A method of inertial orientation for navigation constellations based on observations

Abstract

The present application discloses an inertial orientation method for a navigation constellation based on stargazing measurement, the method comprising: obtaining constellation orbit parameters in an inertial coordinate system determined by intersatellite ranging and an inertial space pointing of an intersatellite relative vector in a star map background, calculating an intersatellite rotation matrix of a single observation baseline at any sampling time, and calculating intersatellite observation values ​​and relative vectors of intersatellite links obtained by a stargazing camera based on the inertial space pointing; constructing an intersatellite orientation observation equation according to the intersatellite observation values, the relative vectors of the intersatellite links and the rotation matrix, and constructing a navigation constellation orientation observation equation group based on the intersatellite orientation observation equation; correcting the rotation matrix based on the navigation constellation orientation observation equation group to obtain a corrected rotation matrix, and correcting the constellation orbit parameters based on the corrected rotation matrix to obtain the corrected constellation orbit parameters.

Description

Technical Field

[0001] The present application relates to the field of satellite navigation technology, and in particular to a navigation constellation inertial orientation method based on stargazing measurement. Background Art

[0002] The autonomous operation capability of navigation constellations is one of the important means for satellite navigation systems to reduce their dependence on ground stations, especially when it is impossible to build stations around the world. Navigation constellations can realize autonomous operation services based on intersatellite links, but intersatellite measurements will lead to rank deficiency in the autonomous orbit determination process of the constellation, that is, the constellation will rotate as a whole, which will affect the performance of the navigation constellation.

[0003] At present, the problem of constellation rotation can be solved by increasing the observation of stars to correct the constellation rotation. For example, assuming that the absolute direction of the satellite optical axis in inertial space can be obtained, the optical axis direction vector is simulated and solved to correct the constellation rotation; or based on the star-to-star relative vector measurement, the relative vector is analyzed through spherical trigonometric geometry to correct the constellation rotation. Although the existing technology currently provides some solutions for correcting constellation rotation, the existing technology is limited to shallow basic principles and basic simulations, and does not involve detailed and feasible technical methods. Summary of the invention

[0004] The technical problem solved by the present application is: in response to the defects in the prior art, the present application provides an inertial orientation method for a navigation constellation based on stargazing measurement. In the solution provided in the embodiment of the present application, based on observations of a small number of on-board stargazing cameras within the constellation and a systematic solution method, absolute inertial orientation in the inertial space of the navigation constellation is achieved, effectively suppressing the overall rotation problem of the autonomous operation of the constellation, which can be used in the next generation of satellite navigation systems to support high-precision and ultra-long-term autonomous operation of the constellation.

[0005] In a first aspect, an embodiment of the present application provides an inertial orientation method for a navigation constellation based on stargazing measurement, the method comprising: obtaining constellation orbit parameters in an inertial coordinate system determined by inter-satellite ranging and an inertial space pointing of an inter-satellite relative vector in a star map background, calculating the inter-satellite rotation matrix of a single observation baseline at any sampling time, and calculating the inter-satellite observation values ​​and the relative vector of the inter-satellite link obtained by a stargazing camera based on the inertial space pointing; constructing an inter-satellite orientation observation equation according to the inter-satellite observation values, the relative vector of the inter-satellite link and the rotation matrix, and constructing a navigation constellation orientation observation equation group based on the inter-satellite orientation observation equation; correcting the rotation matrix based on the navigation constellation orientation observation equation group to obtain a corrected rotation matrix, and correcting the constellation orbit parameters based on the corrected rotation matrix to obtain corrected constellation orbit parameters.

[0006] Optionally, the relative right ascension and declination between any two satellites in the navigation constellation output by the stargazing camera at any sampling moment are obtained; the unit vector of the relative vector between any two satellites is calculated based on the relative right ascension and declination, and the inertial space direction of the inter-satellite relative vector in the background composition of the star map is characterized based on the unit vector.

