CN114462256B - Method, device, equipment and medium for determining non-cooperative low-thrust maneuvering target track - Google Patents
Method, device, equipment and medium for determining non-cooperative low-thrust maneuvering target track Download PDFInfo
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Abstract
The application relates to a method, a device, computer equipment and a storage medium for determining a non-cooperative low-thrust maneuvering target track. The method comprises the following steps: the orbit determination method for the thrust acceleration modeling of the tracked non-cooperative target local orbit coordinate system is provided, an expansion state quantity transfer matrix calculation equation containing an acceleration component under a high-precision perturbation orbit model is deduced, orbit improvement is carried out on the non-cooperative small-thrust maneuvering target through radar observation data and a least square method, and finally orbit prediction is carried out through the determined expansion state quantity, so that the orbit determination of the non-cooperative target of continuous small-thrust maneuvering can be effectively carried out, and the method can be used for solving the problem of the orbit determination of the continuous small-thrust maneuvering of the non-cooperative satellite in a climbing or descending section.
Description
Technical Field
The application relates to the field of space situation perception, in particular to a method, a device, computer equipment and a storage medium for determining a non-cooperative low-thrust maneuvering target orbit of acceleration modeling under a local orbital system.
Background
The precise orbit determination and the high-precision orbit extrapolation of the non-cooperative maneuvering target have important significance on space situation perception tasks such as target cataloging, collision early warning and the like.
The star-chain satellite implements continuous small-thrust maneuvering, but the maneuvering strategy is unknown due to non-cooperation of the target, so that the thrust acceleration of the satellite is difficult to accurately model. The kinetic equation of the absolute orbital motion of the space target is generally described in a J2000 geocentric inertial system; however, in practical mission, in order to save energy, the orbit maneuver of the spacecraft is generally along the orbit trajectory or normal direction; because the spacecraft rotates around the earth and the direction vector of the tracking or normal maneuver in the inertial system also changes in a rotating way, the thrust acceleration vector is directly described in the inertial system, and a converged orbit improvement solution is difficult to obtain through state topology and least square estimation; therefore, the prior art is difficult to realize maneuvering section orbit determination and extrapolation prediction of the non-cooperative low-thrust maneuvering satellite.
Disclosure of Invention
In view of the above, there is a need to provide a method, an apparatus, a computer device and a storage medium for determining a non-cooperative low-thrust maneuvering target trajectory for acceleration modeling under a local track system, so as to improve the improvement and extrapolation effect of the low-thrust maneuvering target trajectory.
A method of non-cooperative low thrust maneuver target trajectory determination, the method comprising:
extracting station coordinates from observation data of a plurality of arc sections of a ground radar, and determining a radar observation vector of a tracked non-cooperative low-thrust maneuvering target according to the station coordinates; the radar observation vector comprises observation values of a plurality of radar observation data to the non-cooperative small-thrust maneuvering target at the moment;
determining the orbit state of the non-cooperative low-thrust maneuvering target at a first moment according to a cataloging database or the radar observation vector; the orbital state comprises a position vector and a velocity vector of the non-cooperative low-thrust maneuver target at a first time;
constructing an expansion state quantity for describing a non-cooperative low-thrust maneuvering target motion system, and constructing a track dynamics model of the non-cooperative low-thrust maneuvering target according to the expansion state quantity; the expansion state quantity comprises a position vector and a velocity vector under a geocentric inertial system and an acceleration vector under a local orbit coordinate system;
performing partial derivative solving on the expanded state quantity by a right function in the orbit dynamics model to obtain a partial derivative matrix, and determining a first-order state transition matrix formula of the expanded state quantity according to the partial derivative matrix;
according to the track state at the first moment, setting the initial acceleration value of the non-cooperative low-thrust maneuvering target at the first moment to be zero, and determining the initial expansion state quantity value of the non-cooperative low-thrust maneuvering target at the first moment;
obtaining an extended state vector forecast value of the non-cooperative low-thrust maneuvering target at a plurality of radar observation data moments according to the initial extended state quantity value at the first moment and the orbit dynamics model, and obtaining a first-order state transition matrix of the plurality of radar observation data moments according to the initial extended state quantity value at the first moment and the first-order state transition matrix formula;
calculating an observation residual error according to the radar observation vector and the extended state vector predicted value, calculating a partial derivative matrix from state deviation to the observation residual error according to the first-order state transition matrix, performing least square iteration improvement on an initial extended state quantity value at the first moment according to the observation residual error and the partial derivative matrix from the state deviation to the observation residual error until an iteration ending condition is met, and outputting an extended state quantity precision value at the first moment;
substituting the precision value of the expansion state quantity at the first moment into the orbit dynamics model to predict the flight trajectory of the non-cooperative low-thrust maneuvering target at any moment.
In one embodiment, the method further comprises the following steps: if the non-cooperative low-thrust maneuvering target has an initial value of cataloguing, acquiring the non-cooperative low-thrust maneuvering target from the cataloguing databaseInitial track state of timeAccording to SGP4 method or other analytic perturbation orbit prediction modelObtaining the non-cooperative low-thrust maneuvering targetTrack state of time of day(ii) a Wherein the content of the first and second substances,is a position vector at a first time instant,is a velocity vector at a first time;
if the non-cooperative low-thrust maneuvering target has no cataloged initial value, a first observation point of a first radar observation arc section in the radar observation vector is observedAnd the last observation pointObtaining a non-cooperative maneuver objectPosition vector of timeAndposition vector of timeFurther adopting Lambert algorithm to obtain non-cooperative maneuvering targetTrack state of time of day(ii) a Wherein the subscriptThe total number of the observed data of the first observed arc segment.
In one embodiment, the method further comprises the following steps: the construction and description of the expansion state quantity of the non-cooperative small-thrust maneuvering target motion system are as follows:(ii) a Wherein the content of the first and second substances,respectively representing a position vector and a velocity vector under the geocentric inertial system;representing an acceleration vector under a local orbit coordinate system;
constructing a track dynamics model of the non-cooperative low-thrust maneuvering target according to the expansion state quantity, wherein the track dynamics model comprises the following steps:
wherein the content of the first and second substances,is a constant of the gravity of the earth,the position velocity vector of the target under the geocentric inertial system is taken as a target;the acceleration of the non-spherical gravity perturbation of the earth,caused by the sun, moon and other starsThe third body gravity perturbs the acceleration,in order to accelerate the air resistance,the solar light pressure perturbation acceleration is measured,representing perturbation acceleration due to tidal forces;for the thrust acceleration vector expressed in RTN,for modeling coefficients for acceleration based on current statistical models, e.g. it is advisable,For a one-step prediction of the acceleration, at each step of the integration,keeping the constant value of the input unchanged;is a transformation matrix from the local orbit coordinate system to the geocentric inertial system, which is expressed as:
in one embodiment, the method further comprises the following steps: and performing partial derivative solution on the expansion state quantity by using a right function in the orbit dynamics model, and calculating a partial derivative matrix as follows:
wherein the content of the first and second substances,a zero matrix of 3 rows and 3 columns is shown,an identity matrix, representing 3 rows and 3 columns、Is a matrix of partial derivatives of gravitational and perturbed acceleration components on the target position velocity vector,,matrix of、Partial derivative matrixes of target thrust acceleration components to target position velocity vectors respectively are allA matrix of (a);
determining a first-order state transition matrix formula of the expanded state quantity according to the partial derivative matrix as follows:
wherein, when the integral is solved by the above formula,the initial value is taken asWhereinRepresenting an identity matrix of 9 rows and 9 columns.
