CN119986733B - Three-dimensional positioning method and device for double-star stationary radiation source based on passive synthetic aperture - Google Patents
Three-dimensional positioning method and device for double-star stationary radiation source based on passive synthetic apertureInfo
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Abstract
The invention provides a double-star stationary radiation source three-dimensional positioning method and device based on a passive synthetic aperture, and relates to the technical field of space electronic reconnaissance. The method comprises the steps of carrying out passive synthetic aperture processing on radiation source signals received by a first satellite and a second satellite from a target radiation source, determining an instantaneous position vector, an instantaneous speed vector and a distance-wise distance of the first satellite and the second satellite at the time of each azimuth, constructing an equation of a first plane and an equation of a second plane where the target radiation source is located according to the instantaneous position vector and the instantaneous speed vector, constructing an equation of a first curved surface where the target radiation source is located and an equation of the second curved surface according to the instantaneous position vector and the distance-wise distance, and forming a nonlinear equation set by combining the equation of the first plane, the equation of the second plane, the equation of the first curved surface and the equation of the second curved surface, and solving the nonlinear equation set to obtain a position coordinate value of the target radiation source. The method can improve the positioning accuracy of the radiation source.
Description
Technical Field
The invention relates to the technical field of space electronic reconnaissance, in particular to a double-star stationary radiation source three-dimensional positioning method and device based on passive synthetic aperture.
Background
In space electronic reconnaissance, the traditional radiation source positioning methods mainly comprise frequency measurement positioning, direction measurement positioning, time difference positioning, time-frequency difference positioning and the like, and the positioning methods are developed relatively mature, but have the defects of low positioning precision, high satellite load requirement and the like, wherein the positioning precision is usually only kilometer level. In order to solve the problem of low positioning accuracy, in recent years, students propose a passive synthetic aperture radiation source positioning method, which uses the position of a radiation source relative to a satellite as a distance direction parameter and a direction parameter, and realizes accurate estimation of the distance direction distance and the direction distance through coherent accumulation.
The conventional passive synthetic aperture radiation source positioning method generally needs to assume that the radiation source is located on the earth surface, and the earth surface meets an ellipsoidal model, however, in practice, because the earth surface contains elevation information, the default radiation source is located on the earth surface, and the elevation information is ignored, so that the positioning accuracy of the radiation source is affected, and the positioning accuracy of the radiation source is not high.
Disclosure of Invention
The invention provides a double-star stationary radiation source three-dimensional positioning method, device and computer program product based on passive synthetic aperture, which are used for solving the defect of low radiation source positioning precision in the prior art and realizing improvement of radiation source positioning precision.
In a first aspect, the invention provides a method for three-dimensionally positioning a double-star stationary radiation source based on a passive synthetic aperture, comprising the following steps:
Respectively carrying out passive synthetic aperture processing on radiation source signals received by a first satellite and a second satellite from a target radiation source, and determining an instantaneous position vector, an instantaneous speed vector and a distance-wise distance of the first satellite and the second satellite respectively at azimuth-wise moments corresponding to the target radiation source;
Constructing an equation of a first plane and an equation of a second plane in which the target radiation source is located according to the instantaneous position vector and the instantaneous speed vector of the first satellite and the second satellite respectively;
constructing an equation of a first curved surface and an equation of a second curved surface where the target radiation source is located according to the instantaneous position vectors and the distance-to-distance of the first satellite and the second satellite respectively;
And forming a nonlinear equation set by combining the equation of the first plane, the equation of the second plane, the equation of the first curved surface and the equation of the second curved surface, and solving the nonlinear equation set to obtain the position coordinate value of the target radiation source.
According to the method for three-dimensionally positioning the dual-satellite stationary radiation source based on the passive synthetic aperture, which is provided by the invention, the radiation source signals from the target radiation source received by the first satellite and the second satellite are respectively subjected to passive synthetic aperture processing, and the instantaneous position vector, the instantaneous speed vector and the distance of the first satellite and the second satellite respectively under the azimuth moment corresponding to the target radiation source are determined, and the method comprises the following steps:
respectively carrying out passive synthetic aperture processing on radiation source signals received by a first satellite and a second satellite from a target radiation source to obtain azimuth time and Doppler slope of the first satellite and the second satellite corresponding to the target radiation source respectively;
Determining an instantaneous position vector and an instantaneous speed vector of the first satellite and the second satellite respectively at the azimuth moment according to the navigation positioning information of the first satellite and the second satellite;
And determining the distance direction distance between the first satellite and the second satellite and the target radiation source respectively according to the instantaneous speed vector and the Doppler slope of the first satellite and the second satellite respectively.