[0007] Optionally, calculating a unit vector of a relative vector between any two satellites based on the relative right ascension and the declination includes:

[0008] The unit vector is calculated by the following formula:

[0009]

[0010] in, represents the unit vector of the relative vector between the i-th satellite in the navigation constellation and the j-th satellite in the navigation constellation at time t; α ij represents the relative right ascension between the i-th satellite in the navigation constellation and the j-th satellite in the navigation constellation; β ij represents the relative declination between the i-th satellite in the navigation constellation and the j-th satellite in the navigation constellation; i represents the i-th satellite in the navigation constellation; j represents the j-th satellite in the navigation constellation, where i=1…M, j=1…M, and M is the number of satellites in the navigation constellation.

[0011] Optionally, the intersatellite rotation matrix of a single observation baseline at any sampling time is calculated, including:

[0012] The rotation angle between the satellite coordinates and the inertial system coordinates is determined by an intersatellite link, and the intersatellite rotation matrix is ​​calculated based on the rotation angle; wherein,

[0013] The inter-satellite rotation matrix R(-ε(t)) is:

[0014]

[0015] Among them, ε(t) represents the rotation angle at time t; θ x represents the rotation component of the rotation matrix between the satellite coordinates and the inertial coordinates determined by the intersatellite link around the X axis; θ y represents the rotation component of the rotation matrix between the satellite coordinates and the inertial coordinates determined by the intersatellite link around the Y axis; θ z It represents the rotation component about the Z axis of the rotation matrix between the satellite coordinates and the inertial coordinates determined by the intersatellite link.

[0016] Optionally, calculating the intersatellite observation value acquired by the star-gazing camera and the relative vector of the intersatellite link based on the inertial space pointing includes:

[0017] Determine the first constellation inertial system orbit unit vector corresponding to the navigation constellation by the intersatellite link, and determine the real second constellation inertial system orbit unit vector corresponding to the navigation constellation;

[0018] The relative vector of the inter-satellite link is calculated based on the first constellation inertial system orbit unit vector, and the inter-satellite observation value is calculated based on the second constellation inertial system orbit unit vector.

[0019] Optionally, constructing an inter-satellite directional observation equation according to the inter-satellite observation value, the relative vector of the inter-satellite link and the rotation matrix includes:

[0020] The intersatellite directional observation equation is:

[0021]

[0022] in, represents the inter-satellite observation value between the i-th satellite in the navigation constellation and the j-th satellite in the navigation constellation, represents the second constellation inertial system orbit unit vector corresponding to the i-th satellite in the navigation constellation, Represents the second constellation inertial system orbit unit vector corresponding to the j-th satellite in the navigation constellation; represents the relative vector of the intersatellite link between the i-th satellite in the navigation constellation and the j-th satellite in the navigation constellation, represents the first constellation inertial system orbit unit vector corresponding to the i-th satellite in the navigation constellation, Represents the first constellation inertial system orbit unit vector corresponding to the j-th satellite in the navigation constellation.

[0023] Optionally, constructing a navigation constellation directional observation equation group based on the inter-satellite directional observation equation includes:

[0024] The navigation constellation orientation observation equation group is:

[0025]

[0026] Optionally, the rotation matrix is ​​corrected based on the navigation constellation directional observation equation group to obtain a corrected rotation matrix, including: performing Taylor expansion on the navigation constellation directional observation equation group to obtain an observation matrix, and calculating an inter-satellite calculation value of the rotation correction; iteratively calculating each angle correction amount in the rotation matrix based on the observation matrix and the inter-satellite calculation value until the correction amount is less than a preset threshold, and determining the corrected rotation matrix when the correction amount is less than the preset threshold.

[0027] Optionally, the constellation orbit parameters are corrected based on the corrected rotation matrix to obtain corrected constellation orbit parameters, including: averaging the rotation matrix correction amount within a preset sampling time interval to obtain the averaged rotation matrix correction amount; correcting the constellation orbit parameters based on the averaged rotation matrix correction amount to obtain the corrected constellation orbit parameters.

[0028] Optionally, performing average processing on the rotation matrix correction amount within a preset sampling time interval to obtain an averaged rotation matrix correction amount includes:

[0029] Solving all rotation matrix corrections within a preset sampling time interval to obtain a first mean, and solving the variance of each rotation matrix correction one by one;

[0030] Determine and eliminate the first rotation matrix correction amount whose difference with the first mean is greater than the variance one by one, solve the second rotation matrix correction amount except the first rotation matrix correction amount within the preset sampling time interval to obtain the second mean, and use the second mean as the averaged rotation matrix correction amount.

