CN112379398B - Earth-moon space satellite navigation positioning method - Google Patents
Earth-moon space satellite navigation positioning method Download PDFInfo
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- CN112379398B CN112379398B CN202011059993.1A CN202011059993A CN112379398B CN 112379398 B CN112379398 B CN 112379398B CN 202011059993 A CN202011059993 A CN 202011059993A CN 112379398 B CN112379398 B CN 112379398B
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Abstract
The invention discloses a navigation and positioning method for earth-moon space satellites, which can meet the navigation and positioning coverage requirements in the large-scale range of the whole earth-moon space by selecting part or all of eight orbit types, namely a moon near-linear orbit, an earth-moon remote retrograde orbit, a round orbit around the moon, an earth high orbit round orbit, an earth large-eccentricity elliptical orbit, an earth-moon translation point L4/L5, an L1/L2 halo orbit and a sun-center orbit, as navigation satellite running orbits, and provides support for realizing the high-precision navigation and positioning of the earth-moon space. And the spatial position of the user can be obtained in real time based on a geometric solving mode, the positioning speed is high, the navigation positioning precision is high, and high-precision navigation service can be provided for the earth-moon space development.
Description
Technical Field
The invention relates to the technical field of earth-moon space satellite navigation, in particular to an earth-moon space satellite navigation positioning method.
Background
Earth-moon space refers to a universe space composed of near-earth space, earth-moon transfer space, and moon space. At present, the global satellite navigation system has real-time and high-precision navigation capability of the ground and the near-earth space, and brings great convenience to human life. However, with the development of aerospace technology and the need for human survival, the human footprint necessarily extends from near-earth space to earth-moon space, or even deeper and farther, space. In the future, people will frequently go to and fro the earth and the moon, and perform activities such as resource development, scientific experiments, material transportation and the like on the moon, so that the earth-moon economic circle is continuously developed. Just like the urgent need for marine navigation when the human beings enter the navigation era, the support of navigation and positioning can not be left for the human beings to develop the moon space, and the requirements on the navigation precision, the real-time performance, the autonomy and the like of the moon space are higher and higher along with the deepening of development activities. When an astronaut and a lunar robot carry out lunar activities, the support of a navigation positioning system is needed to help the astronaut and the lunar robot to accurately determine the position and the speed of the astronaut and the lunar robot and the position and the speed of a target point; when the spacecraft shuttles in the Earth-moon space, the navigation and positioning of the spacecraft are required to be carried out in the whole process and in real time, so that the state of the spacecraft is better mastered and the Earth-moon transfer is realized.
At present, although navigation constellations such as a U.S. GPS system, a Russian glonass system, an European Galileo system, a Chinese Beidou system and the like which run around the earth can support navigation and positioning of a part of the Earth-moon space after being upgraded and modified, the orbit heights of the navigation constellations are distributed within the range of 2-4 kilometers and are smaller than 40 kilometers of the Earth-moon space. When a satellite navigation system around the earth performs earth-moon space and moon surface navigation, the geometric structure is poor, so that the positioning accuracy is poor, and meanwhile, the signal transmitting power may not meet the navigation requirement in the earth-moon space scale and cannot support the navigation and positioning of the back of the moon.
As known from research and study of literature, literature 1 (patent CN201710090284.1) proposes a navigation constellation system based on earth high-orbit satellites and satellites near earth-moon translation points, which can implement the navigation function of earth-moon space, and the basic method is to first use pulsar to implement positioning of navigation constellation, and then determine the position of target satellite according to the inter-satellite distance measurement information of target satellite and navigation constellation. However, the earth high-orbit satellite and the satellite near the earth-moon translational point are basically distributed in a white road surface (i.e. an orbit plane of the earth revolving around the earth) or near the white road surface, the normal height from the white road surface is not more than 4 kilometers, and actually, the dimension of the earth-moon transfer space is about 40 kilometers, so that when the navigation and positioning are carried out by only depending on the earth high-orbit satellite and the satellite near the earth-moon translational point, the observed white road surface normal positioning accuracy is poor, and the three-dimensional position and speed determination accuracy in the earth-moon transfer space is poor. Meanwhile, the whole lunar surface is difficult to be effectively covered by only depending on the earth high orbit satellite and the satellite near the earth-moon translation point, and the high-precision navigation and positioning of the whole lunar surface cannot be realized.
Document 2 [ chenlei, huang ying bo, liu wen xiang, european steel ] and a lunar exploration vehicle orbit positioning analysis of a multi-global navigation satellite system combination, academic newspaper of national defense science and technology university, 2015,37(3):39-44 ] analyzes a scheme for realizing lunar space navigation based on systems such as american GPS, chinese beidou, european galileo and the like, performs analog simulation, researches the availability of a main lobe and a side lobe of a wave beam when each system is jointly positioned, and simultaneously evaluates a precision factor when each system is jointly applied. However, since the orbit height of these navigation systems is small relative to the earth-moon space scale, the earth-moon space navigation system proposed in the document [2] has a poor geometric observation structure, and the accuracy of navigation of earth-moon transfer space and the moon surface is limited, as in the document [1 ]. Meanwhile, one face of the moon always points to the earth, and the other face of the moon always faces back to the earth, so that the navigation and positioning of the back face of the moon cannot be realized by systems such as a GPS, a Beidou and a Galileo.
