An autonomous navigation method for lunar satellite formation and a second-order filter navigation architecture

Abstract

The application relates to a kind of lunar satellite formation autonomous navigation method and second-order filter navigation architecture, and autonomous navigation method includes: obtaining orbit prediction information based on the dynamics model of lunar satellite formation, obtaining collaborative theory observation information based on collaborative observation model, using extended Kalman filter algorithm to carry out fusion processing to orbit prediction information, collaborative theory observation information and on-orbit observation multi-source observation data, and estimating the absolute orbit state of lunar satellite formation;Establish the relative motion model of slave star under the local coordinate system of main star, and establish relative measurement model;And with the absolute orbit state of main star as reference datum, obtain preliminary prediction relative orbit state based on the relative motion model of slave star, obtain relative measurement data containing ranging and angle measurement based on relative measurement model, estimate the relative orbit state of slave star by fusing relative measurement data and preliminary prediction relative orbit state through extended Kalman filter algorithm.Navigation can not rely on ground support.

Description

Technical Field

[0001] This invention relates to the field of satellite technology, and in particular to an autonomous navigation method and a second-order filtered navigation architecture for lunar satellite formations. Background Technology

[0002] Very long-wave radio astronomy observations hold unique scientific value in revealing the early evolution of the universe, studying extreme celestial phenomena, and probing the large-scale magnetic field structure of the universe. Due to interference from the Earth's ionosphere and the limitations of strong electromagnetic noise, ground-based platforms struggle to conduct such precise observations. Utilizing the Moon as a natural electromagnetic shield, deploying a satellite formation in lunar orbit allows for high-resolution observations and precise measurements in a quiet electromagnetic environment. The inter-satellite distances within the formation are continuously compressed and expanded according to mission requirements, exhibiting a "breathing" characteristic to create a spatial interferometric aperture on the order of tens to hundreds of kilometers.

[0003] Unlike traditional lunar satellite formations, the "breathing formation" possesses dynamic characteristics. This flexible formation allows satellites to dynamically adjust their relative positions according to mission requirements, thereby optimizing the efficiency of collaborative work among satellites at different stages. Therefore, precise and efficient autonomous navigation technology is crucial for the normal operation of the lunar "breathing formation," further becoming a key factor in ensuring the success of ultra-long-wave exploration missions.

[0004] While the "breathing formation" approach has improved the accuracy and efficiency of ultra-long-wave observation missions, it still faces several limitations in practical applications. First, traditional relative navigation methods are typically based on the first-order linear Clohessy-Wiltshire (CW) model, which assumes satellites travel along simplified orbits and struggles to accurately describe the nonlinear changes in inter-satellite distances within the "breathing formation." When the formation distance is large or the structure is complex, the CW model cannot effectively capture these changes, leading to a rapid accumulation of navigation errors. Second, relative navigation methods cannot provide absolute orbital information for the formation, resulting in a lack of effective external orbital references for accurate correction when inter-satellite distances are large or relative positions change drastically, thus exacerbating error accumulation. Furthermore, existing absolute navigation methods largely rely on external signal sources (such as ground stations or GNSS measurements), but the coverage of these signals in lunar orbit is limited, making it difficult to provide real-time orbital 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 the lunar "breathing formation" mission. Summary of the Invention

[0005] This invention provides an autonomous navigation method for lunar satellite formations. It estimates the absolute orbital state of the lunar satellite formation by combining a high-precision dynamic model in the lunar inertial coordinate system, collaborative theoretical observation information, and multi-source on-orbit observation information with an extended Kalman filter algorithm. It estimates the relative orbital state of the satellites by combining a relative dynamic model with relative measurement data with an extended Kalman filter algorithm. This method can achieve autonomous orbit determination without relying on ground support, using only inter-satellite measurement information, and has high engineering application value.

[0006] According to the present invention, the aforementioned task is accomplished by an integrated absolute and relative autonomous navigation method for lunar satellite formations, the method comprising:

[0007] Orbit prediction information is obtained based on the dynamic model of the lunar satellite formation, and collaborative theoretical observation information is obtained based on the collaborative observation model. The extended Kalman filter algorithm is used to fuse the orbit prediction information, collaborative theoretical observation information and multi-source observation data from on-orbit observation to estimate the absolute orbital state of the lunar satellite formation, including the absolute orbital state of the primary star and the absolute orbital state of the secondary stars.