According to the three-dimensional positioning method of the dual-satellite stationary radiation source based on the passive synthetic aperture, the distance direction distance between the first satellite and the second satellite and the target radiation source is determined according to the instantaneous velocity vector and the Doppler slope of the first satellite and the second satellite respectively, and the method comprises the following steps:
Determining instantaneous velocity values of the first satellite and the second satellite at the respective azimuth moments according to the instantaneous velocity vectors of the first satellite and the second satellite respectively;
determining a carrier frequency of the target radiation source according to the radiation source signals received by the first satellite and the second satellite;
and determining the distance direction distance between the first satellite and the second satellite and the target radiation source respectively according to the instantaneous speed value and the Doppler slope of the first satellite and the second satellite and the carrier frequency and the light speed of the target radiation source respectively.
According to the three-dimensional positioning method of the double-star stationary radiation source based on the passive synthetic aperture provided by the invention, the equation of the first plane and the equation of the second plane in which the target radiation source is positioned are constructed according to the instantaneous position vector and the instantaneous speed vector of the first satellite and the second satellite respectively, and the method comprises the following steps:
Constructing a first position vector of the target radiation source relative to the first satellite and a second position vector relative to the second satellite according to the difference between the position coordinate variables of the target radiation source and the instantaneous position vectors of the first satellite and the second satellite respectively;
constructing an equation of a first plane in which the target radiation source is located according to the first position vector and the instantaneous velocity vector of the first satellite;
and constructing an equation of a second plane in which the target radiation source is located according to the second position vector and the instantaneous speed vector of the second satellite.
According to the three-dimensional positioning method of the double-star stationary radiation source based on the passive synthetic aperture provided by the invention, the equation of the first curved surface and the equation of the second curved surface where the target radiation source is located are constructed according to the instantaneous position vectors and the distance distances of the first satellite and the second satellite respectively, and the method comprises the following steps:
Constructing a first position vector of the target radiation source relative to the first satellite and a second position vector relative to the second satellite according to the difference between the position coordinate variables of the target radiation source and the instantaneous position vectors of the first satellite and the second satellite respectively;
constructing an equation of a first curved surface where the target radiation source is located according to the first position vector and the distance direction distance of the first satellite;
And constructing an equation of a second curved surface where the target radiation source is located according to the second position vector and the distance direction distance of the second satellite.
According to the method for three-dimensionally positioning the double-star stationary radiation source based on the passive synthetic aperture provided by the invention, the position coordinate value of the target radiation source is obtained by solving the nonlinear equation set, and the method comprises the following steps:
Constructing a Newton equation set according to the nonlinear equation set;
Acquiring an initial predicted position coordinate value, and taking the initial predicted position coordinate value as a predicted position coordinate value in a first iteration;
Substituting the predicted position coordinate value of the current iteration into the Newton equation set in each iteration, and solving to obtain the position coordinate adjustment value of the current iteration;
Determining a predicted position coordinate value of the next iteration according to the position coordinate adjustment value of the current iteration and the predicted position coordinate value of the current iteration;
Returning to execute the step of substituting the predicted position coordinate value of the current round of iteration into the Newton equation set and solving to obtain the position coordinate adjustment value of the current round of iteration so as to enter the next round of iteration until the iteration stop condition is met;
and after the iteration is stopped, determining the predicted position coordinate value obtained in the last iteration as the position coordinate value of the target radiation source.
In a second aspect, the invention provides a two-star stationary radiation source three-dimensional positioning device based on passive synthetic aperture, comprising the following modules:
The data processing module is used for respectively carrying out passive synthetic aperture processing on radiation source signals received by the first satellite and the second satellite from the target radiation source and determining an instantaneous position vector, an instantaneous speed vector and a distance-wise distance of the first satellite and the second satellite respectively at the azimuth-wise moment corresponding to the target radiation source;
the system comprises an equation construction module, an equation construction module and a model calculation module, wherein the equation construction module is used for constructing an equation of a first plane and an equation of a second plane where the target radiation source is positioned according to the instantaneous position vector and the instantaneous speed vector of the first satellite and the instantaneous speed vector of the second satellite respectively;
The position solving module is used for forming a nonlinear equation set by combining the equation of the first plane, the equation of the second plane, the equation of the first curved surface and the equation of the second curved surface, and solving the nonlinear equation set to obtain the position coordinate value of the target radiation source.
The double-satellite static radiation source three-dimensional positioning device based on the passive synthetic aperture is further used for respectively carrying out passive synthetic aperture processing on radiation source signals received by a first satellite and a second satellite from a target radiation source to obtain azimuth time and Doppler slope of the first satellite and the second satellite corresponding to the target radiation source respectively, determining instantaneous position vectors and instantaneous speed vectors of the first satellite and the second satellite under the azimuth time respectively according to navigation positioning information of the first satellite and the second satellite, and determining distance direction distances between the first satellite and the second satellite and the target radiation source respectively according to the instantaneous speed vectors and the Doppler slope of the first satellite and the second satellite respectively.