Document 3 (patent CN201210504473.6) proposes that earth-moon space navigation is realized by jointly calculating estimates of the spatial positions of earth satellites and moon satellites by using inter-satellite ranging data between the earth satellites and the moon satellites and earth-moon dynamic models. The method is theoretically feasible, but only one group of inter-satellite ranging is provided, so that the lunar satellite positioning accuracy obtained through combined solution is very limited; meanwhile, high-precision dynamic models are needed for joint solution, earth satellites or lunar satellites usually have orbit and attitude maneuvering capabilities due to task requirements, and the precision of the output force of a propeller usually cannot meet the requirement of joint solution, namely the earth-moon space navigation method based on the inter-satellite ranging mode is not suitable for satellite positioning with poor propulsion output precision.
The design of a suspended sun sail moon navigation constellation is described in document 4 [ dawn, yao, Chongqing ], seventh China satellite navigation academic annual meeting, S04 satellite orbit and clock error, 2016, 5, 18, to 20, and Hunan Changsha ], in consideration of the defect that the existing earth-orbiting satellite navigation system has a poor geometric observation structure during navigating in a moon space, a moon space navigation system based on a sun sail is provided, the sun sail is arranged on an artificial Lagrange day point of the sun-earth-moon system, and the sun light pressure borne by the sun sail is utilized to counteract the gravity of the moon, so that the sun sail is ensured to be stably located in the moon space for a long time, and the goal of the moon space navigation is achieved. However, since the light pressure and the earth-moon attraction on the solar sail are extremely complex and are difficult to accurately offset, the orbit of the solar sail is difficult to accurately determine, and the positioning accuracy based on the navigation constellation of the solar sail is affected.
Document 5 [ zhanli. earth moon system translation point navigation satellite constellation design and navigation performance analysis ] a doctor academic paper of Nanjing university, 2016 ] proposes a scheme for forming earth moon space navigation constellations by earth moon system satellites, including an earth moon system L1-L2 two-star constellation, an L2-L4-L5 three-star constellation, an L1-L2-L4-L5 four-star constellation, and the like, analyzes the navigation capabilities of different constellations, and provides an important technical reference for future earth moon space navigation system design. However, because these translational points are located in the white road surface, the navigation system based on this scheme has high navigation accuracy in the white road surface, but has extremely poor normal positioning accuracy in the white road surface, and even cannot perform calculation, so that it is difficult to meet the requirement of high-accuracy navigation positioning in the earth-moon space.
Therefore, the navigation positioning requirement of the earth-moon space flight task is urgently needed, an earth-moon space navigation constellation is developed, and high-precision navigation service is provided for earth-moon space development.
Disclosure of Invention
The invention provides a moon-earth space satellite navigation positioning method, which aims to solve the technical problem that the existing moon-earth space navigation constellation is difficult to meet the high-precision navigation positioning requirement in the large-scale range of the whole moon-earth space.
According to one aspect of the invention, a terrestrial-lunar space satellite navigation positioning method is provided, which comprises the following steps:
step S1: selecting partial or all orbits as navigation satellite operation orbits from eight orbit types, namely a moon near-linear orbit, a Earth-moon remote retrograde orbit, a round orbit around the moon, an Earth high orbit round orbit, an Earth large eccentricity ellipse orbit, an Earth-moon translation point L4/L5, an L1/L2 halo orbit and a Sun-center orbit, and deploying one or more navigation satellites on each operation orbit;
step S2: setting the minimum transmitting power of a navigation satellite signal;
step S3: and measuring the distances between the user and the plurality of navigation satellites observed by the user at any moment, and solving to obtain the spatial position of the user at the moment based on the measured distance values.
Further, the method also comprises the following steps:
step S4: and accurately positioning the spatial position of the user based on a dynamic method.
Further, the step S4 specifically includes the following steps:
step S41: obtaining a spatial state observation value of a user based on the spatial position of the user;
step S42: performing dynamics integration based on the earth-moon space dynamics model and the initial state of the user to obtain a space state calculation value of the user;
step S43: and continuously and iteratively adjusting parameters of the earth-moon space dynamic model and the initial state of the user according to the difference between the observed value and the calculated value of the user space state until the difference between the observed value and the calculated value of the user space state meets the navigation precision requirement, and taking the calculated value of the user space state after iteration as a high-precision navigation value.
Further, in step S1, a partial orbit is selected from eight orbit types as the orbit of the navigation satellite by the following steps:
step S11: classifying the eight track types based on a classification rule that the tracks are distributed on the white road surface or in the normal direction of the white road surface;
step S12: selecting different orbit types to combine according to the principle that four spatial distributions in the white road surface close to the moon, in the white road surface close to the earth, in the white road surface normal close to the moon and in the white road surface normal close to the earth exist;
step S13: and calculating the spatial position precision factors of different track type combinations to determine the advantages and disadvantages of the observation geometrical structures of the different track type combinations, and performing iterative optimization on the constellation configuration parameters by combining the earth-moon space coverage requirement.
Further, the earth-moon space coverage requirement refers to that at least four navigation satellites can be observed at any point in earth-moon space at any time;
the spatial position accuracy factor is calculated by the following steps:
assuming that N navigation satellites are arranged in the earth-moon space navigation constellation formed by combining different orbit types, a user corresponds to the navigation satellitesRespectively, in elevation and azimuth ofu→s,i、αu→s,i，i＝1,2,...,N；
Defining a geometric matrix G and a weight system matrix H:
H＝(GTG)-1
the spatial position accuracy factor is
Wherein h is11、h22、h33Representing the first three diagonal elements of the weight system matrix H.
