CN110849377A - Space target relative navigation system and method based on constellation cooperation - Google Patents
Space target relative navigation system and method based on constellation cooperation Download PDFInfo
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Abstract
The invention provides a space target relative navigation system with cooperative constellation, which comprises: the satellite group comprises a main satellite and at least six auxiliary satellites, the main satellite is in communication connection with any one auxiliary satellite, the auxiliary satellites take the main satellite as a center and fly around according to a design configuration, the auxiliary satellites measure position coordinates of the auxiliary satellites relative to the main satellite and send the position coordinates to the main satellite, and the auxiliary satellites also measure altitude angle values and azimuth angle values of a space target relative to the sight line direction of the auxiliary satellite and send the altitude angle values and the azimuth angle values to the main satellite; screening four auxiliary stars by the main star according to a designed selection method; and the relative navigation filter is arranged on the main satellite, and the position of the space target relative to the main satellite under the orbit system is calculated through filtering estimation according to the position measurement values sent by the four screened auxiliary satellites at the same time, so that the only angle measurement relative navigation of the space target through the satellite group is realized. The invention also comprises a multi-angle relative navigation method under the modified spherical coordinate system.
Description
Technical Field
The invention relates to the technical field of spacecraft navigation, in particular to a space target relative navigation system and method based on constellation cooperation.
Background
With the increasing frequency of space exploration, on one hand, micro-nano satellites develop vigorously, and various micro-nano satellite group plans with large scales are developed; on the other hand, the amount of space garbage also increases sharply, and the operation safety of the on-orbit spacecraft is threatened. Space debris is usually an uncontrolled non-cooperative target, and most of the space debris are completely non-cooperative targets, so that on-orbit information related to morphology, kinematics and optics of the space debris cannot be obtained, the space debris is accurately positioned and tracked and detected, and the method is an effective way for avoiding on-orbit collision threats.
Under the condition of super-far relative distance, only relative angle information can be obtained by the tracking star, and the traditional single tracking star positions the target through only goniometric relative navigation, so that the positioning accuracy is seriously influenced due to insufficient observability. Therefore, a constellation is formed by utilizing the micro-nano satellites, a plurality of member satellites in the constellation cooperate with one another to perform remote sight measurement and accurate navigation positioning on space targets such as space rubbish and the like, necessary remote relative navigation information can be provided for active clearing of space debris and maintenance of failed satellites, and important research value and development potential are achieved.
Disclosure of Invention
The invention aims to provide a space target relative navigation system and method based on constellation cooperation, which can carry out high-precision relative positioning on a space target in a micro-nano constellation cooperation angle measurement mode at an ultra-long distance section which can not realize distance measurement.
In order to achieve the above object, the present invention provides a space target relative navigation system with constellation coordination, comprising: the system comprises a constellation, a plurality of relative position measuring sensors, a plurality of angle measuring sensors and a relative navigation filter;
the constellation consists of a plurality of micro-nano satellites; the constellation comprises a main star and at least six auxiliary stars; the main satellite is in communication connection with any auxiliary satellite; the auxiliary star takes the main star as the center and flies around according to the design configuration;
the auxiliary stars are provided with the relative position measuring sensor and the angle measuring sensor; the main star is provided with the angle measuring sensor; the auxiliary star obtains the position coordinate relative to the main star through the relative position measuring sensor of the auxiliary star, and the auxiliary star also sends the measured position coordinate to the main star; the main star and the auxiliary star measure the high-low angle value and the azimuth angle value of the space target relative to the sight line direction of the main star and the auxiliary star through respective angle measuring sensors; the auxiliary star also sends the measured high-low angle value and azimuth angle value to the main star; screening a plurality of auxiliary stars by the main star according to a designed selection method;
the relative navigation filter is arranged on the main satellite, and according to the position coordinate value, the altitude angle value and the azimuth angle value which are sent by the screened auxiliary satellites at the same moment and the altitude angle value and the azimuth angle value of the space target measured by the main satellite at the moment, the position of the space target relative to the main satellite under the orbital system is calculated through filtering estimation, so that only angle measurement relative navigation is carried out on the space target through the satellite group.
The main satellite and the auxiliary satellite are both micro-nano satellites.
The selection of a plurality of satellites is specifically the selection of four satellites.
