CN107607947A - Spaceborne radar imaging parameters On-line Estimation method based on Kalman filtering - Google Patents

Spaceborne radar imaging parameters On-line Estimation method based on Kalman filtering Download PDF

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CN107607947A
CN107607947A CN201710724088.5A CN201710724088A CN107607947A CN 107607947 A CN107607947 A CN 107607947A CN 201710724088 A CN201710724088 A CN 201710724088A CN 107607947 A CN107607947 A CN 107607947A
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CN107607947B (en
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丁金闪
吴晓桐
梁毅
张玉洪
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Xidian University
Xian Cetc Xidian University Radar Technology Collaborative Innovation Research Institute Co Ltd
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Xian Cetc Xidian University Radar Technology Collaborative Innovation Research Institute Co Ltd
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Abstract

The invention discloses a kind of spaceborne radar imaging parameters real-time online method of estimation based on Kalman filtering, its main thought is：Earth inertial coordinates system, earth fixed coordinate system, satellite orbit coordinate system, satellite flight path axis system, satellite fixed coordinate system are established respectively, respectively obtain the transformational relation, satellite orbit coordinate system and the transformational relation in earth inertial coordinates system, satellite flight path axis system and the transformational relation of earth inertial coordinates system of earth fixed coordinate system and earth inertial coordinates system；The measurement equation of k moment satellites is established, and carries out Kalman filtering, obtains position vector of the k+1 moment satellite in earth inertial coordinates system；Radar antenna beam center pointing vector and point target are determined respectively, calculate k+1 moment radar antenna phase centers to the oblique distance vector of point target, and then calculate minimum distance moment t respectively0And B parameter, the B parameter are the spaceborne radar imaging parameters real-time online estimated result based on Kalman filtering.

Description

Spaceborne radar imaging parameters On-line Estimation method based on Kalman filtering
Technical field
The present invention relates to spaceborne radar technical field, more particularly to a kind of spaceborne radar imaging ginseng based on Kalman filtering Number real-time online method of estimation, for random eccentric rate track and oval earth model, and suitable for being satellite-borne synthetic aperture thunder Up to key parameter needed for (SAR) imaging offer.
Background technology
At present, Space-borne SAR Imaging technology develops to high-resolution and multi-mode, the U.S. " lacrosse " satellite-borne SAR orientation point Resolution is better than 1m, and the SAR-Lupe that German DLR launches at the beginning of 2007 is up to 0.5m high-resolution.
Space-borne SAR Imaging model more ripe at present is the equivalent airborne rectilinear orbit model of erection rate, i.e., by positive side Airborne rectilinear orbit model is equivalent to depending on satellite-borne SAR, simply replaces speed with velocity equivalent, and the calculating one of velocity equivalent As need the needs that could meet precision by the method for numerical computations.To the of new generation spaceborne of high-resolution and wide swath SAR system, mismatch error caused by equivalent airborne rectilinear orbit model increase, and extreme case even fails；At traditional imaging Reason method using based on echo data clutter locking and self-focusing technology come reverse kinematic parameter, but its in second-order model Approximation can not further improve the precision of model, and can increase certain operand, so as to increase real time signal processing on star Load.
The content of the invention
In view of the above-mentioned problems of the prior art, it is an object of the invention to propose a kind of star based on Kalman filtering Radar imagery parameter real-time online method of estimation is carried, spaceborne radar imaging parameters real-time online of this kind based on Kalman filtering is estimated Geometry and the posture High Accuracy Parameter that meter method takes full advantage of satellite and track are estimated to obtain needed for imaging calculate Key parameter, the precision of parameters obtained is high, and caused operand greatly reduces compared with the method for parameter estimation based on echo.
To reach above-mentioned technical purpose, the present invention, which adopts the following technical scheme that, to be achieved.
A kind of spaceborne radar imaging parameters real-time online method of estimation based on Kalman filtering, comprises the following steps：
Step 1, earth inertial coordinates system, earth fixed coordinate system, satellite orbit coordinate system, satellite flight path seat are established respectively Mark system, satellite fixed coordinate system, respectively obtain transformational relation, the satellite orbit of earth fixed coordinate system and earth inertial coordinates system Coordinate system and the transformational relation, satellite flight path axis system and the transformational relation of earth inertial coordinates system of earth inertial coordinates system；
Step 2, the measurement equation of the satellitosis at k moment is established, and carries out Kalman filtering, and then k+1 is calculated Position vector of the moment satellite in earth inertial coordinates system；Wherein, k represents time variable, and k is positive integer；
Step 3, radar antenna beam center pointing vector is determined, and by radar antenna beam center pointing vector and the earth The intersection point on surface is designated as point target, and according to position vector of the k+1 moment satellite in earth inertial coordinates system, k+1 is calculated Oblique distance vector of the moment radar antenna phase center to point target；
Step 4, according to the oblique distance vector of k+1 moment radar antenna phase centers to point target, it is calculated respectively recently Apart from moment t0And B parameter, the B parameter are the spaceborne radar imaging parameters real-time online estimation knot based on Kalman filtering Fruit, wherein B parameter and minimum distance moment t0For spaceborne radar imaging parameters, the minimum distance moment is radar antenna phase center To point target oblique distance minimum when correspond at the time of.
The present invention has the following advantages compared with prior art：
First, traditional image processing method is transported using the clutter locking based on echo data and self-focusing technology come reverse Dynamic parameter, but certain operand can be increased, so as to increase the load of real time signal processing on star；In addition, the present invention is calculating A variety of data are handled using Kalman filtering in flow, operand subtracts significantly compared with the method for parameter estimation based on echo It is small, and can be handled online according to the data of real-time update.
Second, Space-borne SAR Imaging model more ripe at present is the equivalent airborne rectilinear orbit model of erection rate, to pole The Spaceborne SAR System of new generation of high-resolution and wide swath, mismatch error caused by equivalent airborne rectilinear orbit model increase, Extreme case even fails.The present invention considers the relative smoothness of satellite motion and the intellectual of satellite orbit parameter, utilizes The high-precision satellite attitude parameter that system measures is imaged required parameters to be calculated.
Brief description of the drawings
The present invention is described in further detail with reference to the accompanying drawings and detailed description.
Fig. 1 is a kind of spaceborne radar imaging parameters real-time online method of estimation flow based on Kalman filtering of the present invention Figure；
Fig. 2 is the five coordinate system schematic diagrames used in the present invention；
Fig. 3 is earth inertial coordinates system and satellite orbit parameter schematic diagram；
Fig. 4 is the eccentric anomaly result figure of any time satellite obtained using the inventive method；
Fig. 5 is the satellite orbit coordinate system schematic diagram using the earth as elliptic orbit focus；
Fig. 6 changes over time relation pair ratio for radar antenna phase center before and after consideration perturbative force to the oblique distance of point target Figure；
Fig. 7 is that the B parameter obtained using the inventive method changes over time result figure, and transverse axis is the time, and the longitudinal axis is
Embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete Site preparation describes, it is clear that described embodiment is only part of the embodiment of the present invention, rather than whole embodiments.It is based on Embodiment in the present invention, those of ordinary skill in the art are obtained every other under the premise of creative work is not made Embodiment, belong to the scope of protection of the invention.
Reference picture 1, for a kind of spaceborne radar imaging parameters real-time online estimation side based on Kalman filtering of the present invention Method flow chart；The wherein described spaceborne radar imaging parameters real-time online method of estimation based on Kalman filtering, including following step Suddenly：
Step 1, earth inertial coordinates system, earth fixed coordinate system, satellite orbit coordinate system, satellite flight path seat are established respectively Mark system, satellite fixed coordinate system, respectively obtain transformational relation, the satellite orbit of earth fixed coordinate system and earth inertial coordinates system Coordinate system and the transformational relation, satellite flight path axis system and the transformational relation of earth inertial coordinates system of earth inertial coordinates system.
Specifically, reference picture 2, for the five coordinate system schematic diagrames used in the present invention；Wherein, five coordinate systems are：Ground Ball inertial coodinate system (IN coordinate systems), earth fixed coordinate system (EF coordinate systems), satellite orbit coordinate system (OS coordinate systems), satellite Flight path axis system (TS coordinate systems), satellite fixed coordinate system (SC coordinate systems).
XINRepresent X-axis in earth inertial coordinates system, YINRepresent Y-axis in earth inertial coordinates system, ZINRepresent that earth inertial is sat Z axis in mark system, earth inertial coordinates system is using the earth's core O as origin, XIN YINPlane overlaps with earth equatorial plane, XINPoint to the Spring Equinox Point, ZINPoint to the earth arctic, YINBy XINAnd ZINDetermined by right-hand rule.
XEFRepresent X-axis in earth fixed coordinate system, YEFRepresent Y-axis in earth fixed coordinate system, ZEFRepresent that the earth is fixed to sit Z axis in mark system, earth fixed coordinate system are fixed on the earth, and using the earth's core O as origin, XEFPass through the equatorial plane and Greenwich Noon line intersects, ZEFWith ZINOverlap, YEFBy XEFAnd ZEFDetermined by right-hand rule；Earth fixed coordinate system is with earth rotation shaft angle Speed omega is around ZEFRotation, and earth fixed coordinate system changes with the rotation of the earth, the every bit on ground is fixed in the earth and sat Expression in mark system is all fixed, X'EFRepresent that the earth is fixed when the earth is with earth rotation axis angular rate w rotation time t to sit Mark the X-axis of system, Y 'EFRepresent the Y-axis of the earth fixed coordinate system when the earth is with earth rotation axis angular rate w rotation time t, Z'EF Represent the Z axis of the earth fixed coordinate system when the earth is with earth rotation axis angular rate w rotation time t.
