CN115451944A - Navigation constellation inertial orientation method based on observed quantity - Google Patents

Navigation constellation inertial orientation method based on observed quantity Download PDF

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CN115451944A
CN115451944A CN202210997692.6A CN202210997692A CN115451944A CN 115451944 A CN115451944 A CN 115451944A CN 202210997692 A CN202210997692 A CN 202210997692A CN 115451944 A CN115451944 A CN 115451944A
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constellation
rotation matrix
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陈秋丽
王海红
马福建
赵兴隆
康成斌
张弓
毕少筠
周会超
张朔
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China Academy of Space Technology CAST
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    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
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Abstract

The application discloses a navigation constellation inertial orientation method based on star observation measurement, which comprises the following steps: acquiring constellation orbit parameters and an inertial space orientation of an inter-satellite relative vector in a fixed star map background under an inertial coordinate system determined by inter-satellite distance measurement, calculating an inter-satellite rotation matrix of a single observation base line at any sampling moment, and calculating an inter-satellite observation value and an inter-satellite link relative vector acquired by a satellite observation camera 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 set based on the inter-satellite directional observation equation; and correcting the rotation matrix based on the navigation constellation directional observation equation set to obtain a corrected rotation matrix, and correcting the constellation orbit parameters based on the corrected rotation matrix to obtain corrected constellation orbit parameters.

Description

Navigation constellation inertial orientation method based on observed quantity
Technical Field
The application relates to the technical field of satellite navigation, in particular to a navigation constellation inertial orientation method based on star observation measurement.
Background
The autonomous operation capability of the navigation constellation is one of important means for reducing the dependence of each satellite navigation system on the ground station, and is particularly important for the situation that the stations cannot be built globally. The navigation constellation can realize autonomous operation service based on inter-satellite links, but due to inter-satellite measurement, rank deficiency exists in the autonomous orbit determination process of the constellation, namely the constellation rotates integrally, and the performance of the navigation constellation is influenced.
At present, constellation correction rotation can be realized by additionally observing a fixed star, so that the problem of constellation rotation is solved, for example, on the premise that the absolute direction of an optical axis of a satellite in an inertial space can be obtained, simulation solution of an optical axis direction vector is carried out to realize constellation correction rotation; or the constellation rotation is corrected by giving an analytic solution of the relative vector through spherical trigonometry based on the measurement of the star-star relative vector. Although the prior art provides a scheme for partially correcting constellation rotation, the prior art is limited to a shallow basic principle and basic simulation, and does not relate to a detailed and realizable technical method.
Disclosure of Invention
The technical problem that this application was solved is: aiming at the defects in the prior art, the navigation constellation inertial orientation method based on star observation measurement is provided, in the scheme provided by the embodiment of the application, absolute inertial orientation of the inertial space of the navigation constellation is realized based on observation and systematic solution methods of a satellite-borne star observation camera in a small number of constellations, the problem of integral rotation of autonomous operation of the constellation is effectively inhibited, and the method can be used for a next generation satellite navigation system and supports high-precision and ultra-long-time autonomous operation of the constellation.
In a first aspect, an embodiment of the present application provides a navigation constellation inertial orientation method based on star observation measurement, where the method includes: acquiring an inertial space orientation formed by constellation orbit parameters and an inter-satellite relative vector in a fixed star atlas background under an inertial coordinate system determined by inter-satellite distance measurement, calculating an inter-satellite rotation matrix of a single observation base line at any sampling time, and calculating an inter-satellite observation value and an inter-satellite link relative vector acquired by a satellite-viewing camera 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 set based on the inter-satellite directional observation equation; and correcting the rotation matrix based on the navigation constellation directional observation equation set to obtain a corrected rotation matrix, and correcting the constellation orbit parameters based on the corrected rotation matrix to obtain corrected constellation orbit parameters.
Optionally, obtaining a relative red longitude and a relative red latitude between any two satellites in a navigation constellation output by the star viewing camera at any sampling moment; calculating a unit vector of a relative vector between any two satellites based on the relative declination degrees and the declination degrees, and characterizing the inertial space orientation of the inter-satellite relative vector in the star atlas background based on the unit vector.
Optionally, calculating a unit vector of a relative vector between any two satellites based on the relative declination degrees and the relative declination degrees, comprises:
calculating the unit vector by:
Figure BDA0003806044780000021
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003806044780000022
a unit vector representing a relative vector between an ith satellite in the navigation constellation and a jth satellite in the navigation constellation at time t; alpha is alpha ij Representing a relative longitude and latitude between an ith satellite in the navigation constellation and a jth satellite in the navigation constellation; beta is a ij Representing navigation starsThe relative hot latitude between the ith satellite in the seat and the jth satellite in the navigation constellation; i represents the ith satellite in the navigation constellation; j represents the j th satellite in the navigation constellation, wherein i =1 \ 8230, M, j =1 \ 8230, M, M is the number of satellites in the navigation constellation.