A multi-angle relative navigation method under a modified spherical coordinate system is realized by adopting a space target relative navigation system with constellation cooperation, and comprises the following steps:
s1, taking the main star as the center, and flying around the main star according to the designed flying around configuration by at least six auxiliary stars;
s2, the auxiliary star measures the position coordinate value relative to the main star and sends the measured position coordinate to the main star; the main satellite and the auxiliary satellite measure the high-low angle value and the azimuth angle value of the space target relative to the sight line direction of the main satellite and the auxiliary satellite; the auxiliary star also sends the measured high-low angle value and azimuth angle value to the main star;
s3, screening four auxiliary stars from the at least six auxiliary stars by the main star;
s4, establishing a correction spherical coordinate system; and the main satellite performs relative navigation calculation according to the position coordinates, the altitude angle values and the azimuth angle values measured by the four screened auxiliary satellites at the same moment, the altitude angle values and the azimuth angle values of the space target measured by the main satellite at the moment and the relation between the corrected spherical coordinate system and the rectangular coordinate system to obtain the three-axis relative position and the three-axis relative speed of the space target relative to the main satellite in the rectangular coordinate system.
Step S1 includes:
s11, uniformly distributing the initial positions of the at least six auxiliary stars on a circle in a plane perpendicular to the track speed direction of the main star by taking the main star as the center of the circle, and setting the radius of the circle according to the estimated space between the space target and the main star;
s12, setting the initial relative speed of the auxiliary satellite relative to the main satellite through a J2 energy matching solving method, compensating the influence of the earth on the J2 gravity perturbation of the auxiliary satellite, and reducing the fuel consumption for maintaining the fly-around configuration;
and S13, starting from the corresponding initial positions, the at least six auxiliary stars fly around the main star by taking the main star as the center of a circle according to the set initial relative speed.
Step S3 includes:
s31, selecting four auxiliary stars from the at least six auxiliary stars by the main star, and calculating the geometric accuracy factors of the four auxiliary stars according to the altitude angle value and the azimuth angle value of the four auxiliary stars measured at the time T; repeating the step S31, and traversing all combinations of the four satellites;
and S32, screening four auxiliary stars with the minimum geometric precision factor value, and respectively recording the four auxiliary stars as a first screening auxiliary star to a fourth screening auxiliary star.
Step S4 includes:
s41, constructing a corrected spherical coordinate system by taking the centroid of the main star as the origin, and
to correct the state quantities of the spherical coordinate system, where p,
respectively the distance value and the change rate of the distance value of the space target relative to the main star, α respectively the altitude angle value and the azimuth angle value of the space target relative to the sight line direction of the main star,
the change rate of the high and low angles of the space target relative to the sight line direction of the main satellite is obtained;
the azimuth angle change rate of the space target relative to the sight line direction of the main satellite is obtained;
s42, constructing a system state equation set of the main satellite in the correction spherical coordinate system by using the geometric conversion relation between the state quantity in the correction spherical coordinate system and the state quantity in the rectangular coordinate system and combining a second-order C-W equation in the rectangular coordinate system:
wherein the content of the first and second substances,
ωcis the angular velocity of the orbit of the main satellite, acx、acy、aczThe components of the main star-orbit control acceleration on three axes are respectively.
S43, order αi(t) representing the elevation angle of the spatial target relative to the ith screening satellite gaze direction, let βi(t) represents the elevation angle of the space target relative to the ith screening satellite sight line direction, and t represents the time, i ∈ [1,4 ]]；
Let [ x)Ai(t),yAi(t),zAi(t)]TScreening the position coordinates of the auxiliary star relative to the main star for the ith, i belongs to [1,4 ]]；
S44, according to αi(t)、βi(t)、[xAi(t),yAi(t),zAi(t)]TAnd
the geometrical relationship between the two is used for constructing a multi-angle observation equation, wherein i belongs to [1,4 ]]：
Wherein, Z (t) represents the target sight angle observed quantity vector of the four screened satellites, h (X (t)) represents the functional relation between the observed quantity and the state quantity, and v (t) represents the unmodeled error quantity.
S45, adopting a firefly filtering algorithm, combining a system state equation set and a multi-angle observation equation, and carrying out filtering calculation to obtain the state quantity under the correction spherical coordinate system
And then according to the relation between the corrected spherical coordinate system and the rectangular coordinate system, calculating to obtain the position and the speed of the space target relative to the main satellite under the rectangular coordinate system:
wherein the ratio of x, y, z,the three-axis relative position and relative velocity of the space target relative to the main star are respectively.