[0031] In a second aspect, the present application provides a computer device, the computer device comprising:

[0032] a memory for storing instructions executed by at least one processor;

[0033] The processor is used to execute the instructions stored in the memory to execute the method described in the first aspect.

[0034] In a third aspect, the present application provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer instructions. When the computer instructions are executed on a computer, the computer executes the method described in the first aspect.

[0035] Compared with the prior art, the embodiments of the present application have at least the following effects:

[0036] In the solution provided in the embodiment of the present application, based on observations of a small number of on-board stargazing cameras within the constellation and a systematic solution method, absolute inertial orientation in the inertial space of the navigation constellation is achieved, effectively suppressing the overall rotation problem of the autonomous operation of the constellation, which can be used in the next generation of satellite navigation systems to support high-precision and ultra-long-term autonomous operation of the constellation. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 A schematic diagram of a flow chart of a navigation constellation inertial orientation method based on stargazing measurement provided in an embodiment of the present application;

[0038] Figure 2AA schematic diagram of simulation results of an X-axis directional observation error when a preset directional observation error is 2mas provided in an embodiment of the present application;

[0039] Figure 2B A schematic diagram of simulation results of a Y-axis directional observation error when a preset directional observation error is 2mas provided in an embodiment of the present application;

[0040] Figure 2C A schematic diagram of simulation results of a Z-axis orientation observation error when a preset orientation observation error is 2mas provided in an embodiment of the present application;

[0041] Figure 2D A schematic diagram of simulation results of a comprehensive directional observation error when a preset directional observation error is 2mas provided in an embodiment of the present application;

[0042] Figure 3A A schematic diagram of simulation results of an X-axis directional observation error when a preset directional observation error of 5mas is provided in an embodiment of the present application;

[0043] Figure 3B A schematic diagram of simulation results of a Y-axis directional observation error when a preset directional observation error of 5mas is provided in an embodiment of the present application;

[0044] Figure 3C A schematic diagram of simulation results of a Z-axis orientation observation error when a preset orientation observation error of 5mas is provided in an embodiment of the present application;

[0045] Figure 3D A schematic diagram of simulation results of a comprehensive directional observation error when a preset directional observation error of 5mas is provided in an embodiment of the present application;

[0046] Figure 4 A schematic diagram of the structure of a computer device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0047] In the solutions provided in the embodiments of this application, the described embodiments are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0048] In order to better understand the above technical scheme, the technical scheme of the present application is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present application and the specific features in the embodiments are detailed descriptions of the technical scheme of the present application, rather than limitations on the technical scheme of the present application. In the absence of conflict, the embodiments of the present application and the technical features in the embodiments can be combined with each other.

[0049] The following is a further detailed description of a navigation constellation inertial orientation method based on star observation measurement provided by an embodiment of the present application in conjunction with the accompanying drawings. The specific implementation of the method may include the following steps (the method flow is as follows: Figure 1 shown):

[0050] Step 101, obtain the constellation orbit parameters in the inertial coordinate system determined by inter-satellite ranging and the inertial space orientation of the inter-satellite relative vector in the star map background, calculate the inter-satellite rotation matrix of a single observation baseline at any sampling time, and calculate the inter-satellite observation values ​​obtained by the star-gazing camera and the relative vector of the inter-satellite link based on the inertial space orientation.

[0051] Since autonomous orbit determination based on intersatellite links may cause constellation rotation, in order to avoid the rotation problem, it is necessary to correct the orbit parameters of the navigation constellation in the inertial coordinate system. As an example, the constellation orbit parameters are the coordinates of each satellite in the navigation constellation in the inertial coordinate system. For example, the navigation constellation completes autonomous orbit determination based on intersatellite links. The number of satellites in the navigation constellation is M, and the satellites in the navigation constellation are numbered 1, ..., M in sequence. The coordinates of each satellite in the inertial coordinate system are (x i ,y i , z i ).