The position solving module is further used for constructing a Newton equation set according to the nonlinear equation set, obtaining initial predicted position coordinate values, taking the initial predicted position coordinate values as predicted position coordinate values in a first round of iteration, substituting the predicted position coordinate values of a current round of iteration into the Newton equation set in each round of iteration, solving to obtain a position coordinate adjustment value of the current round of iteration, determining the predicted position coordinate values of a next round of iteration according to the position coordinate adjustment value of the current round of iteration and the predicted position coordinate values of the current round of iteration, returning to execute the step of substituting the predicted position coordinate values of the current round of iteration into the Newton equation set, solving to obtain the position coordinate adjustment value of the current round of iteration, entering the next round of iteration until the iteration stop condition is met, and determining the predicted position coordinate values obtained in the last round of iteration as the position coordinate values of the target radiation source after the iteration is stopped.
In a third aspect, the invention provides a computer program product comprising a computer program which, when executed by a processor, implements a method of three-dimensional positioning of a dual star stationary radiation source based on a passive synthetic aperture as defined in any one of the above.
According to the method, the device and the computer program product for three-dimensional positioning of the double-star stationary radiation source based on the passive synthetic aperture, which are provided by the invention, the two satellites respectively receive the radiation source signals from the same target radiation source, the passive synthetic aperture is processed, then a nonlinear equation set is constructed for solving, the problem that elevation information cannot be obtained by using only a single satellite for passive synthetic aperture processing is avoided, the position coordinate value containing the elevation information of the target radiation source can be accurately determined, three-dimensional positioning is realized, and the positioning precision of the radiation source is improved.
Drawings
In order to more clearly illustrate the invention or the technical solutions of the prior art, the following description will briefly explain the drawings used in the embodiments or the description of the prior art, and it is obvious that the drawings in the following description are some embodiments of the invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow chart of a method for three-dimensionally positioning a dual-star stationary radiation source based on a passive synthetic aperture.
Fig. 2 is a schematic diagram of a geometric model of a three-dimensional positioning method of a dual-star stationary radiation source based on a passive synthetic aperture.
Fig. 3 (a) and fig. 3 (b) are schematic diagrams of the passive synthetic aperture processing result in the two-star stationary radiation source three-dimensional positioning method based on the passive synthetic aperture.
FIG. 4 is a schematic diagram of the relationship between the iteration number and the positioning error in the three-dimensional positioning method of the double-star stationary radiation source based on the passive synthetic aperture.
Fig. 5 is a schematic structural diagram of a three-dimensional positioning device of a dual-star stationary radiation source based on passive synthetic aperture.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The following describes a passive synthetic aperture-based two-star stationary radiation source three-dimensional positioning method, apparatus and computer program product provided by the present invention in connection with fig. 1-5.
In one embodiment, the method for positioning the dual-star stationary radiation source based on the passive synthetic aperture provided by the invention can be executed by electronic equipment, the electronic equipment can receive the radiation source signals from the target radiation source respectively transmitted by the first satellite and the second satellite, and then the method for positioning the dual-star stationary radiation source based on the passive synthetic aperture in each embodiment of the invention is executed.
In another embodiment, the two-star stationary radiation source three-dimensional positioning method based on the passive synthetic aperture provided by the invention can be executed by a first satellite or a second satellite, the first satellite can receive the radiation source signal from the target radiation source received by the second satellite sent by the second satellite, and the first satellite can execute the two-star stationary radiation source three-dimensional positioning method based on the passive synthetic aperture in each embodiment of the invention according to the radiation source signal from the target radiation source received by the first satellite and the radiation source signal from the target radiation source received by the second satellite. Or the second satellite can receive the radiation source signal from the target radiation source received by the first satellite and sent by the first satellite, and the second satellite can execute the double-star stationary radiation source three-dimensional positioning method based on the passive synthetic aperture according to the radiation source signal from the target radiation source received by the second satellite and the radiation source signal from the target radiation source received by the first satellite.
Fig. 1 is a schematic flow chart of a method for three-dimensionally positioning a dual-star stationary radiation source based on a passive synthetic aperture according to the present invention, as shown in fig. 1, the method includes the following steps:
And 102, respectively performing passive synthetic aperture processing on radiation source signals received by the first satellite and the second satellite from the target radiation source, and determining an instantaneous position vector, an instantaneous speed vector and a distance-wise distance of the first satellite and the second satellite at the azimuth-wise moment respectively corresponding to the target radiation source.
Wherein the target radiation source is a stationary radiation source. The passive synthetic aperture processing is to use the time correlation of signals, and to synthesize the continuously measured short array into a virtual long array through phase compensation and space position compensation, thereby realizing the processing of the azimuth resolution of the target. Azimuth time is the point in time when the satellite is closest to the radiation source. The range-wise distance is the linear distance between the satellite and the target radiation source.