Compared with the prior art, the invention has the advantages that:
1. compared with the traditional single-satellite only lateral angle relative navigation, the method greatly improves the observability degree of the space target and improves the accuracy of only angle measurement relative navigation;
2. compared with the prior multi-satellite relative measurement method, firstly, the optimal design is carried out on the constellation configuration, so that the synchronous observation of different directions on the target can be ensured, and the fuel consumption required by maintaining the constellation configuration is greatly reduced; secondly, selecting the observed quantity of four satellites with the minimum geometric accuracy factor from more than six satellites, ensuring the highest observable degree and effectively improving the navigation accuracy; and thirdly, constructing a system state equation under the correction spherical coordinate system, separating the direct observable state from the indirect observable state, avoiding the transmission of errors and noises between the two states, and further improving the navigation precision by matching with a firefly filtering algorithm.
3. The method greatly makes up the defect of insufficient precision when a single satellite positions a target, exerts the cooperative efficiency of the micro-nano constellation, can be applied to tracking and positioning abandoned satellites and spacecraft and carrier resident final stages with failures, and provides remote high-precision relative navigation information for space debris active removal and in-orbit service of failed satellites.
Drawings
In order to more clearly illustrate the technical solution of the present invention, the drawings used in the description will be briefly introduced, and it is obvious that the drawings in the following description are an embodiment of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts according to the drawings:
FIG. 1 is a schematic structural diagram of a space target relative navigation system with constellation coordination according to an embodiment of the present invention;
FIG. 2 is a schematic view of a fly-by trajectory configuration in accordance with a first embodiment of the present invention;
FIG. 3 is a flow chart of a multi-angle relative navigation method under a modified spherical coordinate system according to the present invention.
FIG. 4 is a flowchart illustrating the multi-angle relative navigation method in the modified spherical coordinate system of step S4 according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, the target T in space refers to a completely non-cooperative target without any a priori information, such as space garbage to be cleaned, obsolete satellites in mission, failed spacecraft, anti-satellite trial residual debris, carrier-resident final stages, and the like.
The invention provides a space target relative navigation system with cooperative constellation, which comprises: the system comprises a constellation, a plurality of relative position measuring sensors, a plurality of angle measuring sensors and a relative navigation filter.
The constellation consists of a plurality of micro-nano satellites; the constellation comprises a main star and at least six auxiliary stars; the main satellite is in communication connection with any auxiliary satellite; the auxiliary star takes the main star as the center and flies around according to the design configuration;
the auxiliary stars are provided with the relative position measuring sensor and the angle measuring sensor; the auxiliary star obtains the position coordinate relative to the main star through the relative position measuring sensor of the auxiliary star, and the auxiliary star also sends the measured position coordinate to the main star; measuring a high-low angle value and an azimuth angle value of the space target relative to the sight line direction of the satellite by the satellite through an angle measuring sensor of the satellite; the auxiliary star also sends the measured high-low angle value and azimuth angle value to the main star; and screening a plurality of auxiliary stars by the main star according to a designed selection method. In the embodiment of the invention, four satellites are screened.
The relative navigation filter is arranged on the main satellite, and the position of the space target relative to the main satellite under the orbital system is calculated through filtering estimation according to the position coordinate value, the altitude angle value and the azimuth angle value which are sent by the four screened auxiliary satellites at the same time, so that the only angle measurement relative navigation of the space target through the satellite group is realized.
As shown in fig. 1, in the first embodiment of the present invention, the constellation includes a primary star a, a secondary star B, and a secondary star G. The main star A and the six auxiliary stars are respectively provided with one relative position measuring sensor and one angle measuring sensor. And acquiring the position coordinates of the auxiliary stars B to G relative to the main star A under the orbital system through respective relative position measuring sensors. As shown in FIG. 1, the position coordinate of the secondary star B relative to the primary star A is [ X ]AB,YAB,ZAB]TThe position coordinate of the satellite G relative to the satellite A is [ X ]AG,YAG,ZAG]TAnd the auxiliary satellites B to G also send the position coordinates which are measured by the auxiliary satellites B to G respectively and are relative to the main satellite A. And the main star A, the auxiliary star B to the auxiliary star G obtain the relative angle measurement value of each to the target T through the angle measurement sensors. The relative angle measurement value specifically refers to a high-low angle value and an azimuth angle value of the space target relative to the direction of the sight of the satellite. And the auxiliary satellites B to G also send the measured relative angle values of the target T to the main satellite A. And the main satellite selects the measurement quantities of four auxiliary satellites from the measurement quantities of six auxiliary satellites according to a designed selection method for resolving relative navigation.
