neighbor can be determined according to the normal vector of each pixel calculating gained, thus by integrating the 3D geometric configuration obtaining body surface: first extract minutiae, and start to calculate using these unique points as center radiation to surrounding respectively, certain a bit on surface elevation by utilizing the height of the point of arest neighbors and surface gradedly estimating; Then be optimized, often walk iterative computation pixel, the averaged power spectrum of the height of this pixel and its all nearest neighbor point is matched, the pixel of non-object edge part, it estimates that the Laplace transform of height is equivalent to the Laplace transform of measuring gradient, the pixel of object edge part, its gradient vertical is in body surface; Final iteration terminates to obtain earth's surface stereo mapping image.

It should be noted last that, above embodiment is only in order to illustrate technical scheme of the present invention and unrestricted.Although with reference to embodiment to invention has been detailed description, those of ordinary skill in the art is to be understood that, modify to technical scheme of the present invention or equivalent replacement, do not depart from the spirit and scope of technical solution of the present invention, it all should be encompassed in the middle of right of the present invention.

Claims (9)

1. based on the stereo mapping imaging system being separated load satellites formation, it is characterized in that, comprising: be separated load satellites formation, satellite antenna (2), surface-based observing station (3); Described separation load satellites formation comprises at least two satellites, and each satellite all includes a spaceborne point probe, a satellite includes a planar array detector wherein; Described satellite antenna (2) is arranged on described surface-based observing station (3);

Sunshine incides earth surface, through earth reflection, the total light intensity on each detection direction is received by the spaceborne point probe on each satellite in described separation load satellites formation, using the detectable signal of result of detection as thing arm, the optical field distribution of the planar array detector detection sunshine comprised in described separation load satellites formation, using result of detection as the detectable signal with reference to arm; By the detectable signal of described thing arm and reference arm by being wirelessly transmitted to ground, received by described satellite antenna (2), described surface-based observing station (3) is according to received data, utilize compressed sensing algorithm to rebuild the two dimensional image that each Satellite Formation Flying observes, then compare the dash area information of these images to build stereo mapping image; Wherein,

Described separation load satellites formation adopts space circle pearl necklace to form into columns or wheel is formed into columns or hybrid wheel is formed into columns; Wherein, described space circle pearl necklace is formed into columns at the ellipse being projected as 1:2 of virtual primary orbital coordinate system xy plane, being projected as of yz plane ellipse, be projected as straight line in xz plane;

If space circle pearl necklace Satellite Formation Flying number is N, adjacent interstellar distance is L, and space circle radius is that R, N decimetre star is uniformly distributed in space circle, then the subtended angle of adjacent star is:

$\mathrm{\θ}=\frac{2\mathrm{\π}}{N}$

If known N and R, then have:

$L=R\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})};$

If known N and L, then have:

$R=\frac{L}{\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})}};$

If known L and R, then have:

$N=\frac{2\mathrm{\π}}{{\cos }^{-1}(1-\frac{1}{2}{\left(\frac{L}{R}\right)}^2)};$

Described wheel is formed into columns: cancel normal component, and making z direction amplitude be zero, xy plane configuration is that 1:2 is oval, and all satellites of formation are all in an orbit plane;

Suppose that R is major axis radius, at phasing degree be 0 ° and 180 ° time, intersatellite spacing is maximum,

$L_{\max }=R\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})}$

$R=\frac{L_{\max }}{\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})}}$

At phasing degree be 90 ° and 270 ° time, intersatellite spacing is minimum,

$L_{\min }=\frac{R}{2}\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})}$

$R=\frac{{2L}_{\min }}{\sqrt{2(1-\cos \frac{2\mathrm{\π}}{N})}};$

Described hybrid wheel formation is divided into two-layer, odd-level and even level, and odd number satellite still keeps wheel to form into columns, and even number satellite increases longitude of ascending node difference on the basis that wheel is formed into columns; The distance that hybrid wheel is formed into columns is uneven, and adjacent interstellar distance is maximum in X-axis, minimum in Y-axis; Hybrid wheel is formed into columns and be there is normal direction component motion.

2. the stereo mapping imaging system based on being separated load satellites formation according to claim 1, it is characterized in that, also comprise optical filter, described optical filter is before described spaceborne point probe.

3. the stereo mapping imaging system based on being separated load satellites formation according to claim 2, it is characterized in that, described optical filter is red, green, blue three-colour filter, or has the optical filter of different wave length.

4. the stereo mapping imaging system based on being separated load satellites formation according to claim 1, it is characterized in that, also comprise camera lens or optical lens, described camera lens or optical lens are before described spaceborne point probe.

5. the stereo mapping imaging system based on separation load satellites formation according to claim 1 or 2 or 4, it is characterized in that, the spaceborne point probe in described separation load satellites formation on each satellite keeps synchronous with unique planar array detector.

6. the stereo mapping imaging system based on separation load satellites formation according to claim 1 or 2 or 4, it is characterized in that, the spaceborne point probe in described separation load satellites formation on each satellite adopt in opto-electronic conversion point probe or bucket detector or single pixel detector or avalanche diode or photomultiplier any one realize.