Further, the minimum transmitting power of the navigation satellite signal is calculated by the following formula:
wherein, PRFor receiver sensitivity, GTTransmitting gain for navigation signals, GRFor receiver antenna gain, λ is the navigation signal wavelength, and d is the farthest distance between the navigation satellite and the user.
Further, the step S3 specifically includes the following steps:
step S31: acquiring the spatial positions of at least four navigation satellites observed by a user at any time;
step S32: measuring distances between the user and the navigation satellites;
step S33: the spatial location of the user is solved based on the distance measurements.
Further, the spatial positions of the navigation satellites in the step S31 are obtained by ground-based radio measurement or autonomously obtained by constellation prediction.
Further, the process of autonomously acquiring the spatial position of the navigation satellite through constellation prediction specifically comprises the following steps:
step S311: acquiring the initial position and the initial speed of each navigation satellite in the earth-moon space navigation constellation based on a foundation radio measurement means;
step S312: establishing a relational expression between the inter-satellite distance and the change rate of the inter-satellite distance of any two navigation satellites and the earth-moon space dynamic model parameters;
step S313: measuring by an inter-satellite distance measuring mode to obtain the inter-satellite distance and the inter-satellite distance change rate between any two navigation satellites;
step S314: jointly solving to obtain earth-moon space dynamic model parameters and initial state correction values of the navigation satellite based on the relational expression and the measurement result;
step S315: and repeating the steps S312-S314 at intervals to obtain the latest earth-moon space dynamic model parameters and the initial state of the navigation satellite, and performing constellation ephemeris forecast by using the latest initial state of the navigation satellite and the earth-moon space dynamic model parameters.
Further, in step S32, the distance between the user and the navigation satellite at any time is obtained through the measurement of the pseudorange, the carrier phase or the doppler shift of the user receiver.
The invention has the following effects:
the earth-moon space satellite navigation positioning method can meet the navigation positioning coverage requirement in the whole earth-moon space large-scale range by selecting part or all of the orbit from eight orbit types, namely a moon near-linear orbit, an earth-moon long-distance retrograde orbit, a moon-circle-around orbit, an earth high-orbit circular orbit, an earth large-eccentricity elliptical orbit, an earth-moon translational point L4/L5, an L1/L2 halo orbit and a sun-center orbit, and provides support for realizing earth-moon space high-precision navigation positioning. And the spatial position of the user can be obtained in real time based on a geometric solving mode, the positioning speed is high, the navigation positioning precision is high, and high-precision navigation service can be provided for the earth-moon space development.
In addition to the objects, features and advantages described above, other objects, features and advantages of the present invention are also provided. The present invention will be described in further detail below with reference to the drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
fig. 1 is a flow chart of a method for positioning earth-moon space satellite navigation according to a preferred embodiment of the invention.
Fig. 2 is a distribution diagram of the moon near-linear orbit and the earth-moon far-distance retrograde orbit in step S1 according to the preferred embodiment of the present invention.
Fig. 3 is a schematic distribution diagram of the elliptical orbits of large eccentricity of the earth in step S1 of the preferred embodiment of the present invention.
FIG. 4 is a distribution diagram of the ground-moon panning points L4/L5 in step S1 according to the preferred embodiment of the present invention.
FIG. 5 is a schematic diagram of the distribution of the L1/L2 halo tracks in step S1 according to the preferred embodiment of the present invention.
Fig. 6 is a sub-flowchart of the process of selecting a partial orbit from eight orbit types as the orbit for the navigation satellite in step S1 according to the preferred embodiment of the present invention.
Fig. 7 is a sub-flowchart of step S3 in accordance with the preferred embodiment of the present invention.
Fig. 8 is a sub-flowchart illustrating the process of autonomously acquiring the spatial positions of the navigation satellites through constellation prediction in step S31 in fig. 7.
Fig. 9 is a sub-flowchart of step S4 in fig. 1.
Detailed Description
The embodiments of the invention will be described in detail below with reference to the accompanying drawings, but the invention can be embodied in many different forms, which are defined and covered by the following description.
As shown in fig. 1, a preferred embodiment of the present invention provides a method for positioning earth-moon space satellite navigation, comprising the following steps:
step S1: selecting partial or all orbits as navigation satellite operation orbits from eight orbit types, namely a moon near-linear orbit, a Earth-moon remote retrograde orbit, a round orbit around the moon, an Earth high orbit round orbit, an Earth large eccentricity ellipse orbit, an Earth-moon translation point L4/L5, an L1/L2 halo orbit and a Sun-center orbit, and deploying one or more navigation satellites on each operation orbit;
step S2: setting the minimum transmitting power of a navigation satellite signal;
step S3: and measuring the distances between the user and the plurality of navigation satellites observed by the user at any moment, and solving to obtain the spatial position of the user at the moment based on the measured distance values.
It is understood that in the step S1, a part or all of the orbits are selected from the eight orbit types as the orbit of the navigation satellite, and one or more navigation satellites are deployed on each orbit, and these navigation satellites constitute the earth-moon space navigation constellation. The selection of the orbit type can meet the navigation positioning coverage requirement in the large scale range of the whole moon space, and provides support for realizing moon space high-precision navigation positioning. In addition, each navigation satellite is at least provided with two types of key loads which are respectively navigation signal emitters used for broadcasting navigation information such as ranging codes, navigation messages, carrier signals and the like and providing information service for the earth-moon space navigation; the inter-satellite range finder can adopt a microwave or laser range finder and is used for obtaining the distance between two navigation satellites and the change rate of the distance, providing observation data for the subsequent inversion of earth-moon space dynamics model parameters such as a moon gravitational field, sunlight pressure and the like, obtaining a high-precision dynamics model and the initial state of the navigation satellites and providing support for the prediction of constellation ephemeris.
