Low-orbit remote sensing satellite fixed star observation attitude planning method and system

Abstract

The invention provides a low-orbit remote sensing satellite fixed star observation attitude planning method and system, and the method comprises the steps: S1, determining a satellite star observation reference axis and a reference cone under a satellite coordinate system; s2, calculating a satellite rolling attitude and a satellite pitching attitude required by the satellite star-observation reference axis to be far away from the earth center under an orbital coordinate system based on the satellite star-observation reference axis and the reference cone; s3, determining a satellite star-observation center moment, and calculating to obtain a satellite star-observation reference area under the inertial coordinate system; s4, selecting a star-observation target area from the satellite star-observation reference area, and calculating a camera star-observation attitude under the inertial coordinate system at the star-observation center moment; and S5, setting satellite parameters, determining star observation duration, and further enabling the satellite to maneuver around the camera under an inertial system for imaging. The method ensures that the space camera and the star sensor are not interfered by geogas light and shielded by the earth in the whole star observation period, camera star observation data and satellite attitude data have high precision, and satellite in-orbit geometric calibration is supported.

Description

Technical Field

[0001] The present invention belongs to the technical field of aerospace optical remote sensing imaging. Specifically, it relates to a method and system for attitude planning of low-earth orbit remote sensing satellites for observing stars. More specifically, it is a method and system for attitude planning of low-earth orbit remote sensing satellites for long-term star observation; the term "long-term" means that the star observation duration of the satellite reaches the order of 10 minutes. Background Technique

[0002] In the field of aerospace optical remote sensing imaging, geometric positioning accuracy is an important indicator of optical remote sensing satellites. With the continuous development of commercial remote sensing, the demand for high-precision geometric positioning is becoming increasingly urgent.

[0003] To achieve high-precision geometric positioning, the satellite needs to perform on-orbit geometric calibration. Stars have the advantages of accurate position, stability, and visibility per orbit, and are natural high-precision control points. Based on star observation, the satellite is expected to achieve low-cost and high-precision on-orbit geometric calibration.

[0004] Optical remote sensing satellites have the need for long-term star observation for the following reasons:

[0005] 1. For long-term star observation, the satellite can obtain a larger number of stars in a single shot, improving the geometric calibration accuracy;

[0006] 2. For long-term star observation, it is possible to evaluate and analyze the time-varying and temperature-varying characteristics of the satellite's geometric positioning accuracy.

[0007] However, for low-earth orbit satellites, during long-term star observation, the satellite continuously moves along the orbit, and to photograph a large area of the star field, the optical axis of the space camera often moves actively. That is, during long-term star observation of low-earth orbit satellites, the relative position relationship between the field of view of the space camera, the field of view of the star sensor, and the Earth continuously changes, and it is very easy for the field of view to be blocked by the Earth or affected by the light of the Earth's atmosphere, thus affecting the geometric calibration accuracy. Therefore, it is urgent to develop a technology for attitude planning of low-earth orbit remote sensing satellites for long-term star observation.

[0008] Regarding the star observation of optical remote sensing satellites, relevant technologies have been proposed:

[0009] Patent document CN117611660A discloses a method for on-orbit evaluation and correction of optical distortion of a space camera based on star observation. This method calculates the projected position of the theoretical value of the star visual vector in the image coordinate system by obtaining multiple frames of images of the space camera observing stars, and evaluates and corrects the optical distortion based on the detected positions and projected positions of the stars in multiple frames. However, this method does not involve the attitude planning of low-earth orbit remote sensing satellites for long-term star observation.

[0010] Patent document CN114858186A discloses a method for on-orbit geometric calibration of a linear array camera in the stellar observation mode. This method realizes the on-orbit geometric calibration of the linear array camera by using the recognizable magnitude and field of view angle of the camera, selecting a suitable sky area for observing stellar control points, and identifying the object coordinates of the stellar control points, accurately extracting the image coordinates, and constructing a geometric distortion model. However, this method does not involve the attitude planning for long-term stellar observations of low-earth orbit remote sensing satellites.

[0011] Patent document CN117824701A discloses an on-orbit internal calibration method for a space camera based on stellar angular distance. This method calculates the principal point and principal distance by shuffling the star map sequence and combining the principal point rotation imaging, calculates the polynomial distortion coefficients, and outputs the calibration results and residual quantities, which is applicable to the on-orbit internal calibration of a space camera under the condition of unable to obtain accurate attitude measurements. However, this method does not involve the attitude planning for long-term stellar observations of low-earth orbit remote sensing satellites.

[0012] Patent document CN118503573A discloses a calculation method and system for a low-earth orbit satellite to continuously observe multiple stellar targets. This method realizes the continuous observation of multiple stellar targets by a low-earth orbit satellite by calculating the vectors from the satellite to each star, screening out the time windows not blocked by the earth, successively judging whether the required rotation angle for star observation meets the servo rotation range, judging whether the shielding angle meets the set threshold, and screening out the observation windows that meet the continuous observation conditions. However, this method does not involve the attitude planning for long-term stellar observations of low-earth orbit remote sensing satellites.

[0013] Patent document CN115861414A discloses an attitude calculation method and system for a remote sensing satellite to observe stars. This method establishes an attitude reference for the satellite to observe stars, constrains the satellite's solar array to face the sun and the camera's field of view to be away from the sun, obtains the target star through the method of star search, and adjusts the satellite's attitude to make the star sensor away from the earth to avoid occlusion. This method fully considers the satellite's safety and engineering feasibility, but it is not suitable for long-term star observation imaging of low-earth orbit satellites and linear array cameras.