XOSRepresent X-axis in satellite orbit coordinate system, YOSRepresent Y-axis in satellite orbit coordinate system, ZOSRepresent that satellite orbit is sat Z axis in mark system, satellite orbit coordinate system is using the earth's core O as origin, XOSPoint to perigee, YOSThe vertical X in satellite orbit faceOS, ZOS By XOSAnd YOSDetermined by right-hand rule；Wherein, satellite orbit face is plane, wherein perigee where the running track of satellite For point nearest with the earth in Earth's orbit face.
XTSRepresent X-axis in satellite flight path axis system, YTSRepresent Y-axis in satellite flight path axis system, ZTSRepresent that satellite flight path is sat The direction of satellite is pointed to as Z in the earth's core by Z axis in mark system, satellite flight path axis system using centroid of satellite as originTSSensing, By ZTSSensing be designated as zenith direction, XTSIt is orthogonal to ZTSThe plane formed with satellite velocity vector, YTSBy XTSAnd ZTSPass through the right side Gimmick then determines；Satellite fixed coordinate system using centroid of satellite as origin, the angle of pitch of yaw angle, satellite when satellite and satellite When roll angle is all 0, satellite fixed coordinate system is completely superposed with satellite flight path axis system.
The intersection point of satellite orbit and equatorial plane when Fig. 2 Satellites to be passed through to equator from south to north, is designated as ascending node；By equator The earth's core angle in face corresponding to the first point of Aries to ascending node line, is designated as right ascension of ascending node Ω；The normal in satellite orbit face with it is red The angle of road plane normal, inclination of satellite orbit i is designated as, is expressed as ZINWith ZOSAngle；Satellite is in orbital plane by ascending node The earth's core angle corresponding to perigean track is run to, is designated as argument of perigee ω.
Conversion between 5 coordinate systems is the rotary course of coordinate system in fact, and any one coordinate system all regards another as Coordinate system obtains by certain rotation；The parameter observed in different coordinates is uniformly transformed into earth inertial coordinates In system, its process is：
When the earth is with earth rotation axis angular rate w rotation time t, the earth fixes EF coordinate systems to earth inertial IN coordinate systems Transformational relation be：
Wherein, XINRepresent X-axis in earth inertial coordinates system, YINRepresent Y-axis in earth inertial coordinates system, ZINRepresent the earth Z axis in inertial coodinate system, XEFRepresent X-axis in earth fixed coordinate system, YEFRepresent Y-axis in earth fixed coordinate system, ZEFRepresent ground Z axis in ball fixed coordinate system, Ω represent right ascension of ascending node, and cos represents cosine function, and sin represents SIN function, and t represents the time Variable, w represent earth rotation axis angular rate；DZ(Ω+wt) represents that the earth fixes Z in EF coordinate systemsEFAfter rotating Ω+ω t radians Obtained spin matrix, its expression formula are：
Satellite orbit coordinate system is to the transformational relation of earth inertial coordinates system：
Wherein, XOSRepresent X-axis in satellite orbit coordinate system, YOSRepresent Y-axis coordinate in satellite orbit coordinate system, ZOSRepresent Z axis in satellite orbit coordinate system, DZ(u) represent satellite orbit coordinate system around ZOSThe spin matrix obtained after rotation u radians, DZ (Ω) represents satellite orbit coordinate system around ZOSThe spin matrix obtained after rotation Ω radians, DX(i) satellite orbit coordinate system is represented Around XOSThe spin matrix obtained after rotation i radians, Ω represent right ascension of ascending node, and i represents inclination of satellite orbit orbit inclination angle, u tables Show satellite orbit argument, be defined as in satellite orbit face satellite from ascending node to corresponding to the movement locus of satellite real time position Heart angle.
Formula (3) shows satellite orbit coordinate system first around ZOSU radians are rotated, further around XOSI radians are rotated, finally around ZOSRotation After Ω radians, satellite orbit coordinate system just overlaps with earth inertial coordinates system.
The attitude parameter of satellite defines in satellite flight path axis system, and the attitude parameter of the satellite includes satellite The angle of pitch of yaw angle, the roll angle of satellite and satellite；X-axis X in satellite flight path axis systemTSUnit vector beSatellite navigates Y-axis Y in mark coordinate systemTSUnit vector beZ axis Z in satellite flight path axis systemTSUnit vector beIt is designated as satellite boat Mark coordinate system unit vectorWherein Represent satellite activity's speed Spend vector,Substar unit vector is represented, the earth fixes substar unit vector in EF coordinate systems and isIts expression formula is：
Wherein, ΦSRepresent the latitude of satellite present position, ΛSRepresent the longitude of satellite present position.
Substar unit vector is in earth inertial IN coordinate systemsIts expression formula is：
Wherein, Dz(wt) represent that the earth fixes EF coordinate systems around ZEFThe spin matrix obtained after rotation wt radians.
Transformational relation by satellite flight path TS coordinate systems to earth inertial IN coordinate systems is：
Wherein, XTSRepresent X-axis in satellite flight path axis system, YTSRepresent Y-axis in satellite flight path axis system, ZTSRepresent satellite Z axis in flight path axis system, D represent earth inertial IN coordinate system unit coordinate vector matrixs, and
Wherein,Represent X-axis X in satellite flight path axis systemTSUnit vector,Represent Y-axis Y in satellite flight path axis systemTS Unit vector,Represent Z axis Z in satellite flight path axis systemTSUnit vector,Represent earth inertial coordinates system Satellite Unit speed vector.
Step 2, determine that satellite position changes over time relation by Kepler's law, obtain satellite in earth inertial coordinates Position vector in system；The observation satellite position coordinates in satellite orbit coordinate system, as shown in figure 3, the satellite rail in Fig. 3 Road coordinate system is using the earth's core as origin, and apogee refers in satellite orbit face and the farthest point of the earth；It is big by Kepler's planetary motion three Law knows that the tracks of satellite are elliptic orbit, and the earth is located in one of focus of the elliptic orbit；Satellite is with ground Ball center moves as focus along elliptic orbit, and meets Kepler's law；By distance of the satellite at perigee to earth surface As satellite flight height h, the semi-major axis a and semi-minor axis b of elliptic orbit are determined under the conditions of known to h, is done using a as radius ellipse The circumscribed circle of circular orbit, point A, point A to elliptic orbit are obtained on circumscribed circle if satellite present position is projected in a vertical direction The line and X at centerOSAngle, be designated as the eccentric anomaly E of satellite；Satellite in satellite orbit face is moved into satellite by perigee The earth's core angle corresponding to the movement locus of current location, it is designated as the true anomaly f of satellite；X-axis X in satellite orbit coordinate systemOSCross Perigee, set when satellite crosses perigee as zero moment, the eccentricity of elliptic orbit is e=c/a, and c represents Jiao of elliptic orbit Away from c=a-b, a-c=h+a_earth, a_earth represent terrestrial equator radius；H=650km in the present embodiment, e= 0.007163, a_earth=6370137km.
Then satellite position vectors are calculatedIts process is：
2.1 determine description satellite position and the Kepler's equations of time relationship：
n(t-tp)=E-esin (E) (8)
By n (t-tp) mean anomaly M, n the expression satellite mean angular velocity of satellite is defined as,
μ represents geocentric gravitational constant, and a represents the semi-major axis of elliptic orbit, and T represents satellite rail The road period of motion, t represent time variable, tpTime of satellite perigee passing is represented, t in the present embodimentp=0；E represents the inclined of satellite Anomaly, e represent the eccentricity of elliptic orbit.
And then obtain the eccentric anomaly of t satellite：
Wherein, E (t) represents the eccentric anomaly of t satellite；The eccentric anomaly that E (t+ △ T) is t+ △ T moment satellites is made, △ T represent time interval, and the Kepler's equations for obtaining satellite is：
Obtained after the sin functions in formula (10) are carried out into linear progression expansion at t：
Abbreviation is carried out to formula (11), obtained：
Due to that can be interfered during satellite transit, directly solved with Kepler's equations and ignore interference to parameter Influence, can be in cases of a disturbance according to the estimate at previous moment and current time observation using Kalman filtering The optimal estimation at current time is tried to achieve, is more nearly actual value；It is used herein as Kalman filtering and seeks eccentric anomaly.
Kalman filtering is carried out to formula (12), obtains the satellitosis equation in Kalman filtering：
Wherein, x (k+1) represents the satellitosis at k+1 moment, the eccentric anomaly E (t+ △ T) of corresponding t+ △ T moment satellites The interference w being subject to k moment satellite when elliptic orbit is runkSuperposition；X (k) represents the satellitosis at k moment, when corresponding to t Carve the eccentric anomaly E (t) of satellite；wkRepresent the interference that k moment satellite is subject to when elliptic orbit is run；By the satellite at 0 moment State is designated as original state x (0), x (0)=0 in the present embodiment.
G (x (k)) is made to represent the satellitosis equation when k moment does not consider interference：
Satellitosis equation in Kalman filtering is measured, obtains the measurement equation y (k) of k moment satellites：
Wherein, vkRepresent the observation noise of k moment satellites, tpRepresent time of satellite perigee passing.
By formula (9) and x (k) and E (t) corresponding relation, y (k) and x (k) relation are obtained：
Y (k)=x (k)-e sin x (k)+vk (16)
H (x (k)) is made to represent the satellitosis x (k) at k moment measurement equation：
H (x (k))=x (k)-e sin x (k) (17)
Wherein, when the observation noise of the corresponding k moment satellites of the satellitosis x (k) at k moment measurement equation h (x (k)) is 0 True value；It is non-linear conversion relation between state because the satellitosis equation in Kalman filtering is understood, so being non-thread Sexual system, handled using EKF.
