Optimization design method and system for layout of three-star sensor of low-dip-angle radar satellite

Abstract

The invention provides an optimal design method and system for layout of three-star sensors of a low-dip-angle radar satellite. The optimal design method comprises the following steps: calculating the orbit position of the satellite in the in-orbit life period; calculating a position vector of the sun in a satellite orbit coordinate system; calculating the unit vector of the optical axis of each star sensor in the orbital coordinate system; constructing an optimization model of the layout of the three-star sensor; and carrying out optimization calculation on the layout optimization problem of the Samsung sensor by using a particle swarm optimization algorithm. The intelligent algorithm is used for design, low-efficiency manual design iteration in the traditional star sensor layout process is avoided, and the design efficiency is improved; an optimal layout scheme can be obtained, and the attitude measurement precision of the star sensor is improved; meanwhile, the method has universality and can be suitable for multi-star sensor layout design of other orbit types.

Description

Technical Field

[0001] The present invention relates to the field of overall satellite design, and more particularly, to an optimized design method and system for the layout of three star sensors on a low-inclination radar satellite. Background Art

[0002] A star sensor is a high-precision attitude sensor, and the layout of star sensors is one of the main contents of the satellite platform structure design. The layout design of multiple star sensors on a low-inclination radar satellite needs to comprehensively consider various stray light constraint conditions such as sunlight, earth-gas light, and the satellite's own stray light, and combine the working characteristics of low-inclination orbit satellites, such as regular 180° yaw maneuvers, one-dimensional swing and drive of solar arrays, etc. By reasonably designing the optical axis directions of multiple star sensors, the attitude measurement accuracy can be improved as much as possible. Therefore, the layout of multiple star sensors on a low-inclination orbit radar satellite is a complex design optimization problem.

[0003] In the current process of star sensor layout, it mainly relies on the personal experience of the overall satellite layout designer. According to the satellite illumination conditions and attitudes provided by the attitude and orbit control designer, the installation positions and angles of the star sensors are manually adjusted in CAD software. This method requires multiple rounds of iteration to determine the optical axis directions of the star sensors, which takes a long time, has low design efficiency, and it is difficult to obtain the optimal solution. Especially for the layout design of multiple star sensors, the design efficiency is even lower. Therefore, it is necessary to introduce an optimization algorithm to solve the problem of multiple star sensor layout to improve the design efficiency.

[0004] The patent document "An Optimized Design Method for the Layout of Multiple Star Sensors on a Spacecraft" (CN108681617A) discloses an optimized solution for the problem of optimizing the layout of multiple star sensors by comprehensively considering the effects of sunlight, earth-gas light, and the satellite body and other large components on the star sensors. This method needs to use a cube to approximately describe the geometric shapes of the satellite body and the solar array, and judge the relative relationship between the line of sight in the star sensor's light shield and the cube. The main limitation is that the calculation amount is large, and the accurate design constraints of the star sensors cannot be obtained through the approximation method, thus affecting the layout design results.

[0005] The patent document "A Calculation Method for Automatic Layout of Star Sensors" (CN109992869A) discloses a method of establishing a sun point model, using the CAD software import method to establish a satellite point model of the satellite body and satellite components such as antennas and solar wings, establishing a star sensor field of view cone angle model using the installation point position and azimuth angle, and calculating the effective field of view cone angle of the star sensor according to the spatial relationship between the sun, the satellite, and the star sensor. By traversing, the maximum effective field of view cone angle of the star sensor is calculated to obtain the optimal layout of the star sensor. This method does not consider the design requirement of the orthogonality of the optical axes between multiple star sensors, and its design results will affect the joint attitude determination accuracy of multiple star sensors.

[0006] The patent document "A method for spatial layout of star sensors based on logical traceability" (CN111027159A) discloses a method through placeholder design and field of view analysis. The star sensor installation points are selected based on whether two reference target stars can be identified and whether the requirements of opto-mechanical-thermal plume tests are met, and the layout of star sensors is determined. This method is only suitable for the layout of single star sensors, not applicable to the multi-star sensor layout problem, and does not consider satellite configuration constraints, only applicable to the preliminary analysis in the initial stage of satellite development.

[0007] The patent document "An optimization method for multi-star sensor layout of spacecraft" (CN114577201A) discloses the construction of a multi-objective optimization model with the maximum availability of double star sensors and the included angle between star sensors approaching orthogonality, and uses the multi-objective genetic algorithm for solution to determine the optimal layout of multi-star sensors. This method does not consider the influence of the 180° yaw maneuver of the satellite on the star sensors regularly, nor does it consider the possible influence of the solar array and satellite body scattered light on the star sensors.