In one embodiment, the method further comprises the following steps: obtaining the extended state vector predicted values of the non-cooperative low-thrust maneuvering target at a plurality of radar observation data moments according to the extended state vector initial value at the first moment and the orbit dynamics model as follows:
wherein the content of the first and second substances,representing an expansion state quantity forecast value of each radar observation data moment;the total number of the data observation time of the radar is;
obtaining a first-order state transition matrix of a plurality of radar observation data moments according to the initial value of the expanded state quantity at the first moment and the first-order state transition matrix formula:
in one embodiment, the method further comprises the following steps: obtaining the radar observation vector as follows:whereinRespectively correspond toAn observed value of a time;
obtaining observed quantity according to the radar observation vectorAnd observation quantity to extended state quantity partial derivative matrix(ii) a Wherein the content of the first and second substances,,;
calculating an observation residual error according to the radar observation vector and the extended state vector predicted value:
calculating a partial derivative matrix from the state deviation to the observation residual according to the first-order state transition matrix as follows:
and performing least square iteration improvement on the initial value of the expanded state quantity at the first moment according to the observation residual and a partial derivative matrix from the state deviation to the observation residual, wherein an iteration formula is as follows:
wherein the content of the first and second substances,representing iteration in least squares estimationkStep (A) tok = 1,2,…,K) The target expansion state quantity of (2),Kis the preset maximum number of iterations,kwhen the ratio is not less than 1,(ii) a Let the azimuth standard difference observed by radar beStandard difference of pitch angle ofStandard deviation of the skew distance ofThen the weight matrix can be expressed as:
when the iteration times are more than the preset times or the relative value of the root mean square error of the observed residual error is less than 10-6Then, finishing iteration and outputting the precision value of the expansion state quantity at the first moment。
In one embodiment, the method further comprises the following steps: the observations include azimuth, pitch, and skew data.
A non-cooperative low thrust maneuver target trajectory determination device, the device comprising:
the system comprises a radar observation vector acquisition module, a tracking module and a tracking module, wherein the radar observation vector acquisition module is used for extracting station coordinates from observation data of a plurality of arc sections of a foundation radar and determining a radar observation vector of a tracked non-cooperative low-thrust maneuvering target according to the station coordinates; the radar observation vector comprises observation values of a plurality of radar observation data to the non-cooperative small-thrust maneuvering target at the moment; determining the orbit state of the non-cooperative low-thrust maneuvering target at a first moment according to a cataloging database or the radar observation vector; the orbital state comprises a position vector and a velocity vector of the non-cooperative low-thrust maneuver target at a first time;
the system comprises a track dynamics model establishing module, a track dynamics model establishing module and a track dynamics model establishing module, wherein the track dynamics model establishing module is used for establishing an expansion state quantity for describing a non-cooperative small-thrust maneuvering target motion system and establishing a track dynamics model of the non-cooperative small-thrust maneuvering target according to the expansion state quantity; the expansion state quantity comprises a position vector and a velocity vector under a geocentric inertial system and an acceleration vector under a local orbit coordinate system;
the first-order state transition matrix formula determining module is used for solving partial derivatives of the expanded state quantities by a right function in the orbit dynamics model to obtain a partial derivative matrix, and determining a first-order state transition matrix formula of the expanded state quantities according to the partial derivative matrix;
the least square iteration module is used for setting the initial acceleration value of the non-cooperative small-thrust maneuvering target at the first moment to be zero according to the track state at the first moment and determining the initial expansion state quantity value of the non-cooperative small-thrust maneuvering target at the first moment; obtaining an extended state vector forecast value of the non-cooperative low-thrust maneuvering target at a plurality of radar observation data moments according to the initial extended state quantity value at the first moment and the orbit dynamics model, and obtaining a first-order state transition matrix of the plurality of radar observation data moments according to the initial extended state quantity value at the first moment and the first-order state transition matrix formula; calculating an observation residual error according to the radar observation vector and the extended state vector predicted value, calculating a partial derivative matrix from state deviation to the observation residual error according to the first-order state transition matrix, performing least square iteration improvement on an initial extended state quantity value at the first moment according to the observation residual error and the partial derivative matrix from the state deviation to the observation residual error until an iteration ending condition is met, and outputting an extended state quantity precision value at the first moment;
and the track prediction module is used for substituting the precision value of the expansion state quantity at the first moment into the track dynamics model to predict the flight track of the non-cooperative low-thrust maneuvering target at any moment.
A computer device comprising a memory and a processor, the memory storing a computer program, the processor implementing the following steps when executing the computer program:
extracting station coordinates from observation data of a plurality of arc sections of a ground radar, and determining a radar observation vector of a tracked non-cooperative low-thrust maneuvering target according to the station coordinates; the radar observation vector comprises observation values of a plurality of radar observation data to the non-cooperative low-thrust maneuvering target at all times;
determining the orbit state of the non-cooperative low-thrust maneuvering target at a first moment according to a cataloging database or the radar observation vector; the trajectory state comprises a position vector and a velocity vector of the non-cooperative low-thrust maneuver target at a first time;
constructing an expansion state quantity for describing a non-cooperative low-thrust maneuvering target motion system, and constructing a track dynamics model of the non-cooperative low-thrust maneuvering target according to the expansion state quantity; the expansion state quantity comprises a position vector and a velocity vector under a geocentric inertial system and an acceleration vector under a local orbit coordinate system;
performing partial derivative solving on the expanded state quantity by a right function in the orbit dynamics model to obtain a partial derivative matrix, and determining a first-order state transition matrix formula of the expanded state quantity according to the partial derivative matrix;
according to the track state at the first moment, setting the initial acceleration value of the non-cooperative low-thrust maneuvering target at the first moment to be zero, and determining the initial expansion state quantity value of the non-cooperative low-thrust maneuvering target at the first moment;
obtaining an extended state vector forecast value of the non-cooperative low-thrust maneuvering target at a plurality of radar observation data moments according to the initial extended state quantity value at the first moment and the orbit dynamics model, and obtaining a first-order state transition matrix of the plurality of radar observation data moments according to the initial extended state quantity value at the first moment and the first-order state transition matrix formula;
calculating an observation residual error according to the radar observation vector and the extended state vector predicted value, calculating a partial derivative matrix from state deviation to the observation residual error according to the first-order state transition matrix, performing least square iteration improvement on an initial extended state quantity value at the first moment according to the observation residual error and the partial derivative matrix from the state deviation to the observation residual error until an iteration ending condition is met, and outputting an extended state quantity precision value at the first moment;
substituting the precision value of the expansion state quantity at the first moment into the orbit dynamics model to predict the flight trajectory of the non-cooperative low-thrust maneuvering target at any moment.
