Autonomous navigation method for lunar satellite formation and second-order filtering navigation architecture

Abstract

The invention relates to an autonomous navigation method for lunar satellite formation and a second-order filtering navigation architecture, and the autonomous navigation method comprises the steps: obtaining orbit prediction information based on a kinetic model of the lunar satellite formation, and obtaining collaborative theory observation information based on a collaborative observation model, carrying out fusion processing on orbit prediction information, collaborative theory observation information and multi-source observation data of in-orbit observation by using an extended Kalman filtering algorithm, and estimating an absolute orbit state of the lunar satellite formation; establishing a relative motion model of the slave satellite under the local coordinate system of the master satellite, and establishing a relative measurement model; and taking the absolute orbit state of the master satellite as a reference datum, obtaining a preliminary prediction relative orbit state based on the relative motion model of the slave satellite, and obtaining relative measurement data including distance measurement and angle measurement based on the relative measurement model, and fusing the relative measurement data and the preliminarily predicted relative orbit state through an extended Kalman filtering algorithm to estimate the relative orbit state of the slave satellite. Navigation may be independent of ground support.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of technology satellites, and particularly relates to a self-navigation method for a lunar satellite formation and a second-order filtering navigation architecture. BACKGROUND

[0002] Ultra-long wave radio astronomy observations have unique scientific value in revealing the early evolution of the universe, studying extreme astrophysical phenomena, and detecting large-scale cosmic magnetic field structures. Due to the interference of the Earth's ionosphere and the limitation of strong electromagnetic environment noise, it is difficult to carry out related precise observations on the ground platform. By deploying a satellite formation in the lunar orbit, high-resolution observations and accurate measurements can be achieved in a quiet electromagnetic environment using the moon as a natural electromagnetic shield. The inter-satellite distance of the formation is constantly compressed and stretched according to the task requirements, showing a feature similar to "breathing" to build a space interferometric aperture of tens to hundreds of kilometers.

[0003] Unlike traditional lunar satellite formations, the "breathing formation" has dynamic characteristics, that is, this flexible formation allows satellites to dynamically adjust their relative positions according to task requirements, thereby optimizing the cooperative working efficiency between satellites at different stages. Therefore, accurate and efficient autonomous navigation technology is crucial for the normal operation of the lunar "breathing formation" and further becomes a key factor in ensuring the success of ultra-long wave detection missions.

[0004] Although the "breathing formation" improves the observation accuracy and efficiency in ultra-long wave observation missions, it still faces several limitations in practical applications. First, traditional relative navigation methods are usually based on a first-order linear Clohessy-Wiltshire (CW) model, which assumes that satellites run along a simplified orbit and cannot accurately describe the nonlinear changes in the distance between satellites in the "breathing formation". When the formation distance is large or the structure is complex, the CW model cannot effectively capture these changes, leading to rapid accumulation of navigation errors. Second, relative navigation methods cannot provide absolute orbit information for the formation, resulting in a lack of effective external orbit reference for accurate correction when the inter-satellite distance is large or the relative position changes dramatically, thereby exacerbating the accumulation of errors. In addition, existing absolute navigation methods largely rely on external signal sources (such as ground stations or GNSS measurements), but the coverage of these signals in the lunar orbit is limited, making it difficult to provide real-time orbit data. Therefore, in the absence of external signal support, how to fully utilize inter-satellite measurement information to achieve stable and reliable autonomous navigation has become a key engineering challenge for lunar "breathing formation" missions. SUMMARY

[0005] The application provides a kind of lunar satellite formation autonomous navigation method, through high-precision dynamics model under the center of the moon inertial coordinate system, collaborative theory observation information, on-orbit observation multi-source observation information is estimated in combination with extended Kalman filter algorithm absolute orbit state of lunar satellite formation, through relative dynamics model and relative measurement data combination extended Kalman filter algorithm estimation relative orbit state of slave star, can not rely on ground support, can only realize autonomous orbit determination by interstellar measurement information, with high engineering application value.