Kalman filtering processing is extended to the satellitosis x (k) at k moment measurement equation, obtains k+1 moment satellites Eccentric anomaly posterior estimate, and using the satellite eccentric anomaly posterior estimate of k+1 moment satellites as k+1 moment satellites Eccentric anomaly E (k+1), its calculating process are：
Wherein,Represent the eccentric anomaly priori estimates of k+1 moment satellites, g (x+(k) k moment satellites) are represented Eccentric anomaly posterior estimateObservational equation,Represent the eccentric anomaly posterior estimate of k moment satellites, P+ (k) the eccentric anomaly posterior estimate of k moment satellites is representedMean square error, W represent to wkObtained after seeking mathematic expectaion Interference covariance matrix, K (k+1) represents the gain matrix of k+1 moment satellites, corresponding k+1 moment Kalman filter gains； P-(k+1) the eccentric anomaly priori estimates of k+1 moment satellites are representedMean square error, V represent to k moment satellites Observation noise vkThe observation noise covariance matrix obtained after mathematic expectaion is sought,Represent
The eccentric anomaly posterior estimate of k+1 moment satellites, y (k+1) represent the measurement equation of k+1 moment satellites, P+(k+ 1) the eccentric anomaly posterior estimate of k+1 moment satellites is representedMean square error,Represent the k+1 moment The eccentric anomaly priori estimates of satelliteMeasurement equation；It is actual observed value with not having There is the difference for the estimate for considering noise, imply observation noise and the information of interference.
The eccentric anomaly posterior estimate of k+1 moment satellites is calculated by formula (18)It is to the k+1 moment Satellitosis x (k+1) optimal estimation, and using the satellite eccentric anomaly posterior estimate of k+1 moment satellites as the k+1 moment The eccentric anomaly E (k+1) of satellite；Reference picture 4, for the eccentric anomaly result of any time satellite obtained using the inventive method Figure.
2.2 by true anomaly and the relation of eccentric anomaly, and the true anomaly f (k+1) of k+1 moment satellites is calculated：
2.3, for preferable two body motion model, are calculated the satellite at k+1 moment with respect to the earth's core immediate movement r (k+ 1)：
And then obtain coordinate of the k+1 moment satellite in satellite orbit coordinate systemFor：
Wherein, a represents the semi-major axis of elliptic orbit, and e represents the eccentricity of elliptic orbit, XOS(k+1) represent that the k+1 moment is defended X-axis in star orbital coordinate system, YOS(k+1) Y-axis coordinate in k+1 moment satellite orbit coordinate systems, Z are representedOS(k+1) when representing k+1 Carve Z axis in satellite orbit coordinate system.
By coordinate of the k+1 moment satellite in satellite orbit coordinate systemTransform in earth inertial coordinates system, obtain To position vector of the k+1 moment satellite in earth inertial coordinates system
Step 3, radar antenna beam center pointing vector is designated asBy radar antenna beam center pointing vectorWith The intersection point of earth surface is designated as point target, and the position vector of point target is designated asRadar antenna phase center is arrived into point target Oblique distance vector is designated asAnd then obtain satellite and fix radar antenna beam center pointing vector in SC coordinate systems
Wherein, θ represents radar antenna beam center pointing vectorWith substar unit vectorAngle, be designated as nadir Angle；Because the roll angle of satellite only changes the size of nadir angle, thus the roll angle of satellite directly according to the change of nadir angle come Processing.
By radar antenna beam center pointing vectorTransformed to by satellite flight path axis system in earth inertial coordinates system, It is all 0 to set the angle of pitch of satellite and the yaw angle of satellite, then obtains radar antenna beam center in earth inertial coordinates system and refer to To vector
D represents earth inertial IN coordinate system unit coordinate vector matrixs.
To coordinate of the k+1 moment satellite in satellite orbit coordinate systemDerivation, obtain k+1 moment satellite and defending Velocity in star orbital coordinate system
Wherein,Represent the coordinate to k+1 moment satellite in satellite orbit coordinate systemDerivation, T are represented The satellite orbit motion cycle.
And then obtain speed v of the k+1 moment satellite in satellite orbit coordinate systemOS(k+1)：
Wherein, μ represents geocentric gravitational constant.
To velocity of the k+1 moment satellite in satellite orbit coordinate systemReconvert is used to the earth after normalization In property coordinate system, k+1 moment satellite activitys velocity is obtained
Wherein, a represents the semi-major axis of elliptic orbit, and e represents the eccentricity of elliptic orbit, DZ(u) represent that satellite orbit is sat Mark system is around ZOSThe spin matrix obtained after rotation u radians, DZ(Ω) represents satellite orbit coordinate system around ZOSObtained after rotating Ω radians The spin matrix arrived, DX(i) represent satellite orbit coordinate system around XOSThe spin matrix obtained after rotation i radians.
Substar unit vector is in earth inertial coordinates system
Wherein,Represent substar unit vector in earth fixed coordinate system, Dz(ω t) represents satellite orbit coordinate system Around ZOSThe spin matrix obtained after rotation ω t radians, w represent earth rotation axis angular rate, ΦSRepresent the latitude of satellite present position Degree, ΛSRepresent the longitude of satellite present position.
According to formula (26) and formula (27), k+1 moment earth inertial IN coordinate system unit coordinate vector matrix D (k+1) are obtained：
The position vector of point target under earth inertial IN coordinate systems is designated asIts expression formula is：
Wherein, RNRepresent that point target represents the latitude of point target position to the distance in the earth's core, Φ, Λ represents point target The longitude of position, Dz(ω t) represents satellite orbit coordinate system around ZOSThe spin matrix obtained after rotation ω t radians, w are represented Earth rotation axis angular rate, t represent time variable, aearthRepresent terrestrial equator semi-major axis.
Reference picture 5, it is that Fig. 5 is satellite orbit coordinate system schematic diagram using the earth as elliptic orbit focus；In Figure 5, For satellite position vectors, the position vector of satellite under earth inertial IN coordinate systems is designated as WithRelation：
Wherein,Radar antenna phase center in earth inertial coordinates systems is represented to the oblique distance vector of point target, R represents that radar antenna phase center represents radar antenna wave beam to the oblique distance of point target, θ Center pointing vectorWith substar unit vectorAngle, be designated as nadir angle；D represents that earth inertial IN coordinate systems unit is sat Mark vector matrix,Represent the radar antenna beam center pointing vector in earth inertial coordinates system；Represent earth inertial IN The position vector of satellite under coordinate system；Due toIt is known, therefore obtains simultaneous equations：
Wherein,The position vector of point target under k+1 moment earth inertial IN coordinate systems is represented, D represents that the earth is used to Property IN coordinate system unit coordinate vector matrixs, D (k+1) represent k+1 moment earth inertial IN coordinate system unit coordinate vector matrixs, R represents radar antenna phase center to the oblique distance of point target.
Simultaneous equations is handled with Kalman filtering mode, is first abbreviated as formula (28)：
Wherein,
Set the unknown state vector at k moment
Wherein, m1(k) the 1st element in the unknown state vector at k moment, position where corresponding k moment point target are represented The latitude Φ (k) put；m2(k) the 2nd element in the unknown state vector at k moment, position where corresponding k moment point target are represented The longitude Λ (k) put；m3(k) the 3rd element in the unknown state vector at k moment, corresponding k moment radar antenna phases are represented Oblique distance R (k) of the center to point target；Φ (k) represents the latitude of k moment point targets position, and Λ (k) represents k moment point mesh The longitude of position is marked, R (k) represents k moment radar antenna phase centers to the oblique distance of point target.
The unknown state vector at k+1 moment is designated as qkRepresent that k moment satellites exist What the latitude that elliptic orbit motion time does not correspond to point target position was subject to disturbs, corresponds to the longitude of point target position What is be subject to disturbs, corresponds to the interference that radar antenna phase center is subject to the oblique distance of point target；By t earth inertial IN coordinates The position vector of the lower satellite of system is designated as
Wherein, Represent k moment earth inertial IN coordinate systems The position vector of lower point target, D represent earth inertial IN coordinate system unit coordinate vector matrixs, and R is represented in radar antenna phase The heart is to the oblique distance of point target, y1(k) position vector of expression k moment satellites X-axis coordinate, y in earth inertial IN coordinate systems2(k) The position vector of expression k moment satellites Y-axis coordinate, y in earth inertial IN coordinate systems3(k) the position arrow of k moment satellites is represented Amount Z axis coordinate, y in earth inertial IN coordinate systems4(k) represent k moment radar antenna phase centers to the oblique distance of point target, Dz (ω k) represents satellite orbit coordinate system around ZOSThe spin matrix obtained after rotation ω t radians, w represent earth rotation axis angular rate, K represents time variable,Represent in earth inertial coordinates systems radar antenna phase center to the oblique distance vector of point target, RNRepresent Distance of the point target to the earth's core.
The measurement equation at k moment is：
Wherein, Represent under k moment earth inertial IN coordinate systems The position vector of satellite, jkRepresent that k moment satellite corresponds to the LATITUDE OBSERVATIONS noise of point target position, corresponding point target respectively The oblique distance observation noise of the longitude observation noise of position, corresponding radar antenna phase center to point target.