7. the stereo mapping imaging system based on separation load satellites formation according to claim 1 or 2 or 4, it is characterized in that, the compressed sensing algorithm that described surface-based observing station (3) adopts adopts any one algorithm realization following: greedy reconstruction algorithm, Matching pursuitalgorithm MP, orthogonal Matching pursuitalgorithm OMP, base track algorithm BP, LASSO, LARS, GPSR, Bayesian Estimation algorithm, magic, IST, TV, StOMP, CoSaMP, LBI, SP, l1_ls, smp algorithm, SpaRSA algorithm, TwIST algorithm, l ₀reconstruction algorithm, l ₁reconstruction algorithm, l ₂reconstruction algorithm; Sparse base adopts any one realization in dct basis, wavelet basis, Fourier transform base, gradient base, gabor transform-based.

8., based on the stereo mapping formation method realized based on the stereo mapping imaging system being separated load satellites formation one of claim 1-7 Suo Shu, comprising:

Step 1), setting is separated the step of load satellites formation;

In this step, according to satellite orbit kinetic model, EVOLUTION ANALYSIS is carried out to flight pattern, according to analysis result, separation load Satellite formation flying is set as that space circle pearl necklace is formed into columns or wheel is formed into columns or hybrid wheel is formed into columns, make under J2 Perturbation Effect, be separated the stability that load satellites formation can keep rank;

Step 2), compression sampling step;

On N number of reflected light direction, each spaceborne point probe collects the party upwards from total light intensity m time of the solar reflection optical on earth's surface, and N number of spaceborne point probe detects the measurement result of m time as measured value y _{m × N}, meanwhile, face battle array detects the optical field distribution of m sunshine, is denoted as calculation matrix A _{m × n};

Step 3), star ground data communication step;

Satellite Formation Flying is by step 2) fructufy after compression sampling time be wirelessly transmitted to ground, by satellite antenna (2) receiving communication signal;

Step 4), sparse reconstruction procedures, generate the two dimensional image in each spaceborne point probe direction corresponding;

Surface-based observing station (3) utilizes natural image compressible or can the priori of rarefaction representation, chooses suitable sparse base Ψ, makes subject image x _{n × N}coefficient x ' is obtained after Ψ conversion _{n × N}the most sparse; At known measurements y _{m × N}, calculation matrix A _{m × n}with under the condition of sparse base Ψ, founding mathematical models y _{m × N}=A _{m × n}Ψ _{n × n}x ' _{n × N}+ e _{n × N}, wherein N is detector number, and n is the signal total length of single width two dimensional image; Convex optimization is carried out, after obtaining x ', then by x by compressed sensing algorithm _{n × N}=Ψ _{n × n}x ' _{n × N}be finally inversed by x _{n × N}, each row wherein are all lined up matrix image by column weight, and its image pixel dimensions is the optical field distribution a of the single frames sunshine photographed _isize, namely in x i-th row corresponding I _i;

Step 5), stereo mapping image-forming step;

If the luminance equation of the pixel image on i-th detector is i.e. step 4) two dimensional image in each spaceborne point probe direction that obtains, wherein i=1,2,3 ..., N, I _sfor the intensity of light source, α is surface reflectivity, for pointing to the unit direction vector of i-th detector from object, for body surface unit normal vector, p, q are image pixel row-coordinate and row coordinate, open two dimensional image for N, are rewritten as by above-mentioned formula:

$I(p.q)=I_{s}a(D\·\hat{n}),$

Wherein, D is the matrix comprising all units direction vector, and I is the matrix comprising respective image intensity signal, and for any pixel (p, q), unit normal vector is surface reflectivity α=D ^-1, the gradient between neighbor can be determined according to the normal vector of each pixel calculating gained, thus by integrating the 3D geometric configuration obtaining body surface; Specifically comprise:

First extract minutiae, and start to calculate using these unique points as center radiation to surrounding respectively, certain a bit on surface elevation by utilizing the height of the point of arest neighbors and surface gradedly estimating; Then be optimized, often walk iterative computation pixel, the averaged power spectrum of the height of this pixel and its all nearest neighbor point is matched, the pixel of non-object edge part, it estimates that the Laplace transform of height is equivalent to the Laplace transform of measuring gradient, the pixel of object edge part, its gradient vertical is in body surface; Final iteration terminates to obtain earth's surface stereo mapping image.

9. stereo mapping formation method according to claim 8, is characterized in that, in described step 1) in, the foundation of described satellite orbit kinetic model comprises the following steps:

Step 1-1), first determine describe be separated load form into columns motion orbital coordinate system:

Coordinate origin is at aircraft barycenter, and Z axis is perpendicular to satellite orbit plane; XY axle is in satellite orbit plane, and X-axis points to aircraft barycenter direction from the earth's core; Y-axis meets right-hand screw rule;

Step 1-2), then derive from dynamic (dynamical) angle and be separated load formation relative motion mechanics equation and approximate analytic solution thereof:

Step 1-3), then from kinematic angle, derive and be separated load formation Relative Kinematics:

R _ref＝a _ref(1-e _refcosE _ref)

R _sat＝a _sat(1-e _satcosE _sat)

R in formula _ref, R _satbe respectively the geocentric distance of principal and subordinate's spacecraft, e _ref, e _satbe respectively the excentricity of principal and subordinate's spacecraft, E _ref, E _satbe respectively the eccentric anomaly of principal and subordinate's spacecraft;

Step 1-4), except earth center gravitation, also must consider the impact of various perturbation factors:

Concerning below 1000km height low orbit satellite, affecting larger has perturbation of earths gravitational field power, atmospherical drag perturbation, in addition, and the 3rd body Gravitational perturbation such as the sun, the moon, the motion of solar radiation pressure perturbation to low orbit satellite also has a certain impact, and need carry out Modifying model for these perturbations.