Optical system design method for interferometric star sensor based on attitude measurement accuracy modeling and multi-constraint collaborative optimization

Abstract

The method for designing an optical system of an interferometric star sensor based on attitude measurement accuracy modeling and multi-constraint collaborative optimization belongs to the technical field of spacecraft autonomous attitude measurement. In order to solve the problem of collaborative design of high precision and miniaturization of the interferometric star sensor, the method comprises the following steps: building an optical system of the interferometric star sensor; establishing an attitude measurement accuracy model of the optical system of the interferometric star sensor; establishing a multi-constraint parameter optimization model of the optical system of the interferometric star sensor; and then performing parameter optimization and solving on the multi-constraint parameter optimization model of the optical system of the interferometric star sensor to complete the design of the optical system of the interferometric star sensor based on the attitude measurement accuracy modeling and the multi-constraint collaborative optimization. The method improves the engineering realizability and design consistency of the interferometric star sensor in the application scenario of high precision and miniaturization.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft autonomous attitude measurement technology, specifically involving a design method for an interferometric star sensor optical system based on attitude measurement accuracy modeling and multi-constraint collaborative optimization. Background Technology

[0002] Star sensors are high-precision measurement devices that calculate a carrier's attitude in inertial space by acquiring and processing images of the starry sky. They are characterized by strong autonomy and no error accumulation, and have been widely used in various spacecraft. With the increasing sophistication of missions, higher demands are being placed on the attitude measurement accuracy of star sensors. However, the accuracy improvement of traditional star sensors based on geometric imaging and spot centroid positioning is limited by both physical principles and engineering constraints. On the one hand, geometric imaging star sensors typically rely on spot centroid positioning algorithms for angle calculation, and their measurement accuracy is easily affected by factors such as detection noise, optical diffraction, and aberrations, making further improvement difficult. On the other hand, increasing the system's focal length or aperture to improve angular resolution directly leads to an increase in device size, weight, and power consumption, making it difficult to meet the miniaturization and lightweight development requirements of modern spacecraft. Therefore, exploring new angle measurement technologies that do not rely on traditional geometric resolution improvement paths has become an important direction for improving attitude measurement accuracy.

[0003] Computational interferometry offers a solution to the aforementioned problems. This technique maps the incident angle information of stellar light to the energy distribution between image points by introducing a phase modulation structure into the optical path, and then calculates the angle based on this distribution information. Because this method utilizes the high sensitivity of light wave phase information to angle changes, it can achieve higher starlight measurement accuracy at a smaller system scale. Although the concept of interferometric star sensors was proposed as early as the 1970s, and some engineering products have verified the feasibility of this technical approach, the design theory and methods of its core optical system are still incomplete. Existing research focuses mainly on the interferometric angle measurement principle or local structural forms, with relatively limited research on the system-level forward design of the front-end optical system of interferometric star sensors. Due to the lack of unified design guidance for wave optics, existing design schemes remain relatively scattered in terms of parameter selection and system configuration, making it difficult to form a universally applicable design method.

[0004] At the engineering application level, the system performance of interferometric star sensors is influenced by a variety of factors, including light source characteristics, detection noise, and the coupling relationships between optical system parameters. Some existing technical solutions fail to systematically consider these factors during physical modeling and system design, relying heavily on experience or local adjustments for parameter configuration. A system-level design framework that simultaneously considers measurement accuracy, system structural dimensions, and engineering feasibility has not yet been established. Therefore, developing a method for the forward design and optimization of interferometric star sensor system parameters, tailored to specific application needs, remains a key issue hindering the engineering application and performance enhancement of this technology. Summary of the Invention

[0005] The problem this invention aims to solve is that existing interferometric star sensor designs lack system-level accuracy prediction models, rely on experience for parameter selection, and are difficult to achieve high-precision and miniaturized collaborative design under multiple physical and engineering constraints. The invention proposes an interferometric star sensor optical system design method based on attitude measurement accuracy modeling and multi-constraint collaborative optimization.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] An interferometric star sensor optical system design method based on attitude measurement accuracy modeling and multi-constraint collaborative optimization includes the following steps:

[0008] S1. Construct an interferometric star sensor optical system;

[0009] S2. For the interferometric star sensor optical system obtained in step S1, establish an attitude measurement accuracy model for the interferometric star sensor optical system;

[0010] S3. Based on the attitude measurement accuracy model of the interferometric star sensor obtained in step S2, establish a multi-constraint parameter optimization model of the interferometric star sensor optical system. Then, perform parameter optimization on the multi-constraint parameter optimization model of the interferometric star sensor optical system to complete the design of the interferometric star sensor optical system based on attitude measurement accuracy modeling and multi-constraint co-optimization.