[0014] Patent document CN105512374A discloses a satellite observation orbit design method under the condition of natural fly-around in the same orbital plane; this scheme includes: designing the initial orbit of the observation satellite to satisfy the natural fly-around condition with the target star; at the initial moment, setting the line-of-sight direction of the target star relative to the observation satellite as the observation direction, and keeping the attitude of the observation satellite in space inertial orientation during the fly-around process; selecting the field of view angle of the observation camera; determining the long-period divergence model of the included angle between the observation direction and the line connecting the target star; and adjusting the attitude of the observation satellite according to the long-period divergence model. This method belongs to the observation of fly-around artificial satellites and is not suitable for long-term imaging of stellar observations.

[0015] None of the above-mentioned existing patents and documents can effectively solve the problem of attitude planning for long-term stellar observations of low-earth orbit remote sensing satellites. This problem urgently needs to be solved. Summary of the Invention

[0016] Aiming at the deficiencies in the prior art, the purpose of the present invention is to provide a method and system for attitude planning of stellar observations of low-earth orbit remote sensing satellites.

[0017] A method for attitude planning of stellar observations of low-earth orbit remote sensing satellites provided by the present invention includes: Step S1: Determine the satellite star-viewing reference axis and reference cone in the satellite coordinate system;

[0018] Step S2: Based on the satellite star-viewing reference axis and reference cone, calculate the satellite roll attitude and satellite pitch attitude required for the satellite star-viewing reference axis in the orbital coordinate system to move away from the earth's center;

[0019] Step S3: Determine the satellite star-viewing center time, and based on the satellite roll attitude and satellite pitch attitude, calculate the satellite star-viewing reference area in the inertial coordinate system;

[0020] Step S4: Select a star-viewing target area from the satellite star-viewing reference area, and calculate the star-viewing center time and the camera star-viewing attitude in the inertial coordinate system;

[0021] Step S5: Set satellite parameters, determine the star-viewing duration, and then make the satellite maneuver around the camera in the inertial system for imaging.

[0022] Preferably, in the step S1, the mathematical expression of the cone angle of the reference cone is:

[0023]

[0024] where β cone is the cone angle of the reference cone, is the unit vector of the satellite star-viewing reference axis, is the unit vector of the optical axis of the camera, and β cam is the protection angle of the camera;

[0025] The mathematical expression of the satellite star-viewing reference axis is:

[0026]

[0027] where The mathematical expression of is:

[0028]

[0029] where is the unit vector of the satellite star-viewing reference axis, is the unit vector of the optical axis of the camera, is the unit vector of the optical axis of star sensor a, is the unit vector of the optical axis of star sensor b, β cam is the camera protection angle, β ssa is the star sensor protection angle; star sensors a and b have the same protection angle; λ is the parameter to be solved, which can be obtained by Newton iteration method or bisection method, etc.;

[0030] In the step S1, when the camera protection angle and the star sensor protection angle are the same, the mathematical expression of the satellite star observation reference axis is simplified as:

[0031]

[0032] where is the unit vector of the satellite star observation reference axis, is the unit vector of the optical axis of the camera, is the unit vector of the optical axis of star sensor a, is the unit vector of the optical axis of star sensor b;

[0033] where the selection of the plus or minus sign is determined by the following formula:

[0034]

[0035] Only keep the unique sign that meets the above judgment conditions. If the plus sign meets the above judgment conditions, then take the plus sign and discard the minus sign result; if the plus sign does not meet the above judgment conditions, then take the minus sign and discard the plus sign result.

[0036] Preferably, in the step S2, the rotation order of the Euler angles of the satellite rolling attitude and the satellite pitching attitude is the 312 rotation sequence;

[0037] In the step S2, the mathematical expressions of the satellite rolling attitude and the satellite pitching attitude are as follows:

[0038]

[0039] where is the roll angle, θ is the pitch angle, is the unit vector of the satellite star observation reference axis, are the unit vectors along the +x axis, +y axis, and +z axis respectively, and the superscript T represents transpose;

[0040] where, let be the first pitch angle formula; let be the second pitch angle formula; the selection of one of the two calculation formulas of the pitch angle θ is determined by the following formula:

[0041]

[0042] Judge whether the first pitch angle formula can satisfy the above expression. If the result is yes, select the first pitch angle formula as the calculation formula for the pitch angle θ; if the result is no, select the second pitch angle formula as the calculation formula for the pitch angle θ.

[0043] Preferably, in the step S3, the mathematical expression of the satellite star-viewing reference area is:

[0044]

[0045] where represents the unit vector of the camera line of sight in the inertial coordinate system, represents the rotation matrix from the orbital coordinate system to the inertial coordinate system at the satellite star-viewing center time, represents the rotation matrix from the satellite coordinate system to the orbital coordinate system, represents the unit vector of the camera line of sight in the camera coordinate system, represents the rotation matrix from the camera coordinate system to the satellite coordinate system;

[0046] where The mathematical expression of is:

[0047]

[0048] where R x 、R y 、R z respectively represent the transformation matrices for rotating angles around the x-axis, y-axis, and z-axis; the ψ represents the yaw attitude, ψ ∈ [0.5π to 1.5π].