The geometrical model adopted by the invention is shown in figure 2, wherein the moment that the low orbit satellite A (first satellite) is nearest to the target radiation source is azimuth momentThe nearest moment of the low orbit satellite B (second satellite) from the target radiation source is azimuth moment. Low orbit satellite a at azimuth momentThe instantaneous position vector is as followsThe instantaneous velocity vector is. Low orbit satellite B at azimuth momentThe instantaneous position vector is as followsInstantaneous velocity vector。
In one embodiment, passive synthetic aperture processing is performed on radiation source signals received by the first satellite and the second satellite from the target radiation source, respectively, so as to obtain azimuth time and Doppler slope of the first satellite and the second satellite corresponding to the target radiation source respectively, and then, according to the azimuth time and Doppler slope of the first satellite and the second satellite respectively, an instantaneous position vector, an instantaneous velocity vector and a distance-wise distance of the first satellite and the second satellite under the azimuth time corresponding to the target radiation source respectively are determined. Wherein the Doppler slope characterizes the rate at which the signal frequency of the radiation source signal received by the satellite changes over time.
And 104, constructing an equation of a first plane and an equation of a second plane in which the target radiation source is positioned according to the instantaneous position vector and the instantaneous speed vector of the first satellite and the second satellite respectively.
Specifically, an equation for a first plane in which the target radiation source is located is constructed based on the instantaneous position vector and the instantaneous velocity vector of the first satellite. And constructing an equation of a second plane in which the target radiation source is located according to the instantaneous position vector and the instantaneous speed vector of the second satellite.
The first plane is perpendicular to the instantaneous speed vector of the first satellite, and the second plane is perpendicular to the instantaneous speed vector of the second satellite.
And 106, constructing an equation of a first curved surface and an equation of a second curved surface where the target radiation source is located according to the instantaneous position vectors and the distance-wise distances of the first satellite and the second satellite respectively.
Specifically, an equation of a first curved surface where the target radiation source is located is constructed according to the instantaneous position vector and the distance-to-distance of the first satellite. And constructing an equation of a second curved surface where the target radiation source is positioned according to the instantaneous position vector and the distance-to-distance of the second satellite.
The distance between any point on the first curved surface and the first satellite is equal to the distance direction distance of the first satellite. The distance between any point on the second curved surface and the second satellite is equal to the distance of the second satellite.
And 108, combining the equation of the first plane, the equation of the second plane, the equation of the first curved surface and the equation of the second curved surface to form a nonlinear equation set, and solving the nonlinear equation set to obtain the position coordinate value of the target radiation source.
In one embodiment, a newton equation set is constructed according to a nonlinear equation set, an initial predicted position coordinate value is set, the newton equation set is solved iteratively until iteration is stopped, and the predicted position coordinate value obtained in the last iteration is determined as the position coordinate value of the target radiation source.
According to the double-star stationary radiation source three-dimensional positioning method based on the passive synthetic aperture, the passive synthetic aperture processing is carried out on the radiation source signals from the same target radiation source respectively received by the two satellites, then the nonlinear equation set is constructed for solving, the problem that elevation information cannot be obtained by using only a single satellite for passive synthetic aperture processing is avoided, position coordinate values containing the elevation information of the target radiation source can be accurately determined, three-dimensional positioning is achieved, and the positioning precision of the radiation source is improved. In addition, compared with the traditional methods of frequency measurement positioning, direction measurement positioning, time difference positioning, time-frequency difference positioning and the like, the method can improve the positioning precision, can also improve the replacement of an array antenna by a single antenna, reduces the volume and further reduces the requirement on satellite load.
In one embodiment, the method comprises the steps of respectively carrying out passive synthetic aperture processing on radiation source signals from a target radiation source received by a first satellite and a second satellite, and determining instantaneous position vectors, instantaneous speed vectors and distance distances of the first satellite and the second satellite at azimuth moments corresponding to the target radiation source respectively; according to the navigation positioning information of the first satellite and the second satellite, determining the instantaneous position vector and the instantaneous speed vector of the first satellite and the second satellite respectively at the respective azimuth time, and according to the instantaneous speed vector and the Doppler slope of the first satellite and the second satellite respectively, determining the distance direction distance between the first satellite and the second satellite and the target radiation source respectively.
For example, the radiation source signals from the target radiation source received by the first satellite A and the second satellite B are respectively processed by passive synthetic aperture to obtain the azimuth moment of the first satellite A corresponding to the target radiation sourceAnd Doppler slopeAnd the azimuth moment corresponding to the second satellite BAnd Doppler slope. Determining the moment of the first satellite A in the azimuth direction according to the navigation positioning information of the first satellite ALower instantaneous position vectorAnd instantaneous velocity vector. Determining the time of the second satellite B in the azimuth according to the navigation positioning information of the second satellite BLower instantaneous position vectorAnd instantaneous velocity vector。
In one embodiment, the navigation positioning information may be GNSS (Global Navigation SATELLITE SYSTEM ) information of satellites.