[0011] Furthermore, the interferometric star sensor optical system constructed in step S1 includes an interferometric component, a beam splitter, a focusing component, and a detector arranged sequentially along the optical axis. The interferometric component consists of two spatially separated phase gratings, with the grating lines of the two gratings arranged symmetrically and tilted relative to the reference axis. The beam splitter is used to spatially divide the interference fringes. The focusing component is used to focus the divided interference beam onto the detector image plane to form four zero-order image points.

[0012] Furthermore, the specific implementation method of step S2 includes the following steps:

[0013] S2.1. Based on the structural form and engineering design requirements of the interferometric star sensor optical system, determine the system's structural parameters and operating parameters;

[0014] S2.2. Based on the principle of interferometric angle measurement, establish a mapping model between the incident angle of a star and the interference phase;

[0015] S2.3. Establish a model for calculating the expected number of electrons at interference image points;

[0016] S2.4. Construct a noise statistical model for the interference image points;

[0017] S2.5. Based on the expected electron number calculation model of the interference image points obtained in step S2.3 and the noise statistical model of the interference image points obtained in step S2.4, the extraction error of the interference phase is modeled.

[0018] S2.6. The attitude measurement accuracy is calculated using the classical attitude accuracy model, and the attitude measurement accuracy model of the interferometric star sensor optical system is obtained.

[0019] Furthermore, the system parameters determined in step S2.1 include the grating period p, the distance between the two gratings z, the relative angle ε between the gratings, the unit size a×b of the beam splitting component, the focal length f of the focusing component, and the detector pixel size s. pix Quantum efficiency of detectors System transmittance and points time .

[0020] Furthermore, in step S2.3, for the multipath interference image points formed by spatial phase shift, the expected number of electrons at the k-th interference image point is expressed as:

[0021]

[0022] Where A represents the DC component and B represents the modulation amplitude. This is the interference phase.

[0023] Furthermore, the expression for the noise statistical model of the interferometric image points constructed in step S2.4 is as follows:

[0024]

[0025] in, This represents the variance of photon shot noise. This represents the variance of dark current noise. Indicates the variance of readout noise. Digital quantization noise variance.

[0026] Furthermore, the specific implementation method of step S2.5 includes the following steps:

[0027] S2.5.1. Phase extraction is performed using the spatial phase-shifting method. The expression for the phase estimation function is as follows:

[0028]

[0029] in, , , , These are the estimated values ​​of the number of electrons at the first pixel, the second pixel, the third pixel, and the fourth pixel, respectively.

[0030] S2.5.2. According to the law of error propagation, the incident angle estimation error can be approximated as follows:

[0031] .

[0032] Furthermore, step S2.6 yields the attitude measurement accuracy model of the interferometric star sensor optical system as follows:

[0033]

[0034] Where E represents the attitude measurement accuracy of the interferometric star sensor optical system. This represents the number of stars within the field of view that participate in the attitude calculation.

[0035] Furthermore, the specific implementation method of step S3 includes the following steps:

[0036] S3.1. Determine the optimization objective function and design variables of the interferometric star sensor based on the task requirements;

[0037] S3.2. Establish the attitude measurement accuracy constraint condition that the attitude measurement accuracy obtained in step S2 is less than or equal to the attitude accuracy index required by the task;

[0038] S3.3. Construct physical and engineering constraints, including constraints on the design difficulty of the focusing component, the number of stars in the field of view, and the phase de-ambiguity constraint;

[0039] S3.4. Combining steps S3.1, S3.2, and S3.3, we obtain the multi-constraint parameter optimization model;

[0040] S3.5. For the multi-constraint parameter optimization model obtained in step S3.4, use a global search algorithm or a multi-starting point local optimization algorithm to perform parameter optimization and select feasible solutions;

[0041] S3.6. The parameter optimization solution obtained in step S3.5 is input into the attitude measurement accuracy model of the interferometric star sensor optical system in step S2 for verification and performance evaluation.