[0006] According to the application, the aforementioned task is solved by an absolute and relative integrated autonomous navigation method for a lunar satellite formation, comprising: obtaining orbit prediction information based on a dynamics model of the lunar satellite formation, obtaining collaborative theory observation information based on a collaborative observation model, and using an extended Kalman filter algorithm to fuse the orbit prediction information, the collaborative theory observation information and multi-source observation data obtained by on-orbit observation, to estimate the absolute orbit state of the lunar satellite formation, including the absolute orbit state of the master star and the absolute orbit state of the slave star; establishing a relative motion model of the slave star in the local coordinate system of the master star, and establishing a relative measurement model; and taking the absolute orbit state of the master star as a reference benchmark, obtaining a preliminary predicted relative orbit state based on the relative motion model of the slave star, obtaining relative measurement data including ranging and angular measurement based on the relative measurement model, and estimating the relative orbit state of the slave star by fusing the relative measurement data and the preliminary predicted relative orbit state through the extended Kalman filter algorithm.

[0007] Further, it further comprises: establishing a dynamics model of the lunar satellite formation in the center of the moon inertial coordinate system J2000; and establishing a collaborative observation model of the lunar satellite formation.

[0008] Further, in the dynamics model, the motion equation of a single star is represented as: , wherein, is the three-dimensional position of the satellite, is the three-dimensional velocity, represents the acceleration of the center of the moon and the non-spherical gravity, represents the acceleration caused by the solar gravitational perturbation and the solar pressure perturbation; and based on the motion equation of a single star, the motion model of the lunar satellite formation is: , wherein, is the differential of the three-dimensional position of the master star, is the differential of the three-dimensional velocity of the master star, is the first differential from the three-dimensional position of the star, is the first differential of the three-dimensional velocity of the star, is the differential of the three-dimensional position of the nth slave star, is the differential of the three-dimensional velocity of the nth slave star.

[0009] Furthermore, establishing a collaborative observation model for the lunar satellite formation includes: When the lunar satellite formation is orbiting the moon, the slave satellites obtain inter-satellite angle information by optically observing the master satellite and obtain inter-satellite distance information by microwave ranging. The angle observation model is: , in, It is The azimuth information between the slave satellite and the master satellite, It is The pitch angle information between the slave satellite and the master satellite, represents the optical observation error, , is the y-axis position of the i-th slave star, is the y-axis position of the primary star, is the x-axis position of the ith satellite, is the x-axis position of the primary star, is the z-axis position of the ith slave star, is the z-axis position of the primary star, is the three-dimensional position of the i-th satellite, is the three-dimensional position of the primary star; The intersatellite distance observation model is: , in, Indicates the The ranging error between the slave satellite and the master satellite; Based on the inter-satellite angle information and distance information, the collaborative observation model of the lunar satellite formation is: , in, , It is the measurement information between the first slave star and the master star, including the inter-satellite distance information and inter-satellite angle information between the first slave star and the master star. It is the measurement information between the second slave star and the master star, including the inter-satellite distance information and inter-satellite angle information between the second slave star and the master star. It is the measurement information between the nth slave star and the master star, including the inter-satellite distance information and inter-satellite angle information between the nth slave star and the master star.

[0010] Further, the absolute orbit state of the lunar satellite formation at the current time is obtained by fusing the orbit prediction information, the cooperative theory observation information and the multi-source observation information obtained by on-orbit observation, using an extended Kalman filtering algorithm. The absolute orbit state of the lunar satellite formation at the current time is obtained by fusing the orbit prediction information, the cooperative theory observation information and the multi-source observation information obtained by on-orbit observation, using an extended Kalman filtering algorithm.

[0011] Further, a relative motion model of the slave satellite in the local coordinate system of the master satellite is established, and a relative measurement model is established, including: According to the motion equations of the master satellite and the slave satellite and the conversion relationship between the lunar center inertial coordinate system J2000 and the local coordinate system of the master satellite, the relative state variable is defined in the local coordinate system of the master satellite wherein is the three-dimensional position of the slave satellite relative to the master satellite, is the three-dimensional velocity of the slave satellite relative to the master satellite; In the local coordinate system of the master satellite, the relative motion equation of the slave satellite in the relative motion model is: , wherein, represents the lunar center distance of the master satellite, represents the lunar gravitational constant, represents the true anomaly angular velocity of the master satellite; Considering that the master satellite runs in a near-circular orbit and the inter-satellite distance is much smaller than the orbit radius of the master satellite, The above relative motion equation is expanded by Taylor series to the third order, and the third-order relative motion equation is obtained by simplifying and arranging: , wherein: , , In the local coordinate system of the master satellite, the inter-satellite angle measurement model and the inter-satellite distance measurement model of the relative measurement model are: , wherein, is the three-dimensional position of the slave satellite relative to the master satellite, is the azimuth angle measurement noise, is the pitch angle measurement noise, is the distance measurement noise.