A multi-angle relative navigation method under a modified spherical coordinate system is realized by adopting a space target relative navigation system with cooperative constellation, as shown in figure 3, and comprises the following steps:
s1, taking the main star as the center, and flying around the main star according to the designed flying around configuration by at least six auxiliary stars;
step S1 includes:
s11, uniformly distributing the initial positions of the at least six auxiliary stars on a circle in a plane perpendicular to the track speed direction of the main star by taking the main star as the center of the circle, and setting the radius of the circle according to the estimated space between the space target and the main star;
s12, setting the initial relative speed of the auxiliary satellite relative to the main satellite through a J2 energy matching solving method, compensating the influence of the earth on the J2 gravity perturbation of the auxiliary satellite, and reducing the fuel consumption for maintaining the fly-around configuration;
and S13, starting from the corresponding initial positions, the at least six auxiliary stars fly around the main star by taking the main star as the center of a circle according to the set initial relative speed. And the initial position and the initial speed of the auxiliary star determine the trajectory configuration of the auxiliary star around the main star. In the first embodiment of the present invention, the trajectory configurations of satellites B to G are shown in fig. 2.
S2, the auxiliary star measures the position coordinate value relative to the main star and sends the measured position coordinate to the main star; measuring a high-low angle value and an azimuth angle value of the space target relative to the sight line direction of the satellite by the satellite; the auxiliary star also sends the measured high-low angle value and azimuth angle value to the main star;
s3, screening four auxiliary stars from the at least six auxiliary stars by the main star;
step S3 includes:
s31, selecting four auxiliary stars from the at least six auxiliary stars by the main star, and calculating the geometric accuracy factors of the four auxiliary stars according to the altitude angle value and the azimuth angle value of the four auxiliary stars measured at the time T; repeating the step S31, and traversing all combinations of the four satellites;
and S32, screening four auxiliary stars with the minimum geometric precision factor value, and respectively recording the four auxiliary stars as a first screening auxiliary star to a fourth screening auxiliary star.
S4, establishing a correction spherical coordinate system; and the main satellite performs relative navigation calculation according to the position coordinates, the altitude angle values and the azimuth angle values measured by the four screened auxiliary satellites at the same moment and the relation between the correction spherical coordinate system and the rectangular coordinate system to obtain the three-axis relative position and the three-axis relative speed of the space target relative to the main satellite in the rectangular coordinate system.
As shown in fig. 4, step S4 includes:
s41, constructing by taking the centroid of the main star as the originCorrecting the spherical coordinate system toTo correct the state quantities of the spherical coordinate system, where p,respectively the distance value and the change rate of the distance value of the space target relative to the main star, α respectively the altitude angle value and the azimuth angle value of the space target relative to the sight line direction of the main star,
the change rate of the high and low angles of the space target relative to the sight line direction of the main satellite is obtained;
the azimuth angle change rate of the space target relative to the sight line direction of the main satellite is obtained;
s42, constructing a system state equation set of the planet in the modified spherical coordinate system by using the geometric conversion relation between the state quantity in the modified spherical coordinate system and the state quantity in the rectangular coordinate system and combining a second-order C-W (Clohessy-Wiltshire) equation in the rectangular coordinate system:
wherein the content of the first and second substances,
ωcis the angular velocity of the orbit of the main satellite, acx、acy、aczThe components of the main star-orbit control acceleration on three axes are respectively.
S43, order αi(t) representing the elevation angle of the spatial target relative to the ith screening satellite gaze direction, let βi(t) represents the elevation angle of the space target relative to the ith screening satellite sight line direction, and t represents the time, i ∈ [1,4 ]]；
Let [ x)Ai(t),yAi(t),zAi(t)]TScreening the position coordinates of the auxiliary star relative to the main star for the ith, i belongs to [1,4 ]]；
S44, according to αi(t)、βi(t)、[xAi(t),yAi(t),zAi(t)]TAndthe geometrical relationship between the two is used for constructing a multi-angle observation equation, wherein i belongs to [1,4 ]]：
Wherein, Z (t) represents the target sight angle observed quantity vector of the four screened satellites, h (X (t)) represents the functional relation between the observed quantity and the state quantity, and v (t) represents the unmodeled error quantity.