A computer-readable storage medium, on which a computer program is stored which, when executed by a processor, carries out the steps of:
extracting station coordinates from observation data of a plurality of arc sections of a ground radar, and determining a radar observation vector of a tracked non-cooperative low-thrust maneuvering target according to the station coordinates; the radar observation vector comprises observation values of a plurality of radar observation data to the non-cooperative small-thrust maneuvering target at the moment;
determining the orbit state of the non-cooperative low-thrust maneuvering target at a first moment according to a cataloging database or the radar observation vector; the orbital state comprises a position vector and a velocity vector of the non-cooperative low-thrust maneuver target at a first time;
constructing an expansion state quantity for describing a non-cooperative low-thrust maneuvering target motion system, and constructing a track dynamics model of the non-cooperative low-thrust maneuvering target according to the expansion state quantity; the expansion state quantity comprises a position vector and a velocity vector under a geocentric inertial system and an acceleration vector under a local orbit coordinate system;
performing partial derivative solving on the expanded state quantity by a right function in the orbit dynamics model to obtain a partial derivative matrix, and determining a first-order state transition matrix formula of the expanded state quantity according to the partial derivative matrix;
according to the track state at the first moment, setting the initial acceleration value of the non-cooperative low-thrust maneuvering target at the first moment to be zero, and determining the initial expansion state quantity value of the non-cooperative low-thrust maneuvering target at the first moment;
obtaining an extended state vector forecast value of the non-cooperative low-thrust maneuvering target at a plurality of radar observation data moments according to the initial extended state quantity value at the first moment and the orbit dynamics model, and obtaining a first-order state transition matrix of the plurality of radar observation data moments according to the initial extended state quantity value at the first moment and the first-order state transition matrix formula;
calculating an observation residual error according to the radar observation vector and the extended state vector predicted value, calculating a partial derivative matrix from state deviation to the observation residual error according to the first-order state transition matrix, performing least square iteration improvement on an initial extended state quantity value at the first moment according to the observation residual error and the partial derivative matrix from the state deviation to the observation residual error until an iteration ending condition is met, and outputting an extended state quantity precision value at the first moment;
substituting the precision value of the expansion state quantity at the first moment into the orbit dynamics model to predict the flight trajectory of the non-cooperative low-thrust maneuvering target at any moment.
The method, the device, the computer equipment and the storage medium for determining the orbit of the non-cooperative low-thrust maneuvering target determine the radar observation vector of the tracked non-cooperative low-thrust maneuvering target from the observation data of a plurality of arc sections of the ground radar, and further determine the orbit state of the target at the first moment; constructing an expansion state quantity describing a non-cooperative small-thrust maneuvering target moving system, and constructing a track dynamics model of the non-cooperative small-thrust maneuvering target according to the expansion state quantity; performing partial derivative solving on the expanded state quantity by a right function in the orbit dynamics model to obtain a partial derivative matrix, and determining a first-order state transition matrix formula of the expanded state quantity according to the partial derivative matrix; obtaining an extended state vector forecast value of a non-cooperative low-thrust maneuvering target at a plurality of radar observation data moments according to the extended state vector initial value and the orbit dynamics model at the first moment, and obtaining a first-order state transition matrix of the radar observation data moments according to the extended state vector initial value and a first-order state transition matrix formula at the first moment; performing track improvement on the non-cooperative low-thrust maneuvering target by radar observation data and a least square method until an iteration ending condition is met, and outputting an expansion state quantity precision value at a first moment; substituting the precision value of the expansion state quantity at the first moment into the orbit dynamics model, and predicting the flight trajectory of the non-cooperative small-thrust maneuvering target at any moment. The invention provides an orbit determination method for carrying out thrust acceleration modeling on a tracked non-cooperative target local orbit coordinate system, which deduces an extended state quantity transfer matrix calculation equation containing an acceleration component under a high-precision perturbation orbit model, carries out orbit improvement on a non-cooperative small-thrust maneuvering target through radar observation data and a least square method, and finally carries out orbit prediction through the determined extended state quantity, thereby effectively carrying out orbit determination on the continuous small-thrust maneuvering non-cooperative target.
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FIG. 1 is a schematic flow chart diagram of a method for determining a target trajectory for a non-cooperative low thrust maneuver in one embodiment;
FIG. 2 is a schematic flow chart diagram of a method for determining a target trajectory for a non-cooperative low thrust maneuver in an exemplary embodiment;
FIG. 3 is a block diagram of a non-cooperative low thrust maneuver target trajectory determination device in one embodiment;
FIG. 4 is a diagram illustrating an internal structure of a computer device according to an embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
In one embodiment, as shown in fig. 1, there is provided a non-cooperative low thrust maneuver target trajectory determination method, comprising the steps of:
and 102, extracting station coordinates from observation data of a plurality of arc sections of the ground radar, and determining a radar observation vector of the tracked non-cooperative low-thrust maneuvering target according to the station coordinates.
Specifically, the site coordinates, the azimuth angle, the pitch angle and the slant range information of the observation non-cooperative maneuvering target are extracted from the observation data of a plurality of arc sections of the ground radar, and the site coordinates of the survey station S are recorded as [ lat, lon, alt ]]Wherein lat is the geographical latitude of the site, lon is the geographical longitude of the site, alt is the geographical elevation of the site; let us rememberiAn observation of radar isWhereinIs as followsiThe azimuth angle observed by the individual radar,is a firstiThe pitch angle as observed by the individual radar,is as followsiThe slant distance observed by each radar is obtained as the total observation vectorWhereinRespectively correspond toThe observed value of the time of day,Nthe total number of observed data points.
And 104, determining the track state of the non-cooperative low-thrust maneuvering target at the first moment according to the inventory database or the radar observation vector.
The orbital state includes a position vector and a velocity vector of the non-cooperative low-thrust maneuver object at the first time.
If the tracked non-cooperative maneuver targets areAn initial value of the catalog, and a non-cooperative target of the mobile terminal is obtained according to the catalog databaseInitial orbit state of time of dayWhereinFor non-cooperative maneuvering objectsThe position vector of the time of day,for non-cooperative maneuvering objectsA velocity vector of a time of day; the method adopts an SGP4 method or other analytic perturbation orbit forecasting modelsForecasting the first radar observation data point momentObtaining a non-cooperative maneuver atTrack state of time of day。
If the tracked non-cooperative maneuvering target has no catalogued initial value, a first observation point based on a first radar observation arc segmentAnd the last observation pointWherein the subscriptIs the total number of observation data of the first observation arc segment, anCan solve the non-cooperative maneuvering target inPosition vector of timePosition vector of timeFurther adopting Lambert algorithm well known in the field of space dynamics to obtain non-cooperative maneuvering targetTrack state of time of day。
And 106, constructing an expansion state quantity describing the non-cooperative small-thrust maneuvering target motion system, and constructing a track dynamics model of the non-cooperative small-thrust maneuvering target according to the expansion state quantity.
The expansion state quantity comprises a position vector and a velocity vector under the geocentric inertial system and an acceleration vector under the local orbit coordinate system.
Since the maneuvering strategy and maneuvering acceleration of a non-cooperative low-thrust maneuvering target are unknown, three components of the acceleration vector under the target local orbit coordinate system are described as:wherein, in the step (A),、、respectively thrust acceleration in a target local orbit coordinate systemxA shaft,yA shaft,zThe component of the axis. The target local orbit coordinate system (hereinafter referred to as RTN system) is defined as the origin at the tracked target centroid,xthe axis is along the connecting line direction of the geocenter and the target centroid,zthe shaft is normal to the track surface,ythe shaft and the other two shafts form a right-hand system. Further expanding the state quantity of the system to be estimated intoWhereinThe position vector of the target in the centroid inertia system (hereinafter referred to as ECI system),for a velocity vector targeted under the ECI series,the acceleration vector of the target under the RTN system is shown.