Optionally, calculating an inter-satellite rotation matrix of a single observation baseline at any sampling time includes:
determining a rotation angle between a satellite coordinate and an inertial system coordinate by using an inter-satellite link, and calculating to obtain an inter-satellite rotation matrix based on the rotation angle; wherein the content of the first and second substances,
the inter-satellite rotation matrix R (-epsilon (t)) is:
Figure BDA0003806044780000023
wherein ε (t) represents the angle of rotation at time t; theta.theta. x Representing a rotation component of a rotation matrix around the X axis between the satellite coordinates and the inertial coordinates determined by the inter-satellite link; theta y Representing a rotation component of a rotation matrix around the Y axis between the satellite coordinates and the inertial coordinates determined by the inter-satellite link; theta.theta. z Representing the rotation component of the rotation matrix around the Z-axis between the satellite coordinates and the inertial coordinates determined by the inter-satellite link.
Optionally, calculating a relative vector between an inter-satellite observation value and an inter-satellite link acquired by a satellite-viewing camera based on the inertial space orientation includes:
determining a first constellation inertia system orbit unit vector corresponding to a navigation constellation and determining a real second constellation inertia system orbit unit vector corresponding to the navigation constellation by an inter-satellite link;
and calculating a relative vector of the inter-satellite link based on the first constellation inertia system orbit unit vector, and calculating the inter-satellite observation value based on the second constellation inertia system orbit unit vector.
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:
the inter-satellite directional observation equation is as follows:
Figure BDA0003806044780000031
wherein the content of the first and second substances,
Figure BDA0003806044780000032
representing inter-satellite observations between the ith satellite in the navigation constellation and the jth satellite in the navigation constellation,
Figure BDA0003806044780000033
Figure BDA0003806044780000034
represents a unit vector of a second constellation inertial system corresponding to the ith satellite in the navigation constellation,
Figure BDA0003806044780000035
representing a second constellation inertia system orbit unit vector corresponding to the jth satellite in the navigation constellation;
Figure BDA0003806044780000036
representing the relative vectors of the inter-satellite links between the ith satellite in the navigation constellation and the jth satellite in the navigation constellation,
Figure BDA0003806044780000037
Figure BDA0003806044780000038
represents a unit vector of a first constellation inertial system corresponding to the ith satellite in the navigation constellation,
Figure BDA0003806044780000039
and the unit vector of the first constellation inertia system corresponding to the jth satellite in the navigation constellation is represented.
Optionally, constructing a navigation constellation directional observation equation set based on the inter-satellite directional observation equation includes:
the navigation constellation directional observation equation set is as follows:
Figure BDA00038060447800000310
optionally, modifying the rotation matrix based on the navigation constellation directional observation equation set to obtain a modified rotation matrix, including: carrying out Taylor expansion on the navigation constellation directional observation equation set to obtain an observation matrix, and calculating a rotation corrected inter-satellite calculation value; iteratively calculating correction amounts of all angles in a rotation matrix based on the observation matrix and the inter-satellite calculation value until the correction amounts are smaller than a preset threshold value, and determining the corrected rotation matrix when the correction amounts are smaller than the preset threshold value.
Optionally, the modifying the constellation trajectory parameter based on the modified rotation matrix to obtain a modified constellation trajectory parameter includes: homogenizing the rotation matrix correction in a preset sampling time interval to obtain a homogenized rotation matrix correction; and correcting the constellation orbit parameters based on the homogenized rotation matrix correction quantity to obtain the corrected constellation orbit parameters.
Optionally, the homogenizing the rotation matrix correction within the preset sampling time interval to obtain a homogenized rotation matrix correction, including:
solving all rotation matrix correction quantities within a preset sampling time interval to obtain a first mean value, and solving a variance for each rotation matrix correction quantity one by one;
and judging and rejecting first rotation matrix corrections of which the difference between the rotation matrix corrections and the first mean value is larger than the variance one by one, solving second rotation matrix corrections except the first rotation matrix corrections in a preset sampling time interval to obtain a second mean value, and taking the second mean value as the homogenized rotation matrix corrections.
In a second aspect, the present application provides a computer device comprising:
a memory for storing instructions for execution by the at least one processor;
a processor for executing instructions stored in a memory to perform the method of the first aspect.
In a third aspect, the present application provides a computer readable storage medium having stored thereon computer instructions which, when run on a computer, cause the computer to perform the method of the first aspect.