[0012] Further, the absolute orbit state of the master satellite is taken as a reference benchmark, and the relative motion model is used to preliminarily predict the relative orbit state at the current time according to the relative orbit state of the slave satellite at the last time. The preliminary predicted relative orbit state and relative measurement data are fused by using an extended Kalman filter algorithm to obtain the relative orbit state of the slave satellite, wherein the relative measurement data are obtained by a relative measurement model.

[0013] The application further provides a second-order filter navigation architecture, comprising: an absolute navigation filter configured to perform the following steps: obtaining orbit prediction information based on a dynamics model of the lunar satellite formation and obtaining collaborative theoretical observation information based on a collaborative observation model; fusing the orbit prediction information, the collaborative theoretical observation information and multi-source observation data obtained by in-orbit observation by using an extended Kalman filter to estimate absolute orbit states of the lunar satellite formation, including absolute orbit states of the master satellite and absolute orbit states of the slave satellite; and transmitting the absolute orbit states of the master satellite to a relative navigation filter; a relative navigation filter configured to perform the following steps: preliminarily predicting the relative orbit state of the slave satellite at the current time based on the relative orbit state of the slave satellite at the last time by using a relative motion model with the absolute orbit states of the master satellite as a reference benchmark; and fusing the preliminary predicted relative orbit state and relative measurement data by using an extended Kalman filter algorithm to estimate the relative orbit state of the slave satellite, wherein the relative measurement data include ranging and angle measurement, and the angle measurement includes azimuth and elevation.

[0014] The application has at least the following beneficial effects: The autonomous navigation method of the lunar satellite formation of the application estimates the absolute orbit states of the lunar satellite formation by combining a high-precision dynamics model in a lunar center inertial coordinate system and collaborative theoretical observation information with an extended Kalman filter algorithm, estimates the relative orbit state of the slave satellite based on a relative dynamics model and relative measurement data with an extended Kalman filter algorithm with the absolute orbit states of the master satellite as a reference benchmark, can realize autonomous orbit determination only by inter-satellite measurement information without relying on ground support, is suitable for navigation requirements of a lunar "breathing formation" mission, can improve the overall calculation precision and robustness of the system by coupling inter-satellite data while maintaining the independence of each navigation algorithm, and has good engineering practical value and promotion prospects. The autonomous navigation method of the application processes various inter-satellite measurement data by using absolute and relative navigation, and realizes fusion and updating of absolute and relative orbit states in a two-stage filter architecture.

[0015] The second-order filter navigation architecture of the application combining absolute and relative orbit state estimation can realize autonomous orbit determination only by using in-orbit measurement information independently of a ground station. BRIEF DESCRIPTION OF DRAWINGS

[0016] To further clarify the above and other advantages and features of the present embodiments, a more particular description of embodiments of the application will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings. It is appreciated that these drawings depict only typical embodiments of the application and are therefore not to be considered limiting of its scope. The drawings incorporate graphics for purposes of clarity that are not necessarily drawn to scale.

[0017] Figure 1 A flow chart of an autonomous navigation method for a lunar satellite constellation according to an embodiment of the application is shown.

[0018] Figure 2 A schematic diagram of a second order filter navigation architecture according to an embodiment of the application is shown.

[0019] Figure 3 Absolute position error and absolute velocity error for a satellite constellation according to an embodiment of the application is shown.

[0020] Figure 4 Relative position error and relative velocity error for a satellite constellation according to an embodiment of the application is shown. DETAILED DESCRIPTION

[0021] It should be noted that the components in the drawings are possibly exaggerated for illustrative purposes and are not necessarily drawn to scale.

[0022] In the present application, the embodiments are merely intended to illustrate the solutions of the present application and should not be understood as limiting.