[0042] The beneficial effects of this invention are:

[0043] This invention presents a design method for an interferometric star sensor optical system based on attitude measurement accuracy modeling and multi-constraint collaborative optimization. By establishing a quantitative correlation between phase extraction error and attitude measurement accuracy during interferometric angle measurement, it achieves predictable and parameterized characterization of attitude measurement performance. Furthermore, it introduces a system parameter collaborative optimization mechanism under multiple constraints, enabling unified design and global optimization of key structural parameters while meeting measurement accuracy and engineering implementation requirements. Compared to existing design methods that rely on experience or local adjustments, this invention effectively reduces system design uncertainty, improves the engineering feasibility and design consistency of interferometric star sensors in high-precision, miniaturized applications, and provides a universal system-level design method for interferometric star sensors with different structural forms. Attached Figure Description

[0044] Figure 1 This is a flowchart illustrating the design method of an interferometric star sensor optical system based on attitude measurement accuracy modeling and multi-constraint collaborative optimization as described in this invention.

[0045] Figure 2 This is a schematic diagram of the structure of the interferometric star sensor optical system described in this invention. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention; that is, the described specific embodiments are merely a part of the embodiments of the invention, and not all of them. The components of the specific embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations, and the invention may also have other embodiments.

[0047] Therefore, the following detailed description of specific embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected specific embodiments of the invention. All other specific embodiments obtained by those skilled in the art based on these specific embodiments without inventive effort are within the scope of protection of this invention.

[0048] To further understand the invention's content, features, and effects, the following specific embodiments are provided, along with accompanying drawings. Figure 1 and attached Figure 2 Detailed explanation is as follows:

[0049] Example 1:

[0050] An interferometric star sensor optical system design method based on attitude measurement accuracy modeling and multi-constraint collaborative optimization includes the following steps:

[0051] S1. Construct an interferometric star sensor optical system;

[0052] Furthermore, the interferometric star sensor optical system constructed in step S1 includes an interferometric component, a beam splitter, a focusing component, and a detector arranged sequentially along the optical axis. The interferometric component consists of two spatially separated phase gratings, with the grating lines of the two gratings arranged symmetrically and tilted relative to the reference axis. The beam splitter is used to spatially divide the interference fringes. The focusing component is used to focus the divided interference beam onto the detector image plane to form four zero-order image points.

[0053] S2. For the interferometric star sensor optical system obtained in step S1, establish an attitude measurement accuracy model for the interferometric star sensor optical system;

[0054] Furthermore, the specific implementation method of step S2 includes the following steps:

[0055] S2.1. Based on the structural form and engineering design requirements of the interferometric star sensor optical system, determine the system's structural parameters and operating parameters;

[0056] Furthermore, the system parameters determined in step S2.1 include the grating period p, the distance between the two gratings z, the relative angle ε between the gratings, the unit size a×b of the beam splitting component, the focal length f of the focusing component, and the detector pixel size s. pix Quantum efficiency of detectors System transmittance and points time .

[0057] S2.2. Based on the principle of interferometric angle measurement, establish a mapping model between the incident angle of a star and the interference phase;

[0058] Furthermore, assuming that stellar light can be approximated as parallel light at the entrance pupil, changes in the stellar incident angle will cause a phase difference change in the diffracted light from the two gratings during propagation between the gratings. Based on the principle of interferometric imaging, an analytical mapping model between the stellar incident angle and the interference phase is constructed to convert the subsequently extracted interference phase into stellar incident angle information. The expression is:

[0059]

[0060] in, For interference phase, , , , These represent the expected number of electrons at the four image points. Let be the angle of incidence. Based on this, an analytical mapping model between the stellar angle of incidence and the interference phase is established, providing a foundation for subsequent angle inversion.

[0061] S2.3. Establish a model for calculating the expected number of electrons at interference image points;

[0062] Furthermore, in step S2.3, for the multipath interference image points formed by spatial phase shift, the expected number of electrons at the k-th interference image point is expressed as:

[0063]

[0064] Where A represents the DC component and B represents the modulation amplitude. This is the interference phase.