As shown in fig. 2, the lunar near-linear orbit is similar to a lunar polar orbit in the earth-moon rotation coordinate system, and can effectively cover two lunar poles for a long time. But different from the polar orbit of the moon, the polar orbit is influenced by the combined action of earth and moon gravitation, and the orbit surface of the nearly straight orbit of the moon is always approximately vertical to the earth and moon connecting line. And usually, two near linear orbits are adopted, the far moon point is respectively positioned at the north pole and the south pole of the moon, and a plurality of navigation satellites are respectively arranged on the south and north near linear orbits at equal time intervals and are used for supporting high-precision navigation of two poles on the surface of the moon, normal navigation of a Earth-moon transfer space white road surface and navigation of an Earth-moon L1/L2 Halo orbital vehicle. The earth-moon long-distance retrograde orbit comprises earth-moon translation points L1 and L2 in the equatorial plane of the moon, and as shown in FIG. 2, the orbit has high stability and can keep long-term stability for decades or even hundreds of years. And a plurality of navigation satellites are deployed on the Earth-moon remote retrograde orbit at equal intervals and are used for supporting the navigation in the Earth-moon transfer space white road surface, the navigation on the moon surface and the navigation of Earth-moon L1 and L2 Halo orbital aircrafts. The orbit is distributed in a plurality of orbit surfaces around the moon, and the ascending points of the orbit surfaces are uniformly distributed along the equator of the moon. And a plurality of navigation satellites are uniformly distributed in each orbital plane to form full coverage on the lunar surface and support high-precision navigation of the lunar surface and the low-orbit lunar satellite. Aiming at the earth-moon space navigation task, reasonable orbit heights and orbit planes of the earth-surrounding high-orbit satellites are selected and distributed uniformly relative to the ascending intersection points, and a plurality of navigation satellites are uniformly deployed on each orbit plane, so that the earth-moon space navigation task has a better geometric distribution structure. As shown in FIG. 3, the large eccentricity elliptical orbit of the earth comprises a large eccentricity north elliptical orbit and a large eccentricity south elliptical orbit, the included angle between the orbit surface and the white road surface is close to 90 degrees, and the far points are respectively positioned at the north pole and the south pole of the earth. On the south and north earth large eccentricity elliptical orbits, a plurality of navigation satellites are respectively arranged at equal time intervals to ensure the navigation positioning precision along the normal direction of the white road surface. As shown in fig. 4, one navigation satellite is respectively arranged at the earth-moon panning points L4 and L5, and since the points L4 and L5 are located in the white road surface, the navigation satellites located at the two positions can ensure the navigation positioning accuracy in the white road surface or in parallel with the white road surface. As shown in fig. 5, the L1/L2 Halo orbits are respectively located on both sides of the moon of the earth-moon line, and a plurality of navigation satellites are respectively arranged on the L1/L2 Halo orbits at equal time intervals to ensure the navigation positioning accuracy in the white road surface and in the normal direction of the white road surface. And the sun center orbit is an earth revolution orbit, and the satellites are respectively deployed at positions corresponding to the front phase and the rear phase of the earth, so that the navigation and positioning accuracy in the white road surface and the normal direction of the white road surface are ensured.
It can be understood that, in the earth-moon space satellite navigation positioning method of this embodiment, a part or all of the orbit is selected as the operation orbit of the navigation satellite from eight orbit types, i.e., a moon near-linear orbit, a earth-moon long-distance retrograde orbit, a moon circular orbit, an earth high orbit circular orbit, an earth large-eccentricity elliptical orbit, an earth-moon translational point L4/L5, an L1/L2 halo orbit, and a sun-center orbit, so that the navigation positioning coverage requirement in the whole earth-moon space large-scale range can be met, and support is provided for realizing earth-moon space high-precision navigation positioning. And the spatial position of the user can be obtained in real time based on a geometric solving mode, the positioning speed is high, the navigation positioning precision is high, and high-precision navigation service can be provided for the earth-moon space development.
It can be understood that if the eight orbit types are all selected as the operation orbits of the navigation satellite, although the navigation positioning coverage requirement of the whole earth-moon space can be ensured to be met, design redundancy exists, the navigation positioning functions of some navigation satellites can be overlapped, the effective utilization rate of the whole navigation constellation is not high, and greater operation and maintenance cost can be brought. Therefore, the invention preferably selects partial orbit from the eight orbit types as the operation orbit of the navigation satellite, which not only can meet the navigation positioning coverage requirement of the whole Earth-moon space, but also has higher effective utilization rate of the whole navigation constellation and reduces the operation and maintenance cost of the whole constellation. Specifically, as shown in fig. 6, in step S1, a partial orbit is selected from eight orbit types as the orbit of the navigation satellite through the following steps:
step S11: classifying the eight track types based on a classification rule that the tracks are distributed on the white road surface or in the normal direction of the white road surface;
step S12: selecting different orbit types to combine according to the principle that four spatial distributions in the white road surface close to the moon, in the white road surface close to the earth, in the white road surface normal close to the moon and in the white road surface normal close to the earth exist;
step S13: and calculating the spatial position precision factors of different track type combinations to determine the advantages and disadvantages of the observation geometrical structures of the different track type combinations, and performing iterative optimization on the constellation configuration parameters by combining the earth-moon space coverage requirement.