[0023] In the present application, the quantifier "one", "a" does not exclude the scenario of multiple elements unless specifically indicated.

[0024] It should also be noted herein that, in the embodiments of the present application, only a part of components or assemblies can be shown for the sake of clarity and simplicity, but those skilled in the art can understand that, under the teaching of the present application, the required components or assemblies can be added according to the specific scenario as needed.

[0025] It should also be noted herein that, within the scope of the present application, the phrases "same", "equal", "equal to" and the like do not mean that the numerical values of the two are absolutely equal, but allow a certain reasonable error, that is, the phrases also cover "substantially same", "substantially equal", "substantially equal to".

[0026] It should also be noted that in the description of the present application, the terms "center", "longitudinal", "lateral", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not mean that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application. In addition, the terms "first", "second" are only for the purpose of description, and cannot be understood as indicating relative importance.

[0027] In addition, the embodiments of the present application describe the process steps in a specific order, but this is only for the convenience of distinguishing between steps, and does not limit the order of the steps. In different embodiments of the present application, the order of the steps can be adjusted according to the adjustment of the process.

[0028] Figure 1 A flow chart of an autonomous navigation method for a lunar satellite formation according to an embodiment of the present application is shown.

[0029] As shown in Figure 1 An autonomous navigation method for a lunar satellite formation includes the following steps: Step 1: Establish a dynamic model of the lunar satellite formation in the lunar center inertial coordinate system J2000.

[0030] A high-precision dynamic model of the formation is established in the lunar center inertial coordinate system J2000, mainly considering high-order lunar non-spherical gravity perturbation, solar three-body gravity perturbation and solar radiation pressure perturbation, etc. In the dynamic model, the motion equation of a single satellite can be expressed as: (1), wherein, is the three-dimensional position of the satellite, is the three-dimensional velocity, represents the lunar center and the non-spherical gravity acceleration, represents the acceleration caused by solar three-body gravity perturbation and solar radiation pressure perturbation.

[0031] Based on the motion equation of a single satellite shown in formula (1), the motion model of the lunar satellite formation is: , wherein, is the differential of the three-dimensional position of the primary satellite, is the differential of the three-dimensional velocity of the primary satellite, is the differential of the three-dimensional position of the first secondary satellite, is the differential of the three-dimensional velocity of the first secondary satellite, is the differential of the 3D position of the nthchaser, is the differential of the 3D velocity of the nthchaser.

[0032] Step 2, establish the cooperative observation model of the lunar satellite formation.

[0033] During the lunar orbiting process, the lunar satellite formation obtains the interstellar angle information through optical observation of the primary star and the interstellar distance information through microwave ranging.

[0034] The angle observation model is: (2), wherein, is the differential of the 3D position of the nthchaser, is the azimuth angle information between the nthchaser and the primary star, is the elevation angle information between the nthchaser and the primary star, represents the optical observation error, , , is the y-axis position of the ithchaser, is the y-axis position of the primary star, is the x-axis position of the ithchaser, is the x-axis position of the primary star, is the z-axis position of the ithchaser, is the z-axis position of the primary star, is the 3D position of the ithchaser, is the 3D position of the primary star.

[0035] The interstellar distance observation model is: (3), wherein, represents the ranging error between the nthchaser and the primary star. Based on the interstellar angle and distance measurement information, the cooperative observation model of the lunar satellite formation is:

[0036] (4), wherein, , , is the measurement information between the first chaser and the primary star, including the interstellar distance information and the interstellar angle information between the first chaser and the primary star, is the measurement information between the second chaser and the primary star, including the interstellar distance information and the interstellar angle information between the second chaser and the primary star, is the measurement information between the nthchaser and the primary star, including the interstellar distance information and the interstellar angle information between the nthchaser and the primary star.

[0037] Step 3, obtaining orbit prediction information based on the dynamic model of the lunar satellite formation shown in formula (1), obtaining collaborative observation information based on the collaborative observation model shown in formula (4), and using an extended Kalman filtering algorithm to fuse the orbit prediction information, the collaborative observation information and the multi-source observation data of on-orbit observation, to estimate the absolute orbit state of the lunar satellite formation, including the absolute orbit state of the primary satellite and the absolute orbit state of the secondary satellite.