[0052] A stargazing camera is also configured in the navigation constellation, wherein the stargazing camera is used to observe the satellites in the navigation constellation, for example, to observe the orbital parameters or position parameters of the satellites. In order to correct the orbital parameters of the navigation constellation in the inertial coordinate system, it is also necessary to obtain the inertial space pointing of the inter-satellite relative vector in the background of the star map. As an example, for an observation baseline, the relative right ascension and declination between any two satellites in the navigation constellation output by the stargazing camera at any sampling time t are obtained, and the unit vector of the relative vector between any two satellites is calculated based on the relative right ascension and declination, and the inertial space pointing of the inter-satellite relative vector in the background of the star map is characterized based on the unit vector.

[0053] As another example, assuming that the relative right ascension and declination between the i-th satellite in the navigation constellation and the j-th satellite in the navigation constellation are output at any sampling time t, the unit vector of the relative vector between any two satellites is calculated based on the relative right ascension and declination, including:

[0054] The unit vector of the relative vector between the i-th satellite in the navigation constellation and the j-th satellite in the navigation constellation is calculated by the following formula:

[0055]

[0056] in, represents the unit vector of the relative vector between the i-th satellite in the navigation constellation and the j-th satellite in the navigation constellation at time t; α ij represents the relative right ascension between the i-th satellite in the navigation constellation and the j-th satellite in the navigation constellation; β ij represents the relative declination between the i-th satellite in the navigation constellation and the j-th satellite in the navigation constellation; i represents the i-th satellite in the navigation constellation; j represents the j-th satellite in the navigation constellation, where i=1…M, j=1…M, and M is the number of satellites in the navigation constellation.

[0057] Step 102: construct an inter-satellite directional observation equation according to the inter-satellite observation value, the relative vector of the inter-satellite link and the rotation matrix, and construct a navigation constellation directional observation equation group based on the inter-satellite directional observation equation.

[0058] Furthermore, a navigation constellation directional observation equation group is constructed, and in order to construct the navigation constellation directional observation equation group, it is necessary to first construct the intersatellite directional observation equation of a single observation machine baseline. As an example, the intersatellite directional observation equation of a single observation machine baseline is constructed based on the intersatellite observation value output by the star-gazing camera, the relative vector of the intersatellite link, and the rotation matrix.

[0059] The rotation angle between the satellite coordinates and the inertial system coordinates is determined by the intersatellite link. Specifically, the rotation angle is expressed by the following formula:

[0060] ε(t)=[θ x ,θ y ,θ z ] T

[0061] Among them, ε(t) represents the rotation angle of the navigation constellation at time t; θ x represents the rotation component of the rotation matrix around the X axis between the satellite coordinates and the inertial coordinates determined by the intersatellite link at time t; θ y represents the rotation component of the rotation matrix around the Y axis between the satellite coordinates and the inertial coordinates determined by the intersatellite link at time t; θ z It represents the rotation component of the rotation matrix around the Z axis between the satellite coordinates and the inertial coordinates determined by the intersatellite link at time t.

[0062] Furthermore, for small rotation angles, the inter-satellite rotation matrix can be calculated based on the rotation angle; wherein the inter-satellite rotation matrix R(-ε(t)) is:

[0063]

[0064] As another example, the inter-satellite observation values ​​obtained by the stargazing camera and the relative vector of the inter-satellite link are calculated based on the inertial space pointing, including: determining the first constellation inertial system orbit unit vector corresponding to the navigation constellation by the inter-satellite link, and determining the real second constellation inertial system orbit unit vector corresponding to the navigation constellation, and calculating the relative vector of the inter-satellite link based on the first constellation inertial system orbit unit vector, and calculating the inter-satellite observation value based on the second constellation inertial system orbit unit vector.

[0065] For example, assuming that at any sampling time t, the inertial orbit unit vector of the navigation constellation satellite determined by the intersatellite link (i.e., the inertial orbit unit vector of the first constellation) is:

[0066]

[0067] in, represents the inertial orbit unit vector of the navigation constellation satellite corresponding to the i-th satellite in the navigation constellation determined by the intersatellite link; It represents the X-axis component of the orbit unit vector of the inertial system of the navigation constellation corresponding to the i-th satellite in the navigation constellation determined by the intersatellite link; It represents the component of the Y-axis of the orbit unit vector of the inertial system of the navigation constellation corresponding to the i-th satellite in the navigation constellation determined by the intersatellite link; It represents the component of the Z-axis of the orbit unit vector of the inertial system of the navigation constellation corresponding to the i-th satellite in the navigation constellation determined by the intersatellite link.