To formula（36）Kalman filtering is carried out, its process is as follows：
K(k+1)=P-(k+1)·HT[H·P-(k+1)HT+J]-1
P-(k+1)=P+(k)+Q
P+(k+1)=P-(k+1)-K(k+1)·H·P-(k+1)
Wherein,Represent the unknown state vector at k+1 momentPrior estimate vector, including during k+1 Carve to the latitude of point target position, the longitude of point target position, radar antenna phase center to point target oblique distance Prior estimate；Represent the k moment to the latitude of point target position, the longitude of point target position, radar antenna Phase center is to the Posterior estimator of the oblique distance of point target, y'(k+1) measurement equation at k+1 moment is represented,Represent t The position vector of satellite, P under earth inertial IN coordinate systems-(k+1) representMean square error, H represent's Observing matrix；P+(k) representMean square error, K (k+1) represents the gain matrix of k+1 moment satellites, corresponding k+1 moment Kalman filter gain；The unknown state vector at k moment is represented, Q is represented to qkAsk the interference obtained after mathematic expectaion Covariance matrix, J are represented to jkSeek the observation noise covariance matrix obtained after mathematic expectaion；Represent the k+1 moment Unknown state vectorPrior estimate vectorIn the 1st element, position where corresponding k+1 moment point target The latitude prior estimate put；Represent the unknown state vector at k+1 momentPrior estimate vectorIn the 2nd element, the longitude prior estimate of corresponding k moment point targets position；When representing k+1 The unknown state vector at quarterPrior estimate vectorIn the 3rd element, corresponding k+1 moment radar antennas Oblique distance prior estimate of the phase center to point target；RNRepresent that point target represents the eccentricity of ellipse track to the distance in the earth's core, e Circle.
By solving formula (37), the unknown state vector at k+1 moment is calculatedPosterior estimator vectorIncluding the k+1 moment in the latitude of point target position, the longitude of point target position, radar antenna phase Posterior estimator of the heart to the oblique distance of point target；The unknown state vector at the k+1 momentPosterior estimator vectorIt is the unknown state vector to the k+1 momentOptimal estimation, and then obtain position where k+1 moment point target Latitude Φ (k+1), the longitude Λ (k+1) of k+1 moment point targets position, the k+1 moment radar antenna phase centers put arrive The oblique distance R (k+1) of point target.
Then the position vector of point target under k+1 moment earth inertial IN coordinate systems is calculated
Because therefore the oblique distance R of radar antenna phase center to point target is, it is known that obtain in k+1 moment radar antenna phases Oblique distance vector of the heart to point target
Specifically, consider that the perturbative force suffered by satellite is mentioned on influence, step 1 caused by the attitude of satellite and orbital elements Elliptical orbit semi-major axis a, elliptical orbit eccentricity e, orbit inclination angle i, right ascension of ascending node Ω, argument of perigee ω It is not invariable during satellite motion etc. orbital elements.Satellite is taken the photograph by space environment is various all the time in orbit The effect of power.These perturbative forces have：The figure of the earth is aspherical and quality it is uneven caused by additional gravitation, the gas of upper atmosphere Power, the sun, the gravitation of the moon, and solar irradiation injection pressure etc..Under perturbative force effect, satellite orbit no longer follows disome The orbital elements such as track, its cycle, eccentricity, right ascension of ascending node, argument of perigee and orbit inclination angle constantly vary.
Therefore, by the perturbative force suffered by satellite on influenceing to take into account caused by the attitude of satellite and orbital elements；First Define geocentric orbital reference system (Oe-XesYesZes), origin OeOn centroid of satellite, the X-axis of geocentric orbital reference system is Xes, ground The Y-axis of heart orbital coordinate system is Yes, the Z axis of geocentric orbital reference system is Zes, Xes,Yes,ZesUnit vector be respectively ur,ut, un, wherein urAlong satellite the earth's core direction；utPerpendicular to u in satellite orbit facer, point to satellite flight velocity attitude；unWith satellite The normal parallel of orbital plane.
In satellite motion, energy and the moment of momentum are constant, and the perturbative force suffered by satellite is by causing energy and moving Measuring the change of square influences satellite orbit key element.
Perturbative force suffered by satellite is decomposed into along XesThe radial direction F of direction of principal axisr, along YesThe horizontal F of direction of principal axist, and Along ZesThe normal direction F of direction of principal axisn；In satellite motion, energy square and the moment of momentum be it is constant, perturbative force by cause energy square and The change of the moment of momentum influences satellite orbit key element.
In graviational interaction of the analysis celestial body to satellite, commonly use gravitation bit function U and represent；The embodiment of the present invention only considers to take the photograph In power by the figure of the earth is aspherical and quality it is uneven caused by additional gravitation, i.e. earth perturbative force, due to only considering ground Ball perturbative force, so only considering the terrestrial gravitation bit function in gravitation bit function.
To LEO, the principal element of earth perturbative force is the flat-shaped of the earth, in terrestrial gravitation bit function, by the earth Item caused by flat-shaped is referred to as with humorous item, and exemplified by only considering with the quadratic term in humorous item, definition perturbation bit function is △ U：
Wherein, J2Represent by the earth it is flat-shaped caused by two sub-band humorous term coefficients, r represents satellite with respect to the earth's core immediate movement, ΦsRepresent the latitude of satellite present position, ReRepresent terrestrial equator radius.
Earth perturbative force is F, and F=grad (△ U), grad represent to seek gradient operation；In geocentric orbital reference system, it will defend Perturbative force suffered by star is decomposed into the radial direction F along X-directionr, along the horizontal F of Y directiont, and the normal direction along Z-direction Fn；In satellite motion, energy and the moment of momentum are constant, and perturbative force influences to defend by causing the change of energy and the moment of momentum Star orbital elements.
The zonal harmonics perturbation power that geocentric orbit coordinate is obtained by perturbation bit function is：
And then the perturbation equation for obtaining satellite is：
Wherein, a represents elliptical orbit semi-major axis, and e represents elliptical orbit eccentricity, and i represents orbit inclination angle, Ω Right ascension of ascending node is represented, ω represents argument of perigee, and n represents satellite mean angular velocity,μ represents ground Heart gravitational constant, T represent the satellite orbit motion cycle.
Formula (41) is substituted into formula (42), the elliptical orbit half that any time under the influence of perturbative force is calculated is long Axle, elliptical orbit eccentricity, orbit inclination angle, the transient change of five orbital elements of right ascension of ascending node and argument of perigee Value；Reference picture 6, to consider that radar antenna phase center changes over time relation pair ratio to the oblique distance of point target before and after perturbative force Figure；As shown in Figure 6, it can be seen that the perturbative force that satellite is subject to can impact to the movement locus of satellite, therefore the present invention will The influence of perturbative force is taken into account in real time, improves precision.
Step 4, according to the position vector and k+1 moment radar antennas of point target under k+1 moment earth inertial IN coordinate systems Minimum distance moment t is calculated to the oblique distance vector of point target in phase center0B parameter, minimum distance moment t0B Parameter is the spaceborne radar imaging parameters real-time online estimated result based on Kalman filtering, is imaged for spaceborne radar, wherein The minimum distance moment be radar antenna phase center to point target oblique distance minimum when correspond at the time of.
Specifically, the important parameter in SAR imagings is the near distance spot of the radar antenna phase center to point target, It is designated as the minimum distance moment；According to the position vector of point target under k+1 moment earth inertial IN coordinate systemsWith the k+1 moment Oblique distance vector of the radar antenna phase center to point targetCalculate minimum distance PCA moment and B parameter, radar antenna Phase center to point target oblique distance minimum when correspond at the time of, now instantaneous Doppler is zero, and the minimum distance moment is generally fixed Justice is at the time of to be instantaneous Doppler be zero.
4.1B parameters are the B functions at minimum distance PCA moment, and the derivation of B functions is as follows：.
ByWithRelationUnderstand, radar antenna phase center is to point target in earth inertial coordinates system Oblique distance vectorIt can be written as：
Wherein,The position vector of point target under earth inertial coordinates system is represented,Represent to defend under earth inertial coordinates system The position vector of star.
Then radar antenna phase center is to the oblique distance of point target
T radar antenna phase center is to the oblique distance rate of change of point target
Wherein,Represent t radar antenna phase center to the oblique distance vector of point target, t radar antenna phase Oblique distance rate of change of the position center to point targetIt is that t radar antenna phase center is led to the oblique distance vector single order of point target Number, t represent time variable, and subscript T represents to ask transposition to operate.
T radar antenna phase center is to the oblique distance acceleration of point target
Wherein, oblique distance acceleration of the t radar antenna phase center to point targetIt is t radar antenna phase Center represents t radar antenna phase to the oblique distance vector second dervative of point target, the B functions of B (t) expression ts, R (t) Oblique distance of the center to point target.
4.2 define the B function B (t) of t：
Wherein,Represent t radar antenna phase center to point target oblique distance vector rate of change,When representing t Carve radar antenna phase center to point target oblique distance vector acceleration,Represent t radar antenna phase center to point The oblique distance rate of change of target.
The minimum distance moment is set as t', by the oblique distance rate of change of t radar antenna phase center to point target most Linearization approximate processing is closely carried out at moment t', obtains minimum distance moment t radar antenna phase center when being t' To the oblique distance vector first derivative of point target
PCA is calculated for convenience of using recursive algorithm, formula (48) can be converted into t' moment radar antenna phase centers to point The oblique distance vector first derivative of target
4.3 initialization：Make i represent ith iteration, make tiAt the time of after expression ith iteration, i initial value is 1, and t1 =0.
4.4 t at the time of be calculated after i+1 time iterationi+1,B(ti) represent tiThe B functions at moment, R (ti) represent tiMoment radar antenna phase center to point target oblique distance,Represent tiMoment radar Antenna phase center to point target oblique distance rate of change,Represent tiOblique distance of the moment radar antenna phase center to point target Acceleration.