[0008] Establish a relative motion model of the slave star in the local coordinate system of the primary star, and establish a relative measurement model; and

[0009] Using the absolute orbital state of the primary star as a reference, a preliminary predicted relative orbital state is obtained based on the relative motion model of the secondary star. Relative measurement data, including distance and angle measurements, are obtained based on the relative measurement model. The relative orbital state of the secondary star is estimated by fusing the relative measurement data and the preliminary predicted relative orbital state through the extended Kalman filter algorithm.

[0010] Furthermore, it also includes:

[0011] A dynamic model of the lunar satellite formation was established in the lunar inertial coordinate system J2000; and

[0012] Establish a collaborative observation model for lunar satellite formations.

[0013] Furthermore, in the dynamic model, the equations of motion for a single star are expressed as:

[0014] ,

[0015] in, It is the satellite's three-dimensional position. It is three-dimensional velocity. Represents the gravitational acceleration at the center of the moon and in a non-spherical shape. Represents the acceleration caused by gravitational perturbations of the Sun, Earth, and Sun bodies, and solar radiation pressure perturbations; and

[0016] Based on the motion equations of a single star, the motion model of the lunar satellite formation is as follows:

[0017] ,

[0018] in, It is the differential of the three-dimensional position of the primary star. It is the differential of the primary star's three-dimensional velocity. It is the first differential from the three-dimensional position of a star. It is the first differential of the three-dimensional velocity of a star. It is the differential of the nth star's three-dimensional position. It is the differential of the three-dimensional velocity of the nth follower star.

[0019] Furthermore, establishing a collaborative observation model for lunar satellite formations includes:

[0020] During their orbit around the moon, the lunar satellite formation obtains inter-satellite angle information through optical observation of the host star and inter-satellite distance information through microwave ranging.

[0021] The angle observation model is as follows:

[0022] ,

[0023] in, It is the first Information on the azimuth angle between the secondary star and the primary star. It is the first The elevation angle information between the secondary star and the primary star. Represents optical observation error. , It is the y-axis position of the i-th star. It is the y-axis position of the primary star. It is the x-axis position of the i-th star. It is the x-axis position of the primary star. It is the z-axis position of the i-th star. It is the z-axis position of the primary star. It is the three-dimensional position of the i-th star. It is the three-dimensional position of the primary star;

[0024] The inter-satellite distance observation model is as follows:

[0025] ,

[0026] in, Indicates the first The distance measurement error between the secondary star and the primary star;

[0027] Based on inter-satellite angle and distance information, the collaborative observation model for lunar satellite formations is as follows:

[0028] ,

[0029] in, , This is the measurement information between the first secondary star and the primary star, including the inter-star distance and inter-star angle information between the first secondary star and the primary star. This is the measurement information between the second secondary star and the primary star, including the inter-star distance and inter-star angle information between the second secondary star and the primary star. It is the measurement information between the nth slave star and the primary star, including the inter-star distance and inter-star angle information between the nth slave star and the primary star.

[0030] Furthermore, using a dynamic model, orbital state prediction is performed based on the absolute orbital state of the lunar satellite formation at the previous moment, thus obtaining orbital prediction information;

[0031] The extended Kalman filter algorithm fuses orbit prediction information, cooperative 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.

[0032] Furthermore, a relative motion model of the slave star in the local coordinate system of the primary star is established, and a relative measurement model is also established, including:

[0033] Based on the equations of motion of the primary and secondary stars, and the transformation relationship between the lunar inertial coordinate system J2000 and the primary star's local coordinate system, relative state variables are defined in the primary star's local coordinate system. ,in It is based on the three-dimensional position of the star relative to the primary star. It is the three-dimensional velocity of the star relative to the host star;

[0034] In the primary star's local coordinate system, the relative motion equations of the secondary stars in the relative motion model are:

[0035] ,

[0036] in, Represents the distance between the center of the main star and the moon. Represents the lunar gravitational constant. Represents the true perihelion angular velocity of the primary star;