Modeling the orbit dynamics equation of the non-cooperative low-thrust maneuvering target as follows:
wherein the content of the first and second substances,is the constant of the earth's gravity,Position velocity vector under target ECI system;the acceleration of the non-spherical gravity perturbation of the earth,the third body gravity perturbation acceleration caused by the sun, the moon and other stars,in order to make the air resistance acceleration,the solar light pressure perturbation acceleration is measured,representing perturbation acceleration due to tidal forces;for the thrust acceleration vector expressed in RTN,for modeling coefficients for acceleration based on current statistical models, e.g. it is advisable,For a one-step prediction of the acceleration, at each step of the integration,keeping the constant value of the input unchanged;the transformation matrix for RTN system to ECI system can be expressed as:
and 108, performing partial derivative solution on the expanded state quantity through a right function in the orbit dynamics model to obtain a partial derivative matrix, and determining a first-order state transition matrix formula of the expanded state quantity according to the partial derivative matrix.
Expanding state quantity of non-cooperative small-thrust maneuvering targetThe state transition equation is satisfied:whereinIs an initialThe state is expanded to any future at any momenttConstantly expanding a first-order state transition matrix of the state; obtaining initial position velocity according to step 1.2 or 1.3Then, can obtainInitial state of timeIf the iterative initial step acceleration is unknown, it can be taken(ii) a First order state conversionMoving matrixSatisfies the following conditions:
wherein the content of the first and second substances,the matrix being a differential equation of dynamicsMiddle right function pair expansion state quantityPartial derivative matrix, integral solution of ordinary differential equationIs taken asWhereinRepresenting an identity matrix of 9 rows and 9 columns.
wherein the content of the first and second substances,a zero matrix of 3 rows and 3 columns is shown,representing an identity matrix of 3 rows and 3 columns,、can be calculated according to professional teaching materials or references related to the space dynamics, such as the following references: NASA Goddard Space Flight center. General Analysis Tool (GMAT) chemical specificities [ R]Greenbelt, MD 20771, month 6 2020.
Matrix array、Partial derivative matrixes of target thrust acceleration components and target position velocity vectors respectively, which are allOf the matrix of (a). By using superscriptsabRepresents a matrix ofaGo to the firstbElements of columns, e.g.Representation matrixRow 2, column 3 elements; note the bookAs components of the target position vector in the ECI system, i.e.(ii) a Note the bookFor the component of the target velocity vector in the ECI system, i.e.(ii) a Note bookFor the component of the target acceleration vector in the target RTN system, i.e.(ii) a Then the、The computational expression for each element is:
and 110, according to the track state at the first moment, setting the initial acceleration value of the non-cooperative low-thrust maneuvering target at the first moment to be zero, and determining the initial expansion state quantity value of the non-cooperative low-thrust maneuvering target at the first moment.
At the first radar observation pointAt the moment, the initial value of the acceleration is set to zero。
And 112, obtaining an extended state vector forecast value of the non-cooperative low-thrust maneuvering target at a plurality of radar observation data moments according to the initial extended state vector value at the first moment and the orbit dynamics model, and obtaining a first-order state transition matrix at the plurality of radar observation data moments according to the initial extended state vector value at the first moment and a first-order state transition matrix formula.
According to the initial valueSimultaneous integral formulaAnd formulaObtaining the expansion state of the target at each radar observation data momentAnd a first order state transition matrix at each radar observation time。
And step 114, calculating an observation residual error according to the radar observation vector and the expanded state vector predicted value, calculating a partial derivative matrix from the state deviation to the observation residual error according to the first-order state transition matrix, performing least square iterative improvement on the initial value of the expanded state quantity at the first moment according to the observation residual error and the partial derivative matrix from the state deviation to the observation residual error until an iteration ending condition is met, and outputting an expanded state quantity precise value at the first moment.
Extending state quantities by forecasted spacecraftCalculating an observation residual according to an observation equationAnd a matrix of partial derivatives of state deviation to observed residual。
Wherein, the radar observed quantity is calculated according to the state quantity under ECI systemAnd observation quantity to extended state quantity partial derivative matrixThe method can be obtained from aerospace dynamics professional textbooks or documents, and the invention is not repeated. For example, reference may be made to: theory and application of Liulin, Tangjing, satellite orbit]The method comprises the following steps: electronics industry Press, 2 nd edition 2015.
Expanding state quantities for non-cooperative low-thrust maneuvering targetsPerforming least square iteration improvement, wherein the iteration formula is as follows:
wherein, the azimuth standard difference observed by the radar isStandard difference of pitch angle ofStandard deviation of the skew distance ofThen the weight matrix can be expressed as:
and repeating the iteration until the iteration converges. For example, can be set asOr the relative value of the root mean square error of the observed residual is less than 10-6Time of flightQuitting, in which case the precise track state of the non-cooperative maneuvering target is obtained as(ii) a Otherwise, the least square iteration is unsuccessful, the method is not applicable any more, and a user needs to detect whether the tracked target is a continuous low-thrust maneuvering target or not, or whether the observed value is correct or not, or whether the initial value of the track iteration is reasonable or not.
And step 116, substituting the precision value of the expansion state quantity at the first moment into the orbit dynamics model, and predicting the flight trajectory of the non-cooperative low-thrust maneuvering target at any moment.
Track condition to be obtainedSubstituting equation as initial valueIntegral prediction to arbitrarytAnd at any moment, the flight track of the non-cooperative low-thrust maneuvering target in the observation blind area can be obtained, the movement direction of the target can be predicted according to the flight track, and possible threats of the target can be evaluated and early warned.
In particular, estimating states based on least squaresThe orbit extrapolation prediction of (1) is only applicable to the situation where the maneuvering strategy of the non-cooperative low-thrust maneuvering target is unchanged, if the maneuvering strategy is not changedThe target uses a different thrust direction or magnitude in the track extrapolation section than in the observation and tracking section, and the track extrapolation accuracy is affected to different degrees.
In the method for determining the orbit of the non-cooperative low-thrust maneuvering target, a radar observation vector of a tracked non-cooperative low-thrust maneuvering target is determined from observation data of a plurality of arc sections of a ground radar, and then the orbit state of the target at a first moment is determined; constructing an expansion state quantity describing a non-cooperative small-thrust maneuvering target moving system, and constructing a track dynamics model of the non-cooperative small-thrust maneuvering target according to the expansion state quantity; performing partial derivative solving on the expansion state quantity by a right function in the orbit dynamics model to obtain a partial derivative matrix, and determining a first-order state transition matrix formula of the expansion state quantity according to the partial derivative matrix; obtaining an extended state vector forecast value of a non-cooperative low-thrust maneuvering target at a plurality of radar observation data moments according to the extended state vector initial value and the orbit dynamics model at the first moment, and obtaining a first-order state transition matrix of the radar observation data moments according to the extended state vector initial value and a first-order state transition matrix formula at the first moment; performing track improvement on the non-cooperative low-thrust maneuvering target by radar observation data and a least square method until an iteration ending condition is met, and outputting an expansion state quantity precision value at a first moment; substituting the precision value of the expansion state quantity at the first moment into the orbit dynamics model, and predicting the flight trajectory of the non-cooperative small-thrust maneuvering target at any moment. The invention provides an orbit determination method for performing thrust acceleration modeling on a tracked non-cooperative target local orbit coordinate system, which deduces an extended state quantity transfer matrix calculation equation containing an acceleration component under a high-precision perturbation orbit model, performs orbit improvement on a non-cooperative small-thrust maneuvering target through radar observation data and a least square method, and performs orbit prediction through the determined extended state quantity, so that the orbit determination can be effectively performed on the non-cooperative target of continuous small-thrust maneuvering, and the orbit determination method can be used for solving the problem of performing the orbit determination of the continuous small-thrust maneuvering on a climbing or descending section of a non-cooperative satellite.
