Method for correcting rotation errors of a constellation of distributed autonomous navigators

Abstract

The application relates to a rotation error correction method of a distributed autonomous navigation constellation, and comprises the following steps: S1, each satellite calculates the orbit plane orientation error of the satellite in orbit and distributes the result to all visible satellites in the constellation in real time; S2, each satellite fits a local constellation rotation quantity according to the orbit plane orientation error of the satellite and the collected orbit plane orientation error; S3, each satellite determines a virtual satellite orbit observation quantity according to the local constellation rotation quantity of the satellite; S4, each satellite constructs a conditional constraint equation of virtual observation according to the virtual satellite orbit observation quantity and the second type of non-singularity orbit root number; and S5, each satellite solves the satellite orbit through filtering according to the conditional constraint equation of virtual observation, so that the overall rotation effect of the constellation is inhibited and corrected. The application can inhibit the rotation effect of the constellation, improve the distributed autonomous orbit determination precision of the satellite, does not increase the inter-satellite data interaction communication pressure, and can stably maintain the constellation configuration for a long time.

Description

Technical Field

[0001] This invention relates to the field of satellite technology, and specifically to a method for correcting rotational errors in a distributed autonomous navigation constellation. Background Technology

[0002] Autonomous navigation relying solely on inter-satellite link measurements, without ground-based reference constellation constraints, will inevitably encounter the problem of unobservable constellation rotation in inertial space. This is mainly due to limited onboard computing resources, the inability to accurately model perturbations, and the inability of inter-satellite ranging to fully determine the changes in orbital orientation parameters (right ascension of the ascending node Ω and orbital inclination i) caused by perturbation model errors, which in turn causes the constellation reference to rotate as a whole in inertial space.

[0003] Currently, the solutions to the constellation rotation error problem related to autonomous orbit determination can be broadly categorized into three types. First, increase the satellite's autonomous orbit determination capability, such as by carrying optical sensitive payloads to measure "starlight direction + geocentric vector" or using X-ray pulsar observations. Second, add a small number of ground anchoring stations, using two-way Ka-link measurements between the anchoring stations and the satellite to establish a fixed connection between the constellation's spatial reference and Earth. Third, utilize long-term predicted ephemeris information from ground-based systems to constrain orbital plane orientation parameters, thus suppressing a certain degree of inertial space constellation rotation error.

[0004] Of the three methods mentioned above, the first method is limited by the measurement accuracy of star sensors and other components, and is still far from practical application. The second method, although it can eliminate the constellation rotation effect through satellite-to-ground observations using a small number of ground-based anchored stations, compromises the constellation's autonomous operation capability.

[0005] The third method, commonly used today, utilizes ground-based predicted ephemeris information to constrain orbital orientation parameters and suppress rotation errors in inertial space constellations. This method includes single-satellite and constellation-wide constraints for orbital orientation constraint correction. In single-satellite constraints, satellites constrain their orbital orientation parameters based on their own ephemeris predictions, effectively overcoming the problem of incompletely measurable orbital orientation parameters. However, due to the varying i and Ω prediction error characteristics among satellites, and the increasing differences over time, the overall constellation rotation correction accuracy becomes uneven, causing gradual deformation of the distributed autonomous orbit determination network structure, making it unsuitable for long-term distributed autonomous orbit determination. In the constellation-wide constraint method, rotational effect correction is performed based on the orbital orientation parameter determination and prediction information of the entire constellation. The rotation correction of all satellites remains strictly consistent. However, this method requires each satellite to obtain real-time orbital orientation parameter predictions and determinations from all satellites via inter-satellite links, which imposes a significant inter-satellite communication burden on distributed autonomous orbit determination.

[0006] In summary, current constellation rotation correction methods significantly increase inter-satellite communication pressure or disrupt constellation configuration, and are not suitable for distributed long-term autonomous orbit determination based on inter-satellite links. Summary of the Invention

[0007] To address the aforementioned issues, this invention proposes a rotation error correction method for a distributed autonomous navigation constellation. This method not only suppresses constellation rotation effects and improves the accuracy of distributed autonomous orbit determination, but also does not increase the pressure on inter-satellite data exchange and communication, thus maintaining the constellation configuration stably over a long period.

[0008] The rotation error correction method for a distributed autonomous navigation constellation according to an embodiment of the present invention includes:

[0009] S1, each satellite calculates its own orbital plane orientation error in orbit and distributes the results to all linked visible satellites in the constellation;

[0010] S2, each satellite fits its own and the collected orbital plane orientation errors to form a local constellation rotation;

[0011] S3, each satellite within the constellation determines its own virtual satellite orbit observations based on its local constellation rotation.