[0049] Preferably, in the step S4, at the star-viewing center time, the camera star-viewing attitude in the inertial coordinate system, the mathematical expression is:

[0050]

[0051] where respectively represent the camera roll, pitch, and yaw attitudes in the inertial coordinate system at the star-viewing center time; represents the rotation matrix from the camera coordinate system to the inertial coordinate system;

[0052] In the step S5, let the satellite maneuver around the camera +y axis in the inertial system;

[0053] The satellite parameters include the satellite maneuver angular velocity and the camera imaging parameters;

[0054] The matching relationship between the satellite maneuver angular velocity and the camera imaging parameters, the mathematical expression is:

[0055]

[0056] Among them, when the camera is a linear array, f cam represents the imaging line frequency of the camera, ω s represents the satellite maneuvering angular velocity, and δ represents the angular resolution of the camera pixel; when the camera is a matrix array, 1 / f cam represents the longest exposure time per frame;

[0057] The value of the determined star observation duration should satisfy the mathematical expression:

[0058]

[0059] Among them, β cone is the reference cone angle, R air is the radius of the earth-atmosphere light, R is the radius of the earth, H is the satellite orbit altitude, and γ t is the angle between the satellite star observation reference axis and the geocenter-satellite vector; t is the satellite star observation duration, and t shadow is the satellite shadow area duration;

[0060] Among them, the mathematical expression of the said γ t is:

[0061]

[0062] Among them, represents the unit vector along the +z axis, ω o is the satellite orbit angular velocity, and ω s is the satellite maneuvering angular velocity.

[0063] According to a low-earth orbit remote sensing satellite star observation attitude planning system provided by the present invention, it includes: Module M1: Determine the satellite star observation reference axis and the reference cone in the satellite coordinate system;

[0064] Module M2: Based on the satellite star observation reference axis and the reference cone, calculate the satellite rolling attitude and the satellite pitching attitude required for the satellite star observation reference axis to move away from the geocenter in the orbital coordinate system;

[0065] Module M3: Determine the satellite star observation center moment, and based on the satellite rolling attitude and the satellite pitching attitude, calculate the satellite star observation reference area in the inertial coordinate system;

[0066] Module M4: Select the satellite star observation reference area, calculate the star observation center moment, and the camera star observation attitude in the inertial coordinate system;

[0067] Module M5: Set satellite parameters, determine the star observation duration, and then make the satellite maneuver around the camera in the inertial system for imaging.

[0068] Preferably, in the module M1, the mathematical expression of the cone angle of the reference cone is:

[0069]

[0070] where β cone is the cone angle of the reference cone, is the unit vector of the satellite star - viewing reference axis, is the unit vector of the optical axis of the camera, and β cam is the protection angle of the camera;

[0071] The mathematical expression of the satellite star - viewing reference axis is:

[0072]

[0073] where The mathematical expression of

[0074]

[0075] where is the unit vector of the satellite star - viewing reference axis, is the unit vector of the optical axis of the camera, is the unit vector of the optical axis of star sensor a, is the unit vector of the optical axis of star sensor b, and β cam is the protection angle of the camera, and β ssa is the protection angle of the star sensor; Star sensor a and star sensor b have the same protection angle; λ is the parameter to be solved, which can be obtained by Newton's iterative method or bisection method, etc.;

[0076] In the module M1, when the protection angle of the camera is the same as the protection angle of the star sensor, the mathematical expression of the satellite star - viewing reference axis is simplified to:

[0077]

[0078] where is the unit vector of the satellite star - viewing reference axis, is the unit vector of the optical axis of the camera, is the unit vector of the optical axis of star sensor a, is the unit vector of the optical axis of star sensor b;

[0079] where The selection of the plus or minus sign is determined by the following formula:

[0080]

[0081] Only retain the unique sign that satisfies the above judgment condition. If the plus sign satisfies the above judgment condition, then Take the positive sign and discard the negative sign result; if the positive sign does not meet the above judgment conditions, then Take the negative sign and discard the positive sign result.

[0082] Preferably, in the module M2, the rotation order of the Euler angles of the satellite rolling attitude and the satellite pitching attitude is the 312 rotation order;

[0083] In the module M2, the mathematical expressions of the satellite rolling attitude and the satellite pitching attitude are as follows:

[0084]

[0085] Among them, is the roll angle, θ is the pitch angle, is the unit vector of the satellite star-viewing reference axis, are the unit vectors along the +x axis, +y axis, and +z axis respectively, and the superscript T represents the transpose;

[0086] Among them, let be the first pitch angle formula; let be the second pitch angle formula; the choice of one of the two calculation formulas of the pitch angle θ is determined by the following formula:

[0087]

[0088] Judge whether the first pitch angle formula can meet the above expression. If the result is yes, the calculation formula of the pitch angle θ selects the first pitch angle formula; if the result is no, the calculation formula of the pitch angle θ selects the second pitch angle formula.

[0089] Preferably, in the module M3, the mathematical expression of the satellite star-viewing reference area is:

[0090]

[0091] Among them, represents the unit vector of the camera line of sight in the inertial coordinate system, represents the rotation matrix from the orbital coordinate system to the inertial coordinate system at the satellite star-viewing center time, represents the rotation matrix from the satellite coordinate system to the orbital coordinate system, represents the unit vector of the camera line of sight in the camera coordinate system, represents the rotation matrix from the camera coordinate system to the satellite coordinate system;

[0092] Among them, The mathematical expression of is:

[0093]

[0094] Among them, Rx , R y , R z respectively represent the transformation matrices for rotating angles around the x-axis, y-axis, and z-axis; ψ represents the yaw attitude, and ψ ∈ [0.5π to 1.5π].