[0038] The extended Kalman filter inputs the absolute orbit state of the lunar satellite formation at the last time and the multi-source observation data of on-orbit observation at the current time, and outputs the absolute orbit state of the lunar satellite formation at the current time.

[0039] Using the dynamic model, the orbit state is predicted according to the absolute orbit state of the lunar satellite formation at the last time, to obtain orbit prediction information, and the orbit prediction information, the collaborative observation information and the multi-source observation data of on-orbit observation are fused by using the extended Kalman filtering algorithm, to obtain a more accurate and reliable absolute orbit state.

[0040] The specific information fusion process of using the extended Kalman filter to fuse the orbit prediction information and the collaborative observation information is as follows: Time prediction: input the absolute orbit state of the formation at the last time , output the prior estimate of the absolute orbit state at the current time , the calculation formula is as follows: Wherein, is a nonlinear state function (motion equation function of the lunar satellite formation); is a state covariance matrix, is a system process noise matrix, is a state transition matrix.

[0041] 2) Measurement correction: based on the prior estimate of the orbit state at the current time , the multi-source observation data at the current time estimate the posterior orbit state at the current time , the calculation formula is as follows: Wherein, is multi-source observation data, is a nonlinear observation function (collaborative observation model), is an observation matrix, is a measurement noise matrix, is an identity matrix, is the uncertainty of state estimation, is the orbit state of the lunar satellite formation at the current time. Multi-source observation data include the inter-satellite distance, azimuth angle and elevation angle of each slave satellite and the primary satellite, which are obtained by real-time measurement sensors. Observation residuals refer to the error between the multi-source observation data obtained by the measurement sensor and the cooperative theoretical observation information calculated by the cooperative observation model. The cooperative theoretical observation information includes the calculated inter-satellite distance, azimuth angle and elevation angle.

[0042] The fusion processing of orbit prediction information and in-orbit observation data by using the extended Kalman filter can fully utilize the complementarity of the dynamics priori and observation information, and still has good stability and convergence performance under complex orbit change conditions, which is suitable for long-term autonomous navigation requirements of lunar orbit formation.

[0043] Step 4, establish the relative motion model of the slave satellite in the local coordinate system of the primary satellite, and establish the relative measurement model.

[0044] According to the motion equations of the primary satellite and the slave satellite and the conversion relationship between the lunar center inertial coordinate system J2000 and the local coordinate system (LVLH) of the primary satellite, the relative state variables in the LVLH coordinate system of the primary satellite can be defined as is the three-dimensional position of the slave satellite relative to the primary satellite, is the three-dimensional velocity of the slave satellite relative to the primary satellite. In the LVLH coordinate system of the primary satellite, the relative motion equation (high-order CW relative motion model) of the slave satellite is: (5), wherein, represents the lunar center distance of the primary satellite, represents the lunar gravitational constant, represents the true anomaly angular velocity of the primary satellite.

[0045] Considering that the primary satellite runs in a near-circular orbit and the inter-satellite distance is much smaller than the radius of the primary satellite orbit, the formula (5) is expanded by three-order Taylor, and the three-order relative motion equation is obtained by simplifying and arranging: (6), wherein, (7), (8), In the LVLH coordinate system of the primary satellite, the inter-satellite angular measurement model and the inter-satellite distance measurement model of the relative measurement model are: (9), wherein, is the three-dimensional position of the slave satellite relative to the primary satellite, is azimuth measurement noise, is elevation measurement noise, is range measurement noise.

[0046] Step 5, taking the absolute orbit state of the primary star as the reference benchmark, obtaining the preliminary predicted relative orbit state based on the relative motion model of the secondary star, obtaining the relative measurement data containing the range and angle based on the relative measurement model, and estimating the relative orbit state of the secondary star by fusing the relative measurement data and the preliminary predicted relative orbit state through the extended Kalman filtering algorithm.

[0047] The input of the extended Kalman filtering algorithm is the relative orbit state of the secondary star in the lunar satellite formation at the last time, and the output is the calculated relative orbit state of the secondary star at the current time, which is used as the input of the next time of the extended Kalman filtering algorithm.