[0065] Furthermore, let the incident light intensity at the k-th interference point be... Then the corresponding expected number of electrons Represented as:

[0066]

[0067] Where h is Planck's constant, c is the speed of light, and λ is the wavelength.

[0068] S2.4. Construct a noise statistical model for the interference image points;

[0069] Furthermore, the expression for the noise statistical model of the interferometric image points constructed in step S2.4 is as follows:

[0070]

[0071] Furthermore, the variance of photon shot noise following a Poisson distribution is:

[0072] ;

[0073] When the image point distribution occupies 1 pixel, dark current magnitude is At that time, the variance of the dark current noise is:

[0074] ;

[0075] Readout noise can be modeled as a zero-mean Gaussian distribution, the variance of which is given by the detector parameters. Quantization noise follows a uniform distribution, the variance of which can be determined by the detector gain.

[0076] This yields the uncertainty in the number of electrons at the interference image point, which is used for subsequent error propagation analysis.

[0077] S2.5. Based on the expected electron number calculation model of the interference image points obtained in step S2.3 and the noise statistical model of the interference image points obtained in step S2.4, the extraction error of the interference phase is modeled.

[0078] Furthermore, the specific implementation method of step S2.5 includes the following steps:

[0079] S2.5.1. Phase extraction is performed using the spatial phase-shifting method. The expression for the phase estimation function is as follows:

[0080]

[0081] in, , , , These are the estimated values ​​of the number of electrons at the first pixel, the second pixel, the third pixel, and the fourth pixel, respectively.

[0082] S2.5.2. According to the law of error propagation, the incident angle estimation error can be approximated as follows:

[0083] ;

[0084] S2.6. The attitude measurement accuracy is calculated using the classical attitude accuracy model, and the attitude measurement accuracy model of the interferometric star sensor optical system is obtained.

[0085] Furthermore, step S2.6 yields the attitude measurement accuracy model of the interferometric star sensor optical system as follows:

[0086]

[0087] Where E represents the attitude measurement accuracy of the interferometric star sensor optical system. This represents the number of stars within the field of view involved in attitude calculation. This completes the end-to-end modeling from the interferometric signal to the system attitude measurement accuracy.

[0088] S3. Based on the attitude measurement accuracy model of the interferometric star sensor obtained in step S2, establish a multi-constraint parameter optimization model of the interferometric star sensor optical system. Then, perform parameter optimization on the multi-constraint parameter optimization model of the interferometric star sensor optical system to complete the design of the interferometric star sensor optical system based on attitude measurement accuracy modeling and multi-constraint co-optimization.

[0089] Furthermore, the specific implementation method of step S3 includes the following steps:

[0090] S3.1. Determine the optimization objective function and design variables of the interferometric star sensor based on the task requirements;

[0091] Furthermore, the optimization objective can be set as at least one of minimizing the system volume or minimizing the accuracy. Using the system volume V as the optimization objective function, we obtain:

[0092] ;

[0093] The above parameters are used as design variables, and their range of values ​​is determined by engineering constraints and manufacturing conditions.

[0094] S3.2. Establish the attitude measurement accuracy constraint condition that the attitude measurement accuracy obtained in step S2 is less than or equal to the attitude accuracy index required by the task;

[0095] S3.3. Construct physical and engineering constraints, including constraints on the design difficulty of the focusing component, the number of stars in the field of view, and the phase de-ambiguity constraint;

[0096] Furthermore, the design difficulty constraints of the focused components are as follows:

[0097] To quantitatively assess the design difficulty of an optical system, the empirical parameter C proposed by DS Volosov is used as an evaluation index. The larger the value, the higher the design difficulty of the optical system, and it should meet the following requirements:

[0098]

[0099] in The upper limit of the design difficulty for the optical system required by the mission.