It can be understood that when the satellite orbits in the local-lunar space navigation constellation are distributed in the white road surface and the normal direction of the white road surface at the same time, the navigation constellation has a better geometric structure, so that the navigation precision is higher. Therefore, in step S11, the eight orbital type distributions are classified according to whether they are on the white road or the white road, or even further according to whether they are closer to the moon or the earth, as shown in table i.
Table one, eight track types and their classification
Then, in step S12, different orbit types are selected for combination according to the principle that four spatial distributions, i.e., the spatial distribution in the white road surface close to the moon, the spatial distribution in the white road surface close to the earth, the spatial distribution in the white road surface normal close to the moon, and the spatial distribution in the white road surface normal close to the earth, all exist, because in the combination of different orbit types, it can be ensured that the navigation constellation has a good observation geometry in the whole lunar space, thereby realizing high-precision navigation. For example, the moon near-linear orbit, the earth large-eccentricity elliptical orbit and the earth-moon translational point L4/L5 can form a moon-space navigation constellation, and the earth-moon translational point L4/L5, the moon-surrounding circular orbit and the earth high-orbit circular orbit can also form a moon-space navigation constellation.
The classification screening mode can preliminarily screen the advantages and disadvantages of different navigation constellation geometrical structures, but specific quantitative index calculation is not carried out, so that the screening accuracy is still to be improved. Therefore, in step S13, the navigation constellation formed by combining different orbit types selected in step S12 is subjected to spatial position accuracy factor (PDOP) requirement calculation, the advantages and disadvantages of different navigation constellation geometric structures are further evaluated through quantization index calculation, and constellation configuration parameters are further optimized iteratively in combination with the earth-moon spatial coverage requirement, so that the navigation accuracy is further improved.
The earth-moon space coverage requirement means that at least four navigation satellites can be observed at any point in the earth-moon space at any time, so that the constellation can be further ensured to effectively cover the whole earth-moon space, and data support is provided for subsequent user space position solution. The requirement of the space position accuracy factor (PDOP) means that any point in the earth-moon space is better relative to the geometric structure of the observable navigation satellite, and the smaller the PDOP value is, the better the PDOP value is. Specifically, the spatial position accuracy factor is obtained by the following steps:
assuming that N navigation satellites are in the earth-moon space navigation constellation formed by combining different orbit types, the elevation angle and the azimuth angle of a user relative to the navigation satellites are respectively thetau→s,i、αu→s,i，i＝1,2,...,N；
Defining a geometric matrix G and a weight system matrix H:
H＝(GTG)-1
the spatial position accuracy factor is
Wherein h is11、h22、h33Representing the first three diagonal elements of the weight system matrix H.
By calculating the PDOP value of different Earth-moon space navigation constellations, when the PDOP value is smaller than a threshold value, the navigation constellation is evaluated to have a better geometric structure. And the iterative optimization process is specifically to reduce the PDOP value and improve the earth-moon space coverage as optimization targets, continuously iteratively optimize the constellation configuration parameters until a certain iteration number is met or the PDOP value is less than a threshold value and at least four navigation satellites can be observed at any point of the earth-moon space at any time, and terminating the iteration. The constellation configuration parameters include, but are not limited to, motion parameters of navigation satellites in a constellation, distance parameters between the navigation satellites, angle parameters between the navigation satellites, and the like.
It can be understood that, in step S1, the orbit distributions of eight types of orbits are classified, then different orbit types are selected for combination according to the principle that four spatial distributions, that is, the spatial distribution in the white road surface close to the moon, the spatial distribution in the white road surface close to the earth, the spatial distribution in the white road surface normal close to the moon, and the spatial distribution in the white road surface normal close to the earth, so as to preliminarily screen out the advantages and disadvantages of different navigation constellation geometric structures, then the spatial position precision factor of the earth-moon space navigation constellation formed by combining different orbit types is further calculated, the advantages and disadvantages of different navigation constellation geometric structures are further evaluated through calculation of the quantization index, and the constellation configuration parameters are iteratively optimized in combination with the earth-moon space coverage requirement, so as to further improve the navigation precision.
It is understood that, in the step S2, the minimum transmitting power of the navigation satellite signal is calculated by the following formula:
wherein, PRFor receiver sensitivity, GTTransmitting gain for navigation signals, GRFor receiver antenna gain, λ is the navigation signal wavelength, and d is the farthest distance between the navigation satellite and the user.
When the navigation signal transmitting power of the navigation satellite is set, the minimum navigation signal transmitting power of the navigation satellite is calculated according to the farthest distance between the navigation satellite and the user in the constellation, so that the user can be ensured to successfully receive the navigation signal transmitted by the navigation satellite observed by the user. And after the navigation signal transmitting power of the navigation satellite is set, transmitting the navigation signal to the user, so that the user can be ensured to successfully receive the effective navigation signal, and the distance between the user and the navigation satellite observed by the user can be measured subsequently.
As shown in fig. 7, the step S3 specifically includes the following steps:
step S31: acquiring the spatial positions of at least four navigation satellites observed by a user at any time;
step S32: measuring distances between the user and the navigation satellites;
step S33: the spatial location of the user is solved based on the distance measurements.