[0012] S4, each satellite constructs conditional constraint equations for virtual observations based on its own virtual satellite orbit observations and second-kind singularity-free orbital elements;

[0013] S5, each satellite performs its own filtering and orbit calculation based on the condition constraint equations of its own virtual observation, thereby suppressing and correcting the overall constellation rotation effect.

[0014] Further, S1 includes:

[0015] S11, each satellite, based on the simplified dynamic model built on-board, integrates the orbital filter value from the previous epoch to the current epoch to determine the satellite reference orbit X at the current epoch. * ;

[0016] S12, each satellite simultaneously traverses and interpolates its predicted orbit for the current epoch based on the long-term predicted ephemeris data provided on the ground.

[0017] S13, will refer to orbit X * and predicted orbit Converting to Kepler orbital elements, the orbital plane orientation error (Δi, ΔΩ) of each satellite is calculated using the following formula:

[0018]

[0019] Among them, (i * ,Ω * ) represents the reference orbit X * The orbital inclination and right ascension of the ascending node, This represents the orbital inclination and right ascension of the ascending node of the long-term predicted orbit X based on ground-based indices;

[0020] S14 distributes the orbital plane orientation error (Δi, ΔΩ) of each satellite to all visible satellites linked to it.

[0021] Further, S2 includes:

[0022] Local constellation rotation (θ) for each satellite x ,θ y ,θ z The fitting calculation formula for ) is:

[0023]

[0024] Where, (θ x ,θ y ,θ z ) represent the three-dimensional rotation errors of the satellite vector around the x, y, and z axes at the current moment.

[0025] Further, S3 includes:

[0026] The satellite's reference orbit X at its previous epoch * Perform rotation processing to generate virtual satellite orbit observations. The formula is:

[0027]

[0028] Where R(θ) is:

[0029] R(θ)=R x (θ x )·R y (θ y )·R z (θ z )

[0030]

[0031]

[0032]

[0033] in, z represents the position and velocity parameters of the satellite's filtered integral orbit.

[0034] These are the position and velocity parameters of the satellite's virtual orbit.

[0035] Further, S4 includes:

[0036] Based on the functional relationship between the second type of orbital elements h and k without singularities, the conditional constraint equations for virtual observation are established, and the functional relationship is as follows:

[0037] h = -N y =sinicosΩ

[0038] k = -N x =sinisinΩ

[0039] Where, N x and N y Let x and y be the components of the satellite orbital plane normal vector in the x and y directions, respectively:

[0040]

[0041]

[0042]

[0043] By combining the linearization of virtual satellite orbit observations, the equation form for the additional conditions is determined:

[0044]

[0045] in, and To utilize and X * Calculated Kepler roots and(i * ,Ω * Substituting into the constraint equation, we get δX, which is the satellite orbit correction to be estimated at the current epoch.

[0046] Further, S5 includes:

[0047] The equation with additional conditions is expressed in the form of M. k =C k δX k In the form of:

[0048]

[0049] And by combining the inter-satellite ranging observation equations, we obtain the equations used for filtering and solving satellite orbits:

[0050]

[0051] Where z represents the inter-satellite ranging observation vector, A represents the partial derivative matrix of inter-satellite ranging with respect to satellite orbit, the random variable Δ represents the one-dimensional noise vector of the constraint condition, and R and P represent the covariance matrices of the observation noise v and the constraint random variable Δ, respectively.

[0052] The rotation error correction method for distributed autonomous navigation constellations of the present invention calculates the local constellation rotation correction amount using the orbital plane orientation parameter information of the satellite itself and the linked visible satellite at the current epoch, generates virtual orbital observations, designs constraint equations with the second type of singularity-free orbital elements, and then establishes a constellation overall rotation error correction method applicable to long-term distributed satellite autonomous orbit determination. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0054] Figure 1 This is a flowchart illustrating the rotation error correction method for a distributed autonomous navigation constellation according to an embodiment of the present invention.

[0055] Figure 2 This is a schematic diagram illustrating the principle of the rotation error correction method for a distributed autonomous navigation constellation according to an embodiment of the present invention. Detailed Implementation

[0056] The description of the embodiments in this specification should be taken in conjunction with the accompanying drawings, which should form part of the complete specification. In the drawings, the shape or thickness of the embodiments may be exaggerated and may be indicated in a simplified or convenient manner. Furthermore, parts of the various structures in the drawings will be described separately; it is worth noting that elements not shown in the figures or not described in words are in a form known to those skilled in the art.

