On-orbit calibration and attitude calculation method of star sensor based on improved particle swarm optimization algorithm

Abstract

A method for on-orbit calibration and attitude calculation of star sensors based on an improved particle swarm algorithm relates to the field of optical sensors. It addresses the problem that existing star sensor calibration processes fail to consider the effects of focal plane tilt and rotation errors, resulting in reduced star sensor measurement accuracy. This method constructs a star sensor error model and, based on geometric relationships, establishes a nonlinear equation system between star point coordinates, projection coordinates, and error factors. The particle swarm algorithm is then used to find the star point projection coordinates. These two sets of coordinates are used to calibrate influencing factors such as principal point, principal distance, focal plane tilt and rotation, and distortion. The star sensor attitude angle is then determined based on the projection coordinates, achieving star sensor calibration and attitude calculation. The present invention utilizes spatial resection to solve the nonlinear equation system and an improved particle swarm algorithm. Using this method, star sensors can be calibrated on-orbit, improving star sensor measurement accuracy.

Description

Technical Field

[0001] The present invention relates to the field of optical sensors, and in particular to an on-orbit calibration and attitude solution method for star sensors based on an improved particle swarm algorithm. Background Art

[0002] Driven by demand and technology, spacecraft are showing a trend toward high-precision development. Star sensors, currently the most accurate instruments for absolute attitude determination, play a crucial role in spacecraft attitude measurement and control systems. Star sensors use the stars as their reference system and the starry sky as their operating object. Their optical parameters require ground calibration before formal use. However, during actual missions, their internal parameters significantly change relative to ground calibration due to vibration and impact during launch, as well as wear and tear from long-term operation in the harsh space environment. To ensure the observation accuracy and reliability of star sensors, they must undergo in-orbit calibration.

[0003] The key to calibrating star sensors is finding a more accurate reference. Two methods exist for on-orbit star sensor calibration: attitude-dependent and attitude-independent. Attitude-dependent methods utilize external attitude information to calibrate the star sensor, requiring precise known attitude parameters. Errors in these external attitude parameters are retained in the final calibration results. Attitude-independent methods estimate star sensor parameters based on the principle of constant star angular distance. Currently, research focuses on factors such as principal point, principal distance, and distortion, without considering the effects of focal plane tilt and rotation errors.

[0004] To address the shortcomings of existing methods, a novel on-orbit star sensor calibration and attitude estimation method based on an improved particle swarm optimization algorithm is proposed. This method considers image tilt and rotation errors during the calibration process, which is more consistent with actual engineering conditions and helps improve the measurement accuracy of star sensors. Summary of the Invention

[0005] In order to solve the problem that the influence of focal plane tilt and rotation errors is not considered during the calibration process of existing star sensors, resulting in reduced measurement accuracy of the star sensor, the present invention provides an on-orbit star sensor calibration and attitude solution method based on an improved particle swarm algorithm, so as to achieve accurate on-orbit calibration of the star sensor and improve the measurement accuracy of the star sensor.

[0006] The on-orbit calibration and attitude calculation method of star sensor based on improved particle swarm optimization is implemented by the following steps:

[0007] Step 1: Expose the star sensor. The photosensitive detector presents the star point on the focal plane, extracts the star point information, and establishes a star sensor error model. The star point information includes: star point coordinates and celestial coordinates determined by star map recognition;

[0008] Step 2: Find the projection coordinates of the star points based on the improved particle swarm algorithm;

[0009] The improved particle swarm algorithm is based on the multi-swarm collaborative particle swarm algorithm and adds a perturbation strategy. If the global optimal position obtained by the current optimization search is not updated in H consecutive iterations, the original search space is narrowed according to the obtained global optimal solution, and the particle position and speed are re-randomized to force the swarm particles to jump out of the local minimum. H is a natural number greater than 1.

[0010] According to the star point coordinates described in step 1, and according to the constructed objective function value, the projection coordinates of the star point on the ideal plane are found within the allowable range;

[0011] Step 3: Solve the nonlinear equations;

[0012] Substituting the star point coordinates and the corresponding projected coordinates into the nonlinear equations in the star sensor error model described in step 1, solving the unknowns, and determining the error parameters of the star sensor's principal point, principal distance, distortion, focal plane tilt, and focal plane rotation;

[0013] Step 4: Obtain an observation vector based on the projection coordinates, obtain a reference vector based on the celestial coordinates obtained in step 1, use the QUEST algorithm to obtain the star sensor attitude angle, and determine the spacecraft attitude in combination with the installation matrix.