[0008] The patent document "A method and system for adaptive layout of multi-star sensor clusters based on occlusion determination" (CN114537715A) discloses the establishment and assembly of an occluded model and an occlusion model, conducts adaptive biasing based on occlusion determination and angular adaptive biasing of a single star sensor within the cluster, manually sets the biasing value in CAD software, and manually judges whether there is occlusion in the star sensor field of view; based on this, the layout of other star sensors is completed. This method has cumbersome operations, the design means is not automated enough, the design efficiency is low, and it may not be able to obtain a feasible solution for the layout of multi-star sensors for satellites with complex configurations. Summary of the Invention

[0009] Aiming at the defects in the prior art, the purpose of the present invention is to provide an optimized design method and system for the layout of three star sensors of a low-inclination radar satellite.

[0010] According to an optimized design method for the layout of three star sensors of a low-inclination radar satellite provided by the present invention, it includes:

[0011] Step S1: Calculate the orbital position during the satellite's on-orbit life;

[0012] Step S2: Calculate the position vector of the sun in the satellite orbit coordinate system;

[0013] Step S3: Calculate the unit vector of the optical axis of each star sensor in the orbit coordinate system;

[0014] Step S4: Construct an optimization model for the layout of three star sensors;

[0015] Step S5: Use the particle swarm optimization algorithm to perform optimization calculations on the optimization problem of the layout of three star sensors.

[0016] Further, the step S1 includes:

[0017] Step S1.1: Establish an orbital element perturbation model under J2 perturbation;

[0018] Step S1.2: Based on the above perturbation model, perform orbit recursion according to the ephemeris parameters at a certain moment to obtain the orbital elements during the in-orbit lifetime of the satellite;

[0019] Step S1.3: According to the above orbital elements, calculate the satellite position and satellite velocity in the J2000.0 geocentric equatorial inertial coordinate system.

[0020] Further, the step S2 includes:

[0021] Step S2.1: Calculate the solar position in the J2000.0 geocentric equatorial inertial coordinate system

[0022] M = 2πFrac(0.9931267 + 99.9973583T)

[0023]

[0024] r = 1.49619×10 11 -2.499×10 9 ×cos(M) - 2.1×10 7 ×cos(2M)

[0025]

[0026] where M is the mean anomaly, L is the ecliptic longitude, r is the sun-earth distance, R x () represents rotation about the X-axis, T is the relative Julian century number corresponding to the calculation time, and Frac(x) represents the fractional part of the real number x;

[0027] Step S2.2: According to the satellite position and satellite velocity in the J2000.0 geocentric equatorial inertial coordinate system, calculate the solar position vector in the satellite orbit coordinate system.

[0028] Further, the step S3 includes:

[0029] Step S3.1: Calculate the optical axis vectors of each star sensor in the satellite body coordinate system Use the azimuth angle α b Y b Z b in the satellite body coordinate system OX i and the pitch angle β i to represent. The azimuth angle α i is defined as the angle between the X b axis and the star sensor optical axis in the Xb Y b The included angle of the projection on the plane, rotated around the Z b axis is positive according to the right - hand rule; the pitch angle β i is defined as the included angle between the star sensor optical axis and the X b Y b plane, and the star sensor optical axis on the +Z b side is positive;

[0030] The expression is:

[0031]

[0032] Step S3.2: Calculate the optical axis vectors of each star sensor in the orbital coordinate system It is converted from according to the 1 - 2 - 3 rotation sequence, and is related to the satellite side - swing state, the solar vector, and whether there is a yaw of 180° attitude maneuver. The calculation formula is:

[0033] Right - hand view:

[0034]

[0035] Left - hand view: [[ID=~42]]

[0036]

[0037] Among them, is the satellite side - swing angle, represents rotation around the X - axis by A<~ sun is the azimuth state quantity of the solar vector. It is defined that when the included angle between the solar vector and the Y orb axis of the orbital coordinate system is no more than 90°, A sun takes 1; when the included angle between the solar vector and the Y orb axis of the orbital coordinate system is greater than 90°, A sun takes the value of - 1.

[0038] Furthermore, the said step S4 includes:

[0039] Step S4.1: Calculate the earth - atmosphere light protection angle λ earth :

[0040]

[0041] Among them, λ0 is the strong - light protection angle of the star sensor, a is the semi - major axis of the satellite orbit, Re is the equatorial radius of the earth, and h is the height of the dense atmosphere;

[0042] Step S4.2: Calculate the included angle between the optical axes of two star sensors, let θ Note: There seems to be a formatting issue with the "~" in the "ID=53" and "ID=42" in the original text. It's maintained as is in the translation but might need to be corrected in the original source for proper understanding.ij is the included angle between the optical axes of star sensor i and star sensor j, and the specific expression is:

[0043]

[0044] Step S4.3: Calculate the penalty factor of the earth's atmosphere light constraint for each star sensor The expression is:

[0045]

[0046] where is the minimum included angle between the optical axis of the star sensor and the geocentric vector;