It is to be understood that in said step S31, the spatial positions of the navigation satellites are obtained by ground-based radio measurements or autonomously obtained by constellation prediction.
As shown in fig. 8, the process of autonomously obtaining the spatial position of the navigation satellite through constellation prediction specifically includes the following steps:
step S311: acquiring the initial position and the initial speed of each navigation satellite in the earth-moon space navigation constellation based on a foundation radio measurement means;
step S312: establishing a relational expression between the inter-satellite distance and the change rate of the inter-satellite distance of any two navigation satellites and the earth-moon space dynamic model parameters;
step S313: measuring by an inter-satellite distance measuring mode to obtain the inter-satellite distance and the inter-satellite distance change rate between any two navigation satellites;
step S314: jointly solving to obtain earth-moon space dynamic model parameters and initial state correction values of the navigation satellite based on the relational expression and the measurement result;
step S315: and repeating the steps S312-S314 at intervals to obtain the latest earth-moon space dynamic model parameters and the initial state of the navigation satellite, and performing constellation ephemeris forecast by using the latest initial state of the navigation satellite and the earth-moon space dynamic model parameters.
Specifically, the initial position x of each navigation satellite in the constellation is obtained through ground-based radio measurement meansi(t0) And an initial velocity vi(t0) That is, obtaining an initial state of the navigation satellite, where i is 1,20The initial position and the initial speed of the constellation ephemeris provide input conditions for long-term full-autonomous and high-precision prediction of the ephemeris at the initial time, and are used for initializing constellation state parameters. But do notThe measurement distance of the ground radio measurement is long, so that the initial state value of the constellation ephemeris has a large error and needs to be corrected through a subsequent dynamics inversion process.
Then, let the moon gravitational field potential coefficient to be considered be C1,C2,...,CnThe coefficient of the field position of the earth's gravity is D1,D2,...,DmThe other dynamic parameters such as sunlight pressure, three-body attraction and the like are S1,S2,...,SpThe initial state of a single navigation satellite in the constellation is x0,v0. Wherein, an initial state x0,v0Are obtained by terrestrial radio measurements for initializing the constellation state parameters, but ground-based telemetry allows x0,v0The initial value of (2) has large error and needs to be corrected through dynamic model calculation. Wherein parameter set { C1,C2,...,Cn；D1,D2,...,Dm；S1,S2,...,SpCompletely determine the dynamic model of the navigation satellite, whereas the set of parameters x0,v0And completely determining the initial state of the navigation satellite, and then obtaining the satellite motion state at any moment under the condition of a known dynamic model and the initial state according to the orbital dynamics. Then from the orbital dynamics follows the equation C1,C2,...,Cn；D1,D2,...,Dm；S1,S2,...,Sp；x0,v0The functional relationship to satellite position x (t) and velocity v (t) is determined. Then, for any two navigation satellites, the values { C ] are corrected from the kinetic model parameters and the initial state1,C2,...,Cn；D1,D2,...,Dm；S1,S2,...,Sp；xi0,vi0,xj0,vj0Rho distance between the two satellitesij＝||xi(t)-xj(t) |, rate of change of inter-satellite distance
Is also determined, i.e.
ρij＝fρ(C1,C2,...,Cn；D1,D2,...,Dm；S1,S2,...,Sp；xi0,vi0,xj0,vj0；t)
Because the position and the speed of the navigation satellite are vectors in a three-dimensional space, the above formula contains n + m + p +12 unknowns, the inter-satellite distance and the inter-satellite distance change rate of (n + m + p +12)/2 sampling points are required for solving the unknowns, and the solved n + m + p +12 unknowns also comprise initial state correction values x of the navigation satellite i and j in addition to earth-moon space dynamic parametersi0,vi0,xj0,vj0The correction value further refines the initial state of the navigation satellites i, j compared to the ground based radio measurements. By repeatedly carrying out the processes, the earth-moon space dynamics parameters and the initial state of the constellation satellite can be continuously updated, and then the accurate prediction of the constellation state is carried out by orbital extrapolation, so that the constellation is operated in a fully autonomous and high-precision manner.
The method comprises the steps of establishing the relational expression for any two navigation satellites in the earth-moon space navigation constellation, obtaining an inter-satellite distance value and an inter-satellite distance change rate value between the two navigation satellites by utilizing high-precision laser inter-satellite distance measurement or microwave inter-satellite distance measurement, and then jointly solving to obtain earth-moon space dynamic model parameters and initial state correction values (C) of the navigation satellites1,C2,...,Cn；D1,D2,...,Dm；S1,S2,...,Sp；xi0,vi0,xj0,vj0) And obtaining a high-precision dynamic model.
After the latest earth-moon space dynamics model parameters are obtained through inter-satellite distance measurement data processing at regular intervals, ephemeris forecast is carried out by combining the corrected initial state of the navigation satellite, so that the long-term high-precision and full-autonomous acquisition of constellation ephemeris is realized, the constellation is supported to run for a long time and run for the earth-moon space navigation independently, and the space position of each navigation satellite in the constellation can be automatically obtained through the constellation forecast.
It can be understood that, in step S31, a constellation navigation task fully autonomous operation method is provided, in which earth-moon dynamical models are inverted on constellations by using inter-satellite distance measurement information between navigation satellites, and then high-precision prediction of constellation ephemeris is performed by using the updated dynamical models and constellation initial state parameters, so that earth-moon space navigation fully autonomous operation independent of the ground is realized.