[0037] Considering that the primary star orbits in a near-circular orbit and the interstellar distances are much smaller than the radius of the primary star's orbit, then Performing a third-order Taylor expansion on the above relative motion equations and simplifying them, we obtain the third-order relative motion equations:

[0038] ,

[0039] in:

[0040] ,

[0041] ,

[0042] In the primary star's local coordinate system, the inter-satellite angle measurement model and inter-satellite distance measurement model relative to the measurement model are as follows:

[0043] ,

[0044] in, It is based on the three-dimensional position of the star relative to the primary star. It is azimuth measurement noise. It is pitch angle measurement noise. It is distance measurement noise.

[0045] Furthermore, using the absolute orbital state of the primary star as a reference, and employing a relative motion model, the relative orbital state of the secondary star at the current moment is preliminarily predicted based on the relative orbital state of the secondary star at the previous moment.

[0046] The preliminary predicted relative orbital state and relative measurement data are fused using the extended Kalman filter algorithm to obtain the relative orbital state of the satellite, where the relative measurement data is obtained through a relative measurement model.

[0047] The present invention also provides a second-order filtered navigation architecture, comprising:

[0048] An absolute navigation filter is configured to perform the following steps:

[0049] Orbit prediction information is obtained from a dynamic model of lunar satellite formations, and collaborative theoretical observation information is obtained from a collaborative observation model.

[0050] Extended Kalman filtering is employed to fuse orbit prediction information, cooperative 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 primary satellite and the secondary satellites; and

[0051] Transmit the absolute orbital state of the primary star to the relative navigation filter;

[0052] The relative navigation filter is configured to perform the following steps:

[0053] Using the absolute orbital state of the primary star as a reference, and employing a relative motion model, the relative orbital state of the secondary star at the current moment is preliminarily predicted based on the relative orbital state of the secondary star at the previous moment; and

[0054] The extended Kalman filter algorithm is used to fuse the preliminary predicted relative orbital state and relative measurement data to estimate the relative orbital state of the satellite. The relative measurement data includes distance measurement and angle measurement, where the angle measurement includes azimuth and elevation angles.

[0055] The present invention has at least the following beneficial effects:

[0056] The autonomous navigation method for lunar satellite formations of this invention estimates the absolute orbital state of the lunar satellite formation by combining a high-precision dynamic model in the lunar-centric inertial coordinate system with cooperative theoretical observation information and an extended Kalman filter algorithm. Using the absolute orbital state of the primary satellite as a reference, the relative orbital state of the secondary satellites is estimated based on a relative dynamic model and relative measurement data combined with the extended Kalman filter algorithm. This method can achieve autonomous orbit determination without relying on ground support, solely through inter-satellite measurement information, and is suitable for the navigation requirements of lunar "breathing formation" missions. This method can improve the overall computational accuracy and robustness of the system by coupling inter-satellite data while maintaining the independence of each navigation algorithm, demonstrating good engineering practical value and promising prospects for widespread application.

[0057] The autonomous navigation method of the present invention utilizes absolute and relative navigation to process various inter-satellite measurement data respectively, and realizes the fusion and update of absolute and relative orbital states in a two-level filtering architecture.

[0058] The second-order filtered navigation architecture of this invention, which combines absolute and relative orbital state estimation, can achieve autonomous orbit determination independently of ground stations and using only on-orbit measurement information. Attached Figure Description

[0059] To further illustrate the above and other advantages and features of the various embodiments of the present invention, a more specific description of the embodiments of the invention will be presented with reference to the accompanying drawings. It is to be understood that these drawings depict only typical embodiments of the invention and are therefore not intended to limit its scope. In the drawings, identical or corresponding parts will be indicated by identical or similar reference numerals for clarity.

[0060] Figure 1 A flowchart of an autonomous navigation method for a lunar satellite formation according to an embodiment of the present invention is shown.

[0061] Figure 2 A schematic diagram of a second-order filtered navigation architecture according to an embodiment of the present invention is shown.

[0062] Figure 3 The absolute position error and absolute velocity error of a satellite formation according to an embodiment of the present invention are shown.

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

[0064] It should be noted that the components in the accompanying drawings may be shown exaggerated for illustrative purposes and may not be to scale.