[0095] Preferably, in the module M4, at the star observation center moment, the attitude of the camera for star observation in the inertial coordinate system is expressed by the mathematical formula:

[0096]

[0097] where respectively represent the roll, pitch, and yaw attitudes of the camera in the inertial coordinate system at the star observation center moment; represents the rotation matrix from the camera coordinate system to the inertial coordinate system;

[0098] In the module M5, let the satellite maneuver around the +y-axis of the camera in the inertial system;

[0099] The satellite parameters include the satellite maneuver angular velocity and the camera imaging parameters;

[0100] The matching relationship between the satellite maneuver angular velocity and the camera imaging parameters is expressed by the mathematical formula:

[0101]

[0102] where, when the camera is a linear array, f cam represents the camera imaging line frequency, ω s represents the satellite maneuver angular velocity, and δ represents the camera pixel angular resolution; when the camera is a area array, 1 / f cam represents the longest exposure time per frame;

[0103] The value of the determined star observation duration should satisfy the mathematical formula:

[0104]

[0105] where, β cone is the reference cone angle, R air is the radius of the earth-atmosphere light, R is the radius of the earth, H is the satellite orbit altitude, γ t is the angle between the satellite star observation reference axis and the geocenter-satellite vector; t is the satellite star observation duration, t shadow is the satellite shadow area duration;

[0106] where, the mathematical formula of the γ t is:

[0107]

[0108] where Denote the unit vector along the +z axis, ω o is the angular velocity of the satellite orbit, ω s is the angular velocity of the satellite maneuver.

[0109] Compared with the prior art, the present invention has the following beneficial effects:

[0110] 1. The present invention ensures that both the space camera and the star sensor are not affected by earth atmosphere light interference and earth occlusion during the entire star observation period. The star observation data of the camera and the satellite attitude data both have high precision, supporting on-orbit geometric calibration of the satellite.

[0111] 2. The present invention has strong adaptability, can be applied to linear array satellites and area array satellites, and can be generally applied to the attitude planning of long-term star observation for optical remote sensing satellites.

[0112] 3. The star observation reference axis, reference cone, and the satellite roll and pitch attitudes required to move the satellite star observation reference axis away from the earth center in the present invention are all fixed values. The yaw attitude ψ of the satellite in the orbital coordinate system at the star observation center moment can be defaulted to ψ = π, with low computing power requirements, which is especially suitable for on-board autonomous mission planning for star observation imaging.

[0113] 4. The present invention adopts a reference cone, fully considering the field of view characteristics of the space camera and the star sensor, can achieve long-term star observation of the satellite, and ensures that both the space camera and the star sensor are not affected by earth atmosphere light interference and earth occlusion during the entire star observation period. BRIEF DESCRIPTION OF THE DRAWINGS

[0114] By reading the detailed description of the non-limiting embodiments with reference to the following drawings, other features, objectives, and advantages of the present invention will become more obvious:

[0115] Figure 1 is the work flow chart provided by the present invention;

[0116] Figure 2 is the schematic diagram of the geometric model of the satellite star observation reference axis and reference cone provided by the present invention;

[0117] Figure 3 is the example diagram of the satellite star observation reference area provided by the present invention;

[0118] Figure 4 is the example diagram of the satellite 900s long-term star observation imaging area provided by the present invention;

[0119] Figure 5 is the example diagram of the curve of the angle between the edge of the satellite reference cone, the edge of the star sensor protection angle cone, the edge of the camera protection angle cone and the earth atmosphere light changing with the imaging time during the star observation period provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0120] The present invention will be described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several changes and improvements can still be made. These all belong to the protection scope of the present invention.

[0121] The purpose of the present invention is to provide a method for long-time stellar observation attitude planning of a low-earth orbit remote sensing satellite, so as to achieve long-time large-range stellar observation in a safe satellite attitude state.

[0122] Embodiment 1, an optical remote sensing satellite has an orbital altitude of 500 km. It is necessary to plan the long-time stellar observation attitude to achieve long-time large-range starfield photography for on-orbit star observation calibration and improve the geometric positioning accuracy of the satellite.

[0123] The following is the application of the present invention for the long-time stellar observation attitude planning of an optical remote sensing satellite. The implementation process is as Figure 1 shown:

[0124] Step S1: In the satellite body coordinate system, determine the satellite's star observation reference axis and reference cone according to the field-of-view characteristics of the space camera and the star sensor;

[0125] Step S2: In the orbital coordinate system, solve the satellite's roll and pitch attitudes required to move the satellite's star observation reference axis away from the earth's center, and the rotation sequence is 312;

[0126] Step S3: Determine the satellite's star observation center time, and calculate the satellite's star observation reference area in the inertial coordinate system;

[0127] Step S4: Select the star observation target area from the satellite's star observation reference area, and calculate the camera's star observation attitude in the inertial coordinate system at the star observation center time, and the rotation sequence is 312;

[0128] Step S5: Set the satellite's maneuvering angular velocity and camera imaging parameters, and determine the satellite's star observation duration; during the star observation period, the satellite maneuvers in the inertial system around the positive direction of the camera +y axis for star observation imaging.

[0129] In the step S1, the reference cone contains the star sensor field-of-view cone and the camera field-of-view cone and is tangent to them. The satellite's star observation reference axis is the unit vector of the reference cone axis. The star sensor field-of-view cone includes a protection angle; the camera field-of-view cone includes a protection angle.