[0057] The descriptions of the embodiments herein, including any references to directions and orientations, are for ease of description only and should not be construed as limiting the scope of the invention. The following description of preferred embodiments involves combinations of features, which may exist independently or in combination; the invention is not particularly limited to the preferred embodiments. The scope of the invention is defined by the claims.

[0058] like Figure 1 As shown, the rotation error correction method for the distributed autonomous navigation constellation of the present invention includes:

[0059] S1, each satellite calculates its own orbital plane orientation error in orbit and distributes the results in real time to all linked visible satellites in the constellation;

[0060] S2, each satellite fits its own and the collected orbital plane orientation errors to form a local constellation rotation;

[0061] S3, each satellite within the constellation determines its own virtual satellite orbit observations based on its local constellation rotation.

[0062] S4, each satellite constructs conditional constraint equations for virtual observations based on its own virtual satellite orbit observations and second-kind singularity-free orbital elements;

[0063] S5, each satellite performs its own filtering and orbit calculation based on the conditional constraint equations of virtual observation, thereby suppressing and correcting the overall constellation rotation effect.

[0064] In this embodiment, S1 involves using long-term predicted ephemeris data from the ground as the true value to calculate the orientation error of the satellite's filtered integral orbit in real time, providing necessary data input for the next step of calculating the local constellation rotation error. This includes:

[0065] S11, each satellite, based on the simplified dynamic model built on-board, integrates the orbital filter value from the previous epoch to the current epoch to determine the satellite reference orbit X at the current epoch. * ;

[0066] S12, each satellite simultaneously traverses and interpolates its predicted orbit for the current epoch based on the long-term predicted ephemeris data provided on the ground.

[0067] S13, will refer to orbit X * and predicted orbit Converting to Kepler orbital elements, the orbital plane orientation error (Δi, ΔΩ) of each satellite is calculated using the following formula:

[0068]

[0069] Among them, (i * ,Ω * ) represents the reference orbit X * The orbital inclination and right ascension of the ascending node, Indicates the predicted orbit The orbital inclination and right ascension of the ascending node;

[0070] S14 distributes the orbital plane orientation error (Δi, ΔΩ) of each satellite to all visible satellites linked to it.

[0071] In this embodiment, S2 involves calculating the local constellation rotation of each satellite based on its own orbital plane orientation error information and that of the visible linked satellites, using the following formula for least-squares fitting:

[0072] Local constellation rotation (θ) for each satellite x ,θ y ,θz The fitting calculation formula for ) is:

[0073]

[0074] In this embodiment, S3, after all satellites simultaneously calculate their respective observed local constellation rotations, includes:

[0075] The satellite's reference orbit X at its previous epoch * Perform rotation processing to generate virtual satellite orbit observations. The formula is:

[0076]

[0077] Where R(θ) is:

[0078] R(θ)=R x (θ x )·R y (θ y )·R z (θ z )

[0079]

[0080]

[0081]

[0082] in, The position and velocity parameters of the satellite's filtered integral orbit. These are the position and velocity parameters of the satellite's virtual orbit.

[0083] In this embodiment, S4 includes:

[0084] Based on the functional relationship between the second type of orbital elements h and k without singularities, the conditional constraint equations for virtual observation are established, and the functional relationship is as follows:

[0085] h = -N y =sinicosΩ

[0086] k = -N x =sinisinΩ

[0087] Where, N x and N y Let x and y be the components of the satellite orbital plane normal vector in the x and y directions, respectively:

[0088]

[0089]

[0090]

[0091] By combining the linearization of virtual satellite orbit observations, the equation form for the additional conditions is determined:

[0092]

[0093] in, and (h) * ,k * ) for use and X * Calculated Kepler roots and(i * ,Ω * Substituting into the constraint equation, we get δX, which is the satellite orbit correction to be estimated at the current epoch.

[0094] In this embodiment, S5 includes:

[0095] The equation with additional conditions is expressed in the form of M. k =C k δX k In the form of:

[0096]

[0097] And by combining the inter-satellite ranging observation equations, we obtain the equations used for filtering and solving satellite orbits:

[0098]

[0099] Where z represents the inter-satellite ranging observation vector, A represents the partial derivative matrix of inter-satellite ranging with respect to satellite orbit, the random variable Δ represents the one-dimensional noise vector of the constraint condition, and R and P represent the covariance matrices of the observation noise v and the constraint random variable Δ, respectively.