If 4.5 tiOblique distance rate of change absolute value of the moment radar antenna phase center to point targetε is to appoint Anticipate small constant, ε ∈ [10-6,10-4], then make i value add 1, return to 4.4.
If tiOblique distance rate of change absolute value of the moment radar antenna phase center to point targetε is arbitrarily small Constant, ε ∈ [10-6,10-4], then iteration ends, and at the time of during by iteration stopping after corresponding i+1 time iteration, it is designated as PCA Moment t0；And then obtain minimum distance PCA moment t0B function B (t0)：
Wherein,Represent PCA moment t0Radar antenna phase center to point target oblique distance vector,Represent PCA Moment t0Radar antenna phase center to point target oblique distance vector rate of change,Represent PCA moment t0Radar antenna phase Oblique distance vector acceleration of the center to point target.
4.6 are understood by formula (50), it is necessary to which the parameter calculated includes PCA moment t0Radar antenna phase center arrives point target Oblique distance vectorPCA moment t0Oblique distance vector rate of change of the radar antenna phase center to point targetAnd minimum distance PCA moment t0Oblique distance vector acceleration of the radar antenna phase center to point targetIt obtains process：
Calculate the position vector rate of change of point target under t earth inertial IN coordinate systems
Wherein, under t earth inertial IN coordinate systems point target position vector rate of changeIt is t earth inertial The position vector first derivative of point target under IN coordinate systems：Φ (t) represents the latitude of t point target position, corresponding k+1 The latitude Φ (k+1) of moment point target position；Λ (t) represents the longitude of t point target position, when corresponding to k+1 The longitude Λ (k+1) of punctum target position；Represent the position vector change of satellite under t earth inertial coordinates system Rate, it is the position vector first derivative of satellite under t earth inertial coordinates system；Represent t radar antenna phase center It is oblique distance vector first derivative of the t radar antenna phase center to point target to the oblique distance vector rate of change of point target；D (t) t earth inertial IN coordinate system unit coordinate vector matrixs, corresponding k+1 moment earth inertial IN coordinate system units are represented Coordinate vector matrix D (k+1)；T earth inertial IN coordinate system unit coordinate vector matrix rates of change are represented,Table Show satellite orbit coordinate system around ZOSThe spin matrix rate of change obtained after rotation ω t radians, w represent earth rotation axis angular rate, t Represent time variable.
It is describedRepresent that t radar antenna phase center is to the oblique distance rate of change of point target, its expression formula：
Wherein,Represent t radar antenna phase center to point target oblique distance vector,Represent t radar Antenna phase center to point target oblique distance vector rate of change, R (t) represent t radar antenna phase center arrive point target Oblique distance.
4.7 are calculated the position vector acceleration of point target under t earth inertial IN coordinate systems
Wherein,The position vector acceleration of satellite under t earth inertial coordinates system is represented, is that the t earth is used to The position vector second dervative of satellite under property coordinate system；RNRepresent that point target represents the bias of elliptic orbit to the distance in the earth's core, e Rate,T earth inertial IN coordinate system unit coordinate vector matrix acceleration is represented,Represent t radar antenna phase Oblique distance vector acceleration of the position center to point target；θ represents radar antenna beam center pointing vectorWith substar Unit Vector AmountAngle, be designated as nadir angle.
Formula (54), which is arranged, can obtain t radar antenna phase center to the oblique distance vector acceleration of point targetFor：
4.8 by PCA moment t0Substitution formula (52), formula (53), formula (55), respectively obtain PCA moment t0In radar antenna phase Oblique distance vector of the heart to point targetPCA moment t0Oblique distance vector rate of change of the radar antenna phase center to point targetPCA moment t0Oblique distance vector acceleration of the radar antenna phase center to point target
Wherein, R represents radar antenna phase center to the oblique distance of point target, D (t0) represent PCA moment t0Earth inertial IN Coordinate system unit coordinate vector matrix,Represent minimum distance PCA moment t0Oblique distance of the radar antenna phase center to point target Rate of change, Represent minimum distance PCA moment t0Oblique distance of the radar antenna phase center to point target Vector,Represent minimum distance PCA moment t0Radar antenna phase center is to the oblique distance vector rate of change of point target, R (t0) table Show minimum distance PCA moment t0Radar antenna phase center to point target oblique distance,Represent minimum distance PCA moment t0Ground Ball inertia IN coordinate system unit coordinate vector matrix rates of change,Represent satellite orbit coordinate system around ZOSRotate ω t0Radian The spin matrix rate of change obtained afterwards,Represent satellite orbit coordinate system around ZOSRotate ω t0The spin moment obtained after radian Battle array acceleration, w represent earth rotation axis angular rate, t0Represent minimum distance PCA moment, Φ (t0) represent the minimum distance PCA moment t0The latitude of point target position, Λ (t0) represent minimum distance PCA moment t0The longitude of point target position, RNRepresent Point target to the earth's core distance,Represent PCA moment t0The position vector rate of change of satellite under earth inertial coordinates system,Represent PCA moment t0The position vector acceleration of satellite under earth inertial coordinates system.
Formula (56), formula (57) and formula (58) are substituted into after formula (50) to the result being calculated, are designated as B parameter, the B parameter For the spaceborne radar imaging parameters real-time online estimated result based on Kalman filtering, wherein B parameter and minimum distance PCA moment t0For spaceborne radar imaging parameters, the minimum distance moment is corresponding when being radar antenna phase center to the oblique distance minimum of point target Moment；Reference picture 7, the B parameter to be obtained using the inventive method change over time result figure, and transverse axis is the time, and the longitudinal axis is
Embodiments of the invention are the foregoing is only, are not intended to limit the scope of the invention, it is every to utilize this hair The equivalent structure or equivalent flow conversion that bright specification and accompanying drawing content are made, or directly or indirectly it is used in other related skills Art field, is included within the scope of the present invention.

Claims (6)

  1. A kind of 1. spaceborne radar imaging parameters real-time online method of estimation based on Kalman filtering, it is characterised in that including with Lower step：
    Step 1, earth inertial coordinates system, earth fixed coordinate system, satellite orbit coordinate system, satellite flight path coordinate are established respectively System, satellite fixed coordinate system, respectively obtain the transformational relation of earth fixed coordinate system and earth inertial coordinates system, satellite orbit is sat The transformational relation, satellite flight path axis system and the transformational relation of earth inertial coordinates system of mark system and earth inertial coordinates system；
    Step 2, the measurement equation of the satellitosis at k moment is established, and carries out Kalman filtering, and then the k+1 moment is calculated Position vector of the satellite in earth inertial coordinates system；Wherein, k represents time variable, and k is positive integer；
    Step 3, radar antenna beam center pointing vector is determined, and by radar antenna beam center pointing vector and earth surface Intersection point be designated as point target, according to position vector of the k+1 moment satellite in earth inertial coordinates system, the k+1 moment is calculated Oblique distance vector of the radar antenna phase center to point target；
    Step 4, according to the oblique distance vector of k+1 moment radar antenna phase centers to point target, minimum distance is calculated respectively Moment t0And B parameter, the B parameter are the spaceborne radar imaging parameters real-time online estimated result based on Kalman filtering, its Middle B parameter and minimum distance moment t0For spaceborne radar imaging parameters, the minimum distance moment is radar antenna phase center to point At the time of correspondence during the oblique distance minimum of target.
  2. 2. a kind of spaceborne radar imaging parameters real-time online method of estimation based on Kalman filtering as claimed in claim 1, Characterized in that, in step 1, the earth inertial coordinates system, earth fixed coordinate system, satellite orbit coordinate system, satellite boat Mark coordinate system, satellite fixed coordinate system, it is established process and is：
    X-axis is X in earth inertial coordinates systemIN, Y-axis is Y in earth inertial coordinates systemIN, Z axis is Z in earth inertial coordinates systemIN, Earth inertial coordinates system is using the earth's core O as origin, XIN YINPlane overlaps with earth equatorial plane, XINPoint to the first point of Aries, ZINPoint to The earth arctic, YINBy XINAnd ZINDetermined by right-hand rule；
    X-axis is X in earth fixed coordinate systemEF, Y-axis is Y in earth fixed coordinate systemEF, Z axis is Z in earth fixed coordinate systemEF, Earth fixed coordinate system is fixed on the earth, and using the earth's core O as origin, XEFIntersected by the equatorial plane with Greenwich meridian, ZEFWith ZINOverlap, YEFBy XEFAnd ZEFDetermined by right-hand rule；Earth fixed coordinate system with earth's axis angular velocity omega around ZEFRotation, when the earth is using earth rotation axis angular rate w rotation time t, the X-axis of earth fixed coordinate system is X'EF, when the earth with The Y-axis of earth fixed coordinate system is Y during earth rotation axis angular rate w rotation time tE'F, when the earth is with earth rotation axis angular rate The Z axis of earth fixed coordinate system is Z' during w rotation time tEF；
    X-axis is X in satellite orbit coordinate systemOS, Y-axis is Y in satellite orbit coordinate systemOS, Z axis is Z in satellite orbit coordinate systemOS, Satellite orbit coordinate system is using the earth's core O as origin, XOSPoint to perigee, YOSThe vertical X in satellite orbit faceOS, ZOSBy XOSAnd YOS Determined by right-hand rule；Wherein, satellite orbit face is plane where the running track of satellite, and wherein perigee is Earth's orbit In face with the nearest point of the earth；
    X-axis is X in satellite flight path axis systemTS, Y-axis is Y in satellite flight path axis systemTS, Z axis is Z in satellite flight path axis systemTS, The direction of satellite is pointed to as Z in the earth's core by satellite flight path axis system using centroid of satellite as originTSSensing, by ZTSSensing It is designated as zenith direction, XTSIt is orthogonal to ZTSThe plane formed with satellite velocity vector, YTSBy XTSAnd ZTSDetermined by right-hand rule；
    The intersection point of satellite orbit and equatorial plane when satellite to be passed through to equator from south to north, is designated as ascending node；By the Spring Equinox in the equatorial plane Point is designated as right ascension of ascending node Ω to the earth's core angle corresponding to ascending node line；The normal in satellite orbit face and equatorial plane method The angle of line, inclination of satellite orbit i is designated as, is expressed as ZINWith ZOSAngle；Satellite is run to closely in orbital plane by ascending node The earth's core angle corresponding to the track in place, is designated as argument of perigee ω.