[0048] Taking the absolute orbit state of the primary star as the reference benchmark, using the relative motion model, according to the relative orbit state of the secondary star at the last time, the relative orbit state at the current time is preliminarily predicted, and the preliminary predicted relative orbit state and the relative measurement data are fused by using the extended Kalman filtering algorithm to obtain a more accurate and reliable relative orbit state. The relative measurement data is obtained through the relative measurement model.

[0049] The absolute orbit state of the primary star provides a reference benchmark for relative navigation, that is, for the estimation of the relative orbit state of the secondary star.

[0050] In summary, the lunar "breathing formation" absolute / relative integrated autonomous navigation method consists of the following three parts: (1) Establishment of absolute / relative orbit dynamics model In the lunar center of inertia coordinate system, a high-precision dynamics model of the "breathing formation" is constructed. This model fully considers the high-order non-spherical gravity of the moon, the perturbation effects of the three-body gravity of the sun and the earth, and the solar pressure, etc., in order to improve the orbit propagation accuracy.

[0051] In the local LVLH coordinate system of the primary star, a high-order CW relative motion model is established based on the third-order Taylor expansion form. Compared with the traditional linear approximation form, this model can more accurately describe the nonlinear relative motion characteristics of the "breathing formation" changing over time, and is suitable for large-scale dynamic configuration transformation situations.

[0052] (2) Establishment of absolute / relative measurement model In the lunar center of inertia coordinate system, taking the absolute orbit state of the formation as the estimation object, a cooperative observation model between the primary star and the secondary star is established. This model is based on interstellar range and angle observation information (including azimuth, elevation), and is used to support the estimation of the absolute navigation state.

[0053] In the local LVLH coordinate system of the primary satellite, the relative navigation required relative measurement model is established by taking the relative position and velocity of the slave satellite with respect to the primary satellite as state variables. The model can provide accurate perception ability for dynamic configuration evolution based on inter-satellite relative distance and angle observation.

[0054] (3) Second-order navigation architecture design Firstly, in the absolute navigation module, the extended Kalman filter algorithm is used to fuse the priori orbital dynamics and on-orbit observation data to estimate the absolute orbital state of the formation in the inertial system.

[0055] Secondly, the orbital state of the primary satellite is short-term predicted to construct the instantaneous LVLH reference system of the primary satellite and provide a reference benchmark for the relative navigation module.

[0056] Then, in the LVLH coordinate system of the primary satellite, the extended Kalman filter algorithm is used to fuse the inter-satellite relative observation information based on the high-order CW model to estimate the relative orbital state of the slave satellite with respect to the primary satellite, thereby improving the navigation accuracy and tracking continuity.

[0057] Finally, through the parallel running of the absolute and relative navigation algorithms and the data interaction of the key state variables, the autonomous and integrated navigation estimation of the lunar "breathing formation" on-orbit state is realized.

[0058] Figure 2 A schematic diagram of a second-order filter navigation architecture according to an embodiment of the application is shown.

[0059] The application also provides a second-order filter navigation architecture comprising an absolute navigation filter and a relative navigation filter. The absolute navigation filter is configured to perform the following steps: Obtaining orbital prediction information based on a dynamic model of a lunar satellite formation and obtaining collaborative theoretical observation information based on a collaborative observation model; Fusing the orbital prediction information, the collaborative theoretical observation information, and the multi-source observation data of on-orbit observation by using an extended Kalman filter to estimate the absolute orbital state of the lunar satellite formation, including the absolute orbital state of the primary satellite and the absolute orbital state of the slave satellite; and Transmitting the absolute orbital state of the primary satellite to the relative navigation filter.

[0060] The relative navigation filter is configured to perform the following steps: Taking the absolute orbital state of the primary satellite as a reference benchmark, using a relative motion model, and preliminarily predicting the relative orbital state of the slave satellite at the current time according to the relative orbital state of the slave satellite at the last time; and Fusing the preliminarily predicted relative orbital state and the relative measurement data by using an extended Kalman filter algorithm to estimate the relative orbital state of the slave satellite.

[0061] Relative measurement data includes distance measurement and angle measurement, where angle measurement includes azimuth and elevation.