In one embodiment, the instantaneous velocity values of the first satellite and the second satellite at the respective azimuth moments may be determined based on the instantaneous velocity vectors of the first satellite and the second satellite, respectively, and then the range distances between the first satellite and the second satellite, respectively, and the target radiation source may be determined based on the instantaneous velocity values and the doppler slopes of the first satellite and the second satellite, respectively. Wherein the range-wise distance of the first satellite is proportional to the square of the instantaneous velocity value of the first satellite. The range-wise distance of the second satellite is proportional to the square of the instantaneous velocity value of the second satellite. The range-to-range of the first satellite is inversely proportional to the absolute value of the doppler slope of the first satellite. The range-to-range of the second satellite is inversely proportional to the absolute value of the doppler slope of the second satellite. The instantaneous velocity value is a modulus of the instantaneous velocity vector.
In the above embodiment, the passive synthetic aperture processing is performed on the radiation source signal to obtain the azimuth time and the doppler slope, and then the instantaneous position vector and the instantaneous velocity vector at the azimuth time can be accurately and efficiently determined according to the navigation positioning information of the satellite, and the distance can be accurately and efficiently determined according to the instantaneous velocity vector and the doppler slope.
In one embodiment, the distance-wise distance between the first satellite and the second satellite and the target radiation source is determined according to the instantaneous speed vector and the Doppler slope of the first satellite and the second satellite respectively, and the method comprises the steps of determining the instantaneous speed value of the first satellite and the instantaneous speed value of the second satellite respectively at the respective azimuth moment according to the instantaneous speed vector of the first satellite and the instantaneous speed vector of the second satellite respectively, determining the carrier frequency of the target radiation source according to the radiation source signals received by the first satellite and the second satellite, and determining the distance-wise distance between the first satellite and the second satellite and the target radiation source according to the instantaneous speed value and the Doppler slope of the first satellite and the Doppler slope of the second satellite respectively and the carrier frequency and the light speed of the target radiation source respectively.
In one embodiment, the range-to-range is proportional to the carrier frequency of the target radiation source. The distance-to-distance is proportional to the square of the instantaneous speed value. The distance-to-distance is inversely proportional to the speed of light. The range-wise distance is inversely proportional to the absolute value of the doppler slope.
In one embodiment, the range-wise distance between the first satellite and the second satellite, respectively, and the target radiation source may be determined according to the following formula:
Wherein, the Representing the range-wise distance between the first satellite a and the target radiation source.Representing the range-wise distance between the second satellite B and the target radiation source.Representing the carrier frequency of the target radiation source.Indicating the speed of light.Representing the instantaneous velocity value of the first satellite a.Representing the instantaneous velocity value of the second satellite B.Representing the doppler slope of the first satellite a.Representing the doppler slope of the second satellite B.
In the above embodiment, the distance-direction distance between the first satellite and the second satellite and the target radiation source can be accurately determined according to the instantaneous velocity value and the doppler slope of the first satellite and the second satellite, and the carrier frequency and the speed of light of the target radiation source, respectively.
In one embodiment, constructing the equation for the first plane and the equation for the second plane in which the target radiation source is located based on the instantaneous position vector and the instantaneous velocity vector of the first satellite and the second satellite, respectively, includes constructing the first position vector and the second position vector of the target radiation source relative to the first satellite and the second satellite, respectively, based on the difference between the position coordinate variable of the target radiation source and the instantaneous position vector of the first satellite and the instantaneous velocity vector of the second satellite, constructing the equation for the first plane in which the target radiation source is located based on the first position vector and the instantaneous velocity vector of the first satellite, and constructing the equation for the second plane in which the target radiation source is located based on the second position vector and the instantaneous velocity vector of the second satellite.
In one embodiment, an equation for the first plane in which the target radiation source is located may be constructed based on the point product between the first position vector and the instantaneous velocity vector of the first satellite being equal to zero. And constructing an equation of a second plane in which the target radiation source is located according to the point product between the second position vector and the instantaneous speed vector of the second satellite being equal to zero.
It will be appreciated that since the first position vector of the target radiation source relative to the first satellite is perpendicular to the instantaneous velocity vector of the first satellite, the equation for the first plane may be constructed by constraining the dot product between the first position vector and the instantaneous velocity vector of the first satellite to be equal to zero. Since the second position vector of the target radiation source relative to the second satellite is perpendicular to the instantaneous velocity vector of the second satellite, an equation for the second plane may be constructed by constraining the dot product between the second position vector and the instantaneous velocity vector of the second satellite to be equal to zero.