  3. 3. a kind of spaceborne radar imaging parameters real-time online method of estimation based on Kalman filtering as claimed in claim 2, Characterized in that, in step 1, the earth fixed coordinate system and transformational relation, the satellite orbit of earth inertial coordinates system are sat Mark system and the transformational relation in earth inertial coordinates system, satellite flight path axis system and the transformational relation of earth inertial coordinates system, point It is not：
    When the earth is with earth rotation axis angular rate w rotation time t, the conversion of earth fixed coordinate system to earth inertial coordinates system is closed It is to be：
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    Wherein, XINRepresent X-axis in earth inertial coordinates system, YINRepresent Y-axis in earth inertial coordinates system, ZINRepresent earth inertial Z axis in coordinate system, XEFRepresent X-axis in earth fixed coordinate system, YEFRepresent Y-axis in earth fixed coordinate system, ZEFRepresent that the earth is consolidated Z axis in position fixing system, Ω represent right ascension of ascending node, and cos represents cosine function, and sin represents SIN function, and t represents time variable, W represents earth rotation axis angular rate；DZ(Ω+wt) represents Z in earth fixed coordinate systemEFThe rotation obtained after rotation Ω+ω t radians Torque battle array, its expression formula are：
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    It is to the transformational relation of earth inertial coordinates system by satellite orbit coordinate system：
    <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>X</mi> <mrow> <mi>I</mi> <mi>N</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>Y</mi> <mrow> <mi>I</mi> <mi>N</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mi>N</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>cos</mi> <mi>&amp;Omega;</mi> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mi>sin</mi> <mi>&amp;Omega;</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>sin</mi> <mi>&amp;Omega;</mi> </mrow> </mtd> <mtd> <mrow> <mi>cos</mi> <mi>&amp;Omega;</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>cos</mi> <mi> </mi> <mi>i</mi> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mi>sin</mi> <mi> </mi> <mi>i</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>sin</mi> <mi> </mi> <mi>i</mi> </mrow> </mtd> <mtd> <mrow> <mi>cos</mi> <mi> </mi> <mi>i</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>cos</mi> <mi> </mi> <mi>u</mi> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mi>sin</mi> <mi> </mi> <mi>u</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>sin</mi> <mi> </mi> <mi>u</mi> </mrow> </mtd> <mtd> <mrow> <mi>cos</mi> <mi> </mi> <mi>u</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>X</mi> <mrow> <mi>O</mi> <mi>S</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>Y</mi> <mrow> <mi>O</mi> <mi>S</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>Z</mi> <mrow> <mi>O</mi> <mi>S</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>D</mi> <mi>Z</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;Omega;</mi> <mo>)</mo> </mrow> <msub> <mi>D</mi> <mi>X</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <msub> <mi>D</mi> <mi>Z</mi> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>X</mi> <mrow> <mi>O</mi> <mi>S</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>Y</mi> <mrow> <mi>O</mi> <mi>S</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>Z</mi> <mrow> <mi>O</mi> <mi>S</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> </mtable> </mfenced>
    Wherein, XOSRepresent X-axis in satellite orbit coordinate system, YOSRepresent Y-axis coordinate in satellite orbit coordinate system, ZOSRepresent satellite Z axis in orbital coordinate system, DZ(u) represent satellite orbit coordinate system around ZOSThe spin matrix obtained after rotation u radians, DZ(Ω) table Show satellite orbit coordinate system around ZOSThe spin matrix obtained after rotation Ω radians, DX(i) represent satellite orbit coordinate system around XOSRotation Turn the spin matrix obtained after i radians, Ω represents right ascension of ascending node, and i represents inclination of satellite orbit orbit inclination angle, and u represents satellite Track argument, it is defined as satellite in satellite orbit face and is pressed from both sides from ascending node to the earth's core corresponding to the movement locus of satellite real time position Angle；
    The transformational relation that satellite flight path axis system is transformed into earth inertial coordinates system is：
    <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>X</mi> <mrow> <mi>I</mi> <mi>N</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>Y</mi> <mrow> <mi>I</mi> <mi>N</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mi>N</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mi>D</mi> <mo>&amp;CenterDot;</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>X</mi> <mrow> <mi>T</mi> <mi>S</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>Y</mi> <mrow> <mi>T</mi> <mi>S</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>Z</mi> <mrow> <mi>T</mi> <mi>S</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow>
    Wherein, XTSRepresent X-axis in satellite flight path axis system, YTSRepresent Y-axis in satellite flight path axis system, ZTSRepresent satellite flight path Z axis in coordinate system, D represent earth inertial coordinates system unit coordinate vector matrix, and
    <mrow> <mi>D</mi> <mo>=</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <msub> <mover> <mi>e</mi> <mo>&amp;RightArrow;</mo> </mover> <mi>x</mi> </msub> <mo>,</mo> <msub> <mover> <mi>e</mi> <mo>&amp;RightArrow;</mo> </mover> <mi>y</mi> </msub> <mo>,</mo> <msub> <mover> <mi>e</mi> <mo>&amp;RightArrow;</mo> </mover> <mi>z</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>I</mi> <mi>N</mi> </mrow> </msub> <mo>=</mo> <mo>&amp;lsqb;</mo> <msub> <mover> <mi>n</mi> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mn>0</mn> <mi>I</mi> <mi>N</mi> </mrow> </msub> <mo>&amp;times;</mo> <msub> <mover> <mi>e</mi> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mi>v</mi> <mi>I</mi> <mi>N</mi> </mrow> </msub> <mo>,</mo> <mrow> <mo>(</mo> <msub> <mover> <mi>n</mi> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mn>0</mn> <mi>I</mi> <mi>N</mi> </mrow> </msub> <mo>&amp;times;</mo> <msub> <mover> <mi>e</mi> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mi>v</mi> <mi>I</mi> <mi>N</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <msub> <mover> <mi>n</mi> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mn>0</mn> <mi>I</mi> <mi>N</mi> </mrow> </msub> <mo>,</mo> <mo>-</mo> <msub> <mover> <mi>n</mi> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mn>0</mn> <mi>I</mi> <mi>N</mi> </mrow> </msub> <mo>&amp;rsqb;</mo> </mrow>
    Wherein,Represent X-axis X in satellite flight path axis systemTSUnit vector,Represent Y-axis Y in satellite flight path axis systemTSList Bit vector,Represent Z axis Z in satellite flight path axis systemTSUnit vector,Represent earth inertial coordinates system Satellite unit Velocity.