[0065] In this invention, the various embodiments are merely intended to illustrate the solutions of the invention and should not be construed as limiting.

[0066] In this invention, unless otherwise specified, the quantifiers “a” and “one” do not exclude scenarios involving multiple elements.

[0067] It should also be noted that, in the embodiments of the present invention, only a portion of the parts or components may be shown for clarity and simplicity. However, those skilled in the art will understand that, under the teachings of the present invention, the required parts or components can be added as needed for specific scenarios.

[0068] It should also be noted that within the scope of this invention, the terms "same", "equal", and "equal to" do not mean that the two values ​​are absolutely equal, but allow for a certain reasonable error. In other words, the terms also cover "substantially the same", "substantially equal", and "substantially equal to".

[0069] It should also be noted that in the description of this invention, the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not explicitly or implicitly suggest that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0070] Furthermore, the embodiments of the present invention describe the process steps in a specific order; however, this is only for the convenience of distinguishing each step, and is not intended to limit the order of the steps. In different embodiments of the present invention, the order of each step can be adjusted according to the process.

[0071] Figure 1 A flowchart of an autonomous navigation method for a lunar satellite formation according to an embodiment of the present invention is shown.

[0072] like Figure 1 As shown, an autonomous navigation method for lunar satellite formations includes the following steps:

[0073] Step 1: Establish a dynamic model of the lunar satellite formation in the lunar inertial coordinate system J2000.

[0074] A high-precision dynamic model of the formation was established in the lunar inertial coordinate system J2000, mainly considering the effects of higher-order lunar non-spherical gravitational perturbations, Sun-Earth three-body gravitational perturbations, and solar radiation pressure perturbations. In the dynamic model, the equations of motion for a single star can be expressed as:

[0075] (1),

[0076] in, It is the satellite's three-dimensional position. It is three-dimensional velocity. Represents the gravitational acceleration at the center of the moon and in a non-spherical shape. This represents the acceleration caused by gravitational perturbations of the Sun, Earth, and Sun bodies, as well as solar radiation pressure perturbations.

[0077] Based on the motion equation of a single star as shown in formula (1), the motion model of the lunar satellite formation is as follows:

[0078] ,

[0079] in, It is the differential of the three-dimensional position of the primary star. It is the differential of the primary star's three-dimensional velocity. It is the first differential from the three-dimensional position of a star. It is the first differential of the three-dimensional velocity of a star. It is the differential of the nth star's three-dimensional position. It is the differential of the three-dimensional velocity of the nth follower star.

[0080] Step 2: Establish a collaborative observation model for the lunar satellite formation.

[0081] During their orbit around the moon, the lunar satellite formation obtains inter-satellite angle information through optical observation of the host satellite and inter-satellite distance information through microwave ranging.

[0082] The angle observation model is as follows:

[0083] (2),

[0084] in, It is the first Information on the azimuth angle between the secondary star and the primary star. It is the first The elevation angle information between the secondary star and the primary star. Represents optical observation error. , It is the y-axis position of the i-th star. It is the y-axis position of the primary star. It is the x-axis position of the i-th star. It is the x-axis position of the primary star. It is the z-axis position of the i-th star. It is the z-axis position of the primary star. It is the three-dimensional position of the i-th star. It is the three-dimensional position of the primary star.

[0085] The inter-satellite distance observation model is as follows:

[0086] (3),

[0087] in, Indicates the first The distance measurement error between the secondary star and the primary star.

[0088] Based on inter-satellite angle and distance measurements, the collaborative observation model for the lunar satellite formation is as follows:

[0089] (4),

[0090] in, , This is the measurement information between the first secondary star and the primary star, including the inter-star distance and inter-star angle information between the first secondary star and the primary star. This is the measurement information between the second secondary star and the primary star, including the inter-star distance and inter-star angle information between the second secondary star and the primary star. It is the measurement information between the nth slave star and the primary star, including the inter-star distance and inter-star angle information between the nth slave star and the primary star.