[0100] The star count constraint for the field of view is as follows:

[0101] Ensuring a sufficient number of navigation stars within the field of view is a prerequisite for achieving star map recognition and high-precision attitude calculation. Taking typical algorithms as an example, triangle-matching-based recognition algorithms require at least three stars to be detected simultaneously within the field of view; while the more robust Pyramid star map recognition algorithm typically requires at least four stars. To transform this discrete star counting requirement into a continuous parameter constraint, an empirical formula for stellar density based on the SKY2000 visible light star catalog is introduced. Given a limiting detection magnitude, the expected number of detectable stars within the field of view is expressed as:

[0102]

[0103] in, This refers to the field of view of the optical system.

[0104] Considering the randomness and non-uniformity of stellar distribution in the celestial sphere, simply constraining the average value is insufficient to guarantee the system's on-orbit availability. Based on the Poisson process assumption of stellar distribution, the cumulative probability of detecting at least N stars within the field of view should satisfy:

[0105]

[0106] in, The probability that the number of observable stars within the field of view meets the requirements for star map recognition;

[0107] The phase defuzzification constraints are as follows:

[0108] Due to the periodicity of the interference fringes, the phase values ​​directly calculated by the four-step phase-shifting algorithm are distributed in... The phase principal value is required, therefore the equivalent position error introduced by the traditional geometric centroid algorithm must be strictly controlled within half an interference fringe period. This is equivalent in the phase domain to requiring the absolute value of the phase error to be less than [a certain value]. The mathematical inequality corresponding to this constraint is:

[0109]

[0110] in, This represents the maximum positioning error bound of the traditional geometric centroid positioning algorithm, which uses pixels as the unit.

[0111] The above constraints collectively define the feasible domain of the design variables.

[0112] S3.4. Combining steps S3.1, S3.2, and S3.3, we obtain the multi-constraint parameter optimization model;

[0113] Furthermore, the optimization problem can be uniformly represented as:

[0114]

[0115] in, This indicates the required attitude measurement accuracy of the system.

[0116] This model achieves a unified description of system structural parameters, system design difficulty, and attitude measurement accuracy;

[0117] S3.5. For the multi-constraint parameter optimization model obtained in step S3.4, use a global search algorithm or a multi-starting point local optimization algorithm to perform parameter optimization and select feasible solutions;

[0118] Furthermore, firstly, a set of feasible solutions that satisfy the constraints is obtained through parameter space sampling or random search; then, using the feasible solutions as initial points, gradient-type or sequential quadratic programming algorithms are used to locally optimize the objective function.

[0119] S3.6. The parameter optimization solution obtained in step S3.5 is input into the attitude measurement accuracy model of the interferometric star sensor optical system in step S2 for verification and performance evaluation.

[0120] Furthermore, the effectiveness and stability of the parameter optimization method are evaluated by comparing the system volume, attitude measurement accuracy, and interference sensitivity before and after optimization.

[0121] It should be noted that relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0122] Although this application has been described above with reference to specific embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of this application. In particular, as long as there is no structural conflict, the features in the specific embodiments disclosed in this application can be combined with each other in any way. The lack of an exhaustive description of these combinations in this specification is merely for the sake of brevity and resource conservation. Therefore, this application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A design method for an interferometric star sensor optical system based on attitude measurement accuracy modeling and multi-constraint collaborative optimization, characterized in that, Includes the following steps: S1. Construct an interferometric star sensor optical system; S2. For the interferometric star sensor optical system obtained in step S1, establish an attitude measurement accuracy model for the interferometric star sensor optical system; S3. Based on the attitude measurement accuracy model of the interferometric star sensor obtained in step S2, establish a multi-constraint parameter optimization model of the interferometric star sensor optical system. Then, perform parameter optimization on the multi-constraint parameter optimization model of the interferometric star sensor optical system to complete the design of the interferometric star sensor optical system based on attitude measurement accuracy modeling and multi-constraint co-optimization.

2. The design method for an interferometric star sensor optical system based on attitude measurement accuracy modeling and multi-constraint collaborative optimization as described in claim 1, characterized in that, The interferometric star sensor optical system constructed in step S1 includes an interferometric component, a beam splitter, a focusing component, and a detector arranged sequentially along the optical axis. The interferometric component consists of two spatially separated phase gratings, with the grating lines of the two gratings arranged symmetrically and tilted relative to the reference axis. The beam splitter is used to spatially divide the interference fringes. The focusing component is used to focus the divided interference beam onto the detector image plane to form four zero-order image points.