S45, adopting a firefly filtering algorithm, combining a system state equation set and a multi-angle observation equation, and carrying out filtering calculation to obtain the state quantity under the correction spherical coordinate system
And then according to the relation between the corrected spherical coordinate system and the rectangular coordinate system, calculating to obtain the position and the speed of the space target relative to the main satellite under the rectangular coordinate system:
wherein the ratio of x, y, z,
the three-axis relative position and relative velocity of the space target relative to the main star are respectively.
Compared with the prior art, the invention has the advantages that:
1. compared with the traditional single-satellite only lateral angle relative navigation, the method greatly improves the observability degree of the space target and improves the accuracy of only angle measurement relative navigation;
2. compared with the prior multi-satellite relative measurement method, firstly, the optimal design is carried out on the constellation configuration, so that the synchronous observation of different directions on the target can be ensured, and the fuel consumption required by maintaining the constellation configuration is greatly reduced; secondly, selecting the observed quantity of four satellites with the minimum geometric accuracy factor from more than six satellites, ensuring the highest observable degree and effectively improving the navigation accuracy; and thirdly, constructing a system state equation under the correction spherical coordinate system, separating the direct observable state from the indirect observable state, avoiding the transmission of errors and noises between the two states, and further improving the navigation precision by matching with a firefly filtering algorithm.
3. The method greatly makes up the defect of insufficient precision when a single satellite positions a target, exerts the cooperative efficiency of the micro-nano constellation, can be applied to tracking and positioning abandoned satellites and spacecraft and carrier resident final stages with failures, and provides remote high-precision relative navigation information for space debris active removal and in-orbit service of failed satellites.
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications and substitutions can be easily made by those skilled in the art within the technical scope of the invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (7)
1. A constellation-coordinated spatial target relative navigation system, comprising: the system comprises a constellation, a plurality of relative position measuring sensors, a plurality of angle measuring sensors and a relative navigation filter;
the constellation comprises a main star and at least six auxiliary stars; the main satellite is in communication connection with any auxiliary satellite; the auxiliary star takes the main star as the center and flies around according to the design configuration;
the auxiliary stars are provided with the relative position measuring sensor and the angle measuring sensor; the main star is provided with the angle measuring sensor; the auxiliary star obtains the position coordinate relative to the main star through the relative position measuring sensor of the auxiliary star, and the auxiliary star also sends the measured position coordinate to the main star; the main star and the auxiliary star measure the high-low angle value and the azimuth angle value of the space target relative to the sight line direction of the main star and the auxiliary star through respective angle measuring sensors; the auxiliary star also sends the measured high-low angle value and azimuth angle value to the main star; screening a plurality of auxiliary stars by the main star according to a designed selection method;
the relative navigation filter is arranged on the main satellite, and according to the position coordinate value, the altitude angle value and the azimuth angle value which are sent by the screened auxiliary satellites at the same moment and the altitude angle value and the azimuth angle value of the space target measured by the main satellite at the moment, the position of the space target relative to the main satellite under the orbital system is calculated through filtering estimation, so that only angle measurement relative navigation is carried out on the space target through the satellite group.
2. The constellation-coordinated spatial target relative navigation system of claim 1, wherein the primary satellite and the secondary satellite are both micro-nano satellites.
3. The constellation-coordinated spatial target relative navigation system of claim 1, wherein a number of satellites, in particular four satellites, are selected.