[0091] Step 3: Obtain orbit prediction information based on the dynamic model of the lunar satellite formation shown in formula (1), obtain collaborative theoretical observation information based on the collaborative observation model shown in formula (4), and use the extended Kalman filter algorithm to fuse the orbit prediction information, collaborative theoretical observation information and multi-source observation data of on-orbit observation to estimate the absolute orbital state of the lunar satellite formation, including the absolute orbital state of the primary star and the absolute orbital state of the secondary stars.

[0092] The extended Kalman filter takes the absolute orbital state of the lunar satellite formation at the previous moment and the multi-source observation data of the current on-orbit observation as input, and outputs the absolute orbital state of the lunar satellite formation at the current moment.

[0093] Using a dynamic model, orbital state prediction is performed based on the absolute orbital state of the lunar satellite formation at the previous moment, resulting in orbital prediction information. Then, the extended Kalman filter algorithm is used to fuse the orbital prediction information, cooperative theoretical observation information, and multi-source observation data from on-orbit observations to obtain a more accurate and reliable absolute orbital state.

[0094] The specific information fusion process for fusing orbit prediction information and cooperative theoretical observation information using extended Kalman filtering is as follows:

[0095] Time prediction: Input the absolute orbital state of the formation at the previous moment. Output the prior estimate of the absolute orbital state at the current moment. The calculation formula is as follows:

[0096]

[0097] in, It is a nonlinear state function (the motion equation function of the lunar satellite formation); Let be the state covariance matrix. The system process noise matrix is... Let be the state transition matrix.

[0098] 2) Measurement correction: Prior estimation based on the current orbital state Multi-source observation data at the current moment Estimate the posterior orbital state at the current moment. The calculation formula is as follows:

[0099]

[0100] in, For multi-source observation data, This is a nonlinear observation function (cooperative observation model). For the observation matrix, To measure the noise matrix, It is the identity matrix. It is the uncertainty of state estimation. This represents the current orbital status of the lunar satellite formation. (Multi-source observation data) This includes the inter-star distances, azimuth angles, and elevation angles of each satellite relative to the primary star, obtained through real-time measurement sensors. Observation residuals. This refers to the error between multi-source observation data obtained through measurement sensors and the cooperative theoretical observation information calculated through a cooperative observation model. The cooperative theoretical observation information includes the calculated inter-satellite distances, azimuth angles, and elevation angles.

[0101] Using extended Kalman filtering to fuse orbit prediction information with on-orbit observation data can fully utilize the complementarity between dynamic priors and observation information. It still has good stability and convergence performance under complex orbital change conditions, and is suitable for the long-term autonomous navigation needs of lunar orbit formations.

[0102] Step 4: Establish a relative motion model of the slave star in the local coordinate system of the primary star, and establish a relative measurement model.

[0103] Based on the equations of motion of the primary and secondary stars, and the transformation relationship between the lunar inertial coordinate system J2000 and the primary star's local coordinate system (LVLH), relative state variables can be defined in the primary star's LVLH coordinate system. ,in It is based on the three-dimensional position of the star relative to the primary star. This refers to the three-dimensional velocity of the satellite relative to the host star. In the host star's LVLH coordinate system, the equations of motion for the satellite (higher-order CW relative motion model) are:

[0104] (5),

[0105] in, Represents the distance between the center of the main star and the moon. Represents the lunar gravitational constant. This represents the true perihelion angular velocity of the primary star.

[0106] Considering that the primary star orbits in a near-circular orbit and the interstellar distances are much smaller than the radius of the primary star's orbit, then By performing a third-order Taylor expansion on equation (5) and simplifying it, we obtain the third-order relative motion equation:

[0107] (6),

[0108] in,

[0109] (7),

[0110] (8),

[0111] In the primary star's LVLH coordinate system, the inter-satellite angular measurement model and inter-satellite ranging model for the relative measurement model are as follows:

[0112] (9),

[0113] Among them, in formula (9) It is based on the three-dimensional position of the star relative to the primary star. It is azimuth measurement noise. It is pitch angle measurement noise. It is distance measurement noise.

[0114] Step 5: Using the absolute orbital state of the primary star as a reference, obtain the preliminary predicted relative orbital state based on the relative motion model of the secondary star, obtain the relative measurement data including distance and angle measurements based on the relative measurement model, and estimate the relative orbital state of the secondary star by fusing the relative measurement data and the preliminary predicted relative orbital state through the extended Kalman filter algorithm.