[0130] The mathematical expression of the reference cone angle is:

[0131]

[0132] where, β cone is the reference cone angle, is the unit vector of the satellite star - viewing reference axis, is the unit vector of the camera's optical axis, and β cam is the camera protection angle;

[0133] The calculation method of the satellite star - viewing reference axis is as follows:

[0134]

[0135] Among them, The mathematical expression of is:

[0136]

[0137] Among them, is the unit vector of the satellite star - viewing reference axis, is the unit vector of the camera's optical axis, is the unit vector of the optical axis of star sensor a, is the unit vector of the optical axis of star sensor b, and β cam is the camera protection angle, and β ssa is the star sensor protection angle. Star sensor a and star sensor b have the same protection angle. λ is the parameter to be solved and can be obtained by methods such as Newton iteration method or bisection method.

[0138] In the step S1, when the camera protection angle and the star sensor protection angle are the same, the mathematical expression of the satellite star - viewing reference axis is simplified to:

[0139]

[0140] Among them, is the unit vector of the satellite star - viewing reference axis, is the unit vector of the camera's optical axis, is the unit vector of the optical axis of star sensor a, is the unit vector of the optical axis of star sensor b.

[0141] Among them, The selection of the plus or minus sign is determined by the following formula:

[0142]

[0143] Specifically, only retain the unique sign that meets the above judgment conditions. If the plus sign meets the above judgment conditions, take the plus sign and discard the negative - sign result; if the plus sign does not meet the above judgment conditions, take the negative sign and discard the positive - sign result;

[0144] In the step S2, the calculation formulas for the satellite roll and pitch attitudes in the orbital system are as follows:

[0145]

[0146] Among them, is the roll angle, θ is the pitch angle, is the unit vector of the satellite star - viewing reference axis, are the unit vectors along the +x - axis, +y - axis, and +z - axis respectively, and the superscript T represents transpose.

[0147] Among them, let be the first pitch - angle formula; let be the second pitch - angle formula; the selection of one of the two calculation formulas of the pitch angle θ is determined by the following formula:

[0148]

[0149] Judge whether the first pitch - angle formula can satisfy the above - mentioned expression. If the result is yes, the calculation formula of the pitch angle θ selects the first pitch - angle formula; if the result is no, the calculation formula of the pitch angle θ selects the second pitch - angle formula.

[0150] In the step S3, to ensure safety, the satellite star - viewing period is located in the shadow area, and preferably the central moment of the shadow area is the central moment of satellite star - viewing.

[0151] In the step S3, the satellite star - viewing reference area is calculated by the following formula:

[0152]

[0153] Among them, The mathematical expression of is:

[0154]

[0155] In the formula, represents the unit vector of the camera line of sight in the inertial coordinate system, represents the unit vector of the camera line of sight in the camera coordinate system, represents the rotation matrix from the camera coordinate system to the satellite coordinate system, represents the rotation matrix from the satellite coordinate system to the orbital coordinate system, represents the rotation matrix from the orbital coordinate system to the inertial coordinate system at the central moment of satellite star - viewing. respectively represent the roll, pitch, and yaw attitudes of the satellite in the orbital coordinate system, θ is determined by step S2, and the value range of ψ is 0 - 2π. R x (α), R y (α), R z (α) represent the transformation matrices for rotating α angles around the x - axis, y - axis, and z - axis respectively.

[0156] Respectively obtain the unit vector of the camera's optical axis and the unit vector of the detector pointing at the edge of the field of view in the camera coordinate system.

[0157] In the step S4, the camera's star observation attitude in the inertial coordinate system at the star observation center moment is expressed as:

[0158]

[0159] In other words, the mathematical expression is:

[0160]

[0161] Among them, The mathematical expression of is:

[0162]

[0163] Among them, respectively represent the camera's roll, pitch, and yaw attitudes in the inertial coordinate system at the star observation center moment, and the rotation order is 312; represents the rotation matrix from the camera coordinate system to the inertial coordinate system, represents the rotation matrix from the camera coordinate system to the satellite coordinate system, represents the rotation matrix from the satellite coordinate system to the orbital coordinate system, represents the rotation matrix from the orbital coordinate system to the inertial coordinate system. respectively represent the satellite's roll, pitch, and yaw attitudes in the orbital coordinate system at the star observation center moment, θ is determined by step S2, and the yaw attitude ψ is determined by the selected star observation target area.

[0164] In the step S4, to achieve long-time star observation imaging, select the star observation target area from the star observation reference area corresponding to the satellite yaw attitude ψ ∈ [0.5π~1.5π] in the orbital coordinate system at the star observation center moment; when there is no special requirement for the star observation target area, take the satellite yaw attitude ψ = π.

[0165] In the step S5, the method for setting the camera imaging parameters is as follows: the imaging frame rate of the area array camera is set according to requirements; the imaging line frequency of the line array camera needs to match the satellite maneuvering angular velocity and satisfy the following formula:

[0166]

[0167] Among them, when the camera is a line array, f cam represents the camera imaging line frequency, ω s represents the satellite maneuvering angular velocity, and δ represents the camera pixel angular resolution; when the camera is an area array, 1 / f cam represents the longest exposure time per frame.