  4. 4. a kind of spaceborne radar imaging parameters real-time online method of estimation based on Kalman filtering as claimed in claim 3, Characterized in that, in step 2, the measurement equation of the satellitosis at the k moment is h (x (k))：
    H (x (k))=x (k)-esinx (k)；Wherein, x (k) represents the satellitosis at k moment, the inclined near point of corresponding t satellite Angle E (t)；E represents the eccentricity of elliptic orbit,
    Position vector of the k+1 moment satellite in earth inertial coordinates system, it obtains process and is：
    2.1 establish equation group：
    <mrow> <msup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>-</mo> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>+</mo> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <mn>2</mn> <mi>&amp;pi;</mi> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mi>&amp;Delta;</mi> <mi>T</mi> </mrow> <mi>T</mi> </mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <mi>e</mi> <mi> </mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <msup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>+</mo> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mn>1</mn> <mo>-</mo> <mi>e</mi> <mi> </mi> <mi>cos</mi> <msup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>+</mo> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow>
    <mrow> <msup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>+</mo> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>-</mo> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>+</mo> <mi>K</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;lsqb;</mo> <mi>y</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mi>h</mi> <mrow> <mo>(</mo> <msup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>-</mo> </msup> <mo>(</mo> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow>
    K (k+1)=cP-(k+1)·[c2·P-(k+1)+V]-1
    P-(k+1)=a2·P+(k)+W
    P+(k+1)=P-(k+1)-K(k+1)·c·P-(k+1)
    <mrow> <mi>a</mi> <mo>=</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <msub> <mo>|</mo> <mrow> <msup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>+</mo> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mn>2</mn> <mi>&amp;pi;</mi> <mfrac> <mrow> <mi>&amp;Delta;</mi> <mi>T</mi> </mrow> <mi>T</mi> </mfrac> <mo>&amp;CenterDot;</mo> <mi>e</mi> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <msup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>+</mo> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>e</mi> <mo>&amp;CenterDot;</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <msup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>+</mo> </msup> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> </mrow>
    <mrow> <mi>c</mi> <mo>=</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>h</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <msub> <mo>|</mo> <mrow> <msup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>-</mo> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mi>e</mi> <mo>&amp;CenterDot;</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <msup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>-</mo> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    Wherein,Represent the eccentric anomaly priori estimates of k+1 moment satellites, g (x+(k) the inclined of k moment satellites) is represented Anomaly posterior estimateObservational equation,Represent the eccentric anomaly posterior estimate of k moment satellites, P+(k) table Show the eccentric anomaly posterior estimate of k moment satellitesMean square error, W represent to wkAsk the interference obtained after mathematic expectaion Covariance matrix, K (k+1) represent the gain matrix of k+1 moment satellites, corresponding k+1 moment Kalman filter gains；P-(k+ 1) the eccentric anomaly priori estimates of k+1 moment satellites are representedMean square error, V represents observation to k moment satellites Noise vkThe observation noise covariance matrix obtained after mathematic expectaion is sought,After the eccentric anomaly for representing k+1 moment satellites Estimate is tested, y (k+1) represents the measurement equation of k+1 moment satellites, P+(k+1) the eccentric anomaly posteriority of k+1 moment satellites is represented EstimateMean square error,Represent the eccentric anomaly priori estimates of k+1 moment satellites Measurement equation；
    Above-mentioned equation group is solved, and then the eccentric anomaly posterior estimate of k+1 moment satellites is calculatedIt is to k+1 The satellitosis x (k+1) at moment optimal estimation, and using the satellite eccentric anomaly posterior estimate of k+1 moment satellites as k+1 The eccentric anomaly E (k+1) of moment satellite；
    2.2 are calculated the true anomaly f (k+1) of k+1 moment satellites：
    <mrow> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>e</mi> </mrow> <mrow> <mn>1</mn> <mo>-</mo> <mi>e</mi> </mrow> </mfrac> </msqrt> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mfrac> <mrow> <mi>E</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </mfrac> <mo>;</mo> </mrow>
    2.3 are calculated the satellite at k+1 moment with respect to the earth's core immediate movement r (k+1)：
    <mrow> <mi>r</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>a</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mi>e</mi> <mi> </mi> <mi>cos</mi> <mi> </mi> <mi>f</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow>
    And then obtain coordinate of the k+1 moment satellite in satellite orbit coordinate systemFor：
    <mrow> <msub> <mover> <mi>s</mi> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mi>O</mi> <mi>S</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>X</mi> <mrow> <mi>O</mi> <mi>S</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Y</mi> <mrow> <mi>O</mi> <mi>S</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Z</mi> <mrow> <mi>O</mi> <mi>S</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>r</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>cos</mi> <mi> </mi> <mi>f</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>r</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>sin</mi> <mi> </mi> <mi>f</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mi>a</mi> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>cos</mi> <mrow> <mo>(</mo> <mi>E</mi> <mo>(</mo> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>-</mo> <mi>e</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msqrt> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mn>2</mn> </msup> </mrow> </msqrt> <mi>sin</mi> <mrow> <mo>(</mo> <mi>E</mi> <mo>(</mo> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mrow>
    Wherein, a represents the semi-major axis of elliptic orbit, and e represents the eccentricity of elliptic orbit, XOS(k+1) k+1 moment satellite rails are represented X-axis in road coordinate system, YOS(k+1) Y-axis coordinate in k+1 moment satellite orbit coordinate systems, Z are representedOS(k+1) represent that the k+1 moment is defended Z axis in star orbital coordinate system；
    By coordinate of the k+1 moment satellite in satellite orbit coordinate systemTransform in earth inertial coordinates system, obtain k+ Position vector of the 1 moment satellite in earth inertial coordinates system
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>s</mi> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mi>I</mi> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>X</mi> <mrow> <mi>I</mi> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Y</mi> <mrow> <mi>I</mi> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Z</mi> <mrow> <mi>I</mi> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <msub> <mi>D</mi> <mi>Z</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;Omega;</mi> <mo>)</mo> </mrow> <msub> <mi>D</mi> <mi>X</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <msub> <mi>D</mi> <mi>Z</mi> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>X</mi> <mrow> <mi>O</mi> <mi>S</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Y</mi> <mrow> <mi>O</mi> <mi>S</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Z</mi> <mrow> <mi>O</mi> <mi>S</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>D</mi> <mi>Z</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;Omega;</mi> <mo>)</mo> </mrow> <msub> <mi>D</mi> <mi>X</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <msub> <mi>D</mi> <mi>Z</mi> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>r</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>cos</mi> <mi> </mi> <mi>f</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>r</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>sin</mi> <mi> </mi> <mi>f</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> </mtable> <mo>.</mo> </mrow>
  5. 5. a kind of spaceborne radar imaging parameters real-time online method of estimation based on Kalman filtering as claimed in claim 4, Characterized in that, in step 3, the oblique distance vector of the k+1 moment radar antenna phase center to point target, its process is：
    Set the unknown state vector at k moment
    <mrow> <mover> <mi>m</mi> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>m</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>m</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>m</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>&amp;Phi;</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&amp;Lambda;</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
    Wherein, m1(k) the 1st element in the unknown state vector at k moment, the latitude of corresponding k moment point targets position are represented Spend Φ (k)；m2(k) the 2nd element in the unknown state vector at k moment, the warp of corresponding k moment point targets position are represented Spend Λ (k)；m3(k) the 3rd element in the unknown state vector at k moment is represented, corresponding k moment radar antenna phase centers arrive The oblique distance R (k) of point target；Φ (k) represents the latitude of k moment point targets position, and Λ (k) is represented where k moment point target The longitude of position, R (k) represent k moment radar antenna phase centers to the oblique distance of point target；
    The unknown state vector at k+1 moment is designated as qkRepresent k moment satellites in ellipse What the latitude that track motion time does not correspond to point target position was subject to disturb, the longitude of corresponding point target position by Disturb, the interference that corresponding radar antenna phase center is subject to the oblique distance of point target；It will be defended under t earth inertial coordinates system The position vector of star is designated as
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>s</mi> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mi>I</mi> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mover> <mi>x</mi> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mi>I</mi> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>R</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>D</mi> <mo>&amp;CenterDot;</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>D</mi> <mi>z</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mi>k</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mo>&amp;CenterDot;</mo> <mi>cos</mi> <mi>&amp;Phi;</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>cos</mi> <mi>&amp;Lambda;</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mo>&amp;CenterDot;</mo> <mi>cos</mi> <mi>&amp;Phi;</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>sin</mi> <mi>&amp;Lambda;</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>sin</mi> <mi>&amp;Phi;</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mi>R</mi> <mo>&amp;CenterDot;</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mover> <mi>d</mi> <mo>&amp;RightArrow;</mo> </mover> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mover> <mi>d</mi> <mo>&amp;RightArrow;</mo> </mover> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mover> <mi>d</mi> <mo>&amp;RightArrow;</mo> </mover> <mn>3</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>&amp;CenterDot;</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>D</mi> <mi>z</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mi>k</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mo>&amp;CenterDot;</mo> <mi>cos</mi> <mi> </mi> <msub> <mi>m</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>cos</mi> <mi> </mi> <msub> <mi>m</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mo>&amp;CenterDot;</mo> <mi>cos</mi> <mi> </mi> <msub> <mi>m</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>sin</mi> <mi> </mi> <msub> <mi>m</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>sin</mi> <mi> </mi> <msub> <mi>m</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mi>R</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;lsqb;</mo> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <msub> <mover> <mi>d</mi> <mo>&amp;RightArrow;</mo> </mover> <mn>1</mn> </msub> <mo>-</mo> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <msub> <mover> <mi>d</mi> <mo>&amp;RightArrow;</mo> </mover> <mn>3</mn> </msub> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mo>&amp;lsqb;</mo> <msub> <mi>D</mi> <mi>z</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mi>k</mi> <mo>)</mo> </mrow> <mo>|</mo> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <msub> <mover> <mi>d</mi> <mo>&amp;RightArrow;</mo> </mover> <mn>3</mn> </msub> <mo>-</mo> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <msub> <mover> <mi>d</mi> <mo>&amp;RightArrow;</mo> </mover> <mn>1</mn> </msub> <mo>&amp;rsqb;</mo> <mo>&amp;CenterDot;</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mi>cos</mi> <mi> </mi> <msub> <mi>m</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>cos</mi> <mi> </mi> <msub> <mi>m</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mi>cos</mi> <mi> </mi> <msub> <mi>m</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>sin</mi> <mi> </mi> <msub> <mi>m</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>sin</mi> <mi> </mi> <msub> <mi>m</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>m</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mi>C</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>f</mi> <mrow> <mo>(</mo> <mover> <mi>m</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>34</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mover> <mi>m</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>y</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>y</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>y</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>y</mi> <mn>4</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mi>cos</mi> <mi> </mi> <msub> <mi>m</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>cos</mi> <mi> </mi> <msub> <mi>m</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mi>cos</mi> <mi> </mi> <msub> <mi>m</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>sin</mi> <mi> </mi> <msub> <mi>m</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>sin</mi> <mi> </mi> <msub> <mi>m</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>m</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