[0068] The real inertial orbit unit vector of the navigation constellation satellite (i.e. the second constellation inertial orbit unit vector) is:

[0069]

[0070] in, Represents the real navigation constellation satellite inertial system orbit unit vector corresponding to the i-th satellite in the navigation constellation; Represents the X-axis component of the real navigation constellation satellite inertial system orbit unit vector corresponding to the i-th satellite in the navigation constellation; Represents the Y-axis component of the real navigation constellation satellite inertial system orbit unit vector corresponding to the i-th satellite in the navigation constellation; It represents the component of the Z-axis of the real navigation constellation satellite inertial system orbit unit vector corresponding to the i-th satellite in the navigation constellation.

[0071] Based on the first constellation inertial system orbit unit vector, the relative vector of the intersatellite link between the i-th satellite in the navigation constellation and the j-th satellite in the navigation constellation is calculated: for:

[0072]

[0073] Calculate the inter-satellite observation values ​​of the i-th satellite in the navigation constellation and the j-th satellite in the navigation constellation based on the orbit unit vector of the second constellation inertial system for:

[0074]

[0075] Based on this, the intersatellite directional observation equation is constructed according to the intersatellite observation value, the relative vector of the intersatellite link and the rotation matrix:

[0076]

[0077] As another example, since the navigation constellation contains multiple satellites, it is necessary to construct the navigation constellation directional observation equation group according to the inter-satellite directional observation equations corresponding to any two satellites. For example, assuming that the number of satellites in the navigation constellation is M, the navigation constellation directional observation equation group is as follows:

[0078]

[0079] It should be understood that the above-mentioned navigation constellation directional observation equation group is a directional observation equation group composed of multiple baselines. Each equation in the equation group is a single-baseline inter-satellite directional observation equation. The left side of each equation is the observation value obtained by the inertial camera, and the right side is the rotation matrix and the relative vector calculation value obtained by the inter-satellite link.

[0080] Step 103: Based on the navigation constellation directional observation equation group, the rotation matrix is ​​corrected to obtain a corrected rotation matrix, and based on the corrected rotation matrix, the constellation orbit parameters are corrected to obtain corrected constellation orbit parameters.

[0081] As an example, Taylor expansion is performed on the navigation constellation directional observation equation group to obtain an observation matrix, and an inter-satellite calculation value of the rotation correction is calculated; based on the observation matrix and the inter-satellite calculation value, each angle correction in the rotation matrix is ​​iteratively calculated until the correction is less than a preset threshold, and the corrected rotation matrix is ​​determined when the correction is less than the preset threshold.

[0082] For example, the first-order Taylor expansion of the navigation constellation directional observation equation group corresponding to any observation sampling time t can obtain the observation matrix:

[0083]

[0084] in, represents the calculated value of the relative rotation correction between satellite i and satellite j in the navigation constellation; It represents the X-axis component of the calculated value of the relative rotation correction between satellite i and satellite j in the navigation constellation; It represents the Y-axis component of the calculated value of the relative rotation correction between satellite i and satellite j in the navigation constellation; It represents the component of the Z-axis of the calculated value of the relative rotation correction between satellite i and satellite j in the navigation constellation.

[0085]

[0086] is the calculated value of satellite i after rotation correction; It represents the component of the calculated value of satellite i after rotation correction on the X axis; It represents the component of the calculated value of satellite i after rotation correction on the Y axis; It represents the component of the calculated value of satellite i after rotation correction on the Z axis; is the calculated value of satellite j after rotation correction; It represents the component of the calculated value of satellite j after rotation correction on the X axis; It represents the component of the calculated value of satellite j after rotation correction on the Y axis; It represents the component of the calculated value of satellite j after rotation correction on the Z axis.

[0087] And for the first correction:

[0088]

[0089] In addition, the difference y between the observation values ​​of satellite i and satellite j output by the star-gazing camera and the calculated value of relative rotation correction is:

[0090]

[0091] The correction value Δε of each angle of the single calculation rotation matrix can be obtained as:

[0092] Δε=[Δθ x Δθ y Δθ z ] T =(H(t) T H(t) -1 H(t)·y

[0093] Among them, Δθ x Indicates the correction amount of the rotation component of the rotation matrix around the X axis in a single calculation; Δθ y Indicates the correction amount of the rotation component of the rotation matrix around the Y axis in a single calculation; Δθ z Indicates the correction amount for a single calculation of the rotation matrix around the Z axis.