In one embodiment, the method further comprises the following steps: the observations include azimuth, pitch, and skew data.
It should be understood that, although the steps in the flowchart of fig. 1 are shown in order as indicated by the arrows, the steps are not necessarily performed in order as indicated by the arrows. The steps are not performed in the exact order shown and described, and may be performed in other orders, unless explicitly stated otherwise. Moreover, at least a portion of the steps in fig. 1 may include multiple sub-steps or multiple stages that are not necessarily performed at the same time, but may be performed at different times, and the order of performance of the sub-steps or stages is not necessarily sequential, but may be performed in turn or alternately with other steps or at least a portion of the sub-steps or stages of other steps.
In one embodiment, as shown in fig. 2, there is provided a method for determining a non-cooperative low thrust maneuver target trajectory, comprising:
step 1: and acquiring radar observation data and an initial orbit of the non-cooperative low-thrust maneuvering target.
1.1 extracting station address coordinates and information of azimuth angle, pitch angle and slant distance of observation non-cooperative maneuvering target from observation data of a plurality of arc sections of ground radar, wherein the station address coordinates of a survey station S are [46.8 deg,130.32 deg,101 m](ii) a Let us rememberiThe radar observation data isWhereinIs as followsiThe azimuth angle observed by the individual radar,is as followsiThe pitch angle as observed by the individual radar,is as followsiThe slant distance observed by each radar is obtained as the total observation vectorWhereinRespectively correspond toThe observed value of the time of day,Nthe total number of observed data points. And (4) switching to step 1.2 because the non-cooperative maneuvering target has an initial value of cataloguing.
1.2 obtaining non-cooperative maneuver targets from inventory databaseThe initial orbit state at that time is:
the method adopts an SGP4 method or other analytic perturbation orbit forecasting modelsForecasting the first radar observation data point momentObtaining a non-cooperative maneuver atThe track state at the moment is:
step 2: and establishing a high-precision perturbation orbit dynamics model of the non-cooperative small-thrust maneuvering target.
2.1 describes the three components of the acceleration vector in the target local orbit coordinate system as:wherein, in the step (A),respectively thrust acceleration on target local orbit coordinate systemxA shaft,yA shaft,zComponent of the axis, the initial value of acceleration being taken as。
2.2 modeling the orbit dynamics equation of the non-cooperative low thrust maneuvering target as:
wherein the content of the first and second substances,is a constant of the gravity of the earth,for the acceleration modeling coefficient based on the current statistical model, take,For a one-step prediction of the acceleration, at each step of the integration,keeping the constant value of the input unchanged;the transformation matrix for RTN system to ECI system can be expressed as:
and step 3: and calculating a first-order state transition matrix of the expanded state quantity under the high-precision perturbation model.
3.1 expansion State quantity of non-cooperative Low thrust maneuver targetsThe state transition equation is satisfied:whereinIs an initialThe state is expanded to any future at any momenttConstantly expanding a first-order state transition matrix of the state; obtaining initial position velocity according to step 1.2 or 1.3Then, can obtainInitial state of timeIf the iterative initial step acceleration is unknown, it can be taken(ii) a First order state transition matrixSatisfies the following conditions:
wherein the content of the first and second substances,the matrix being a differential equation of dynamicsMiddle right function pair expansion state quantityPartial derivative matrix, integral solution of ordinary differential equationIs taken asWhereinAn identity matrix of 9 rows and 9 columns is represented,the matrix is calculated by step 3.2.
wherein the content of the first and second substances,a zero matrix of 3 rows and 3 columns is shown,representing an identity matrix of 3 rows and 3 columns,can be calculated according to professional teaching materials or references related to the space dynamics, such as the following references: NASA Goddard Space Flight center. General Analysis Tool (GMAT) chemical specificities [ R]Greenbelt, MD 20771, month 6 2020.
3.3 matrixPartial derivative matrixes of target thrust acceleration components and target position velocity vectors respectively, which are allOf the matrix of (a).
And 4, step 4: orbit determination is performed based on a weighted least squares estimate.
4.1 at the first observation PointAt the moment, the initial value of the acceleration isTarget initial position velocity obtained according to step 1.2 or 1.3In the second of least squares estimation iterationkStep (a)k = 1,2,…,K) Recording the target expansion state asWhereinKIs the set maximum number of iterations.kWhen the ratio is not less than 1,。
4.2 according to the initial valueSimultaneous integral formulaAnd formulaAnd acquiring the expansion state of the target at each radar observation data momentAnd a first order state transition matrix at each radar observation time。
4.3 expanding State quantities by forecasted spacecraftCalculating an observation residual according to an observation equationAnd a matrix of partial derivatives of the state deviation to the observed residual。
Wherein, the radar observed quantity is calculated according to the state quantity under ECI systemAnd observation quantity to extended state quantity partial derivative matrixThe method can be obtained from aerospace dynamics professional textbooks or documents, and the invention is not repeated. For example, reference may be made to: theory and application of Liulin, Tangjing, satellite orbit]Beijing: electronics industry publishers, 2 nd edition 2015.
4.4 expansion State quantities for non-cooperative Low-thrust maneuver targetsPerforming least square iterative improvement, wherein the iterative formula is as follows:
wherein the azimuth standard difference observed by the radar isStandard difference of pitch angle ofStandard deviation of slope distance ofThen the weight matrix can be expressed as:
4.5 repeat steps 4.2 to 4.4 until the iteration converges. For example, can be set asOr the relative value of the root mean square error of the observed residual error is less than 1e-6Quitting, wherein the initial value of the precise track of the non-cooperative maneuvering target is obtained(ii) a Otherwise, the least square iteration is unsuccessful, the method is not applicable any more, and a user needs to detect whether the tracked target is a continuous low-thrust maneuvering target or not, or whether the observed value is correct or not, or whether the initial value of the track iteration is reasonable or not.
And 5: orbit state based on least square estimationAnd extrapolating and forecasting the future flight track of the non-cooperative low-thrust maneuvering target.
5.1 track status obtained in step 4Substituting equation as initial valueIntegral prediction to arbitrarytAnd the flight track of the non-cooperative low-thrust maneuvering target in the observation blind area can be obtained at any moment, the movement direction of the target can be predicted according to the flight track, and possible threats of the target can be evaluated and early warned.