    Wherein, Represent point target under k moment earth inertial coordinates system Position vector, D represents earth inertial coordinates systems unit coordinate vector matrix, and R represents radar antenna phase center to point target Oblique distance, y1(k) position vector of expression k moment satellites X-axis coordinate, y in earth inertial coordinates system2(k) represent that the k moment is defended The position vector of star Y-axis coordinate, y in earth inertial coordinates system3(k) represent the position vector of k moment satellites in earth inertial Z axis coordinate in coordinate system, y4(k) represent k moment radar antenna phase centers to the oblique distance of point target, Dz(ω k) represents satellite rail Road coordinate system is around ZOSThe spin matrix obtained after rotation ω t radians, w represent earth rotation axis angular rate, and k represents time variable,Represent in earth inertial coordinates systems radar antenna phase center to the oblique distance vector of point target, RNRepresent that point target arrives the earth's core Distance；
    The measurement equation at k moment is：
    Wherein, Represent satellite under k moment earth inertial coordinates system Position vector, jkRepresent that k moment satellite corresponds to position where the LATITUDE OBSERVATIONS noise of point target position, corresponding point target respectively Longitude observation noise, the oblique distance observation noise of corresponding radar antenna phase center to point target put；
    Kalman filtering is carried out to the measurement equation at k moment, obtains equation below group：
    <mrow> <msup> <mover> <mover> <mi>m</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>^</mo> </mover> <mo>-</mo> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mover> <mover> <mi>m</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>^</mo> </mover> <mo>+</mo> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow>
    <mrow> <msup> <mover> <mover> <mi>m</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>^</mo> </mover> <mo>+</mo> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mover> <mover> <mi>m</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>^</mo> </mover> <mo>-</mo> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>+</mo> <mi>K</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mo>&amp;lsqb;</mo> <msup> <mi>y</mi> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mi>C</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>f</mi> <mrow> <mo>(</mo> <msup> <mover> <mover> <mi>m</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>^</mo> </mover> <mo>-</mo> </msup> <mo>(</mo> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow>
    K (k+1)=P-(k+1)·HT[H·P-(k+1)HT+J]-1
    P-(k+1)=P+(k)+Q
    P+(k+1)=P-(k+1)-K(k+1)·H·P-(k+1)
    <mrow> <mi>H</mi> <mo>=</mo> <mi>C</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mi>d</mi> <mi>f</mi> <mrow> <mo>(</mo> <mover> <mi>m</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mover> <mi>m</mi> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <msub> <mo>|</mo> <mrow> <msup> <mover> <mover> <mi>m</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>^</mo> </mover> <mo>-</mo> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> </mrow>
    <mrow> <mi>f</mi> <mrow> <mo>(</mo> <msup> <mover> <mover> <mi>m</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>^</mo> </mover> <mo>-</mo> </msup> <mo>(</mo> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mi>c</mi> <mi>o</mi> <mi>s</mi> <msubsup> <mover> <mover> <mi>m</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>^</mo> </mover> <mn>1</mn> <mo>-</mo> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <msubsup> <mover> <mover> <mi>m</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>^</mo> </mover> <mn>2</mn> <mo>-</mo> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mi>c</mi> <mi>o</mi> <mi>s</mi> <msubsup> <mover> <mover> <mi>m</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>^</mo> </mover> <mn>1</mn> <mo>-</mo> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <msubsup> <mover> <mover> <mi>m</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>^</mo> </mover> <mn>2</mn> <mo>-</mo> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <msubsup> <mover> <mover> <mi>m</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>^</mo> </mover> <mn>1</mn> <mo>-</mo> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mover> <mover> <mi>m</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>^</mo> </mover> <mn>3</mn> <mo>-</mo> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
    Wherein,Represent the unknown state vector at k+1 momentPrior estimate vector, including k+1 moment pair The latitude of point target position, the longitude of point target position, the elder generation of radar antenna phase center to the oblique distance of point target Test estimation；Represent the k moment to the latitude of point target position, the longitude of point target position, radar antenna phase Center is to the Posterior estimator of the oblique distance of point target, y'(k+1) measurement equation at k+1 moment is represented,Represent the t earth The position vector of satellite, P under inertial coodinate system-(k+1) representMean square error, H representObservation square Battle array；P+(k) representMean square error, K (k+1) represents the gain matrix of k+1 moment satellites, corresponding k+1 moment Kalmans Filter gain；The unknown state vector at k moment is represented, Q is represented to qkSeek the interference covariance obtained after mathematic expectaion Matrix, J are represented to jkSeek the observation noise covariance matrix obtained after mathematic expectaion；Represent the unknown shape at k+1 moment State vectorPrior estimate vectorIn the 1st element, the latitude of corresponding k+1 moment point targets position Spend prior estimate；Represent the unknown state vector at k+1 momentPrior estimate vectorIn 2nd element, the longitude prior estimate of corresponding k moment point targets position；Represent the unknown state at k+1 moment VectorPrior estimate vectorIn the 3rd element, corresponding k+1 moment radar antenna phase centers to point The oblique distance prior estimate of target；RNRepresent that point target represents the eccentricity of elliptic orbit to the distance in the earth's core, e；
    By equation group, the unknown state vector at k+1 moment is calculatedPosterior estimator vectorIncluding The k+1 moment arrives point target to the latitude of point target position, the longitude of point target position, radar antenna phase center The Posterior estimator of oblique distance；The unknown state vector at the k+1 momentPosterior estimator vectorIt is to k+1 The unknown state vector at momentOptimal estimation, and then obtain the latitude Φ (k+ of k+1 moment point targets position 1), the longitude Λ (k+1) of k+1 moment point targets position, the oblique distance R of k+1 moment radar antenna phase centers to point target (k+1)；
    Then the position vector of point target under k+1 moment earth inertial coordinates system is calculated
    <mrow> <msub> <mover> <mi>x</mi> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mi>I</mi> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>D</mi> <mi>z</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mo>(</mo> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mo>&amp;CenterDot;</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;Phi;</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>cos</mi> <mi>&amp;Lambda;</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mo>&amp;CenterDot;</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;Phi;</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>sin</mi> <mi>&amp;Lambda;</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>sin</mi> <mi>&amp;Phi;</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
    And then k+1 moment radar antenna phase centers are obtained to the oblique distance vector of point target
    <mrow> <mover> <mi>R</mi> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mi>R</mi> <mo>&amp;CenterDot;</mo> <mi>D</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow>
  6. 6. a kind of spaceborne radar imaging parameters real-time online method of estimation based on Kalman filtering as claimed in claim 5, Characterized in that, in step 4, minimum distance moment t0B parameter, it obtains process and is：
    4.1 define the B function B (t) of t：Wherein,Represent t thunder Up to antenna phase center to the oblique distance vector rate of change of point target,Represent t radar antenna phase center to point target Oblique distance vector acceleration,Represent t radar antenna phase center to the oblique distance rate of change of point target；
    Initialization：Make i represent ith iteration, make tiAt the time of after expression ith iteration, i initial value is 1, and t1=0；
    4.2 t at the time of be calculated after i+1 time iterationi+1,B(ti) represent tiWhen The B functions at quarter, R (ti) represent tiMoment radar antenna phase center to point target oblique distance,Represent tiMoment radar antenna Phase center to point target oblique distance rate of change,Represent tiMoment radar antenna phase center accelerates to the oblique distance of point target Degree；
    If 4.3 tiOblique distance rate of change absolute value of the moment radar antenna phase center to point targetε is arbitrarily small Constant, ε ∈ [10-6,10-4], then make i value add 1, return to 4.2；
    If tiOblique distance rate of change absolute value of the moment radar antenna phase center to point targetε is arbitrarily small normal Number, ε ∈ [10-6,10-4], then iteration ends, and at the time of during by iteration stopping after corresponding i+1 time iteration, be designated as recently Apart from moment t0；And then B parameter is calculated, it is designated as B (t0)：
    <mrow> <mi>B</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mover> <mover> <mi>R</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mover> <mover> <mi>R</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mover> <mi>R</mi> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mover> <mover> <mi>R</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow>
    <mrow> <mover> <mi>R</mi> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mi>R</mi> <mo>&amp;CenterDot;</mo> <mi>D</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
    <mrow> <mover> <mover> <mi>R</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mover> <mi>R</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>D</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <mi>R</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mover> <mi>D</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <msub> <mover> <mi>D</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>z</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;omega;t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mo>&amp;CenterDot;</mo> <mi>cos</mi> <mi>&amp;Phi;</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>cos</mi> <mi>&amp;Lambda;</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mo>&amp;CenterDot;</mo> <mi>cos</mi> <mi>&amp;Phi;</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>sin</mi> <mi>&amp;Lambda;</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>sin</mi> <mi>&amp;Phi;</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <msub> <mover> <mover> <mi>s</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow>
    <mrow> <mover> <mover> <mi>R</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mover> <mi>D</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mi>z</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;omega;t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mo>&amp;CenterDot;</mo> <mi>cos</mi> <mi>&amp;Phi;</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;Lambda;</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mo>&amp;CenterDot;</mo> <mi>cos</mi> <mi>&amp;Phi;</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>sin</mi> <mi>&amp;Lambda;</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>sin</mi> <mi>&amp;Phi;</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <msub> <mover> <mover> <mi>s</mi> <mo>&amp;RightArrow;</mo> </mover> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mrow> <mi>I</mi> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow>
    Wherein, R represents radar antenna phase center to the oblique distance of point target, D (t0) represent minimum distance moment t0Earth inertial IN Coordinate system unit coordinate vector matrix,Represent minimum distance moment t0Radar antenna phase center becomes to the oblique distance of point target Rate, Represent minimum distance moment t0Radar antenna phase center to point target oblique distance vector,Represent minimum distance moment t0Radar antenna phase center is to the oblique distance vector rate of change of point target, R (t0) represent most low coverage From moment t0Radar antenna phase center to point target oblique distance,Represent minimum distance moment t0Earth inertial coordinates system is single Position coordinate vector matrix rate of change,Represent satellite orbit coordinate system around ZOSRotate ω t0The spin matrix obtained after radian Rate of change,Represent satellite orbit coordinate system around ZOSRotate ω t0The spin matrix acceleration obtained after radian, w represent ground Revolutions axis angular rate, t0Represent minimum distance moment, Φ (t0) represent minimum distance moment t0The latitude of point target position Degree, Λ (t0) represent minimum distance moment t0The longitude of point target position, RNRepresent point target to the earth's core distance, Represent minimum distance moment t0The position vector rate of change of satellite under earth inertial coordinates system,Represent minimum distance moment t0 The position vector acceleration of satellite under earth inertial coordinates system.
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