[0094] Furthermore, in the solution provided in the embodiment of the present application, the preset result cannot be achieved by correcting each angle of the rotation matrix once, and multiple iterations are required to correct each angle of the rotation matrix. Specifically, if there are multiple iterations, the relationship between the rotation angles obtained by two adjacent iterations is as follows:

[0095] ε k+1 =ε k + Δε=[θ xk θ yk θ zk ] T +[Δθ x Δθ y Δθ z ] T

[0096] Among them, ε k+1 Represents the value of the rotation angle after k+1 iterations, where k increases by 1 for each iteration; ε k Represents the value of the rotation angle obtained after k iterations; θ xk Represents the rotation component of the rotation matrix around the X axis after k iterations; θ yk Represents the rotation component of the rotation matrix around the Y axis after k iterations; θ zk Represents the rotation component of the rotation matrix around the Z axis after k iterations.

[0097] At time t, the initial value of the rotation angle ε(t) is assumed to be ε1(t)=[0, 0, 0], where ε1(t) represents the rotation angle obtained after one iterative calculation at time t.

[0098] Use the calculated relative vector pointing correction obtained:

[0099]

[0100] Iterate to solve the rotation angle correction value until the correction value is less than the set threshold Δ = (10 -10 , 10 -10 , 10 -10 )(as), the iteration ends, and the rotation angle ε(t) at this sampling time point is obtained.

[0101] Further, as an example, the constellation orbit parameters are corrected based on the corrected rotation matrix to obtain the corrected constellation orbit parameters, including: averaging the rotation matrix correction amount within a preset sampling time interval to obtain the averaged rotation matrix correction amount; correcting the constellation orbit parameters based on the averaged rotation matrix correction amount to obtain the corrected constellation orbit parameters.

[0102] Assume that the number of inertial cameras in the navigation constellation is M, the sampling interval of each camera is N seconds, and the navigation constellation performs an inertial space orientation correction solution every TN period (in seconds). The rotation matrix correction value is averaged within the time period of an inertial space orientation correction solution. This prevents the limited number of cameras in the constellation from being unable to observe the entire constellation at a specific moment, resulting in a deviation between the rotation angle obtained at a certain sampling moment and the overall rotation of the constellation. Assuming that there are P corrections in the TN time period, where P is a positive integer not less than 1, the variance of the P corrections is:

[0103]

[0104]

[0105] Wherein, E(ε) represents the mean of P rotation angle correction values ​​in the TN time period; σ(ε) represents the variance of P rotation angle correction values ​​in the TN time period.

[0106] Determine the rotation amount ε at each sampling moment one by one k Is the difference from the mean E(ε) greater than σ(ε)? If so, the sampling moment is an invalid sample.

[0107] Resolve the P rotation angle corrections in the TN time period to remove invalid samples and obtain S valid samples, where 1≤S≤P. Recalculate the mean rotation angle of the S valid sampling moments:

[0108]

[0109] Where, ε(TN) and E′(ε) both represent the mean rotation angle of S valid sampling moments in the TN time period; θ x (TN) represents the mean value of the rotation angle on the X-axis at S valid sampling moments in the TN time period; θ y (TN) represents the mean value of the rotation angle on the Y axis at S valid sampling moments in the TN time period; θ z (TN) represents the average value of the rotation angle on the Z axis at S valid sampling moments within the TN time period.

[0110] Next, the inertial system orbit correction of all satellites in the constellation is performed. For each satellite orbit in the TN period, the inertial system coordinate value of each satellite after the star-gazing and orientation observation is calculated using the rotation matrix of the constellation relative to the inertial coordinate system and the satellite orbit modulus obtained in the end.

[0111]

[0112] In the solution provided in the embodiment of the present application, based on observations of a small number of on-board stargazing cameras within the constellation and a systematic solution method, absolute inertial orientation in the inertial space of the navigation constellation is achieved, effectively suppressing the overall rotation problem of the autonomous operation of the constellation, which can be used in the next generation of satellite navigation systems to support high-precision and ultra-long-term autonomous operation of the constellation.