In one embodiment, the equation for the first plane is as follows:
Wherein, the Representing the instantaneous velocity vector of the first satellite a.Representing the instantaneous position vector of the first satellite a.Representing the position coordinate variables of the target radiation source.A first position vector of the target radiation source relative to the first satellite is represented. T represents the transpose.
In one embodiment, the equation for the second plane is as follows:
Wherein, the Representing the instantaneous velocity vector of the second satellite B.Representing the instantaneous position vector of the second satellite B.Representing the position coordinate variables of the target radiation source.Representing a second position vector of the target radiation source relative to the second satellite. T represents the transpose.
In the embodiment, the equation of the first plane in which the target radiation source is positioned is constructed according to the first position vector and the instantaneous speed vector of the first satellite, and the equation of the second plane in which the target radiation source is positioned is constructed according to the second position vector and the instantaneous speed vector of the second satellite, so that the equation of the first plane and the equation of the second plane in which the target radiation source is positioned can be accurately obtained.
In one embodiment, the constructing an equation of the first curved surface and an equation of the second curved surface in which the target radiation source is located based on the instantaneous position vectors and the distance-wise distances of the first satellite and the second satellite, respectively, includes constructing a first position vector of the target radiation source relative to the first satellite and a second position vector of the target radiation source relative to the second satellite based on the difference between the position coordinate variables of the target radiation source and the instantaneous position vectors of the first satellite and the second satellite, respectively, constructing an equation of the first curved surface in which the target radiation source is located based on the distance-wise distances of the first position vector and the first satellite, and constructing an equation of the second curved surface in which the target radiation source is located based on the distance-wise distances of the second position vector and the second satellite.
In one embodiment, an equation for the first curved surface on which the target radiation source is located may be constructed based on the first position vector having a dot product with itself equal to the square of the distance to the distance of the first satellite. And constructing an equation of a second curved surface where the target radiation source is positioned according to the square of the distance direction distance of the second satellite and the dot product of the second position vector and the second position vector.
In one embodiment, the equation for the first curved surface is as follows:
Wherein, the Representing the instantaneous position vector of the first satellite a.Representing the position coordinate variables of the target radiation source.A first position vector of the target radiation source relative to the first satellite is represented.Representing the range-wise distance between the first satellite a and the target radiation source. T represents the transpose.
In one embodiment, the equation for the second curved surface is as follows:
Wherein, the Representing the instantaneous position vector of the second satellite B.Representing the position coordinate variables of the target radiation source.Representing a second position vector of the target radiation source relative to the second satellite.Representing the range-wise distance between the second satellite B and the target radiation source. T represents the transpose.
In the above embodiment, the equation of the first curved surface where the target radiation source is located is constructed according to the distance between the first position vector and the first satellite, and the equation of the second curved surface where the target radiation source is located is constructed according to the distance between the second position vector and the second satellite, so that the equation of the first curved surface and the equation of the second curved surface where the target radiation source is located can be accurately constructed.
In one embodiment, solving the nonlinear equation set to obtain the position coordinate value of the target radiation source comprises the steps of constructing a Newton equation set according to the nonlinear equation set, obtaining initial predicted position coordinate values, substituting the initial predicted position coordinate values into the Newton equation set in each iteration to obtain the position coordinate adjustment value of the current iteration, determining the predicted position coordinate values of the next iteration according to the position coordinate adjustment value of the current iteration and the predicted position coordinate values of the current iteration, returning to execute the steps of substituting the predicted position coordinate values of the current iteration into the Newton equation set, solving to obtain the position coordinate adjustment value of the current iteration, entering the next iteration until the iteration stopping condition is met, and determining the predicted position coordinate values obtained in the last iteration as the position coordinate value of the target radiation source after the iteration is stopped.
In one embodiment, in each iteration, the predicted position coordinate value of the next iteration may be determined from the sum of the position coordinate adjustment value of the current iteration and the predicted position coordinate value of the current iteration.
In one embodiment, the system of nonlinear equations is as follows:
The conversion of the nonlinear equation set into vector form is as follows:
Wherein, the Representing the position coordinate variables of the target radiation source.
Can then be foundIs a derivative matrix of (a). The derivative matrix may be a Jacobi (Jacobi) matrix or the like.
ObtainingJacobian matrix of (a)The following are provided:
According to AndConstructing a Newton equation set:
Where k represents the iteration round number. Representing the predicted position coordinate values of the kth iteration.Representing the position coordinate adjustment value of the kth iteration.
Acquiring initial predicted position coordinate valuesWill beSubstituting the coordinate values of the predicted position in the first iteration into a Newton equation set:
Solving the Newton equation set to obtain the position coordinate adjustment value of the first round:
Then, according to the predicted position coordinate value in the first round of iteration With position coordinate adjustment values in a first round of iterationDetermining the predicted position coordinate value in the next iteration:
Iteratively executing the step of solving the Newton equation set to obtain a position coordinate adjustment value, then obtaining a predicted position coordinate value in the next iteration until the iteration stop condition is met, and obtaining the predicted position coordinate value in the last iterationIs determined as a position coordinate value of the target radiation source.