Compared with the prior art, the embodiment of the application has at least the following effects:
in the scheme provided by the embodiment of the application, based on a small number of satellite-borne star observation camera observation and systematic solution methods in the constellation, absolute inertial orientation of a navigation constellation inertial space is realized, the problem of integral rotation of autonomous operation of the constellation is effectively inhibited, and the method can be used for a next generation satellite navigation system and supports high-precision and ultra-long-time autonomous operation of the constellation.
Drawings
Fig. 1 is a schematic flowchart of a navigation constellation inertial orientation method based on star observation measurement according to an embodiment of the present application;
fig. 2A is a schematic diagram of a simulation result of an X-axis directional observation error when a preset directional observation error is 2mas according to an embodiment of the present application;
fig. 2B is a schematic diagram of a simulation result of a Y-axis directional observation error when a preset directional observation error is 2mas according to an embodiment of the present application;
fig. 2C is a schematic diagram of a simulation result of a Z-axis directional observation error when a preset directional observation error is 2mas according to an embodiment of the present application;
fig. 2D is a schematic diagram of a simulation result of a comprehensive directional observation error when a preset directional observation error is 2mas according to an embodiment of the present application;
fig. 3A is a schematic diagram of a simulation result of an X-axis directional observation error when a preset directional observation error is 5mas according to an embodiment of the present application;
fig. 3B is a schematic diagram of a simulation result of a Y-axis directional observation error when a preset directional observation error is 5mas according to an embodiment of the present application;
fig. 3C is a schematic diagram of a simulation result of a Z-axis directional observation error when a preset directional observation error is 5mas according to an embodiment of the present application;
fig. 3D is a schematic diagram of a simulation result of a comprehensive directional observation error when a preset directional observation error is 5mas according to the embodiment of the present application;
fig. 4 is a schematic structural diagram of a computer device according to an embodiment of the present application.
Detailed Description
In the solutions provided in the embodiments of the present application, the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
In order to better understand the technical solutions, the technical solutions of the present application are described in detail below with reference to the drawings and specific embodiments, and it should be understood that the specific features in the embodiments and examples of the present application are detailed descriptions of the technical solutions of the present application, and are not limitations of the technical solutions of the present application, and the technical features in the embodiments and examples of the present application may be combined with each other without conflict.
The navigation constellation inertial orientation method based on star observation measurement provided by the embodiments of the present application is further described in detail below with reference to the drawings of the specification, and the specific implementation manner of the method may include the following steps (the method flow is shown in fig. 1):
step 101, acquiring constellation orbit parameters and an inertial space orientation of an inter-satellite relative vector in a fixed star map background under an inertial coordinate system determined by inter-satellite distance measurement, calculating an inter-satellite rotation matrix of a single observation base line at any sampling moment, and calculating an inter-satellite observation value and an inter-satellite link relative vector acquired by a satellite observation camera based on the inertial space orientation.
Since autonomous orbit determination is completed based on inter-satellite links, the problem of constellation rotation exists, and in order to avoid the problem of rotation, the orbit parameters of the navigation constellation in an inertial coordinate system need to be corrected. By way of example, constellation tracksThe track parameter is the coordinate of each satellite in the navigation constellation in the inertial coordinate system, for example, the navigation constellation completes autonomous orbit determination based on the inter-satellite link, the number of the satellites in the navigation constellation is M, the serial number of each satellite in the navigation constellation is 1, \ 8230;, M, the coordinate of each satellite in the inertial coordinate system is (x) i ，y i ，z i )。
A satellite viewing camera is also configured in the navigation constellation, wherein the satellite viewing camera is used for observing satellites in the navigation constellation, for example, observing orbit parameters or position parameters of the satellites. In order to correct the orbit parameters of the navigation constellation in the inertial coordinate system, the inertial space direction of the inter-satellite relative vector formed in the background of the fixed star map is also required to be obtained. By way of example, for an observation baseline, relative declination and declination between any two satellites in a navigation constellation output by the tsvis star camera at any sampling time are obtained, a unit vector of a relative vector between any two satellites is calculated based on the relative declination and declination, and inertial space orientation of the inter-satellite relative vector in a star atlas background is represented based on the unit vector.