[0113] In order to verify the effect of the above method, the beneficial effects of the solution provided in the embodiment of the present application are explained below by taking examples.

[0114] For example, with N = 1s as the sampling interval, assuming that two star-gazing cameras are configured in the constellation, the constellation rotation angle within the period of TN = 100s is calculated. When the preset directional observation error is 2 milliseconds (mas), the simulation results based on the solution provided in the example of this application are as follows: Figure 2A , Figure 2B , Figure 2C as well as Figure 2D shown. Figure 2A A schematic diagram of simulation results of an X-axis directional observation error when a preset directional observation error is 2mas provided in an embodiment of the present application; Figure 2B A schematic diagram of simulation results of a Y-axis directional observation error when a preset directional observation error is 2mas provided in an embodiment of the present application; Figure 2C A schematic diagram of simulation results of a Z-axis orientation observation error when a preset orientation observation error is 2mas provided in an embodiment of the present application; Figure 2D The following is a schematic diagram of the simulation results of the comprehensive directional observation error when the preset directional observation error is 2mas provided in the embodiment of the present application. It should be understood that Figure 2D The comprehensive directional observation error is given by Figure 2A , Figure 2B as well as Figure 2C The X, Y and Z axis directional observation errors (RMS values ​​in the figure) are combined. Figure 2D When the preset directional observation error is 2mas, the comprehensive directional observation error obtained by combining the directional observation errors of the X, Y and Z axes is 2.1mas, that is, the comprehensive directional observation error obtained by the simulation of the scheme provided in the example of this application differs from the preset directional observation error by 0.1mas, which is within the preset error range. Therefore, it is effective to correct the rotation matrix based on the scheme provided in the embodiment of this application.

[0115] Further, when the preset directional observation error is 5 milliarcseconds (mas), the simulation results of the solution provided in the example of this application are as follows: Figure 3A , Figure 3B , Figure 3C as well as Figure 3D shown. Figure 3AA schematic diagram of simulation results of an X-axis directional observation error when a preset directional observation error of 5mas is provided in an embodiment of the present application; Figure 3B A schematic diagram of simulation results of a Y-axis directional observation error when a preset directional observation error of 5mas is provided in an embodiment of the present application; Figure 3C A schematic diagram of simulation results of a Z-axis orientation observation error when a preset orientation observation error of 5mas is provided in an embodiment of the present application; Figure 3D The following is a schematic diagram of the simulation results of the comprehensive directional observation error when the preset directional observation error is 5mas provided in the embodiment of the present application. It should be understood that Figure 3D The comprehensive directional observation error is given by Figure 3A , Figure 3B as well as Figure 3C The X, Y and Z axis directional observation errors (RMS values ​​in the figure) are combined. Figure 3D When the preset directional observation error is 5mas, the comprehensive directional observation error obtained by combining the directional observation errors of the X, Y and Z axes is 5mas, that is, the comprehensive directional observation error obtained by the simulation of the scheme provided in the example of the present application is the same as the preset directional observation error, so it is effective to correct the rotation matrix based on the scheme provided in the embodiment of the present application.

[0116] See also Figure 4 The present application provides a computer device, the computer device comprising:

[0117] A memory 401, used to store instructions executed by at least one processor;

[0118] Processor 402, configured to execute instructions stored in the memory Figure 1 The method described.

[0119] The present application provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer instructions, and when the computer instructions are executed on a computer, the computer executes Figure 1 The method described.