[0168] In the step S5, to ensure the safety of the satellite and that it is not affected by earth atmosphere light interference and earth occlusion during the entire stargazing period, the stargazing duration of the satellite needs to satisfy the following formula

[0169]

[0170] where γ t has the following mathematical expression:

[0171]

[0172] where t is the stargazing duration of the satellite, t shadow is the duration of the satellite's shadow area, γ t is the angle between the satellite's stargazing reference axis and the geocenter-satellite vector, β cone is the cone angle of the reference cone, H is the satellite orbit altitude, R is the radius of the earth, R air is the radius of the earth atmosphere light, usually taken as 6381 - 6391 km, ω s is the angular velocity of the satellite's maneuver, ω o is the angular velocity of the satellite's orbit. represents the rotation matrix from the camera coordinate system to the satellite coordinate system, represents the rotation matrix from the satellite coordinate system to the orbit coordinate system. is the unit vector along the +z axis, and the superscript T represents the transpose.

[0173] In the steps S1 - S2, for any satellite, the satellite's stargazing reference axis, reference cone, and the satellite's roll and pitch attitudes required to move the stargazing reference axis away from the geocenter are all fixed values, which are calculated and pre-stored in advance.

[0174] This optical remote sensing satellite is equipped with 1 space camera and 1 dual-head star sensor, denoted as star sensor a and star sensor b respectively. The earth atmosphere light protection angle β cam of the space camera is 16°, and the earth atmosphere light protection angle β ssa of the star sensor is β ssb = 22°.

[0175] The unit vector of the optical axis of the space camera of this optical remote sensing satellite The unit vector of the optical axis of star sensor a The unit vector of the optical axis of star sensor b are respectively:

[0176]

[0177] The geometric model of the satellite's stargazing reference axis and reference cone is as Figure 2 shown. The reference cone is tangent to the star sensor protection angle cone and the camera protection angle cone, and the satellite's stargazing reference axis is the unit vector of the reference cone axis.

[0178] According to step S1, the reference conical angle β is calculated cone = 87.2178°, and the unit vector of the star observation reference axis is

[0179]

[0180] According to step S2, in the orbital coordinate system, the required satellite roll angle and pitch angle θ of the star observation reference axis of the optical remote sensing satellite away from the earth center are respectively

[0181]

[0182] According to step S3, the central moment of the shadow area is selected as the star observation central moment, and the satellite star observation reference area is calculated, as shown in Figure 3 The satellite star observation reference area straddles the Milky Way with dense stars and the declination -70° area with sparse stars.

[0183] According to step S4, for long-time star observation imaging, the yaw attitude ψ of the satellite in the orbital coordinate system at the star observation central moment is selected as 180.0000°, and the three-axis attitude of the camera for star observation in the inertial coordinate system are respectively

[0184]

[0185] According to step S5, the satellite maneuvering angular velocity ω s = 0.1° / s is set. The camera is a linear array, and the camera imaging line frequency f cam = 1764Hz, which is matched with the angular resolution δ = 0.2041″, and the imaging time is set as t = 900s

[0186] During the star observation period, the satellite maneuvers around the positive direction of the camera +y axis at an angular velocity of ω s = 0.1° / s in the inertial system for star observation imaging. The long-time star observation imaging area of the satellite for 900s is as shown in Figure 4 It is in a long strip shape, and the central coordinates are (right ascension 53.3335°, declination 11.0621°).

[0187] The curves of the angles between the edges of the satellite reference cone, the star sensor protection angle cone, the camera protection angle cone and the earth-air light during the star observation period changing with the imaging time are as shown in Figure 5 The minimum angle is 8.18° > 0°, indicating that the camera and star sensor in the satellite are not interfered by the earth-air light and blocked by the earth during the whole star observation period.

[0188] The present invention also provides a low-earth orbit remote sensing satellite's attitude planning system for stellar observation. The low-earth orbit remote sensing satellite's attitude planning system for stellar observation can be implemented by executing the process steps of the low-earth orbit remote sensing satellite's attitude planning method for stellar observation. That is, those skilled in the art can understand the low-earth orbit remote sensing satellite's attitude planning method for stellar observation as a preferred implementation manner of the low-earth orbit remote sensing satellite's attitude planning system for stellar observation.

[0189] A low-earth orbit remote sensing satellite's attitude planning system for stellar observation provided by the present invention includes: Module M1: Determine the satellite's star-viewing reference axis and reference cone in the satellite coordinate system.

[0190] Module M2: Based on the satellite's star-viewing reference axis and reference cone, calculate the satellite's roll attitude and pitch attitude required for the satellite's star-viewing reference axis in the orbital coordinate system to move away from the earth's center.

[0191] Module M3: Determine the satellite's star-viewing center time, and based on the satellite's roll attitude and pitch attitude, calculate the satellite's star-viewing reference area in the inertial coordinate system.

[0192] Module M4: Select the satellite's star-viewing reference area, calculate the star-viewing center time, and the camera's star-viewing attitude in the inertial coordinate system.

[0193] Module M5: Set satellite parameters, determine the star-viewing duration, and then make the satellite maneuver around the camera in the inertial system for imaging.

[0194] Those skilled in the art know that in addition to implementing the system and its various devices, modules, and units provided by the present invention in the form of pure computer-readable program code, the method steps can be logically programmed to enable the system and its various devices, modules, and units provided by the present invention to be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers, etc., to achieve the same functions. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be regarded as the structures within the hardware component; the devices, modules, and units for implementing various functions can also be regarded as both software modules for implementing the method and the structures within the hardware component.