[0115] The Extended Kalman Filter (EKF) algorithm takes as input the relative orbital state and relative measurement data (inter-satellite distance, azimuth, and elevation) of the satellites in the lunar satellite formation at the previous moment, and outputs the relative orbital state of the satellites calculated at the current moment, which is used as the input for the EKF algorithm at the next moment.

[0116] Using the absolute orbital state of the primary star as a reference, and employing a relative motion model, the relative orbital state of the secondary star at the previous moment is initially predicted based on its relative orbital state. Then, an extended Kalman filter algorithm is used to fuse the initially predicted relative orbital state with the relative measurement data, resulting in a more accurate and reliable relative orbital state. The relative measurement data is obtained through a relative measurement model.

[0117] The absolute orbital state of the primary star provides a reference for relative navigation, that is, it provides a reference for estimating the relative orbital state of the secondary stars.

[0118] In summary, the lunar "breathing formation" absolute / relative integrated autonomous navigation method consists of the following three parts:

[0119] (1) Establishment of absolute / relative orbital dynamics model

[0120] A high-precision dynamic model of the "breathing formation" is constructed in the lunar inertial coordinate system. This model fully considers the perturbation effects of the Moon's higher-order non-spherical gravity, the Sun-Earth three-body gravity, and solar radiation pressure to improve the accuracy of orbital propagation.

[0121] In the local LVLH coordinate system of the primary star, a high-order CW relative motion model is established based on a third-order Taylor expansion. Compared with the traditional linear approximation, this model can more accurately describe the time-varying nonlinear relative motion characteristics of the "breathing formation" and is suitable for large-scale dynamic configuration transformations.

[0122] (2) Establishment of absolute / relative measurement model

[0123] In the lunar-centric inertial coordinate system, a collaborative observation model between the primary and secondary stars is established, taking the absolute orbital state of the formation as the estimation object. This model, based on inter-satellite ranging and angular observation information (including azimuth and elevation angles), is used to support the estimation of the absolute navigation state.

[0124] In the primary star's local LVLH coordinate system, a relative measurement model is established using the relative position and velocity of the secondary star relative to the primary star as state variables. This model, also based on inter-star relative distance and angle observations, provides a precise perception of dynamic configuration evolution.

[0125] (3) Second-order navigation architecture design

[0126] First, in the absolute navigation module, the extended Kalman filter algorithm is used to fuse the prior orbital dynamics data with the on-orbit observation data to estimate the absolute orbital state of the formation in the inertial frame.

[0127] Secondly, short-term forecasts of the primary star's orbital state are made to construct the primary star's instantaneous LVLH reference frame and provide a reference benchmark for the relative navigation module.

[0128] Then, in the primary star's LVLH coordinate system, based on a high-order CW model, the extended Kalman filter algorithm is used to fuse inter-satellite relative observation information to estimate the relative orbital state of the slave star relative to the primary star, thereby improving navigation accuracy and tracking continuity.

[0129] Ultimately, through the parallel operation of absolute and relative navigation algorithms and the data interaction of key state variables, autonomous and integrated navigation estimation of the lunar "breathing formation" in orbit is achieved.

[0130] Figure 2 A schematic diagram of a second-order filtered navigation architecture according to an embodiment of the present invention is shown.

[0131] The present invention also provides a second-order filtered navigation architecture comprising: an absolute navigation filter and a relative navigation filter. The absolute navigation filter is configured to perform the following steps:

[0132] Orbit prediction information is obtained from a dynamic model of lunar satellite formations, and collaborative theoretical observation information is obtained from a collaborative observation model.

[0133] Extended Kalman filtering is employed to fuse orbit prediction information, cooperative 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 primary satellite and the secondary satellites; and

[0134] The absolute orbital state of the primary star is transmitted to the relative navigation filter.

[0135] The relative navigation filter is configured to perform the following steps:

[0136] Using the absolute orbital state of the primary star as a reference, and employing a relative motion model, the relative orbital state of the secondary star at the current moment is preliminarily predicted based on the relative orbital state of the secondary star at the previous moment; and

[0137] The extended Kalman filter algorithm is used to fuse the preliminary predicted relative orbital state and the relative measurement data to estimate the relative orbital state of the satellite.