[0047] Step S4.4: Calculate the penalty factor of the sunlight constraint Kγ for each pair of star sensors ij , Kγ ij The expression is:

[0048]

[0049] Step S4.5: Calculate the penalty factor of the star map fusion constraint Kθ for each pair of star sensors ij , Kθ ij The expression is:

[0050]

[0051] where θ min is the threshold;

[0052] Step S4.6: Calculate the penalty factor of the satellite body stray light constraint Kη for each star sensor i , Kη i The expression is:

[0053]

[0054] where, let η i The calculation method of is as follows:

[0055]

[0056] where is the satellite body Y b axis vector;

[0057] Step S4.7: Calculate the penalty factor k of the solar array stray light constraint for each star sensor iArray , in the satellite body coordinate system, considering the constraint of the strong light protection angle λ0 of the star sensor, the rotation area of the solar array is represented by the set S:

[0058] S: {(α, β)|α bmin-λ0 ≤ α ≤ α bmax +λ0, β bmin -λ0 ≤ β ≤ β bmax +λ0}

[0059] Wherein, α bmin , α bmax , β bmin , β bmax respectively represent the minimum and maximum values of the azimuth and elevation angles of the solar array entity relative to the installation position of the star sensor. When the optical axis of the i-th star sensor points to , the star sensor is not affected by the stray light of the solar array, and thus the k iArray expression is:

[0060]

[0061] Step S4.8: Calculate the performance index J of the three-star sensor layout optimization problem min , J min expression is:

[0062]

[0063] According to an optimized design system for the three-star sensor layout of a low-inclination radar satellite provided by the present invention, it includes:

[0064] Module M1: Calculate the orbital position during the on-orbit life of the satellite;

[0065] Module M2: Calculate the position vector of the sun in the satellite orbit coordinate system;

[0066] Module M3: Calculate the unit vector of the optical axis of each star sensor in the orbit coordinate system;

[0067] Module M4: Construct an optimization model for the three-star sensor layout;

[0068] Module M5: Use the particle swarm optimization algorithm to perform optimization calculations on the three-star sensor layout optimization problem.

[0069] Furthermore, the module M1 includes:

[0070] Module M1.1: Establish an orbital element perturbation model under J2 perturbation;

[0071] Module M1.2: Based on the above perturbation model, perform orbit recurrence according to the ephemeris parameters at a certain moment to obtain the orbital elements during the on-orbit life of the satellite;

[0072] Module M1.3: Calculate the satellite position and satellite velocity in the J2000.0 geocentric equatorial inertial coordinate system according to the above orbital elements.

[0073] Further, the module M2 includes:

[0074] Module M2.1: Calculate the solar position in the geocentric equatorial inertial coordinate system of J2000.0

[0075] M = 2πFrac(0.9931267 + 99.9973583T)

[0076]

[0077] r = 1.49619×10 11 -2.499×10 9 ×cos(M) - 2.1×10 7 ×cos(2M)

[0078]

[0079] where M is the mean anomaly, L is the ecliptic longitude, r is the Earth - Sun distance, R x () represents rotation about the X - axis, T is the relative Julian century number corresponding to the calculation time, and Frac(x) represents the fractional part of the real number x;

[0080] Module M2.2: Calculate the solar position vector in the satellite orbital coordinate system based on the satellite position and satellite velocity in the geocentric equatorial inertial coordinate system of J2000.0.

[0081] Further, the module M3 includes:

[0082] Module M3.1: Calculate the optical axis vectors of each star sensor in the satellite body coordinate system The azimuth angle α in the satellite body coordinate system OX b Y b Z b is represented by, and the azimuth angle α i is defined as the angle between the X - axis and the projection of the star sensor optical axis on the X i Y i plane, and rotation about the Z b axis is positive according to the right - hand rule; the pitch angle β b Y b is defined as the angle between the star sensor optical axis and the X b Y i plane, and the star sensor optical axis on the +Z b Y b side is positive; b The expression is:

[0083]

[0084] ​​​

[0085] Module M3.2: Calculate the optical axis vectors of each star sensor in the orbital coordinate system It is converted according to the 1-2-3 rotation sequence, and is related to the satellite side-sway state, the solar vector, and whether there is a yaw 180° attitude maneuver. The calculation formula is as follows: The calculation formula is:

[0086] Right view:

[0087]

[0088] Left view:

[0089]

[0090] Among them, is the satellite side-sway angle, represents a rotation around the X-axis by A sun is the azimuth state quantity of the solar vector. It is defined that when the included angle between the solar vector and the Y-axis of the orbital coordinate system orb is not greater than 90°, A sun takes 1; when the included angle between the solar vector and the Y-axis of the orbital coordinate system orb is greater than 90°, A sun takes the value of -1.