[0062] In summary, the computational process of the second-order navigation architecture of the lunar "breathing formation" includes the following key steps: first, the absolute orbital state of the formation is estimated by combining the absolute navigation algorithm with the dynamic model and observation information; then, the orbit of the master satellite is short-term predicted to provide a reference benchmark for relative navigation; then, based on the relative dynamic model and inter-satellite observation data, the relative orbital state of the slave satellite is estimated through the relative navigation algorithm; finally, the absolute and relative integrated positioning of the formation is achieved, completing the accurate characterization of the formation configuration.

[0063] Figure 3 The absolute position error and absolute velocity error of a satellite formation according to one embodiment of the present invention are shown. Figure 4 The relative position error and relative velocity error of a satellite formation according to one embodiment of the present invention are shown.

[0064] In the lunar center inertial system, the initial orbit error of the "breathing formation" is set to 1km and 1m / s. During the intersatellite measurement process, the ranging error is 3m ( ), the angle measurement error is ( Taking the three-star formation as an example, after parallel filter navigation simulation, the absolute and relative navigation errors are as follows Figure 3 and Figure 4 shown.

[0065] The simulation results show that the navigation algorithm can converge quickly, and the absolute position error is 719.455m ( ), the absolute speed error is 0.550m / s ( ); The relative position error is 1.327m ( ), the relative speed error is 0.00235m / s ( ).

[0066] In summary, the lunar "breathing formation" absolute / relative integrated autonomous navigation method proposed in this invention can achieve precise autonomous orbit determination and provide a technical reference for future lunar exploration missions.

[0067] Although certain embodiments of the present invention have been described in this application, those skilled in the art will appreciate that these embodiments are provided by way of example only. Numerous variations, alternatives, and modifications will be contemplated by those skilled in the art in light of the teachings of this disclosure without departing from the scope of the present invention. The appended claims are intended to define the scope of the present invention and are intended to encompass methods and structures within the scope of these claims and their equivalents.

Claims

1. An autonomous navigation method for a lunar satellite formation, characterized in that: The steps include: The system obtains orbital prediction information based on the dynamic model of the lunar satellite formation and cooperative observation information based on the cooperative observation model. The extended Kalman filter algorithm is used to fuse the orbital prediction information, cooperative observation information, and multi-source observation data of on-orbit observations to estimate the absolute orbital state of the lunar satellite formation, including the absolute orbital state of the master satellite and the absolute orbital state of the slave satellite. Establishing a relative motion model of the slave satellite in the local coordinate system of the master satellite and establishing a relative measurement model; and Taking the absolute orbital state of the master satellite as a reference, a preliminary predicted relative orbital state is obtained based on the relative motion model of the slave satellite. Relative measurement data including ranging and angle measurement are obtained based on the relative measurement model. The relative orbital state of the slave satellite is estimated by fusing the relative measurement data and the preliminary predicted relative orbital state through the extended Kalman filter algorithm.

2. The autonomous navigation method for a lunar satellite formation according to claim 1, characterized in that: Also includes: In the lunar center inertial coordinate system J2000, a dynamic model of the lunar satellite formation is established; as well as Establish a collaborative observation model for lunar satellite formations.

3. The autonomous navigation method for a lunar satellite formation according to claim 2, characterized in that: In the dynamic model, the equation of motion of a single star is expressed as: ， in, is the three-dimensional position of the satellite, is the three-dimensional velocity, represents the lunar center and the non-spherical gravitational acceleration, represents the acceleration caused by the gravitational perturbation of the Sun-Earth triad and the solar radiation pressure perturbation; and Based on the motion equation of a single satellite, the motion model of the lunar satellite formation is: ， in, is the differential of the three-dimensional position of the primary star, is the differential of the primary star's three-dimensional velocity, is the first differential from the three-dimensional position of the star, is the first differential of the three-dimensional velocity of the star, is the differential of the three-dimensional position of the nth slave star, is the differential of the three-dimensional velocity of the nth slave star.