5.2 in particular, estimating the state based on least squaresThe track extrapolation prediction is only applicable to the situation that the maneuvering strategy of the non-cooperative small-thrust maneuvering target is not changed, and if the target uses a thrust direction or magnitude different from that of the observation tracking section in the track extrapolation section, the track extrapolation accuracy is influenced to different degrees.
Determined by the above stepsForecasting the track state to the moment of the last observation point to obtain the track state as follows:
using the value as an initial value, substituting the initial value into an equationAnd (4) performing orbit prediction, wherein 12 o 'clock is performed from 54968.566 seconds to 30 o' clock 6/2021, and the prediction is compared with the real TLE orbit data of the satellite chain satellite No. 48465 at the moment, so that the prediction accuracy can be obtained. Obtaining forecast track as
By looking up the TLE orbit data of the satellite with the number of 48465 satellite chains, the real orbit of the satellite at the same moment is obtained
Alternatively, the satellite orbit may be predicted based on a conventional free orbit extrapolation method, and the prediction errors calculated for the method of the present invention and the conventional free extrapolation method are shown in table 1.
TABLE 1 prediction accuracy of the method of the present invention after determination of the orbit of 48465 satellite chain satellites
As can be seen from Table 1, the method can effectively determine the orbit of the non-cooperative maneuvering target, and the forecasting precision of the determined orbit more than half a day is obviously superior to that of the traditional method without considering the influence of the orbit maneuvering.
Therefore, the application example can prove that the method for determining the orbit of the non-cooperative small-thrust maneuvering target, provided by the invention, can effectively model and represent the acceleration influence of the orbit determination problem of the non-cooperative maneuvering target, and has higher orbit determination precision.
In one embodiment, as shown in fig. 3, there is provided a non-cooperative low-thrust maneuvering target trajectory determination device, comprising: a radar observation vector obtaining module 302, a trajectory dynamics model establishing module 304, a first order state transition matrix formula determining module 306, a least squares iteration module 308, and a trajectory prediction module 310, wherein:
a radar observation vector obtaining module 302, configured to extract site coordinates from observation data of multiple arc segments of a ground-based radar, and determine a radar observation vector of a tracked non-cooperative low-thrust maneuvering target according to the site coordinates; the radar observation vector comprises observation values of a plurality of radar observation data to the non-cooperative low-thrust maneuvering target at all times; determining the track state of the non-cooperative low-thrust maneuvering target at a first moment according to the cataloging database or the radar observation vector; the orbit state comprises a position vector and a velocity vector of the non-cooperative low-thrust maneuvering target at a first moment;
the track dynamics model establishing module 304 is used for establishing an expansion state quantity for describing a motion system of the non-cooperative low-thrust maneuvering target and establishing a track dynamics model of the non-cooperative low-thrust maneuvering target according to the expansion state quantity; the expansion state quantity comprises a position vector and a velocity vector under a geocentric inertial system and an acceleration vector under a local orbit coordinate system;
the first-order state transition matrix formula determining module 306 is configured to perform partial derivative solution on the expanded state quantity by using a right function in the orbit dynamics model to obtain a partial derivative matrix, and determine a first-order state transition matrix formula of the expanded state quantity according to the partial derivative matrix;
the least square iteration module 308 is configured to determine an initial value of an expansion state quantity of the non-cooperative low-thrust maneuvering target at the first moment according to the track state at the first moment and by setting an initial value of acceleration of the non-cooperative low-thrust maneuvering target at the first moment to zero; obtaining an extended state vector prediction value of a non-cooperative low-thrust maneuvering target at a plurality of radar observation data moments according to the initial extended state quantity value and the orbit dynamics model at the first moment, and obtaining a first-order state transition matrix of the plurality of radar observation data moments according to the initial extended state quantity value and a first-order state transition matrix formula at the first moment; calculating an observation residual error according to a radar observation vector and an expanded state vector predicted value, calculating a partial derivative matrix from state deviation to the observation residual error according to a first-order state transition matrix, performing least square iteration improvement on an expanded state quantity initial value at a first moment according to the observation residual error and the partial derivative matrix from the state deviation to the observation residual error until an iteration ending condition is met, and outputting an expanded state quantity precise value at the first moment;
and the trajectory prediction module 310 is configured to substitute the precision value of the expansion state quantity at the first moment into the orbit dynamics model, and predict the flight trajectory of the non-cooperative low-thrust maneuvering target at any moment.
The radar observation vector obtaining module 302 is further configured to obtain the non-cooperative low-thrust maneuvering target from the inventory database if the non-cooperative low-thrust maneuvering target has an inventory initial valueInitial track state of timeAccording to SGP4 method or other analytic perturbation orbit prediction modelObtain a non-cooperative low-thrust maneuvering targetTrack state of time of day(ii) a Wherein the content of the first and second substances,is a position vector at a first time instant,is a velocity vector at a first time; if the non-cooperative low-thrust maneuvering target does not existWith catalogued initial values, based on a first observation point of a first radar observation arc segment in a radar observation vectorAnd the last observation pointObtaining a non-cooperative maneuver objectPosition vector of timeAndposition vector of timeFurther adopting Lambert algorithm to obtain non-cooperative maneuvering targetTrack state of time of day(ii) a Wherein the subscriptThe total number of the observed data of the first observed arc segment.
The orbit dynamics model building module 304 is further configured to build an expansion state quantity describing a non-cooperative small-thrust maneuvering target motion system as follows:(ii) a Wherein the content of the first and second substances,respectively representing a position vector and a velocity vector under the geocentric inertial system;representing an acceleration vector under a local orbit coordinate system;
constructing a track dynamics model of a non-cooperative low-thrust maneuvering target according to the expansion state quantity is as follows:
wherein the content of the first and second substances,is a constant of the gravity of the earth,the position velocity vector of the target under the geocentric inertial system is taken as a target;the acceleration of the non-spherical gravity perturbation of the earth,the third body gravity perturbation acceleration caused by the sun, the moon and other stars,in order to accelerate the air resistance,the solar light pressure perturbation acceleration is measured,representing perturbation acceleration due to tidal forces;for the thrust acceleration vector expressed under the RTN system,for modeling coefficients for acceleration based on current statistical models, e.g. it is advisable,For a one-step prediction of the acceleration, at each step of the integration,keeping the constant value of the input unchanged;is a transformation matrix from the local orbit coordinate system to the geocentric inertial system, which is expressed as:
the first-order state transition matrix formula determining module 306 is further configured to perform partial derivative solution on the expanded state quantities by using a right function in the orbit dynamics model, and calculate a partial derivative matrix as:
wherein the content of the first and second substances,a zero matrix of 3 rows and 3 columns is shown,an identity matrix, representing 3 rows and 3 columns、For gravitational and gravitational acceleration components versus target positionThe matrix of the partial derivatives of the velocity vector,,matrix ofPartial derivative matrixes of target thrust acceleration components to target position velocity vectors respectively are allA matrix of (a);
the first-order state transition matrix formula for determining the expanded state quantity according to the partial derivative matrix is as follows:
wherein, when the integral is solved by the above formula,the initial value is taken asIn whichRepresenting an identity matrix of 9 rows and 9 columns.