[0091] Furthermore, the module M4 includes:

[0092] Module M4.1: Calculate the earth-atmosphere light protection angle λ earth :

[0093]

[0094] Among them, λ0 is the strong light protection angle of the star sensor, a is the semi-major axis of the satellite orbit, Re is the equatorial radius of the earth, and h is the height of the dense atmosphere;

[0095] Module M4.2: Calculate the included angle between the optical axes of two star sensors. Let θ ij be the included angle between the optical axes of star sensor i and star sensor j. The specific expression is:

[0096]

[0097] Module M4.3: Calculate the earth-atmosphere light constraint penalty factor of each star sensor The expression is:

[0098]

[0099] Among them, is the minimum angle between the optical axis of the star sensor and the geocentric vector;

[0100] Module M4.4: Calculate the sunlight constraint penalty factor Kγ for each pair of star sensors ij , Kγ ij The expression is:

[0101]

[0102] Module M4.5: Calculate the star map fusion constraint penalty factor Kθ for each pair of star sensors ij , Kθ ij The expression is:

[0103]

[0104] where θ min is the threshold;

[0105] Module M4.6: Calculate the body stray light constraint penalty factor Kη for each star sensor i , Kη i The expression is:

[0106]

[0107] where, let η i The calculation method includes:

[0108]

[0109] where, is the satellite body Y b axis vector;

[0110] Module M4.7: Calculate the solar array stray light constraint penalty factor k for each star sensor iArray , in the satellite body coordinate system, considering the constraint of the strong light protection angle λ0 of the star sensor, the rotation area of the solar array is represented by the set S:

[0111] S: {(α, β)|α bmin -λ0 ≤ α ≤ α bmax +λ0, β bmin -λ0 ≤ β ≤ β bmax +λ0}

[0112] where, α bmin , α bmax , β bmin , β bmax respectively represent the minimum and maximum values of the azimuth angle and pitch angle of the solar array entity relative to the installation position of the star sensor. When the optical axis of the i-th star sensor points to When the star sensor is not affected by the stray light of the solar array, the value of k can be obtained accordingly. iArray The expression is as follows:

[0113]

[0114] Module M4.8: Calculate the performance index J for the layout optimization problem of the three-star sensor. min , J min The expression is as follows:

[0115]

[0116] Compared with the prior art, the present invention has the following beneficial effects:

[0117] Based on the working characteristics of a low-inclination radar satellite, such as left and right side-looking, regular yaw of 180° in attitude, and swing of the solar panels, and by comprehensively considering various constraint conditions of the star sensors on the low-inclination radar satellite, including star map fusion, earth-atmosphere light, sunlight, stray light of the satellite body, and stray light of the solar array, etc., the present invention optimally designs the optical axis pointing angles of each star sensor, providing a solution for the layout optimization of the three-star sensors on the low-inclination orbit radar satellite. This method uses an intelligent algorithm for design, avoiding the inefficient manual design iteration in the traditional star sensor layout process, improving the design efficiency; it can obtain the optimal layout scheme, improving the star sensor attitude measurement accuracy; at the same time, it has universality and can be applied to the layout design of multiple star sensors of other orbit types. BRIEF DESCRIPTION OF THE DRAWINGS

[0118] By reading the detailed description of the non-limiting embodiments with reference to the following drawings, other features, objects, and advantages of the present invention will become more apparent:

[0119] Figure 1 It is a flowchart of the optimal design method for the layout of the three-star sensors on the low-inclination radar satellite of the present invention;

[0120] Figure 2 It is the satellite orbit coordinate system of the present invention;

[0121] Figure 3 It is the representation of the optical axis vector of the star sensor in the satellite body coordinate system of the present invention;

[0122] Figure 4 It is the optimal pointing of the optical axes of the three-star sensors of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0123] The present invention will be described in detail below with reference to specific embodiments. The following examples will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those skilled in the art, several changes and improvements can be made without departing from the scope of the present invention. These all fall within the scope of protection of the present invention.

[0124] An optimization design method for the layout of three sensors in a low-inclination radar satellite, such as Figure 1 Shown, including:

[0125] Step S1: Calculate the orbital position of the satellite during its on-orbit life. The specific steps include steps S1.1 to S1.2.

[0126] Step S1.1: Establish an orbital element perturbation model under J2 perturbation.

[0127] Step S1.2: Based on the above perturbation model, orbit recursion is performed according to the ephemeris parameters at a certain moment to obtain the orbital elements during the satellite's on-orbit life.

[0128] Step S1.3: Calculate the satellite position and satellite velocity in the J2000.0 geocentric equatorial inertial coordinate system based on the above orbital elements.