4. A multi-angle relative navigation method under a modified spherical coordinate system is realized by adopting the space target relative navigation system with cooperative constellation according to any one of claims 1 to 3, and is characterized by comprising the following steps:
s1, taking the main star as the center, and flying around the main star according to the designed flying around configuration by at least six auxiliary stars;
s2, the auxiliary star measures the position coordinate value relative to the main star and sends the measured position coordinate to the main star; the main satellite and the auxiliary satellite measure the high-low angle value and the azimuth angle value of the space target relative to the sight line direction of the main satellite and the auxiliary satellite; the auxiliary star also sends the measured high-low angle value and azimuth angle value to the main star;
s3, screening four auxiliary stars from the at least six auxiliary stars by the main star;
s4, establishing a correction spherical coordinate system; and the main satellite performs relative navigation calculation according to the position coordinates, the altitude angle values and the azimuth angle values measured by the four screened auxiliary satellites at the same moment, the altitude angle values and the azimuth angle values of the space target measured by the main satellite at the moment and the relation between the corrected spherical coordinate system and the rectangular coordinate system to obtain the three-axis relative position and the three-axis relative speed of the space target relative to the main satellite in the rectangular coordinate system.
5. The method for multi-angle relative navigation in a modified spherical coordinate system as claimed in claim 4, wherein step S1 comprises:
s11, uniformly distributing the initial positions of the at least six auxiliary stars on a circle in a plane perpendicular to the track speed direction of the main star by taking the main star as the center of the circle, and setting the radius of the circle according to the estimated space between the space target and the main star;
s12, setting the initial relative speed of the auxiliary satellite relative to the main satellite through a J2 energy matching solving method, compensating the influence of the earth on the J2 gravity perturbation of the auxiliary satellite, and reducing the fuel consumption for maintaining the fly-around configuration;
and S13, starting from the corresponding initial positions, the at least six auxiliary stars fly around the main star by taking the main star as the center of a circle according to the set initial relative speed.
6. The method for multi-angle relative navigation in a modified spherical coordinate system as claimed in claim 4, wherein step S3 comprises:
s31, selecting four auxiliary stars from the at least six auxiliary stars by the main star, and calculating the geometric accuracy factors of the four auxiliary stars according to the altitude angle value and the azimuth angle value of the four auxiliary stars measured at the time t; repeating the step S31, and traversing all combinations of the four satellites;
and S32, screening four auxiliary stars with the minimum geometric precision factor value, and respectively recording the four auxiliary stars as a first screening auxiliary star to a fourth screening auxiliary star.
7. The method for multi-angle relative navigation in a modified spherical coordinate system as claimed in claim 6, wherein step S4 comprises:
s41, constructing a corrected spherical coordinate system by taking the centroid of the main star as the origin, and
to correct the state quantities of the spherical coordinate system, where p,
respectively the distance value and the change rate of the distance value of the space target relative to the main star, α respectively the altitude angle value and the azimuth angle value of the space target relative to the sight line direction of the main star,
the change rate of the high and low angles of the space target relative to the sight line direction of the main satellite is obtained;
the azimuth angle change rate of the space target relative to the sight line direction of the main satellite is obtained;
s42, constructing a system state equation set of the main satellite in the correction spherical coordinate system by using the geometric conversion relation between the state quantity in the correction spherical coordinate system and the state quantity in the rectangular coordinate system and combining a second-order C-W equation in the rectangular coordinate system:
wherein the content of the first and second substances,
ωcis the angular velocity of the orbit of the main satellite, acx、acy、aczThe components of the main star-orbit control acceleration on three axes are respectively;
s43, order αi(t) representing the elevation angle of the spatial target relative to the ith screening satellite gaze direction, let βi(t) represents the elevation angle of the space target relative to the ith screening satellite sight line direction, and t represents the time, i ∈ [1,4 ]]；
Let [ x)Ai(t),yAi(t),zAi(t)]TScreening the position coordinates of the auxiliary star relative to the main star for the ith, i belongs to [1,4 ]]；
S44, according to αi(t)、βi(t)、[xAi(t),yAi(t),zAi(t)]TAnd
the geometrical relationship between the two is used for constructing a multi-angle observation equation, wherein i belongs to [1,4 ]]：
Wherein Z (t) represents target sight angle observed quantity vectors of four screened auxiliary stars, h (X (t)) represents a functional relation between observed quantity and state quantity, and v (t) represents an unmodeled error quantity;
s45, adopting a firefly filtering algorithm, combining a system state equation set and a multi-angle observation equation, and carrying out filtering calculation to obtain the state quantity under the correction spherical coordinate system
And then according to the relation between the corrected spherical coordinate system and the rectangular coordinate system, calculating to obtain the position and the speed of the space target relative to the main satellite under the rectangular coordinate system:
wherein the ratio of x, y, z,
the three-axis relative position and relative velocity of the space target relative to the main star are respectively.
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