[0120] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A navigation constellation inertial orientation method based on stargazing measurement, characterized in that: include: Obtain the constellation orbit parameters in the inertial coordinate system determined by intersatellite ranging and the inertial space orientation of the intersatellite relative vector in the background of the star map, calculate the intersatellite rotation matrix of a single observation baseline at any sampling time, and calculate the intersatellite observation values ​​obtained by the star-gazing camera and the relative vector of the intersatellite link based on the inertial space orientation; Constructing an inter-satellite directional observation equation according to the inter-satellite observation value, the relative vector of the inter-satellite link and the rotation matrix, and constructing a navigation constellation directional observation equation group based on the inter-satellite directional observation equation; The rotation angle between the satellite coordinates and the inertial system coordinates is determined by an intersatellite link, and the intersatellite rotation matrix is ​​calculated based on the rotation angle; wherein the intersatellite rotation matrix R(-ε(t)) is: Among them, ε(t) represents the rotation angle at time t; θ x represents the rotation component of the rotation matrix between the satellite coordinates and the inertial coordinates determined by the intersatellite link around the X axis; θ y represents the rotation component of the rotation matrix between the satellite coordinates and the inertial coordinates determined by the intersatellite link around the Y axis; θ z represents the rotation component of the rotation matrix between the satellite coordinates and the inertial coordinates determined by the intersatellite link around the Z axis; Determine a first constellation inertial system orbit unit vector corresponding to the navigation constellation by an inter-satellite link, and determine a real second constellation inertial system orbit unit vector corresponding to the navigation constellation; calculate the relative vector of the inter-satellite link based on the first constellation inertial system orbit unit vector, and calculate the inter-satellite observation value based on the second constellation inertial system orbit unit vector; An inter-satellite directional observation equation is constructed according to the inter-satellite observation value, the relative vector of the inter-satellite link and the rotation matrix. The inter-satellite directional observation equation is: in, represents the inter-satellite observation value between the i-th satellite in the navigation constellation and the j-th satellite in the navigation constellation, represents the second constellation inertial system orbit unit vector corresponding to the i-th satellite in the navigation constellation, Represents the second constellation inertial system orbit unit vector corresponding to the j-th satellite in the navigation constellation; represents the relative vector of the intersatellite link between the i-th satellite in the navigation constellation and the j-th satellite in the navigation constellation, represents the first constellation inertial system orbit unit vector corresponding to the i-th satellite in the navigation constellation, Represents the first constellation inertial system orbit unit vector corresponding to the jth satellite in the navigation constellation; The navigation constellation directional observation equations are: Taylor expansion is performed on the navigation constellation directional observation equation group to obtain an observation matrix, and an inter-satellite calculation value of the rotation correction is calculated; based on the observation matrix and the inter-satellite calculation value, each angle correction amount in the rotation matrix is ​​iteratively calculated until the correction amount is less than a preset threshold, and a corrected rotation matrix is ​​determined when the correction amount is less than the preset threshold; Performing average processing on the rotation matrix correction amount within the preset sampling time interval to obtain an averaged rotation matrix correction amount; The constellation orbit parameters are corrected based on the averaged rotation matrix correction amount to obtain corrected constellation orbit parameters.

2. The method according to claim 1, characterized in that in, Obtain the relative right ascension and declination between any two satellites in the navigation constellation output by the star-gazing camera at any sampling time; The unit vector of the relative vector between any two satellites is calculated based on the relative right ascension and the right declination, and the inertial space direction of the inter-satellite relative vector in the background of the star map is characterized based on the unit vector.

3. The method according to claim 2, characterized in that Calculating a unit vector of a relative vector between any two satellites based on the relative right ascension and the declination, comprising: The unit vector is calculated by the following formula: in, represents the unit vector of the relative vector between the i-th satellite in the navigation constellation and the j-th satellite in the navigation constellation at time t, where t represents an arbitrary sampling time; α ij represents the relative right ascension between the i-th satellite in the navigation constellation and the j-th satellite in the navigation constellation; β ij represents the relative declination between the i-th satellite in the navigation constellation and the j-th satellite in the navigation constellation; i represents the i-th satellite in the navigation constellation; j represents the j-th satellite in the navigation constellation, where i=1…M, j=1…M, and M is the number of satellites in the navigation constellation.

4. The method according to claim 1, characterized in that The rotation matrix correction amount within the preset sampling time interval is averaged to obtain an averaged rotation matrix correction amount, including: Solving all rotation matrix corrections within a preset sampling time interval to obtain a first mean, and solving the variance of each rotation matrix correction one by one; Determine and eliminate the first rotation matrix correction amount whose difference with the first mean is greater than the variance one by one, solve the second rotation matrix correction amount except the first rotation matrix correction amount within the preset sampling time interval to obtain the second mean, and use the second mean as the averaged rotation matrix correction amount.

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