[0138] Relative measurement data includes distance measurement and angle measurement, where angle measurement includes azimuth and elevation angle.

[0139] In summary, the computational process of the lunar "breathing formation" second-order navigation architecture 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 observational information; then, the orbit of the primary star is predicted in a short time to provide a reference benchmark for relative navigation; next, the relative orbital state of the secondary stars is estimated by the relative navigation algorithm based on the relative dynamic model and inter-satellite observation data; finally, the absolute and relative integrated positioning of the formation is achieved, completing the accurate characterization of the formation configuration.

[0140] Figure 3 The absolute position error and absolute velocity error of a satellite formation according to an embodiment of the present invention are shown. Figure 4 The relative position error and relative velocity error of a satellite formation according to an embodiment of the present invention are shown.

[0141] In the lunar inertial frame, the initial orbital error for the "breathing formation" was set to 1 km and 1 m / s. During inter-satellite measurements, the ranging error was 3 m. ), the angle measurement error is ( Taking Samsung formation as an example, after parallel filter navigation simulation, the absolute and relative navigation errors are as follows: Figure 3 and Figure 4 As shown.

[0142] Simulation results show that the navigation algorithm can converge quickly, with an absolute position error of 719.455m. The absolute velocity error is 0.550 m / s. The relative position error is 1.327m. The relative velocity error is 0.00235 m / s. ).

[0143] In summary, the lunar "breathing formation" absolute / relative integrated autonomous navigation method proposed in this invention can achieve accurate autonomous orbit determination and can provide a technical reference for future lunar exploration missions.

[0144] While some embodiments of the present invention have been described in this application, those skilled in the art will understand that these embodiments are merely illustrative. Numerous variations, alternatives, and improvements will arise in those skilled in the art under the teachings of this invention without departing from its scope. The appended claims are intended to define the scope of the invention and thereby cover methods and structures within the scope of the claims themselves and their equivalents.

Claims

1. An autonomous navigation method for lunar satellite formations, characterized in that, Includes the following steps: Orbit prediction information is obtained based on the dynamic model of the lunar satellite formation, and collaborative theoretical observation information is obtained based on the collaborative observation model. The extended Kalman filter algorithm is used to fuse the orbit prediction information, collaborative theoretical observation information and multi-source observation data from on-orbit observation to estimate the absolute orbital state of the lunar satellite formation, including the absolute orbital state of the primary star and the absolute orbital state of the secondary stars. Establish a relative motion model of the slave star in the local coordinate system of the primary star, and establish a relative measurement model; and Using the absolute orbital state of the primary star as a reference, a preliminary predicted relative orbital state is obtained based on the relative motion model of the secondary star. Relative measurement data, including distance and angle measurements, are obtained based on the relative measurement model. The relative orbital state of the secondary star 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 lunar satellite formations according to claim 1, characterized in that, Also includes: A dynamic model of the lunar satellite formation is established in the lunar inertial coordinate system J2000. as well as Establish a collaborative observation model for lunar satellite formations.

3. The autonomous navigation method for lunar satellite formations according to claim 2, characterized in that, In the dynamic model, the equations of motion for a single star are expressed as: ， in, It is the satellite's three-dimensional position. It is three-dimensional velocity. Represents the gravitational acceleration at the center of the moon and in a non-spherical shape. Represents the acceleration caused by gravitational perturbations of the Sun, Earth, and Sun bodies, and solar radiation pressure perturbations; and Based on the motion equations of a single star, the motion model of the lunar satellite formation is as follows: ， in, It is the differential of the three-dimensional position of the primary star. It is the differential of the primary star's three-dimensional velocity. It is the first differential from the three-dimensional position of a star. It is the first differential of the three-dimensional velocity of a star. It is the differential of the nth star's three-dimensional position. It is the differential of the three-dimensional velocity of the nth follower star.