The least square iteration module 308 is further configured to obtain an extended state vector predicted value of the non-cooperative low-thrust maneuvering target at a plurality of radar observation data moments according to the extended state vector initial value and the orbit dynamics model at the first moment as follows:
wherein the content of the first and second substances,representing an expansion state quantity forecast value of each radar observation data moment;the total number of times of observing data for the radar;
according to the initial value of the expanded state quantity at the first moment and a first-order state transition matrix formula, obtaining a first-order state transition matrix at a plurality of radar observation data moments as follows:
the least squares iteration module 308 is further configured to obtain a radar observation vector as:in whichRespectively correspond toAn observed value of a time;
obtaining observed quantity according to radar observed vectorAnd observation quantity to extended state quantity partial derivative matrix(ii) a Wherein the content of the first and second substances,,;
calculating an observation residual error according to the radar observation vector and the extended state vector predicted value:
and calculating a partial derivative matrix from the state deviation to the observation residual error according to the first-order state transition matrix, wherein the partial derivative matrix is as follows:
according to the observation residual error and a partial derivative matrix from the state deviation to the observation residual error, performing least square iteration improvement on the initial value of the expanded state quantity at the first moment, wherein the iteration formula is as follows:
wherein the content of the first and second substances,expressed in the second of least squares estimation iterationskStep (a)k = 1,2,…,K) The target expansion state quantity of (2),Kis the preset maximum number of iterations,kwhen the ratio is not less than 1,(ii) a Let the azimuth standard difference observed by radar beStandard difference of pitch angle ofStandard deviation of the skew distance ofThen the weight matrix can be expressed as:
when the iteration times are more than the preset times or the relative value of the root mean square error of the observed residual error is less than 1e-6Then, finishing iteration and outputting the precision value of the expansion state quantity at the first moment。
For specific limitations of the non-cooperative low-thrust maneuvering target trajectory determination device, reference may be made to the above limitations of the non-cooperative low-thrust maneuvering target trajectory determination method, and details thereof are not repeated here. The various modules in the non-cooperative low-thrust maneuvering target trajectory determination device can be realized in whole or in part by software, hardware and a combination thereof. The modules can be embedded in a hardware form or independent from a processor in the computer device, and can also be stored in a memory in the computer device in a software form, so that the processor can call and execute operations corresponding to the modules.
In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as shown in fig. 4. The computer device includes a processor, a memory, a network interface, a display screen, and an input device connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device comprises a nonvolatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of an operating system and computer programs in the non-volatile storage medium. The network interface of the computer device is used for communicating with an external terminal through a network connection. The computer program is executed by a processor to implement a non-cooperative low thrust maneuver target trajectory determination method. The display screen of the computer equipment can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer equipment can be a touch layer covered on the display screen, a key, a track ball or a touch pad arranged on the shell of the computer equipment, an external keyboard, a touch pad or a mouse and the like.
Those skilled in the art will appreciate that the architecture shown in fig. 4 is merely a block diagram of some of the structures associated with the disclosed aspects and is not intended to limit the computing devices to which the disclosed aspects apply, as particular computing devices may include more or less components than those shown, or may combine certain components, or have a different arrangement of components.
In an embodiment, a computer device is provided, comprising a memory storing a computer program and a processor implementing the steps of the above method embodiments when executing the computer program.
In an embodiment, a computer-readable storage medium is provided, on which a computer program is stored, which computer program, when being executed by a processor, carries out the steps of the above-mentioned method embodiments.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by hardware instructions of a computer program, which can be stored in a non-volatile computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in the embodiments provided herein may include non-volatile and/or volatile memory, among others. Non-volatile memory can include read-only memory (ROM), Programmable ROM (PROM), Electrically Programmable ROM (EPROM), Electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), Dynamic RAM (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced SDRAM (ESDRAM), Synchronous Link DRAM (SLDRAM), Rambus Direct RAM (RDRAM), direct bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).
All possible combinations of the technical features in the above embodiments may not be described for the sake of brevity, but should be considered as being within the scope of the present disclosure as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (10)
1. A method for determining a non-cooperative low thrust maneuver target trajectory, the method comprising:
extracting station coordinates from observation data of a plurality of arc sections of a ground radar, and determining a radar observation vector of a tracked non-cooperative low-thrust maneuvering target according to the station coordinates; the radar observation vector comprises observation values of a plurality of radar observation data to the non-cooperative small-thrust maneuvering target at the moment;
determining the track state of the non-cooperative low-thrust maneuvering target at a first moment according to a cataloging database or the radar observation vector; the trajectory state comprises a position vector and a velocity vector of the non-cooperative low-thrust maneuver target at a first time;
constructing an expansion state quantity for describing a non-cooperative low-thrust maneuvering target motion system, and constructing a track dynamics model of the non-cooperative low-thrust maneuvering target according to the expansion state quantity; the expansion state quantity comprises a position vector and a velocity vector under a geocentric inertial system and an acceleration vector under a local orbit coordinate system;
performing partial derivative solving on the expanded state quantity by a right function in the orbit dynamics model to obtain a partial derivative matrix, and determining a first-order state transition matrix formula of the expanded state quantity according to the partial derivative matrix;
according to the track state at the first moment, setting the initial acceleration value of the non-cooperative low-thrust maneuvering target at the first moment to be zero, and determining the initial expansion state quantity value of the non-cooperative low-thrust maneuvering target at the first moment;
obtaining an extended state vector forecast value of the non-cooperative low-thrust maneuvering target at a plurality of radar observation data moments according to the initial extended state quantity value at the first moment and the orbit dynamics model, and obtaining a first-order state transition matrix of the plurality of radar observation data moments according to the initial extended state quantity value at the first moment and the first-order state transition matrix formula;
calculating an observation residual error according to the radar observation vector and the extended state vector predicted value, calculating a partial derivative matrix from state deviation to the observation residual error according to the first-order state transition matrix, performing least square iteration improvement on an initial extended state quantity value at the first moment according to the observation residual error and the partial derivative matrix from the state deviation to the observation residual error until an iteration ending condition is met, and outputting an extended state quantity precision value at the first moment;
substituting the precision value of the expansion state quantity at the first moment into the orbit dynamics model to predict the flight trajectory of the non-cooperative low-thrust maneuvering target at any moment.
2. The method of claim 1, wherein the orbital state of the non-cooperative low-thrust maneuver target at a first time is determined from a cataloged database or the radar observation vectors; the orbital state includes a position vector and a velocity vector of the non-cooperative low-thrust maneuver object at a first time, including:
if the non-cooperative low-thrust maneuvering target has an initial value of cataloguing, acquiring the non-cooperative low-thrust maneuvering target from the cataloguing databaseInitial track state of timeBy the SGP4 method according toObtaining the non-cooperative low-thrust maneuvering targetTrack state of time of day(ii) a Wherein the content of the first and second substances,is a position vector at a first time instant,is a velocity vector at a first time;
if the non-cooperative low-thrust maneuvering target has no cataloged initial value, a first observation point of a first radar observation arc section in the radar observation vector is observedAnd the last observation pointObtaining a non-cooperative maneuver objectPosition vector of timeAndposition vector of timeFurther adopting Lambert algorithm to obtain non-cooperative maneuvering targetTrack state of time of day(ii) a Wherein the subscriptThe total number of the observed data of the first observed arc segment.