By way of example, if the relative declination and declination between the ith satellite in the navigation constellation and the jth satellite in the navigation constellation are output at an arbitrary sampling time t, a unit vector of a relative vector between any two satellites is calculated based on the relative declination and declination, and the method includes:
calculating a unit vector of a relative vector between an ith satellite in the navigation constellation and a jth satellite in the navigation constellation by:
Figure BDA0003806044780000071
wherein the content of the first and second substances,
Figure BDA0003806044780000072
a unit vector representing a relative vector between an ith satellite in the navigation constellation and a jth satellite in the navigation constellation at time t; alpha is alpha ij Representing the relative between the ith satellite in the navigation constellation and the jth satellite in the navigation constellationRed longitude; beta is a ij Representing the relative hot latitude between the ith satellite in the navigation constellation and the jth satellite in the navigation constellation; i represents the ith satellite in the navigation constellation; j represents the j th satellite in the navigation constellation, wherein i = 1\8230, M, j =1 \8230, and M, M is the number of satellites in the navigation constellation.
And 102, 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 set based on the inter-satellite directional observation equation.
Furthermore, a navigation constellation directional observation equation set is constructed, and an inter-satellite directional observation equation of a single observation machine base line is required to be constructed in order to construct the navigation constellation directional observation equation set. By way of example, an inter-satellite directional observation equation of a single observer baseline is constructed based on inter-satellite observations output by a star-viewing camera, relative vectors of inter-satellite links, and a rotation matrix.
And determining the rotation angle between the satellite coordinates and the inertial system coordinates by using the inter-satellite link. Specifically, the rotation angle is expressed by the following formula:
ε(t)＝[θ x ，θ y ，θ z ] T
wherein ε (t) represents the rotation angle of the navigation constellation at time t; theta x Representing the rotation component of the rotation matrix around the X axis between the satellite coordinates determined by the inter-satellite link and the inertial coordinates at time t; theta y Representing the rotation component of the rotation matrix around the Y axis between the satellite coordinates determined by the inter-satellite link and the inertial coordinates at time t; theta z Representing 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.
Further, for a small rotation angle, an inter-satellite rotation matrix can be obtained through calculation based on the rotation angle; wherein the inter-satellite rotation matrix R (-epsilon (t)) is:
Figure BDA0003806044780000073
by way of further example, calculating a relative vector between an inter-satellite observation value and an inter-satellite link acquired by a satellite-viewing camera based on the inertial space orientation includes: determining a first constellation inertia system orbit unit vector corresponding to a navigation constellation by an inter-satellite link, determining a real second constellation inertia system orbit unit vector corresponding to the navigation constellation, calculating a relative vector of the inter-satellite link based on the first constellation inertia system orbit unit vector, and calculating the inter-satellite observation value based on the second constellation inertia system orbit unit vector.
For example, assuming an arbitrary sampling time t, the unit vector of the inertial system orbit of the navigation constellation satellite (i.e. the unit vector of the inertial system orbit of the first constellation) determined by the inter-satellite link is:
Figure BDA0003806044780000081
wherein the content of the first and second substances,
Figure BDA0003806044780000082
representing a unit vector of an inertial system of a navigation constellation satellite corresponding to the ith satellite in the navigation constellation determined by the inter-satellite link;
Figure BDA0003806044780000083
representing the component of the unit vector of the inertial system orbit of the navigation constellation satellite corresponding to the ith satellite in the navigation constellation determined by the inter-satellite link on the X axis;
Figure BDA0003806044780000084
representing the component of the unit vector of the inertial system orbit of the navigation constellation satellite corresponding to the ith satellite in the navigation constellation determined by the inter-satellite link on the Y axis;
Figure BDA0003806044780000085
and the component of the unit vector of the inertial system orbit of the navigation constellation satellite corresponding to the ith satellite in the navigation constellation determined by the inter-satellite link on the Z axis is represented.
The unit vector of the true inertial system orbit of the navigation constellation satellite (i.e. the unit vector of the second constellation inertial system orbit) is:
Figure BDA0003806044780000086
wherein the content of the first and second substances,
Figure BDA0003806044780000087
representing a real navigation constellation satellite inertia system orbit unit vector corresponding to the ith satellite in the navigation constellation;
Figure BDA0003806044780000088
representing the component of the unit vector of the real inertial system orbit of the navigation constellation satellite corresponding to the ith satellite in the navigation constellation on the X axis;
Figure BDA0003806044780000089
representing the component of the unit vector of the real inertial system orbit of the navigation constellation satellite corresponding to the ith satellite in the navigation constellation on the Y axis;
Figure BDA00038060447800000810
and the component of the unit vector of the inertia system orbit of the real navigation constellation satellite corresponding to the ith satellite in the navigation constellation on the Z axis is represented.