4. The autonomous navigation method for lunar satellite formations according to claim 2, characterized in that, Establishing a collaborative observation model for lunar satellite formations includes: During their orbit around the moon, the lunar satellite formation obtains inter-satellite angle information through optical observation of the host star and inter-satellite distance information through microwave ranging. The angle observation model is as follows: ， in, It is the first Information on the azimuth angle between the secondary star and the primary star. It is the first The elevation angle information between the secondary star and the primary star. Represents optical observation error. , It is the y-axis position of the i-th star. It is the y-axis position of the primary star. It is the x-axis position of the i-th star. It is the x-axis position of the primary star. It is the z-axis position of the i-th star. It is the z-axis position of the primary star. It is the three-dimensional position of the i-th star. It is the three-dimensional position of the primary star; The inter-satellite distance observation model is as follows: ， in, Indicates the first The distance measurement error between the secondary star and the primary star; Based on inter-satellite angle and distance information, the collaborative observation model for lunar satellite formations is as follows: ， in, , This is the measurement information between the first secondary star and the primary star, including the inter-star distance and inter-star angle information between the first secondary star and the primary star. This is the measurement information between the second secondary star and the primary star, including the inter-star distance and inter-star angle information between the second secondary star and the primary star. It is the measurement information between the nth slave star and the primary star, including the inter-star distance and inter-star angle information between the nth slave star and the primary star.

5. The autonomous navigation method for lunar satellite formations according to claim 1, characterized in that, Using a dynamic model, orbital state prediction is performed based on the absolute orbital state of the lunar satellite formation at the previous moment, thus obtaining orbital prediction information; The extended Kalman filter algorithm fuses orbit prediction information, cooperative 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 lunar satellite formations according to claim 1, characterized in that, Establish a relative motion model of the slave star in the local coordinate system of the primary star, and establish a relative measurement model including: Based on the equations of motion of the primary and secondary stars, and the transformation relationship between the lunar inertial coordinate system J2000 and the primary star's local coordinate system, relative state variables are defined in the primary star's local coordinate system. ,in It is based on the three-dimensional position of the star relative to the primary star. It is the three-dimensional velocity of the star relative to the host star; In the primary star's local coordinate system, the relative motion equations of the secondary stars in the relative motion model are: ， in, Represents the distance between the center of the main star and the moon. Represents the lunar gravitational constant. Represents the true perihelion angular velocity of the primary star; Considering that the primary star orbits in a near-circular orbit and the interstellar distances are much smaller than the radius of the primary star's orbit, then Performing a third-order Taylor expansion on the above relative motion equations and simplifying them, we obtain the third-order relative motion equations: ， in: ， ， In the primary star's local coordinate system, the inter-satellite angle measurement model and inter-satellite distance measurement model relative to the measurement model are as follows: ， in, It is based on the three-dimensional position of the star relative to the primary star. It is azimuth measurement noise. It is pitch angle measurement noise. It is distance measurement noise.

7. The autonomous navigation method for lunar satellite formations according to claim 1, characterized in that, Using the absolute orbital state of the primary star as a reference, and employing a relative motion model, the relative orbital state of the secondary star at the current moment is preliminarily predicted based on the relative orbital state of the secondary star at the previous moment. The preliminary predicted relative orbital state and relative measurement data are fused using the extended Kalman filter algorithm to obtain the relative orbital state of the satellite, where the relative measurement data is obtained through a relative measurement model.

8. A second-order filtered navigation architecture, characterized in that, include: An absolute navigation filter is configured to perform the following steps: Orbit prediction information is obtained based on the dynamic model of lunar satellite formation and collaborative theoretical observation information is obtained based on the collaborative observation model; Extended Kalman filtering is used to fuse orbit prediction information, cooperative 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 primary satellite and the secondary satellites. as well as Transmit the absolute orbital state of the primary star to the relative navigation filter; The relative navigation filter is configured to perform the following steps: Using the absolute orbital state of the primary star as a reference, and employing a relative motion model, the relative orbital state of the secondary star at the current moment is preliminarily predicted based on the relative orbital state of the secondary star at the previous moment. as well as The extended Kalman filter algorithm is used to fuse the preliminary predicted relative orbital state and relative measurement data to estimate the relative orbital state of the satellite. The relative measurement data includes distance measurement and angle measurement, where the angle measurement includes azimuth and elevation angles.

Images