[0195] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the above specific implementation manners. Those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. Without conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A method for attitude planning of a low-orbit remote sensing satellite for stellar observation, characterized in that, Including: Step S1: Determine the satellite star - viewing reference axis and the reference cone in the satellite coordinate system; Step S2: Based on the satellite star - viewing reference axis and the reference cone, calculate the satellite roll attitude and the satellite pitch attitude required for the satellite star - viewing reference axis to move away from the earth center in the orbital coordinate system; Step S3: Determine the satellite star - viewing center time, and based on the satellite roll attitude and the satellite pitch attitude, calculate the satellite star - viewing reference area in the inertial coordinate system; Step S4: Select the star - viewing target area from the satellite star - viewing reference area, and calculate the star - viewing center time and the camera star - viewing attitude in the inertial coordinate system; Step S5: Set the satellite parameters, determine the star - viewing duration, and then make the satellite maneuver around the camera in the inertial system for imaging.

2. The method for attitude planning of low-orbit remote sensing satellite for stellar observation according to claim 1, characterized in that In the step S1, the mathematical expression of the cone angle of the reference cone is: Among them, β cone is the reference cone angle of the reference cone, is the unit vector of the reference axis for satellite star observation, is the unit vector of the optical axis of the camera, and β cam is the protection angle of the camera; The mathematical expression of the satellite star - viewing reference axis is: Among them, The mathematical expression is: Among them, is the unit vector of the satellite star observation reference axis, is the unit vector of the optical axis of the camera, is the unit vector of the optical axis of star sensor a, is the unit vector of the optical axis of star sensor b, β cam is the protection angle of the camera, β ssa is the protection angle of the star sensor; star sensor a and star sensor b have the same protection angle; λ is the parameter to be solved, which can be obtained by the Newton iteration method or the bisection method, etc.; In the step S1, when the camera protection angle and the star sensor protection angle are the same, the mathematical expression of the satellite star - viewing reference axis is simplified to: Among them, is the unit vector of the satellite star-viewing reference axis, is the unit vector of the optical axis of the camera, is the unit vector of the optical axis of star sensor a, is the unit vector of the optical axis of star sensor b; Among them, The selection of the plus or minus sign is determined by the following formula: Only retain the unique symbol that meets the above judgment conditions. If the positive sign meets the above judgment conditions, then take the positive sign and discard the negative sign result; if the positive sign does not meet the above judgment conditions, then take the negative sign and discard the positive sign result.

3. The method for attitude planning of low-orbit remote sensing satellite's stellar observation according to claim 2, wherein In the step S2, the rotation sequence of the Euler angles of the satellite roll attitude and the satellite pitch attitude is the 312 rotation sequence; In the step S2, the mathematical expressions of the satellite roll attitude and the satellite pitch attitude are as follows: wherein, is the roll angle, θ is the pitch angle, is the unit vector of the satellite star - viewing reference axis, are the unit vectors along the +x - axis, +y - axis, and +z - axis respectively, and the superscript T represents transpose; where, let be the first pitch angle formula; let be the second pitch angle formula; the selection of one of the two calculation formulas for the pitch angle θ is determined by the following formula: Judge whether the first pitch - angle formula can satisfy the above expressions. If the result is yes, the calculation formula of the pitch angle θ selects the first pitch - angle formula; if the result is no, the calculation formula of the pitch angle θ selects the second pitch - angle formula.

4. The method for attitude planning of low-orbit remote sensing satellite for stellar observation according to claim 3, characterized in that In the step S3, the mathematical expression of the satellite star - viewing reference area is: Among them, represents the unit vector of the camera's line of sight in the inertial coordinate system, represents the rotation matrix from the orbital coordinate system to the inertial coordinate system at the satellite's star observation center time, represents the rotation matrix from the satellite coordinate system to the orbital coordinate system, represents the unit vector of the camera's line of sight in the camera coordinate system, represents the rotation matrix from the camera coordinate system to the satellite coordinate system; Among them, The mathematical expression is: Among them, R x , R y , R z respectively represent the transformation matrices for rotating angles around the x-axis, y-axis, and z-axis; the ψ represents the yaw attitude, ψ ∈ [0.5π to 1.5π].

5. The method for attitude planning of a low-orbit remote sensing satellite for stellar observation according to claim 4, characterized in that In the step S4, the mathematical expression of the camera star - viewing attitude in the inertial coordinate system at the star - viewing center time is: Among them, respectively represent the camera roll, pitch, and yaw attitudes in the inertial coordinate system at the central time of stargazing; represents the rotation matrix from the camera coordinate system to the inertial coordinate system; In the step S5, make the satellite maneuver around the camera + y - axis in the inertial system; The satellite parameters include the satellite maneuver angular velocity and the camera imaging parameters; The matching relationship between the satellite maneuver angular velocity and the camera imaging parameters is expressed mathematically as: Among them, when the camera is a linear array, f cam represents the imaging line frequency of the camera, ω s represents the angular velocity of satellite maneuver, and δ represents the angular resolution of camera pixels; when the camera is a area array, 1 / f cam represents the longest exposure time of a single frame; The value of the determined star - viewing duration should satisfy the mathematical expression: Among them, β cone is the reference conical angle of the cone, R air is the radius of the ground-air light, R is the radius of the earth, H is the satellite orbit height, γ t is the angle between the satellite's star-viewing reference axis and the geocenter-satellite vector; t is the satellite's star-viewing duration, t shadow is the duration of the satellite's shadow area; Among them, the γ t has the following mathematical expression: Among them, represents the unit vector along the +z axis, and ω o is the angular velocity of the satellite orbit, and ω s is the angular velocity of satellite maneuvering.