Calculating relative vectors of inter-satellite links of the ith satellite in the navigation constellation and the jth satellite in the navigation constellation based on the orbit unit vector of the inertial system of the first constellation
Figure BDA00038060447800000811
Comprises the following steps:
Figure BDA00038060447800000812
calculating inter-satellite observation values of ith satellite in navigation constellation and jth satellite in navigation constellation based on orbit unit vector of second constellation inertial system
Figure BDA00038060447800000813
Comprises the following steps:
Figure BDA0003806044780000091
based on the inter-satellite directional observation equation, the 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 as follows:
Figure BDA0003806044780000092
as another example, since the navigation constellation includes a plurality of satellites, a navigation constellation directional observation equation set needs to be constructed according to the inter-satellite directional observation equation corresponding to any two satellites. For example, assuming that the number of satellites in the navigation constellation is M, the system of directional observation equations of the navigation constellation is as follows:
Figure BDA0003806044780000093
it should be understood that the navigation constellation directional observation equation set is a directional observation equation set composed of multiple baselines, each equation in the equation set is a single-baseline inter-satellite directional observation equation, the left side of each equation is an observed value obtained by an inertial camera, and the right side of each equation is a relative vector calculated value obtained by a rotation matrix and an inter-satellite link.
And 103, correcting the rotation matrix based on the navigation constellation directional observation equation set to obtain a corrected rotation matrix, and correcting the constellation orbit parameters based on the corrected rotation matrix to obtain corrected constellation orbit parameters.
As an example, taylor expansion is performed on the navigation constellation directional observation equation set to obtain an observation matrix, and a rotation corrected inter-satellite calculation value is calculated; iteratively calculating correction amounts of all angles in a rotation matrix based on the observation matrix and the inter-satellite calculation value until the correction amounts are smaller than a preset threshold value, and determining the corrected rotation matrix when the correction amounts are smaller than the preset threshold value.
For example, a navigation constellation directional observation equation set corresponding to any observation sampling time t is subjected to first-order taylor expansion, and an observation matrix is obtained as follows:
Figure BDA0003806044780000094
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003806044780000095
Figure BDA0003806044780000096
a computed value representing a relative rotation correction between satellite i and satellite j in a navigation constellation;
Figure BDA0003806044780000097
a component on the X-axis representing a computed value of a relative rotation correction between satellite i and satellite j in the navigation constellation;
Figure BDA0003806044780000101
a component on the Y axis representing a computed value of a relative rotation correction between satellite i and satellite j in the navigation constellation;
Figure BDA0003806044780000102
a component of the computed value representing the correction of relative rotation between satellite i and satellite j in the navigation constellation on the Z-axis.
Figure BDA0003806044780000103
Figure BDA0003806044780000104
Calculating a value of the satellite i after rotation correction;
Figure BDA0003806044780000105
a component of a calculation value of the satellite i subjected to rotation correction on the X axis;
Figure BDA0003806044780000106
a component representing a calculated value of the satellite i subjected to rotation correction on the Y axis;
Figure BDA0003806044780000107
a component of a calculated value of the satellite i subjected to rotation correction in the Z axis;
Figure BDA0003806044780000108
the calculated value of the satellite j after rotation correction;
Figure BDA0003806044780000109
representing the component of the computed value of the satellite j subjected to rotation correction on the X axis;
Figure BDA00038060447800001010
a component representing a calculated value of the satellite j subjected to rotation correction on the Y axis;
Figure BDA00038060447800001011
and represents the component of the calculated value of the satellite j subjected to rotation correction on the Z axis.
And for the first correction:
Figure BDA00038060447800001012
in addition, the difference y between the observation values of the satellite i and the satellite j output by the satellite viewing camera and the calculation value of the relative rotation correction is as follows:
Figure BDA00038060447800001013
the correction quantity delta epsilon of each angle of the rotation matrix calculated in one time can be obtained as follows:
Δε＝[Δθ x Δθ y Δθ z ] T ＝(H(t) T H(t)) -1 H(t)·y
wherein, delta theta x A correction representing a rotation component of the single calculation rotation matrix about the X-axis; delta theta y A correction amount representing a rotation component of the single calculation rotation matrix around the Y axis; delta theta z Representing the correction of the rotational component of the rotation matrix about the Z-axis in a single calculation.
Further, in the solution provided in the embodiment of the present application, a preset result cannot be achieved by performing correction on each angle of the rotation matrix once, and at this time, correction on each angle of the rotation matrix needs to be iterated many times. Specifically, if there is a relationship between rotation angles obtained by performing two iterations of a plurality of iterations, the relationship is as follows:
ε k+1 ＝ε k +Δε＝[θ xk θ yk θ zk ] T +[Δθ x Δθ y Δθ z ] T
wherein epsilon k+1 Representing the value obtained by the rotation angle through k +1 iterations, and adding 1 to k every iteration; epsilon k Representing the value of the rotation angle obtained through k iterations; theta.theta. xk Representing the rotation component of the rotation matrix around the X axis after k iterations; theta yk Representing the rotation component of the rotation matrix around the Y axis through k iterations; theta zk Representing the rotational component of the rotation matrix around the Z-axis over k iterations.