In one embodiment, the iteration stop condition may be that a difference between the predicted position coordinate value in the current round of iteration and the predicted position coordinate value in the previous round of iteration is less than a preset threshold.
In one embodiment, the iteration stop condition may be as follows:
Wherein, the Representing the predicted position coordinate values in the current round of iterations.Representing the predicted position coordinate values in the previous iteration.Representing a preset threshold.Representing the dimension of the predicted position coordinate values.Representing the value of the ith bit in the predicted position coordinate values in the current round of iterations.Representing the value of the ith bit in the predicted position coordinate values in the previous iteration.
In the above embodiment, the newton equation set is constructed according to the nonlinear equation set, and then the newton equation set is solved iteratively, and the predicted position coordinate value obtained in the last iteration is determined as the position coordinate value of the target radiation source, so that the position coordinate value of the target radiation source can be accurately determined, and the positioning accuracy of the radiation source is improved.
The efficiency of the present invention is verified by simulation experimental data as follows. In the simulation experiment, the position coordinate of the radiation source under an ECEF coordinate system (Earth-Centered, earth-Fixed coordinate system) is [ -2164952.31,4394341.81,4099970.57], the carrier frequency of the radiation source is 1.6GHz, the sampling rate of baseband signals is 96KHz, the duration of received signals in the over-top time period of a low-orbit satellite A (a first satellite) and a low-orbit satellite B (a second satellite) is 6s, the instantaneous speed values of the low-orbit satellite A and the low-orbit satellite B are 7258.96 m/s and 7383.64 m/s, and the azimuth time is momentAnd1.3141S and 1.4471s, respectively, from distance to distanceAndThe duration of the passive synthetic aperture treatments was 0.69s for 539.315km and 550.515km respectively. The received radiation source signals of the low-orbit satellite A and the low-orbit satellite B are subjected to passive synthetic aperture processing to obtain Doppler slope-azimuth time processing result graphs as shown in fig. 3 (a) and 3 (B), wherein fig. 3 (a) is the Doppler slope-azimuth time processing result graph of the low-orbit satellite A, and fig. 3 (B) is the Doppler slope-azimuth time processing result graph of the low-orbit satellite B, and according to fig. 3 (a) and 3 (B), the azimuth time and the Doppler slope estimated by the passive synthetic aperture processing are respectively、、、. Calculating to obtain the distance direction distance as、. Given initial predicted position coordinate valuesObtainingThe method comprises the following steps:
Obtaining The Jacobi matrix of (a) is:
Will be AndSubstituting into Newton equation set to obtain the solution:
The method further comprises the following steps:
And iteratively executing the steps until the iteration stop condition is met, wherein the position coordinate value of the output target radiation source is [ -2165170.48,4394692.05,4100205.73], and the estimated error is 474.95m. The variation of the positioning estimation error with the number of iterations is shown in fig. 4.
The three-dimensional positioning device of the double-star stationary radiation source based on the passive synthetic aperture, which is provided by the invention, is described below, and the three-dimensional positioning device of the double-star stationary radiation source based on the passive synthetic aperture, which is described below, and the three-dimensional positioning method of the double-star stationary radiation source based on the passive synthetic aperture, which is described above, can be correspondingly referred to each other.
As shown in fig. 5, the present invention provides a dual-star stationary radiation source three-dimensional positioning device 500 based on passive synthetic aperture, comprising the following modules:
the data processing module 502 is configured to perform passive synthetic aperture processing on radiation source signals received by the first satellite and the second satellite from the target radiation source, and determine an instantaneous position vector, an instantaneous velocity vector, and a distance-wise distance of the first satellite and the second satellite at azimuth-wise moments corresponding to the target radiation source, respectively.
The equation construction module 504 is configured to construct an equation of a first plane and an equation of a second plane in which the target radiation source is located according to the instantaneous position vector and the instantaneous velocity vector of the first satellite and the second satellite, respectively, and construct an equation of a first curved surface and an equation of a second curved surface in which the target radiation source is located according to the instantaneous position vector and the distance of the first satellite and the second satellite, respectively.
The position solving module 506 is configured to form a nonlinear equation set by combining the equation of the first plane, the equation of the second plane, the equation of the first curved surface and the equation of the second curved surface, and solve the nonlinear equation set to obtain a position coordinate value of the target radiation source.