[0129] Step S2: Calculate the sun's coordinate system OX in the satellite orbit orb Y orb Z orb Position vector under Satellite orbit coordinate system OX orb Y orb Z orb like Figure 2 As shown, it is defined as: the origin O is the satellite center of mass; Z orb The X axis is in the satellite orbit plane and points to the center of the Earth; orb The axis is in the satellite orbit plane, perpendicular to the Z orb Axis, pointing to the direction of satellite flight; Y orb The axis is determined according to the right-hand rule. The specific steps include steps S2.1 to S2.2.

[0130] Step S2.1: Calculate the position of the sun in the J2000.0 geocentric equatorial inertial coordinate system The calculation formula is

[0131] M=2πFrac(0.9931267+99.9973583T)

[0132]

[0133] r=1.49619×10 11 -2.499×109 × cos(M) - 2.1×10 7 × cos(2M)

[0134]

[0135] Where M is the mean anomaly, L is the ecliptic longitude, r is the distance between the Sun and the Earth, T is the relative Julian century number corresponding to the calculation time, and Frac(x) represents the fractional part of the real number x.

[0136] Step S2.2: Calculate the solar position vector in the satellite orbit coordinate system based on the satellite position and velocity in the J2000.0 geocentric equatorial inertial coordinate system

[0137] Step S3: Calculate the unit vectors of the optical axes of each star sensor in the orbit coordinate system The specific steps include steps S3.1 to S3.2.

[0138] Step S3.1: Calculate the optical axis vectors of each star sensor in the satellite body coordinate system The available azimuth angle α in the satellite body coordinate system OX b Y b Z b and the pitch angle β i are represented as shown in i . The azimuth angle α Figure 3 is defined as the angle between the X i axis and the projection of the star sensor optical axis on the X b Y b plane, and the rotation around the Z b axis is positive according to the right-hand rule; the pitch angle β b is defined as the angle between the star sensor optical axis and the X i Y b plane, and the star sensor optical axis on the +Z b side is positive. b The expression is

[0139] Step S3.2: Calculate the optical axis vectors of each star sensor in the orbit coordinate system

[0140]

[0141] It is converted from by the 1-2-3 rotation sequence, and is related to the satellite side-looking state (right-side view or left-side view), the solar vector, and whether there is a 180° yaw attitude maneuver. The calculation formula is:

[0142] Right-side view: ​

[0143]

[0144] Left side view:

[0145]

[0146] in, is the satellite's side tilt angle, Indicates rotation around the X axis A sun is the azimuth state quantity of the sun vector, and defines the sun vector With orbital coordinate system Y orb When the axis angle is not greater than 90°, A sun Take 1; the sun vector and the orbital coordinate system Y orb When the axis angle is greater than 90°, A sun The value is -1.

[0147] Step S4: Construct an optimization model for the three-star sensor layout. By introducing constraints such as atmospheric light, sunlight, stellar reflection, solar array field of view obstruction, and star map fusion requirements through a penalty function, a performance indicator model for the three-star sensor layout optimization problem is constructed. The specific steps include steps S4.1 to S4.8.

[0148] Step S4.1: Calculate the ground-air light protection angle λ earth λ earth The expression is

[0149]

[0150] Among them, λ0 is the strong light protection angle of the star sensor, which is one of the performance parameters of the star sensor; a is the major axis of the satellite orbit; Re is the equatorial radius of the earth; h is the height of the dense atmosphere, which is generally 100 km.

[0151] Step S4.2: Calculate the angle between the optical axes of the two star sensors. Let θ ij is the angle between the optical axes of star sensor i and star sensor j, and the specific expression is

[0152]

[0153] Step S4.3: Calculate the ground-air light constraint penalty factor for each star sensor In order to avoid the influence of the earth's atmospheric light, the minimum angle between the optical axis of the star sensor and the geocentric vector is required. Greater than the ground-air light protection angle λ earth . The expression is

[0154]

[0155] Step S4.4: Calculate the sunlight constraint penalty factor \(K_{\gamma}\) for each pair of star sensors ij . To avoid the influence of sunlight, it is required that sunlight does not enter the fields of view of two star sensors simultaneously. This can meet the requirement that at least two star sensors are available when the satellite is in the left-view or right-view attitude. Generally, it is required that the included angle \(\theta\) between the optical axes of any two star sensors ij is not less than twice the strong-light protection angle. The expression of \(K_{\gamma}\) ij is

[0156]

[0157] Step S4.5: Calculate the star map fusion constraint penalty factor \(K_{\theta}\) for each pair of star sensors ij . Star map fusion requires that the included angle between the optical axes of each pair of star sensors is as close to 90° as possible to improve the attitude measurement accuracy. In the case of limited layout, it is required that the included angle between the optical axes of each pair of star sensors is not less than the threshold \(\theta\) min . The expression of \(K_{\theta}\) ij is

[0158]