[0100] In the distributed autonomous navigation constellation rotation error correction method of this invention, the satellite uses long-term predicted ephemeris data from the ground as a reference to calculate the filtered integral reference orbit orientation error and distributes it to linked visible satellites. The satellite uses its own current epoch and the collected orbital plane orientation error information from linked visible satellites to fit and calculate the local constellation rotation correction. Based on the fitted local constellation rotation correction and the filtered integral orbit, a virtual orbit observation is constructed. Conditional constraint equations for the virtual observation are established using the second type of singularity-free orbital elements. Autonomous orbit determination is achieved satellite-by-satellite by fusing long-term orbital plane orientation prediction information with inter-satellite ranging, thus constraining and suppressing the overall constellation rotation effect. Therefore, this invention can suppress constellation rotation effects and improve the accuracy of distributed autonomous orbit determination without increasing the pressure on inter-satellite data interaction and communication, and can maintain the constellation configuration stably for a long period.

[0101] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for correcting rotation errors in a distributed autonomous navigation constellation, characterized in that, The method includes: S1, each satellite calculates its own orbital plane orientation error in orbit and distributes the results in real time to all linked visible satellites in the constellation; S2, each satellite fits its own and the collected orbital plane orientation errors to form a local constellation rotation; S3, each satellite within the constellation determines its own virtual satellite orbit observations based on its local constellation rotation. S4, each satellite constructs conditional constraint equations for virtual observations based on its own virtual satellite orbit observations and second-kind singularity-free orbital elements; S5, each satellite performs its own filtering and orbit calculation based on the condition constraint equations of virtual observation, thereby suppressing and correcting the overall constellation rotation effect; S1 includes: S11, each satellite, based on the simplified dynamic model built on-board, integrates the orbital filter value from the previous epoch to the current epoch to determine the satellite reference orbit at the current epoch. ; S12, each satellite simultaneously traverses and interpolates its predicted orbit for the current epoch based on the long-term predicted ephemeris data provided on the ground. ; S13, reference orbit and predicted orbit Convert to Keplerian orbital elements and calculate the orbital plane orientation error for each satellite. The formula is: in, Indicates reference orbit The orbital inclination and right ascension of the ascending node, This indicates the long-term predicted orbit based on ground-based data. The orbital inclination and right ascension of the ascending node; S14, the orbital plane orientation error of each satellite. Distribute to all visible satellites that have established a link with it.

2. The rotation error correction method for a distributed autonomous navigation constellation according to claim 1, characterized in that, S2 includes: Local constellation rotation for each satellite The fitting calculation formula is: in, These represent the three-dimensional rotation errors of the satellite vector around the x, y, and z axes at the current moment.

3. The rotation error correction method for a distributed autonomous navigation constellation according to claim 2, characterized in that, S3 includes: The satellite uses its filtered orbit and integral prediction to obtain a reference orbit. Perform rotation processing to generate virtual satellite orbit observations. The formula is: in, for: in, The position and velocity parameters of the satellite's filtered integral orbit. These are the position and velocity parameters of the satellite's virtual orbit.

4. The rotation error correction method for a distributed autonomous navigation constellation according to claim 3, characterized in that, S4 includes: According to the second kind of orbital elements without singularities , The functional relationship is used to establish the conditional constraint equations for virtual observation, and the functional relationship is as follows: in, Indicates the orbital inclination angle. Indicates the right ascension of the ascending node; and The normal vector of the satellite orbital plane is respectively in and The directional component is: By combining the linearization of virtual satellite orbit observations, the equation form for the additional conditions is determined: in, and To utilize and Calculated Kepler roots and Substituting into the constraint equations, we obtain... This represents the satellite orbital corrections to be estimated at the current epoch.

5. The rotation error correction method for a distributed autonomous navigation constellation according to claim 4, characterized in that, S5 includes: The equation with additional conditions is expressed in the form of: In the form of, where: And by combining the inter-satellite ranging observation equations, the error equations used for filtering and calculating satellite orbits are obtained: in, Represents the inter-satellite ranging observation vector. The matrix representing the partial derivatives of inter-satellite ranging with respect to satellite orbits, and the random variable. A one-dimensional noise vector representing the constraint conditions. and These represent observation noise, respectively. and constraints on random variables The covariance matrix.

Images