3. The design method for an interferometric star sensor optical system based on attitude measurement accuracy modeling and multi-constraint collaborative optimization according to claim 1 or 2, characterized in that, The specific implementation method of step S2 includes the following steps: S2.

1. Based on the structural form and engineering design requirements of the interferometric star sensor optical system, determine the system's structural parameters and operating parameters; S2.

2. Based on the principle of interferometric angle measurement, establish a mapping model between the incident angle of a star and the interference phase; S2.

3. Establish a model for calculating the expected number of electrons at interference image points; S2.

4. Construct a noise statistical model for the interference image points; S2.

5. Based on the expected electron number calculation model of the interference image points obtained in step S2.3 and the noise statistical model of the interference image points obtained in step S2.4, the extraction error of the interference phase is modeled. S2.

6. The attitude measurement accuracy is calculated using the classical attitude accuracy model, and the attitude measurement accuracy model of the interferometric star sensor optical system is obtained.

4. The design method for an interferometric star sensor optical system based on attitude measurement accuracy modeling and multi-constraint collaborative optimization as described in claim 3, characterized in that, The system parameters determined in step S2.1 include the grating period p, the distance between the two gratings z, the relative angle ε between the gratings, the unit size of the beam splitting component a×b, the focal length of the focusing component f, and the detector pixel size s. pix Quantum efficiency of detectors System transmittance and points time .

5. The design method for an interferometric star sensor optical system based on attitude measurement accuracy modeling and multi-constraint collaborative optimization according to claim 4, characterized in that, In step S2.3, for the multipath interference image points formed by spatial phase shift, the expected number of electrons at the k-th interference image point is expressed as: Where A represents the DC component and B represents the modulation amplitude. This is the interference phase.

6. The design method for an interferometric star sensor optical system based on attitude measurement accuracy modeling and multi-constraint collaborative optimization according to claim 5, characterized in that, The expression for the noise statistical model of the interferometric image points constructed in step S2.4 is: in, This represents the variance of photon shot noise. This represents the variance of dark current noise. Indicates the variance of readout noise. Digital quantization noise variance.

7. The design method for an interferometric star sensor optical system based on attitude measurement accuracy modeling and multi-constraint collaborative optimization according to claim 6, characterized in that, The specific implementation method of step S2.5 includes the following steps: S2.5.

1. Phase extraction is performed using the spatial phase-shifting method. The expression for the phase estimation function is as follows: in, , , , These are the estimated values ​​of the number of electrons at the first pixel, the second pixel, the third pixel, and the fourth pixel, respectively. S2.5.

2. According to the law of error propagation, the incident angle estimation error can be approximated as follows: 。 8. The design method for an interferometric star sensor optical system based on attitude measurement accuracy modeling and multi-constraint collaborative optimization according to claim 7, characterized in that, Step S2.6 yields the attitude measurement accuracy model of the interferometric star sensor optical system as follows: Where E represents the attitude measurement accuracy of the interferometric star sensor optical system. This represents the number of stars within the field of view that participate in the attitude calculation.

9. The design method for an interferometric star sensor optical system based on attitude measurement accuracy modeling and multi-constraint collaborative optimization according to claim 8, characterized in that, The specific implementation method of step S3 includes the following steps: S3.

1. Determine the optimization objective function and design variables of the interferometric star sensor based on the task requirements; S3.

2. Establish the attitude measurement accuracy constraint condition that the attitude measurement accuracy obtained in step S2 is less than or equal to the attitude accuracy index required by the task; S3.

3. Construct physical and engineering constraints, including constraints on the design difficulty of the focusing component, the number of stars in the field of view, and the phase de-ambiguity constraint; S3.

4. Combining steps S3.1, S3.2, and S3.3, we obtain the multi-constraint parameter optimization model; S3.

5. For the multi-constraint parameter optimization model obtained in step S3.4, use a global search algorithm or a multi-starting point local optimization algorithm to perform parameter optimization and select feasible solutions; S3.

6. The parameter optimization solution obtained in step S3.5 is input into the attitude measurement accuracy model of the interferometric star sensor optical system in step S2 for verification and performance evaluation.

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