[0159] Step S4.6: Calculate the body stray light constraint penalty factor \(K_{\eta}\) for each star sensor i . To avoid the backscattered light of the satellite body from entering the field of view of the star sensor, it is required that the included angle \(\eta\) between the optical axis of the star sensor and the \(Y_b\) axis of the satellite body i is not greater than 90° - \(\lambda_0\). The expression of \(K_{\eta}\) i is

[0160]

[0161] Among them, let \(\eta\) i can be obtained by the following formula

[0162]

[0163] Step S4.7: Calculate the solar array stray light constraint penalty factor \(k\) for each star sensor iArray . After the solar array swings to \(\pm Y_b\) axis, to avoid the stray light interference caused by it to the field of view of the star sensor, it is required that the optical axis of the star sensor avoids pointing to the rotation area of the solar array. In the satellite body coordinate system, considering the constraint of the strong-light protection angle \(\lambda_0\) of the star sensor, the rotation area of the solar array can be represented by the set \(S\):

[0164] \(S: \{(\alpha, \beta)|\alpha\) bmin - \(\lambda_0 \leq \alpha \leq \alpha\) bmax + \(\lambda_0, \beta\) bmin - \(\lambda_0 \leq \beta \leq \beta\) bmax + \(\lambda_0\}\)

[0165] Among them, α bmin , α bmax , β bmin , β bmax respectively represent the minimum and maximum values of the azimuth angle and pitch angle of the solar array entity relative to the installation position of the star sensor. When the optical axis of the i-th star sensor points to , the star sensor is not affected by the stray light of the solar array. Thus, the k iArray expression is

[0166]

[0167] Step S4.8: Calculate the performance index J of the three-star sensor layout optimization problem min . In order to improve the attitude measurement accuracy, it is required that the included angle between the optical axes of any two star sensors should be as close to 90° as possible. On this basis, the above penalty factor is introduced, and the J min expression is as follows

[0168]

[0169] Step S5: Use the particle swarm optimization algorithm to optimize the three-star sensor layout optimization problem and obtain the minimum value of the performance index. The corresponding and are the optimal optical axis pointing directions of the three star sensors, as Figure 4 shown.

[0170] For the three-star sensor layout problem of low-inclination orbit satellites, the present invention combines the usage requirements of star sensors for radar satellites under left and right side views, takes improving the attitude measurement accuracy of multiple star sensors as the optimization goal, adopts the penalty function method to introduce design constraints such as star map fusion, earth atmosphere light, sunlight, body stray light, and solar array stray light, and uses the particle swarm algorithm to obtain the optimal installation pointing angles of the three-star sensors. The present invention provides a relatively general multi-star sensor layout optimization design scheme for low-inclination orbit satellites, which can obtain the optimal installation angles of multiple star sensors simultaneously while meeting various engineering constraints.

[0171] The present invention also provides an optimized design system for the three-star sensor layout of a low-inclination radar satellite. The optimized design system for the three-star sensor layout of the low-inclination radar satellite can be realized by executing the process steps of the optimized design method for the three-star sensor layout of the low-inclination radar satellite. That is, those skilled in the art can understand the optimized design method for the three-star sensor layout of the low-inclination radar satellite as the preferred implementation manner of the optimized design system for the three-star sensor layout of the low-inclination radar satellite. The system includes:

[0172] Module M1: Calculate the orbital position of the satellite during its on-orbit life.

[0173] Module M2: Calculate the position vector of the sun in the satellite orbit coordinate system.

[0174] Module M3: Calculate the unit vectors of the optical axes of each star sensor in the orbit coordinate system.

[0175] Module M4: Construct an optimization model for the layout of three star sensors.

[0176] Module M5: Use the particle swarm optimization algorithm to perform optimization calculations on the layout optimization problem of three star sensors.

[0177] 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 kind of 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 either software modules for implementing the method or structures within the hardware component.

[0178] 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 embodiments, and 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 arbitrarily with each other.

Claims

1. An optimized design method for the layout of three-star sensors of a low-inclination radar satellite, characterized in that, Including: Step S1: Calculate the orbital position during the on-orbit lifetime of the satellite; Step S2: Calculate the position vector of the sun in the satellite orbit coordinate system; Step S3: Calculate the unit vectors of the optical axes of each star sensor in the orbit coordinate system; Step S4: Construct an optimization model for the layout of three star sensors; Step S5: Use the particle swarm optimization algorithm to perform optimization calculations on the layout optimization problem of three star sensors.

2. The optimized design method for the three-star sensor layout of a low-inclination radar satellite according to claim 1, wherein The said Step S1 includes: Step S1.1: Establish an orbital element perturbation model under J2 perturbation; Step S1.2: Based on the above perturbation model, perform orbital recursion according to the ephemeris parameters at a certain moment to obtain the orbital elements during the on-orbit lifetime of the satellite; Step S1.3: According to the above orbital elements, calculate the satellite position and satellite velocity in the J2000.0 geocentric equatorial inertial coordinate system.