3. The method according to claim 2, characterized by constructing an expansion state quantity describing a non-cooperative small-thrust maneuvering target moving system, and constructing an orbit dynamics model of the non-cooperative small-thrust maneuvering target according to the expansion state quantity; the expansion state quantity comprises a position vector and a velocity vector under a geocentric inertial system and an acceleration vector under a local orbit coordinate system, and comprises the following steps:
the construction and description of the expansion state quantity of the non-cooperative small-thrust maneuvering target motion system are as follows:(ii) a Wherein the content of the first and second substances,、respectively representing a position vector and a velocity vector under the geocentric inertial system;representing an acceleration vector under a local orbit coordinate system;
constructing a track dynamics model of the non-cooperative low-thrust maneuvering target according to the expansion state quantity, wherein the track dynamics model comprises the following steps:
wherein, the first and the second end of the pipe are connected with each other,is a constant of the gravity of the earth,、the position velocity vector of the target under the geocentric inertial system is taken as a target;the acceleration of the non-spherical gravity perturbation of the earth,the third body gravitation perturbation acceleration caused by the sun, moon and other stars,in order to make the air resistance acceleration,the solar light pressure perturbation acceleration is measured,representing perturbation acceleration due to tidal forces;for the thrust acceleration vector expressed in RTN,for the acceleration modeling coefficients based on the current statistical model,for a one-step prediction of the acceleration, at each step of the integration,keeping the constant value of the input unchanged;is a transformation matrix from the local orbit coordinate system to the geocentric inertial system, which is expressed as:
4. the method according to claim 3, wherein a partial derivative solution is performed on the expanded state quantity through a right function in the orbit dynamics model to obtain a partial derivative matrix, and a first-order state transition matrix formula of the expanded state quantity is determined according to the partial derivative matrix, including:
and performing partial derivative solution on the expansion state quantity by using a right function in the orbit dynamics model, and calculating a partial derivative matrix as follows:
wherein, the first and the second end of the pipe are connected with each other,a zero matrix of 3 rows and 3 columns is shown,an identity matrix representing 3 rows and 3 columns、Is a matrix of partial derivatives of gravitational and perturbed acceleration components on the target position velocity vector,,matrix of、Partial derivative matrixes of target thrust acceleration components to target position velocity vectors respectively are allA matrix of (a);
determining a first-order state transition matrix formula of the expanded state quantity according to the partial derivative matrix as follows:
5. The method of claim 4, wherein obtaining extended state vector prediction values of the non-cooperative low-thrust maneuvering target at a plurality of radar observation data moments according to the initial extended state quantity value at the first moment and the orbit dynamics model, and obtaining a first-order state transition matrix at the plurality of radar observation data moments according to the initial extended state quantity value at the first moment and the first-order state transition matrix formula comprises:
obtaining the extended state vector predicted values of the non-cooperative low-thrust maneuvering target at a plurality of radar observation data moments according to the extended state vector initial value at the first moment and the orbit dynamics model as follows:
wherein the content of the first and second substances,representing an expansion state quantity forecast value of each radar observation data moment;the total number of the data observation time of the radar is;
obtaining a first-order state transition matrix of a plurality of radar observation data moments according to the initial value of the expanded state quantity at the first moment and the first-order state transition matrix formula:
6. the method of claim 5, wherein calculating an observation residual according to the radar observation vector and the extended state vector predicted value, calculating a partial derivative matrix from a state deviation to the observation residual according to the first-order state transition matrix, performing least square iteration improvement on an initial extended state quantity value at the first moment according to the observation residual and the partial derivative matrix from the state deviation to the observation residual until an iteration end condition is met, and outputting an extended state quantity precise value at the first moment comprises:
obtaining the radar observation vector as follows:whereinRespectively correspond toAn observed value of a time;
obtaining observed quantity according to the radar observation vectorAnd observation quantity to extended state quantity partial derivative matrix(ii) a Wherein the content of the first and second substances,,;
calculating an observation residual error according to the radar observation vector and the extended state vector predicted value:
calculating a partial derivative matrix from the state deviation to the observation residual according to the first-order state transition matrix as follows:
and performing least square iteration improvement on the initial value of the expanded state quantity at the first moment according to the observation residual and a partial derivative matrix from the state deviation to the observation residual, wherein an iteration formula is as follows:
wherein the content of the first and second substances,representing iteration in least squares estimationkThe target of the step is to expand the state quantity,k = 1,2,…,K,Kis the maximum iteration number which is preset,kwhen the ratio is not less than 1,(ii) a Let the azimuth standard difference observed by radar beStandard difference of pitch angle ofStandard deviation of the skew distance ofThen the weight matrix can be expressed as:
7. The method of any of claims 1-6, wherein the observations comprise azimuth, pitch, and skew data.
8. A non-cooperative low thrust maneuver target trajectory determination device, comprising:
the system comprises a radar observation vector acquisition module, a data acquisition module and a data processing module, wherein the radar observation vector acquisition module is used for extracting station address coordinates from observation data of a plurality of arc sections of a ground radar and determining a radar observation vector of a tracked non-cooperative low-thrust maneuvering target according to the station address coordinates; the radar observation vector comprises observation values of a plurality of radar observation data to the non-cooperative low-thrust maneuvering target at all times; determining the track state of the non-cooperative low-thrust maneuvering target at a first moment according to a cataloging database or the radar observation vector; the orbital state comprises a position vector and a velocity vector of the non-cooperative low-thrust maneuver target at a first time;
the track dynamics model building module is used for building an expansion state quantity for describing a non-cooperative low-thrust maneuvering target motion system and building a track dynamics model of the non-cooperative low-thrust maneuvering target according to the expansion state quantity; the expansion state quantity comprises a position vector and a velocity vector under a geocentric inertial system and an acceleration vector under a local orbit coordinate system;
the first-order state transition matrix formula determining module is used for solving partial derivatives of the expanded state quantities by a right function in the orbit dynamics model to obtain a partial derivative matrix, and determining a first-order state transition matrix formula of the expanded state quantities according to the partial derivative matrix;
the least square iteration module is used for determining an initial value of the expansion state quantity of the non-cooperative low-thrust maneuvering target at the first moment according to the track state at the first moment and setting the initial value of the acceleration of the non-cooperative low-thrust maneuvering target at the first moment to be zero; obtaining an extended state vector forecast value of the non-cooperative low-thrust maneuvering target at a plurality of radar observation data moments according to the initial extended state quantity value at the first moment and the orbit dynamics model, and obtaining a first-order state transition matrix of the plurality of radar observation data moments according to the initial extended state quantity value at the first moment and the first-order state transition matrix formula; calculating an observation residual error according to the radar observation vector and the extended state vector predicted value, calculating a partial derivative matrix from state deviation to the observation residual error according to the first-order state transition matrix, performing least square iteration improvement on an initial extended state quantity value at the first moment according to the observation residual error and the partial derivative matrix from the state deviation to the observation residual error until an iteration ending condition is met, and outputting an extended state quantity precision value at the first moment;
and the track prediction module is used for substituting the precision value of the expansion state quantity at the first moment into the track dynamics model to predict the flight track of the non-cooperative low-thrust maneuvering target at any moment.
9. A computer device comprising a memory and a processor, the memory storing a computer program, wherein the processor implements the steps of the method of any one of claims 1 to 7 when executing the computer program.
10. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the method of any one of claims 1 to 7.
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