In step S32, after the navigation satellite transmits the navigation signal, the distance between the user and the navigation satellite at any time is obtained by measuring the pseudorange, the carrier phase, or the doppler shift of the user receiver.
In addition, based on steps S13 and S31, N navigation satellites can be observed at any point (x, y, z) in Earth-moon space at any time, N is 4, and the spatial positions of the navigation satellites can be obtained autonomously through ephemeris forecast or through ground-based radio measurement, and is set as (x)s j,ys j,zs j) Wherein j is 1, 2.
In step S33, a distance calculation expression between the user and the navigation satellite is established:
where c is the speed of light, δ t is the time difference between the navigation satellite and the user, (x)s j,ys j,zs j) To the spatial position of the navigation satellite, (x, y, z) to the spatial position of the user.
There are only four unknowns, namely the user spatial location (x, y, z) and the time difference δ t. At least 4 navigation satellites can be observed at any point (x, y, z) of the earth-moon space at any time, the equations are established for the N observed navigation satellites, the spatial position (x, y, z) of the user can be obtained through simultaneous solution, and high-precision navigation positioning can be carried out after the accurate position of the user is obtained.
It can be understood that, in the step S3, the user spatial position is solved by a geometric method, which can achieve real-time acquisition of the user spatial position, and the positioning speed is fast and the navigation positioning accuracy is high.
However, the geometric method is considered to have a large error degree in solving the spatial position, and in an actual process, the position precision error is in a range of several meters to dozens of meters. Therefore, in order to further improve the positioning accuracy, it is preferable that the method further includes:
step S4: and accurately positioning the spatial position of the user based on a dynamic method.
Specifically, as shown in fig. 9, the step S4 specifically includes the following steps:
step S41: obtaining a spatial state observation value of a user based on the spatial position of the user;
step S42: performing dynamics integration based on the earth-moon space dynamics model and the initial state of the user to obtain a space state calculation value of the user;
step S43: and continuously and iteratively adjusting parameters of the earth-moon space dynamic model and the initial state of the user according to the difference between the observed value and the calculated value of the user space state until the difference between the observed value and the calculated value of the user space state meets the navigation precision requirement, and taking the calculated value of the user space state after iteration as a high-precision navigation value.
The spatial velocity of the user is obtained by performing difference processing based on the spatial position of the user obtained in step S3, and the spatial state (i.e., spatial position and spatial velocity) observation value X of the user is obtained*(t) of (d). And then obtaining a spatial state calculation value X (t) of the user through kinetic integration according to the earth-moon spatial dynamics model and the initial state of the user, wherein the initial state of the user is obtained through ground-based radio measurement. Then continuously adjusting according to the difference between the observed value and the calculated value of the user space stateAnd the moon space dynamic model enables the difference between the observed value and the calculated value to be minimum, namely the navigation precision requirement is met, and the calculated value of the user space state is the earth-moon space state navigation value obtained based on the dynamic method.
The specific process is as follows:
set earth-moon space user position vector r and velocity vector
The state variable of the composition is
It is the initial condition X (t)0) And a function of the earth-moon space dynamics parameter P, i.e.
X＝X(X0,P,t)
X(t0) The amount of change of P Δ X0The state change amount caused by Δ P is
The state transition matrix Φ and the parameter sensitivity matrix S are defined as follows:
the calculation method of the state transition matrix phi and the parameter sensitivity matrix S is as follows:
(1) Φ and S form the matrix Ψ (t), i.e.:
Ψ(t)＝(Φ(t)S(t))
(2) the matrix Ψ (t) satisfies the following differential equation:
the initial condition is psi (t)0)＝(I6×606×k). Wherein 0 is a zero matrix, I is an identity matrix,
is the acceleration of motion, t, of the navigation satellite0The initial moment of the navigation satellite motion is P, the earth-moon space dynamics parameters are P, and the number of P is k.
(3) By solving the differential equation, a matrix Ψ (t) is obtained, and a state transition matrix Φ and a parameter sensitivity matrix S are obtained.
Setting the calculation value of the user space state in the Earth-moon space as X (t) and the observation value as X*(t) then
ΔX＝X*(t)-X(t)＝ΦΔX0+SΔP
For earth-moon space users, the equations can be established at any time in an observation time sequence, the equations are combined, and the initial state adjustment quantity delta X of the users is obtained by solving0And the earth-moon space dynamics parameter adjustment amount delta P. And then, performing orbit integration according to the adjusted initial state of the user and the earth-moon space dynamics parameters to obtain a new user state calculation value X (t). Repeating the above processes until the user state calculation value is X (t) and the observation value X*And (t) until the difference meets the navigation precision requirement, for example, the difference between the two is smaller than a threshold value, and the obtained user space state calculation value is the high-precision navigation value. Therefore, the earth-moon space high-precision navigation positioning based on the dynamic method is realized.