3. The optimized design method for the three-star sensor layout of a low-inclination radar satellite according to claim 1, characterized in that The said Step S2 includes: Step S2.1: Calculate the solar position in the geocentric equatorial inertial coordinate system of J2000.0 M = 2πFrac(0.9931267 + 99.9973583T) r = 1.49619×10 11 -2.499×10 9 ×cos(M) - 2.1×10 7 ×cos(2M) where M is the mean anomaly, L is the ecliptic longitude, r is the Earth-Sun distance, and R x () indicates rotation about the X-axis, T is the relative Julian century number corresponding to the calculation time, and Frac(x) represents the fractional part of the real number x; Step S2.2: According to the satellite position and satellite velocity in the J2000.0 geocentric equatorial inertial coordinate system, calculate the sun position vector in the satellite orbit coordinate system.

4. The optimized design method for the three-star sensor layout of a low-inclination radar satellite according to claim 1, characterized in that, The said Step S3 includes: Step S3.1: Calculate the optical axis vectors of each star sensor in the satellite body coordinate system Use the azimuth angle α b Y b Z b in the satellite body coordinate system OX i , pitch angle β i to represent. The azimuth angle α i is defined as the angle between the X b axis and the projection of the star sensor optical axis on the X b Y b plane, and the rotation around the Z b axis is positive according to the right-hand rule; the pitch angle β i is defined as the angle between the star sensor optical axis and the X b Y b plane, and the star sensor optical axis on the +Z b side is positive; The expression is: Step S3.2: Calculate the optical axis vectors of each star sensor in the orbital coordinate system It is Converted according to the 1-2-3 rotation sequence, and Related to the satellite's side-sway state, the solar vector, and whether it performs a 180° yaw attitude maneuver, The calculation formula is as follows: Right view: Left view: Among them, is the satellite side-sway angle, indicating rotation around the X-axis A sun is the azimuth state quantity of the solar vector. Define the solar vector and the angle between the Y-axis of the orbital coordinate system orb is not greater than 90°. When A sun takes 1; when the angle between the solar vector and the Y-axis of the orbital coordinate system orb is greater than 90°, A sun takes the value of -1.

5. The optimized design method for the three-star sensor layout of a low-inclination radar satellite according to claim 1, characterized in that, The said Step S4 includes: Step S4.1: Calculate the ground-light protection angle λ earth : Where λ0 is the strong light protection angle of the star sensor, a is the semi-major axis of the satellite orbit, Re is the equatorial radius of the earth, and h is the height of the dense atmosphere; Step S4.2: Calculate the included angle between the optical axes of every two star sensors, and let θ ij be the included angle between the optical axes of star sensor i and star sensor j. The specific expression is as follows: Step S4.3: Calculate the earth atmosphere light constraint penalty factors for each star sensor The expression is as follows: Among them, is the minimum angle between the optical axis of the star sensor and the geocentric vector; Step S4.4: Calculate the sunlight constraint penalty factor \(K_{\gamma}\) for each pair of star sensors ij , \(K_{\gamma}\) ij The expression is as follows: Step S4.5: Calculate the star map fusion constraint penalty factor \(K_{\theta}\) for pairwise star sensors ij , \(K_{\theta}\) ij The expression is as follows: where θ min is a threshold value; Step S4.6: Calculate the star sensor's stray light constraint penalty factor \(K_{\eta}\). i , \(K_{\eta}\) i The expression is as follows: Among them, let η i be calculated as follows: Among them, is the satellite body Y b axial vector; Step S4.7: Calculate the stray light constraint penalty factor k of each star sensor iArray , in the satellite body coordinate system, considering the constraint of the strong light protection angle λ0 of the star sensor, the rotation area of the solar array is represented by the set S: S: {(a, β)|α bmin -λ0 ≤ α ≤ α bmax +λ0, β bmin -λ0 ≤ β ≤ β bmax +λ0} Among them, α bmin , α bmax , β bmin , β bmax respectively represent the minimum and maximum values of the azimuth angle and the pitch angle of the solar array entity relative to the installation position of the star sensor. When the optical axis of the i-th star sensor points to , the star sensor is not affected by the stray light of the solar array, and thus the k iArray expression is as follows: Step S4.8: Calculate the performance index J of the layout optimization problem of the three-star sensor min , J min The expression is as follows:

6. An optimized design system for the layout of three-star sensors of a low-inclination radar satellite, characterized in that, Including: Module M1: Calculate the orbital position during the on-orbit lifetime of the satellite; Module M2: Calculate the position vector of the sun in the satellite orbit coordinate system; Module M3: Calculate the unit vectors of the optical axes of each star sensor in the orbit coordinate system; Module M4: Construct an optimization model for the layout of three star sensors; Module M5: Use the particle swarm optimization algorithm to perform optimization calculations on the layout optimization problem of three star sensors.