At time t, let the initial value of the rotation angle ε (t) be ε 1 (t)＝[0，0，0]Wherein, epsilon 1 And (t) represents the rotation angle obtained after one iteration calculation at the time t.
With the obtained calculated relative vector pointing correction value:
Figure BDA0003806044780000111
iteratively solving the rotation angle correction value until the correction value is less than a set threshold delta = (10) -10 ，10 -10 ，10 -10 ) (as), finishing the iteration and obtaining the rotating angle epsilon (t) of the current sampling time point.
Further, as an example, the modifying the constellation trajectory parameter based on the modified rotation matrix to obtain a modified constellation trajectory parameter includes: carrying out homogenization treatment on the rotation matrix correction within a preset sampling time interval to obtain a homogenized rotation matrix correction; and correcting the constellation orbit parameters based on the homogenized rotation matrix correction quantity to obtain the corrected constellation orbit parameters.
Assuming that the number of inertial cameras in the navigation constellation is M, the sampling interval of each camera is N seconds, and simultaneously setting the navigation constellation to perform inertial space directional correction calculation once per TN time period (unit is second). And (4) homogenizing the correction value of the rotation matrix in the primary inertial space orientation correction calculation time period. The method prevents the deviation between the rotation angle obtained at a certain sampling moment and the integral rotation of the constellation caused by the fact that the limited number of cameras in the constellation cannot observe the whole constellation at a specific moment. Assuming that there are P corrections in the TN period, where P is a positive integer not less than 1, solving the variance for the P corrections as:
Figure BDA0003806044780000112
Figure BDA0003806044780000113
wherein E (epsilon) represents the mean value of the P rotation angle correction quantities in the TN time period; σ (ε) represents the variance of the P rotation angle correction amounts in the TN period.
Judging the rotation quantity epsilon of each sampling moment one by one k If the difference from the mean value E (epsilon) is larger than sigma (epsilon), and if so, the sampling time is an invalid sample.
And re-solving and eliminating invalid samples in the P rotation angle correction quantities in the TN time period to obtain S valid samples, wherein S is more than or equal to 1 and less than or equal to P. And recalculating the rotation angle mean value of S effective sampling moments:
Figure BDA0003806044780000121
wherein epsilon (TN) and E' (epsilon) both represent the rotation angle mean values at S valid sampling moments within the TN time period; theta x (TN) represents the mean of the rotation angles of the S active sampling instants on the X-axis within the TN period; theta y (TN) represents the average of the rotation angles of the S active sampling instants in the TN period on the Y axis; theta z (TN) represents the mean value of the rotation angle on the Z axis at the S active sampling instants within the TN time period.
Then, the orbit correction of the inertial system of the full constellation satellite is performed. And calculating the coordinate value of the inertial system of each satellite after the satellite is observed in the direction of the satellite by utilizing the finally obtained rotation matrix of the constellation relative to the inertial system and the satellite orbit model length for each satellite orbit in the TN time period.
Figure BDA0003806044780000122
In the scheme provided by the embodiment of the application, based on a small number of satellite-borne star observation camera observation and systematic solution methods in the constellation, absolute inertial orientation of a navigation constellation inertial space is realized, the problem of integral rotation of autonomous operation of the constellation is effectively inhibited, and the method can be used for a next generation satellite navigation system and supports high-precision and ultra-long-time autonomous operation of the constellation.
In order to verify the effects of the above method, the following description will take examples to illustrate the beneficial effects of the solution provided in the embodiments of the present application.
For example, with N =1s as a sampling interval, assuming that two star cameras are configured in a constellation, a constellation rotation angle in a period of TN =100s is calculated, and when a preset directional observation error is 2 milli-second (mas), simulation results based on the scheme provided in the example of the present application are shown in fig. 2A, fig. 2B, fig. 2C, and fig. 2D. Fig. 2A is a schematic diagram of a simulation result of an X-axis directional observation error when a preset directional observation error is 2mas according to an embodiment of the present application; fig. 2B is a schematic diagram of a simulation result of a Y-axis directional observation error when a preset directional observation error is 2mas according to an embodiment of the present application; fig. 2C is a schematic diagram of a simulation result of a Z-axis directional observation error when a preset directional observation error is 2mas according to an embodiment of the present application; fig. 2D is a schematic diagram of a simulation result of a comprehensive directional observation error when a preset directional observation error is 2mas according to an embodiment of the present application. It should be understood that the combined orientation observation error in fig. 2D is obtained by combining the X, Y and Z axis orientation observation errors (values corresponding to RMS in the figure) in fig. 2A, 2B and 2C. Further, referring to fig. 2D, when the preset directional observation error is 2mas, the comprehensive directional observation error obtained by synthesizing the directional observation errors of the X, Y and Z axes is 2.1mas, that is, the difference between the comprehensive directional observation error obtained by the simulation based on the solution provided in the embodiment of the present application and the preset directional observation error is 0.1mas, which is within the preset error range, so that it is effective to correct the rotation matrix based on the solution provided in the embodiment of the present application.