6. A low-earth orbit remote sensing satellite stellar observation attitude planning system, characterized in that, Including: Module M1: Determine the satellite star - viewing reference axis and the reference cone in the satellite coordinate system; Module M2: Based on the satellite star - viewing reference axis and the reference cone, calculate the satellite roll attitude and the satellite pitch attitude required for the satellite star - viewing reference axis to move away from the earth center in the orbital coordinate system; Module M3: Determine the satellite star - viewing center time, and based on the satellite roll attitude and the satellite pitch attitude, calculate the satellite star - viewing reference area in the inertial coordinate system; Module M4: Select the satellite star - viewing reference area, calculate the star - viewing center time and the camera star - viewing attitude in the inertial coordinate system; Module M5: Set the satellite parameters, determine the star - viewing duration, and then make the satellite maneuver around the camera in the inertial system for imaging.

7. The low-orbit remote sensing satellite stellar observation attitude planning system according to claim 6, characterized in that, In the module M1, the mathematical expression of the cone angle of the reference cone is: where β cone is the reference cone angle of the reference cone, is the unit vector of the satellite star - viewing reference axis, is the unit vector of the optical axis of the camera, and β cam is the protection angle of the camera; The mathematical expression of the satellite star - viewing reference axis is: Among them, The mathematical expression is: Among them, is the unit vector of the satellite star-viewing reference axis, is the unit vector of the optical axis of the camera, is the unit vector of the optical axis of star sensor a, is the unit vector of the optical axis of star sensor b, β cam is the protection angle of the camera, β ssa is the protection angle of the star sensor; star sensor a and star sensor b have the same protection angle; λ is the parameter to be solved, which can be obtained by Newton iteration method or bisection method, etc.; In the module M1, when the camera protection angle and the star sensor protection angle are the same, the mathematical expression of the satellite star - viewing reference axis is simplified to: Among them, is the unit vector of the satellite star observation reference axis, is the unit vector of the optical axis of the camera, is the unit vector of the optical axis of star sensor a, is the unit vector of the optical axis of star sensor b; Among them, The selection of the plus or minus sign is determined by the following formula: Only retain the unique symbol that meets the above judgment conditions. If the positive sign meets the above judgment conditions, then take the positive sign and discard the negative sign result; if the positive sign does not meet the above judgment conditions, then take the negative sign and discard the positive sign result.

8. The low-earth orbit remote sensing satellite stellar observation attitude planning system according to claim 7, characterized in that In the module M2, the rotation sequence of the Euler angles of the satellite roll attitude and the satellite pitch attitude is the 312 rotation sequence; In the module M2, the mathematical expressions for the satellite's rolling attitude and pitching attitude are as follows: Among them, is the roll angle, θ is the pitch angle, is the unit vector of the satellite star - viewing reference axis, are the unit vectors along the +x - axis, +y - axis, and +z - axis respectively, and the superscript T represents transpose; Among them, let be the first pitch angle formula; let be the second pitch angle formula; either one of the calculation formulas of the pitch angle θ is determined by the following formula: Determine whether the first pitch angle formula can satisfy the above expressions. If the result is yes, the calculation formula for the pitch angle θ selects the first pitch angle formula; if the result is no, the calculation formula for the pitch angle θ selects the second pitch angle formula.

9. The low-earth orbit remote sensing satellite stellar observation attitude planning system according to claim 8, characterized in that In the module M3, the mathematical expression for the satellite's star-viewing reference area is: Among them, represents the unit vector of the camera line of sight in the inertial coordinate system, represents the rotation matrix from the orbital coordinate system to the inertial coordinate system at the satellite star observation center moment, represents the rotation matrix from the satellite coordinate system to the orbital coordinate system, represents the unit vector of the camera line of sight in the camera coordinate system, represents the rotation matrix from the camera coordinate system to the satellite coordinate system; Among them, The mathematical expression is: Among them, R x , R y , R z respectively represent the transformation matrices for rotating angles around the x-axis, y-axis, and z-axis; the ψ represents the yaw attitude, ψ ∈ [0.5π to 1.5π].

10. The low-orbit remote sensing satellite stellar observation attitude planning system according to claim 9, wherein, In the module M4, at the star-viewing center moment, the mathematical expression for the star-viewing attitude of the camera in the inertial coordinate system is: wherein, respectively represent the camera roll, pitch, and yaw attitudes in the inertial coordinate system of the stargazing center moment; represents the rotation matrix from the camera coordinate system to the inertial coordinate system; In the module M5, let the satellite maneuver around the +y axis of the camera in the inertial system; The satellite parameters include the satellite maneuver angular velocity and the camera imaging parameters; The matching relationship between the satellite maneuver angular velocity and the camera imaging parameters is expressed mathematically as: Among them, when the camera is a linear array, f cam represents the imaging line frequency of the camera, ω s represents the angular velocity of satellite maneuver, and δ represents the angular resolution of camera pixels; when the camera is a area array, 1 / f cam represents the longest exposure time of a single frame; The value of the determined star-viewing duration should satisfy the mathematical expression: Among them, β cone is the reference cone angle of the cone, R air is the radius of the earth's atmosphere light, R is the radius of the earth, H is the satellite orbit altitude, γ t is the angle between the satellite's star - viewing reference axis and the geocenter - satellite vector; t is the satellite's star - viewing duration, t shadow is the duration of the satellite's shadow area; Among them, the γ t has a mathematical expression of: Among them, represents the unit vector along the +z axis, ω o is the angular velocity of the satellite orbit, ω s is the angular velocity of satellite maneuver.

Images