In one embodiment, the data processing module 502 is further configured to perform passive synthetic aperture processing on radiation source signals received by the first satellite and the second satellite from the target radiation source, respectively, to obtain azimuth time and doppler slope of the first satellite and the second satellite corresponding to the target radiation source, determine an instantaneous position vector and an instantaneous velocity vector of the first satellite and the second satellite at the respective azimuth time according to navigation positioning information of the first satellite and the second satellite, and determine a distance direction distance between the first satellite and the second satellite and the target radiation source according to the instantaneous velocity vector and the doppler slope of the first satellite and the second satellite, respectively.
In one embodiment, the data processing module 502 is further configured to determine an instantaneous velocity value of the first satellite and the second satellite at each azimuth moment according to the instantaneous velocity vector of the first satellite and the second satellite, respectively, determine a carrier frequency of the target radiation source according to the radiation source signals received by the first satellite and the second satellite, and determine a distance direction distance between the first satellite and the second satellite and the target radiation source according to the instantaneous velocity value and the doppler slope of the first satellite and the second satellite, respectively, and the carrier frequency and the speed of light of the target radiation source, respectively.
In one embodiment, the equation construction module 504 is further configured to construct a first position vector of the target radiation source relative to the first satellite and a second position vector of the target radiation source relative to the second satellite based on a difference between the position coordinate variables of the target radiation source and the instantaneous position vectors of the first satellite and the second satellite, respectively, construct an equation of a first plane in which the target radiation source is located based on the first position vector and the instantaneous velocity vector of the first satellite, and construct an equation of a second plane in which the target radiation source is located based on the second position vector and the instantaneous velocity vector of the second satellite.
In one embodiment, the equation construction module 504 is further configured to construct a first position vector of the target radiation source relative to the first satellite and a second position vector of the target radiation source relative to the second satellite based on a difference between the position coordinate variables of the target radiation source and the instantaneous position vectors of the first satellite and the second satellite, respectively, construct an equation of a first curved surface where the target radiation source is located based on the distance-wise distances of the first position vector and the first satellite, and construct an equation of a second curved surface where the target radiation source is located based on the distance-wise distances of the second position vector and the second satellite.
In one embodiment, the position solving module 506 is further configured to construct a newton equation set according to the nonlinear equation set, obtain an initial predicted position coordinate value, take the initial predicted position coordinate value as a predicted position coordinate value in a first iteration, substitute the predicted position coordinate value of the current iteration into the newton equation set in each iteration, solve to obtain a position coordinate adjustment value of the current iteration, determine a predicted position coordinate value of a next iteration according to the position coordinate adjustment value of the current iteration and the predicted position coordinate value of the current iteration, return to execute the step of substituting the predicted position coordinate value of the current iteration into the newton equation set, solve to obtain the position coordinate adjustment value of the current iteration, enter the next iteration until an iteration stop condition is satisfied, and determine the predicted position coordinate value obtained in the last iteration as the position coordinate value of the target radiation source after the iteration is stopped.
In another aspect, the invention also provides a computer program product, which comprises a computer program, wherein the computer program can be stored on a non-transient computer readable storage medium, and when the computer program is executed by a processor, the computer can execute the two-star stationary radiation source three-dimensional positioning method based on the passive synthetic aperture, which is provided by the methods, and comprises the steps of respectively carrying out passive synthetic aperture processing on radiation source signals received by a first satellite and a second satellite from a target radiation source, determining an instantaneous position vector, an instantaneous velocity vector and a distance of the first satellite and the second satellite respectively under the moment corresponding to the azimuth of the target radiation source, respectively, constructing an equation of a first plane and an equation of a second plane where the target radiation source is located according to the instantaneous position vector and the instantaneous velocity vector of the first satellite, respectively, constructing an equation of a first curved surface where the target radiation source is located and an equation of a second curved surface according to the instantaneous position vector and the distance of the first satellite, respectively, and solving a linear set of coordinate values of the equations of the first curved surface and the second curved surface to form a non-linear set of nonlinear radiation coordinate values, and obtaining a non-linear set of the nonlinear set of position of the radiation coordinate values.
The apparatus embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art will understand and implement the present invention without undue burden.
From the above description of the embodiments, it will be apparent to those skilled in the art that the embodiments may be implemented by means of software plus necessary general hardware platforms, or of course may be implemented by means of hardware. Based on this understanding, the foregoing technical solution may be embodied essentially or in a part contributing to the prior art in the form of a software product, which may be stored in a computer readable storage medium, such as ROM/RAM, a magnetic disk, an optical disk, etc., including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method described in the respective embodiments or some parts of the embodiments.
It should be noted that the above-mentioned embodiments are merely for illustrating the technical solution of the present invention, and not for limiting the same, and although the present invention has been described in detail with reference to the above-mentioned embodiments, it should be understood by those skilled in the art that the technical solution described in the above-mentioned embodiments may be modified or some technical features may be equivalently replaced, and these modifications or substitutions do not make the essence of the corresponding technical solution deviate from the spirit and scope of the technical solution of the embodiments of the present invention.
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