7. The optimized design system for the three-star sensor layout of a low-inclination radar satellite according to claim 6, wherein The said Module M1 includes: Module M1.1: Establish an orbital element perturbation model under J2 perturbation; Module M1.2: Based on the above perturbation model, perform orbital recursion according to the ephemeris parameters at a certain moment to obtain the orbital elements during the on-orbit lifetime of the satellite; Module M1.3: According to the above orbital elements, calculate the satellite position and satellite velocity in the J2000.0 geocentric equatorial inertial coordinate system.

8. The optimized design system for the three-star sensor layout of a low-inclination radar satellite according to claim 6, wherein The said Module M2 includes: Module M2.1: Calculate the solar position in the geocentric equatorial inertial coordinate system of J2000.0 M = 2πFrac(0.9931267 + 99.9973583T) r = 1.49619×10 11 -2.499×10 9 ×cos(M) - 2.1×10 7 ×cos(2M) where M is the mean anomaly, L is the ecliptic longitude, r is the Earth-Sun distance, R x () indicates rotation about the X-axis, T is the relative Julian century number corresponding to the calculation time, and Frac(x) represents the fractional part of the real number x; Module M2.2: According to the satellite position and satellite velocity in the J2000.0 geocentric equatorial inertial coordinate system, calculate the sun position vector in the satellite orbit coordinate system.

9. The optimized design system for the three-star sensor layout of a low-inclination radar satellite according to claim 6, characterized in that, The said Module M3 includes: Module M3.1: Calculate the optical axis vectors of each star sensor in the satellite body coordinate system Use the azimuth angle α b Y b Z b in the satellite body coordinate system OX i , pitch angle β i to represent. The azimuth angle α i is defined as the angle between the X b axis and the projection of the star sensor optical axis on the X b Y b plane, and the rotation around the Z b axis is positive according to the right-hand rule; the pitch angle β i is defined as the angle between the star sensor optical axis and the X b Y b plane, and the star sensor optical axis on the +Z b side is positive; The expression is: Module M3.2: Calculate the optical axis vectors of each star sensor in the orbital coordinate system It is converted from According to the 1-2-3 rotation sequence, and It is related to the satellite's side-sway state, the solar vector, and whether there is a 180° yaw attitude maneuver, The calculation formula is as follows: Right view: Left view: Among them, is the satellite side-sway angle, indicating rotation around the X-axis A sun is the azimuth state quantity of the solar vector. It is defined that when the included angle between the solar vector and the Y-axis of the orbital coordinate system orb is not greater than 90°, A sun takes 1; when the included angle between the solar vector and the Y-axis of the orbital coordinate system orb is greater than 90°, A sun takes the value of -1.

10. The optimized design system for the three-star sensor layout of a low-inclination radar satellite according to claim 6, characterized in that, The said Module M4 includes: Module M4.1: Calculate the ground-air light protection angle λ earth : Where λ0 is the strong light protection angle of the star sensor, a is the semi-major axis of the satellite orbit, Re is the equatorial radius of the earth, and h is the height of the dense atmosphere; Module M4.2: Calculate the included angle between the optical axes of two star sensors, and let θ ij be the included angle between the optical axes of star sensor i and star sensor j. The specific expression is as follows: Module M4.3: Calculate the penalty factor of the earth atmosphere light constraint for each star sensor The expression is as follows: Among them, is the minimum angle between the optical axis of the star sensor and the geocentric vector; Module M4.4: Calculate the sunlight constraint penalty factor Kγ for pairwise star sensors ij , Kγ ij The expression is: Module M4.5: Calculate the star map fusion constraint penalty factor Kθ for pairwise star sensors ij , Kθ ij The expression is: where θ min is a threshold value; Module M4.6: Calculate the penalty factor Kη of the star sensor's stray light constraint for each star sensor i , Kη i The expression is: Among them, let η i be calculated as follows: Among them, is the satellite body Y b axial vector; Module M4.7: Calculate the stray light constraint penalty factor k of each star sensor's solar array iArray , in the satellite body coordinate system, considering the constraint of the strong light protection angle λ0 of the star sensor, the rotation area of the solar array is represented by the set S: S: {(α, β) | α bmin -λ0 ≤ α ≤ α bmax +λ0, β bmin -λ0 ≤ β ≤ β bmax +λ0} Among them, α bmin , α bmax , β bmin , β bmax respectively represent the minimum and maximum values of the azimuth angle and pitch angle of the solar array entity relative to the installation position of the star sensor. When the optical axis of the i-th star sensor points to , the star sensor is not affected by the stray light of the solar array, and thus the k iArray expression is: Module M4.8: Calculate the performance metric J for the layout optimization problem of the Samsung sensor min , J min The expression is:

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