It can be understood that, in step S4, the observed value of the user space state obtained by the geometric solution is compared with the calculated value of the space state obtained by the kinetic integral calculation, the parameters of the earth-moon space kinetic model and the initial state of the user are continuously iteratively adjusted based on the difference between the observed value and the calculated value, the parameters of the earth-moon space kinetic model and the initial state of the user are continuously corrected, the precision of the earth-moon space kinetic model is continuously iteratively optimized, the calculated value obtained by the orbital integral calculation after the iterative optimization is finished is used as the final navigation value, the precision can reach the centimeter level, and compared with the previous geometric solution of the space position, the navigation positioning precision is greatly improved.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (8)
1. A method for satellite navigation and positioning in earth-moon space is characterized in that,
the method comprises the following steps:
step S1: selecting partial or all orbits as navigation satellite operation orbits from eight orbit types, namely a moon near-linear orbit, a Earth-moon remote retrograde orbit, a round orbit around the moon, an Earth high orbit round orbit, an Earth large eccentricity ellipse orbit, an Earth-moon translation point L4/L5, an L1/L2 halo orbit and a Sun-center orbit, and deploying one or more navigation satellites on each operation orbit;
step S2: setting the minimum transmitting power of a navigation satellite signal;
step S3: measuring the distance between a user at any moment and a plurality of navigation satellites observed by the user, and solving to obtain the spatial position of the user at the moment based on the measured distance value;
step S4: accurately positioning the spatial position of the user based on a power method;
the step S4 specifically includes the following steps:
step S41: obtaining a spatial state observation value of a user based on the spatial position of the user;
step S42: performing kinetic integration on the basis of the earth-moon space kinetic model and the initial state of the user to obtain a spatial state calculation value of the user, wherein the earth-moon space kinetic model is formed by a parameter set { C }1,C2,...,Cn；D1,D2,...,Dm；S1,S2,...,SpDetermination, C1,C2,...,CnIs the coefficient of the gravitational field potential of the moon, D1,D2,...,DmIs the coefficient of the field position of the gravitational force, S1,S2,...,SpIs a kinetic parameter;
step S43: and continuously and iteratively adjusting parameters of the earth-moon space dynamics model and the initial state of the user according to the difference between the space state observed value and the space state calculated value of the user until the difference between the space state observed value and the space state calculated value of the user meets the navigation precision requirement, and taking the space state calculated value of the user after the iteration is finished as a high-precision navigation value.
2. The Earth-moon space satellite navigation positioning method of claim 1,
in step S1, a partial orbit is selected from eight orbit types as the orbit of the navigation satellite by the following steps:
step S11: classifying the eight track types based on a classification rule that the tracks are distributed on the white road surface or in the normal direction of the white road surface;
step S12: selecting different orbit types to combine according to the principle that four spatial distributions in the white road surface close to the moon, in the white road surface close to the earth, in the white road surface normal close to the moon and in the white road surface normal close to the earth exist;
step S13: and calculating the spatial position precision factors of different track type combinations to determine the advantages and disadvantages of the observation geometrical structures of the different track type combinations, and performing iterative optimization on the constellation configuration parameters by combining the earth-moon space coverage requirement.
3. The Earth-moon space satellite navigation positioning method of claim 2,
the earth-moon space coverage requirement means that at least four navigation satellites can be observed at any point in earth-moon space at any time;
the spatial position accuracy factor is calculated by the following steps:
assuming that N navigation satellites are arranged in the earth-moon space navigation constellation formed by combining different orbit types, a user can use the navigation satellitesThe elevation and azimuth of the star are thetau→s,i、αu→s,i，i＝1,2,...,N；
Defining a geometric matrix G and a weight system matrix H:
H＝(GTG)-1
the spatial position accuracy factor is
Wherein h is11、h22、h33Representing the first three diagonal elements of the weight system matrix H.
4. The Earth-moon space satellite navigation positioning method of claim 1,
the minimum transmitting power of the navigation satellite signal is calculated by the following formula:
wherein, PRFor receiver sensitivity, GTTransmitting gain for navigation signals, GRFor receiver antenna gain, λ is the navigation signal wavelength, and d is the farthest distance between the navigation satellite and the user.
5. The Earth-moon space satellite navigation positioning method of claim 1,
the step S3 specifically includes the following steps:
step S31: acquiring the spatial positions of at least four navigation satellites observed by a user at any time;
step S32: measuring distances between a user and at least four observed navigation satellites;
step S33: the spatial location of the user is solved based on the distance measurements.
6. The Earth-moon space satellite navigation positioning method of claim 5,
the spatial positions of the navigation satellites in the step S31 are obtained by ground-based radio measurement or autonomously obtained by constellation prediction.
7. The Earth-moon space satellite navigation positioning method of claim 6,
the process of autonomous acquisition of the spatial position of the navigation satellite by constellation forecasting specifically comprises the following steps:
step S311: acquiring the initial position and the initial speed of each navigation satellite in the earth-moon space navigation constellation based on a foundation radio measurement means;
step S312: establishing a relational expression between the inter-satellite distance and the change rate of the inter-satellite distance of any two navigation satellites and the earth-moon space dynamic model parameters;
step S313: measuring by an inter-satellite distance measuring mode to obtain the inter-satellite distance and the inter-satellite distance change rate between any two navigation satellites;
step S314: jointly solving to obtain earth-moon space dynamic model parameters and initial state correction values of the navigation satellites based on the relational expression between the inter-satellite distance and the inter-satellite distance change rate of any two navigation satellites and the measured inter-satellite distance and inter-satellite distance change rate between any two navigation satellites;
step S315: and repeating the steps S312-S314 at intervals to obtain the latest earth-moon space dynamic model parameters and the initial state of the navigation satellite, and performing constellation ephemeris forecast by using the latest initial state of the navigation satellite and the earth-moon space dynamic model parameters.
8. The Earth-moon space satellite navigation positioning method of claim 5,
in step S32, the distance between the user and the navigation satellite at any time is obtained through the measurement of the pseudorange, the carrier phase, or the doppler shift of the user receiver.
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