4. The autonomous navigation method for a lunar satellite formation according to claim 2, characterized in that: The collaborative observation model for the lunar satellite formation is established by: When the lunar satellite formation is orbiting the moon, the slave satellites obtain inter-satellite angle information by optically observing the master satellite and obtain inter-satellite distance information by microwave ranging. The angle observation model is: ， in, It is The azimuth information between the slave satellite and the master satellite, It is The pitch angle information between the slave satellite and the master satellite, represents the optical observation error, , is the y-axis position of the i-th slave star, is the y-axis position of the primary star, is the x-axis position of the ith satellite, is the x-axis position of the primary star, is the z-axis position of the ith slave star, is the z-axis position of the primary star, is the three-dimensional position of the i-th satellite, is the three-dimensional position of the primary star; The intersatellite distance observation model is: ， in, Indicates the The ranging error between the slave satellite and the master satellite; Based on the inter-satellite angle information and distance information, the collaborative observation model of the lunar satellite formation is: ， in, , It is the measurement information between the first slave star and the master star, including the inter-satellite distance information and inter-satellite angle information between the first slave star and the master star. It is the measurement information between the second slave star and the master star, including the inter-satellite distance information and inter-satellite angle information between the second slave star and the master star. It is the measurement information between the nth slave star and the master star, including the inter-satellite distance information and inter-satellite angle information between the nth slave star and the master star.

5. The autonomous navigation method for a lunar satellite formation according to claim 1, characterized in that: Using the dynamic model, the orbital state is predicted based on the absolute orbital state of the lunar satellite formation at the previous moment to obtain orbital prediction information; The extended Kalman filter algorithm integrates orbit prediction information, collaborative theoretical observation information, and multi-source observation information from on-orbit observations to obtain the absolute orbital state of the lunar satellite formation at the current moment.

6. The autonomous navigation method for a lunar satellite formation according to claim 1, characterized in that: Establishing the relative motion model of the slave satellite in the local coordinate system of the master satellite and establishing the relative measurement model include: According to the motion equations of the master and slave satellites and the transformation relationship between the lunar center inertial coordinate system J2000 and the master satellite local coordinate system, the relative state variables are defined in the master satellite local coordinate system. ,in is the three-dimensional position of the slave star relative to the master star, is the three-dimensional velocity of the slave star relative to the master star; In the local coordinate system of the master satellite, the relative motion equation of the slave satellite in the relative motion model is: ， in, Represents the distance between the main star and the moon. represents the lunar gravitational constant, represents the true periapsis angular velocity of the primary star; Considering that the main star is running in a near-circular orbit and the distance between the stars is much smaller than the orbit radius of the main star, , perform a third-order Taylor expansion on the above relative motion equation and simplify it to obtain the third-order relative motion equation: ， in: ， ， In the local coordinate system of the host satellite, the inter-satellite angle measurement model and inter-satellite distance measurement model of the relative measurement model are: ， in, is the three-dimensional position of the slave star relative to the master star, is the azimuth measurement noise, is the pitch angle measurement noise, is the distance measurement noise.

7. The autonomous navigation method for a lunar satellite formation according to claim 1, characterized in that: Taking the absolute orbital state of the master satellite as a reference, using the relative motion model, and based on the relative orbital state of the slave satellite at the previous moment, a preliminary prediction of the relative orbital state at the current moment is made; The extended Kalman filter algorithm is used to fuse the preliminary predicted relative orbit state and the relative measurement data to obtain the relative orbit state of the slave satellite, where the relative measurement data is obtained through the relative measurement model.

8. A second-order filtering navigation architecture, characterized in that: include: An absolute navigation filter configured to perform the following steps: Obtain orbit prediction information based on the dynamics model of the lunar satellite formation and obtain collaborative theoretical observation information based on the collaborative observation model; The extended Kalman filter is used to fuse orbit prediction information, collaborative theoretical observation information, and multi-source observation data from on-orbit observations to estimate the absolute orbital state of the lunar satellite formation, including the absolute orbital state of the master satellite and the absolute orbital state of the slave satellite. as well as Transmitting the absolute orbital state of the primary satellite to the relative navigation filter; A relative navigation filter is configured to perform the following steps: Taking the absolute orbital state of the master satellite as a reference, using the relative motion model, and based on the relative orbital state of the slave satellite at the previous moment, the relative orbital state of the slave satellite at the current moment is preliminarily predicted; as well as The extended Kalman filter algorithm is used to fuse the preliminary predicted relative orbit state and relative measurement data to estimate the relative orbit state of the slave satellite. The relative measurement data includes ranging and angle measurement, and the angle measurement includes azimuth and pitch angle.

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