Further, the simulation results based on the scheme provided in the example of the present application when the predetermined directional observation error is 5 milli-seconds (mas) are shown in fig. 3A, 3B, 3C, and 3D. Fig. 3A is a schematic diagram of a simulation result of an X-axis directional observation error when a preset directional observation error is 5mas according to an embodiment of the present application; fig. 3B is a schematic diagram of a simulation result of a Y-axis directional observation error when a preset directional observation error is 5mas according to an embodiment of the present application; fig. 3C is a schematic diagram of a simulation result of a Z-axis directional observation error when a preset directional observation error is 5mas according to an embodiment of the present application; fig. 3D is a schematic diagram of a simulation result of a comprehensive directional observation error when a preset directional observation error is 5mas according to the embodiment of the present application. It should be understood that the combined orientation observation error in fig. 3D is obtained by combining the X, Y and Z axis orientation observation errors (values corresponding to RMS in the figures) in fig. 3A, 3B and 3C. Further, referring to fig. 3D, when the preset directional observation error is 5mas, the comprehensive directional observation error obtained by synthesizing the directional observation errors of the X, Y, and Z axes is 5mas, that is, the comprehensive directional observation error obtained by the simulation based on the scheme provided in the embodiment of the present application is the same as the preset directional observation error, so that it is effective to correct the rotation matrix based on the scheme provided in the embodiment of the present application.
Referring to fig. 4, the present application provides a computer device comprising:
a memory 401 for storing instructions for execution by at least one processor;
a processor 402 for executing instructions stored in memory to perform the method described in fig. 1.
A computer-readable storage medium having stored thereon computer instructions which, when executed on a computer, cause the computer to perform the method of fig. 1.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present application without departing from the spirit and scope of the application. Thus, if such 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 intended to include such modifications and variations as well.

Claims (10)

1. A navigation constellation inertial orientation method based on star observation measurement is characterized by comprising the following steps:
acquiring constellation orbit parameters and an inertial space orientation of an inter-satellite relative vector in a fixed star map background under an inertial coordinate system determined by inter-satellite distance measurement, calculating an inter-satellite rotation matrix of a single observation base line at any sampling moment, and calculating an inter-satellite observation value and a relative vector of an inter-satellite link acquired by a satellite observation camera 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 set based on the inter-satellite directional observation equation;
and correcting the rotation matrix based on the navigation constellation directional observation equation set to obtain a corrected rotation matrix, and correcting the constellation orbit parameters based on the corrected rotation matrix to obtain corrected constellation orbit parameters.
2. The method of claim 1, wherein,
acquiring relative longitude and latitude between any two satellites in a navigation constellation output by a satellite viewing camera at any sampling moment;
calculating a unit vector of a relative vector between any two satellites based on the relative declination degrees and the declination degrees, and characterizing the inertial space orientation of the inter-satellite relative vector in the star atlas background based on the unit vector.
3. The method of claim 2, wherein calculating a unit vector of a relative vector between any two satellites based on the relative declination degrees comprises:
calculating the unit vector by:
Figure FDA0003806044770000011
wherein the content of the first and second substances,
Figure FDA0003806044770000012
a unit vector representing a relative vector between an ith satellite in the navigation constellation and a jth satellite in the navigation constellation at a time t, wherein the time t represents any sampling time; alpha is alpha ij Representing the relative longitude and declination between the ith satellite in the navigation constellation and the jth satellite in the navigation constellation; beta is a ij Representing the relative hot latitude between the ith satellite in the navigation constellation and the jth satellite in the navigation constellation; i represents the ith satellite in the navigation constellation; j represents the j th satellite in the navigation constellation, wherein i =1 \ 8230, M, j =1 \ 8230, M, M is the number of satellites in the navigation constellation.
4. The method of any one of claims 1 to 3, wherein computing an inter-satellite rotation matrix for a single observation baseline at any sampling time comprises:
determining a rotation angle between a satellite coordinate and an inertial system coordinate by using an inter-satellite link, and calculating to obtain an inter-satellite rotation matrix based on the rotation angle; wherein the content of the first and second substances,
the inter-satellite rotation matrix R (- ε (t)) is:
Figure FDA0003806044770000021
wherein ε (t) represents the angle of rotation at time t; theta x Representing a rotation component of a rotation matrix around the X axis between the satellite coordinates and the inertial coordinates determined by the inter-satellite link; theta y Representing a rotation component of a rotation matrix around the Y axis between the satellite coordinates and the inertial coordinates determined by the inter-satellite link; theta.theta. z Representing the rotation component of the rotation matrix around the Z-axis between the satellite coordinates and the inertial coordinates determined by the inter-satellite link.
5. The method of claim 4, wherein computing relative vectors of inter-satellite observations and inter-satellite links acquired by a star finder camera based on the inertial space orientation comprises:
determining a first constellation inertia system orbit unit vector corresponding to a navigation constellation and a real second constellation inertia system orbit unit vector corresponding to the navigation constellation by an inter-satellite link;
and calculating a relative vector of the inter-satellite link based on the first constellation inertia system orbit unit vector, and calculating the inter-satellite observation value based on the second constellation inertia system orbit unit vector.
6. The method of claim 5, wherein constructing an inter-satellite directional observation equation from the inter-satellite observations, the relative vectors of the inter-satellite links, and a rotation matrix comprises:
the inter-satellite directional observation equation is as follows:
Figure FDA0003806044770000022
wherein the content of the first and second substances,
Figure FDA0003806044770000023
representing inter-satellite observations between the ith satellite in the navigation constellation and the jth satellite in the navigation constellation,
Figure FDA0003806044770000024
Figure FDA0003806044770000025
represents a unit vector of a second constellation inertial system corresponding to the ith satellite in the navigation constellation,
Figure FDA0003806044770000026
representing a second constellation inertia system orbit unit vector corresponding to the jth satellite in the navigation constellation;
Figure FDA0003806044770000031
representing the relative vectors of the inter-satellite links between the ith satellite in the navigation constellation and the jth satellite in the navigation constellation,
Figure FDA0003806044770000032
Figure FDA0003806044770000033
represents a unit vector of a first constellation inertial system corresponding to the ith satellite in the navigation constellation,
Figure FDA0003806044770000034
and the unit vector of the first constellation inertia system corresponding to the jth satellite in the navigation constellation is represented.
7. The method of claim 6, wherein constructing a navigation constellation directional observation equation set based on the inter-satellite directional observation equation comprises:
the navigation constellation directional observation equation set is as follows:
Figure FDA0003806044770000035
8. the method of claim 7, wherein modifying the rotation matrix based on the navigational constellation directional observation equation set to obtain a modified rotation matrix comprises:
carrying out Taylor expansion on the navigation constellation directional observation equation set to obtain an observation matrix, and calculating a rotation corrected inter-satellite calculation value;
iteratively calculating correction amounts of all angles in a rotation matrix based on the observation matrix and the inter-satellite calculation value until the correction amounts are smaller than a preset threshold value, and determining the corrected rotation matrix when the correction amounts are smaller than the preset threshold value.
9. The method of claim 7, wherein modifying the constellation orbital parameters based on the modified rotation matrix to obtain modified constellation orbital parameters comprises:
carrying out homogenization treatment on the rotation matrix correction within a preset sampling time interval to obtain a homogenized rotation matrix correction;
and correcting the constellation orbit parameters based on the homogenized rotation matrix correction quantity to obtain the corrected constellation orbit parameters.
10. The method of claim 9, wherein averaging the rotation matrix modifiers over a predetermined sampling time interval to obtain averaged rotation matrix modifiers comprises:
solving all rotation matrix correction quantities in a preset sampling time interval to obtain a first mean value, and solving a variance for each rotation matrix correction quantity one by one;
and judging and rejecting first rotation matrix corrections of which the difference between the rotation matrix corrections and the first mean value is larger than the variance one by one, solving second rotation matrix corrections except the first rotation matrix corrections in a preset sampling time interval to obtain a second mean value, and taking the second mean value as the homogenized rotation matrix corrections.
CN202210997692.6A 2022-08-19 2022-08-19 Navigation constellation inertial orientation method based on observed quantity Pending CN115451944A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116552817A (en) * 2023-07-12 2023-08-08 银河航天(北京)网络技术有限公司 Method, apparatus and storage medium for optimizing satellite orbit control

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116552817A (en) * 2023-07-12 2023-08-08 银河航天(北京)网络技术有限公司 Method, apparatus and storage medium for optimizing satellite orbit control
CN116552817B (en) * 2023-07-12 2023-09-08 银河航天(北京)网络技术有限公司 Method, apparatus and storage medium for optimizing satellite orbit control

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