[0014] Beneficial effects of the present invention:

[0015] 1. The error factors of image plane tilt and rotation are taken into account during the calibration process, and the error model is corrected to be more in line with actual engineering conditions.

[0016] Second, it is initialized based on the captured star map, does not rely on prior information or external information, requires less data, and is consistent with actual on-orbit conditions.

[0017] 3. Using optimization algorithms to link the star point coordinates with the projection positions of the star points on the ideal plane can be applied to situations with large measurement errors, enriching the research on on-orbit calibration and attitude solution methods of star sensors. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 This is a flow chart of a method for on-orbit calibration and attitude calculation of a star sensor based on an improved particle swarm algorithm according to an embodiment of the present invention;

[0019] Figure 2 Schematic diagram of an on-orbit calibration and attitude calculation method for a star sensor based on an improved particle swarm algorithm according to an embodiment of the present invention;

[0020] Figure 3 is a star sensor error model diagram according to an embodiment of the present invention;

[0021] Figure 4 This is a schematic diagram of narrowing the search space using the improved particle swarm algorithm according to an embodiment of the present invention;

[0022] Figure 5 Schematic diagram of constructing an objective function according to an embodiment of the present invention. DETAILED DESCRIPTION

[0023] The present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

[0024] To address the more complex error factors of focal plane tilt and rotation in star sensors, an embodiment of the present invention provides a method for on-orbit calibration and attitude solution of star sensors based on an improved particle swarm optimization algorithm. The specific solution is as follows.

[0025] Figure 1 The present invention provides a flowchart of a method for on-orbit calibration and attitude calculation of a star sensor based on an improved particle swarm algorithm. Figure 1 As shown in Figure 1, the method consists of four parts: obtaining the coordinates of the star point, finding the projection coordinates of the star point on the ideal plane using the improved particle swarm algorithm, determining the error of the star sensor, and determining the attitude angle of the spacecraft. The specific steps are as follows:

[0026] Step S1: exposing the star sensor. The photosensitive detector presents the star point on the focal plane. Star point information is obtained by star point extraction. The star point information includes: star point coordinates, i.e., the coordinates of the star point on the focal plane; and celestial coordinates determined after star map recognition.

[0027] Step S2, using an improved particle swarm algorithm, based on the star point coordinates and the objective function value, to find the projection coordinates of the star point on the ideal plane within an allowable range;

[0028] Step S3, substituting the star point coordinates and the corresponding projection coordinates into a nonlinear equation system established according to geometric relationships, solving unknown quantities, and determining error parameters such as the principal point, principal distance, distortion, focal plane rotation, and focal plane tilt of the star sensor;

[0029] Step S4: obtaining an observation vector according to the projection coordinates, obtaining a reference vector according to the celestial coordinates, obtaining a star sensor attitude angle using a QUEST algorithm, and determining a spacecraft attitude angle in combination with an installation matrix.

[0030] like Figure 2 As shown, Figure 2 The present invention provides a flow chart of a method for on-orbit calibration and attitude calculation of a star sensor based on an improved particle swarm algorithm. Figure 2As shown in the figure, the value range of the improved particle swarm algorithm is determined according to the known star point coordinates, and the initial projection coordinates are randomly generated within the value range; the star point coordinates and the projection coordinates of the star point form a nonlinear equation, and the unknown quantity is solved to obtain the numerical solution of the star point coordinates. The star point coordinates and the numerical solution of the star point coordinates are subtracted to construct the objective function; the improved particle swarm algorithm searches for the optimal projection coordinates within the value range according to the objective function value until the termination condition is met; based on the observation vector determined by the projection coordinates and the reference vector after star map recognition, the attitude is solved using the QUEST algorithm to determine the attitude of the star sensor.

[0031] like Figure 3 As shown, in the embodiment of the present invention, the error factors of the star sensor error model include the principal point (x0, y0), principal distance (f0), distortion (k1, k2), focal plane tilt and focal plane rotation. The errors of focal plane rotation and tilt can be represented by the Euler angle between two planes; in the ideal plane S a Build on O a -X a Y a Z a Coordinate system, actual focal plane S b Build on O b -X b Y b Z b Coordinate system. The error of focal plane rotation and focal plane tilt can be expressed by the Euler angle between the two planes: the angle from the actual focal plane to the ideal focal plane is defined by Z b -X b -Y b The angles of rotation are κ, ω, The corresponding transformation matrix is ​​C, c 11 ~c 33 Corresponding to each item in the matrix C; distortion includes radial distortion, decentering distortion, and thin prism distortion. Since radial distortion has the greatest impact and high-order distortion may lead to numerical instability, we choose radial second-order distortion here. According to the geometric relationship, the actual value and theoretical value of the star point can be expressed by formula (1), that is, the relationship between the star point coordinate A and the projection coordinate A' is:

[0032]

[0033] Among them, x I 、y I is the theoretical coordinate of the star point in the ideal plane (star point projection coordinate), x', y' are the star point coordinates, x i 、y iare the coordinates of the star point in the focal plane after distortion removal, X, Y, and Z are the coordinates of the star point in the ideal plane, x0 and y0 are the intersections of the principal optical axis and the ideal plane, f is the theoretical principal distance of the star sensor; f0 is the drift of the principal point of the focal plane in the Z-axis direction; k1 and k2 are the optical radial distortion coefficients.

[0034] In an embodiment of the present invention, the method of finding the star point projection coordinates based on the improved particle swarm algorithm includes:

[0035] The allowable range of the improved particle swarm algorithm search is the star point coordinate ± boundary value Δ, where Δ is determined based on the star sensor design accuracy 3δ, the number of stars n, and the focal length f:

[0036] The improved particle swarm algorithm is based on the multi-swarm collaborative particle swarm algorithm and adds a perturbation factor strategy. Assuming that the global optimal position currently found has not been updated in H consecutive iterations, the original search space is narrowed based on the global optimal solution obtained, and the particle positions and velocities are re-randomized to force the swarm particles out of the local minimum. H is a natural number greater than 1, which is called the perturbation factor.

[0037] like Figure 4 As shown in FIG, the rule for reducing the original search space is: comparing the distance between the current global optimal position and the boundary, selecting the side with the shorter distance, and determining a new value range with the global optimal position as the center;

[0038] The multi-swarm collaborative particle swarm algorithm divides the population into a master group and multiple slave groups with a master-slave model, and uses the symbiotic relationship between the master and slave groups to exchange and transmit information.

[0039] The formula for updating the speed and position of particles in a multi-swarm collaborative particle swarm algorithm is:

[0040]

[0041] Where: v and x represent velocity and position, subscript iS represents particle i from swarm S, superscript k and k+1 are the number of iterations; w is the inertia coefficient, c1 and c2 are learning factors, r1 and r2 are uniform random numbers in the range of [0, 1], pbest is the individual optimal value, and gbest is the global optimal value.

[0042] The formula for updating the speed and position of the main group particles in the multi-group collaborative particle swarm algorithm is:

[0043]

[0044] Where M represents the main group, S represents the slave group, and their definitions are the same as above; Φ is the migration factor, which is defined as:

[0045]

[0046] In step S2, the steps of improving the particle swarm algorithm are:

[0047] Step 1: Set the algorithm parameters and initialize the positions and velocities of the master and slave group particles;

[0048] Step 2: Evaluate the fitness of each particle in the master group and the slave group, and solve the global optimal value of each slave group and the global optimal position of the entire population;

[0049] Step 3: Use formula (2) to update all the particles in the swarm and evaluate the fitness of each particle in the swarm;

[0050] Step 4: The global optimal position of the slave group is transferred to the master group, and each particle of the master group is updated according to formula (3) and formula (4), and then the fitness value of each particle of the master group is evaluated;

[0051] Step 5: If k-kl>H, k represents the current iteration number of the main group, and kl represents the initial iteration number when the main group is updated to the current global optimal position; if the global optimal position of the main group is not updated, execute Step 6, otherwise execute Step 7.

[0052] Step 6: Compare the distances between the global optimal position and the upper and lower boundaries in the search space, select the shorter distance, and reset the search space and particle speed of the main group.

[0053] Step 7: If the termination condition is met, return the global optimal value and fitness value of the main group; otherwise, return to step 3.

[0054] In step S3, the nonlinear equations are solved based on spatial resection, and the steps are as follows:

[0055] Step 1) Obtain known data: star point coordinates and projection coordinates;

[0056] Step 2) Determine the initial value of the unknown number.

[0057] Step 3) Calculate the approximate value of the star point coordinates point by point according to formula (5);

[0058] Step 4) Calculate the coefficients and constant terms of the error equation point by point to obtain the correction number of the unknown number;

[0059] Step 5) Use the sum of the approximate value of the unknown and the corrected value as the new value of the unknown to determine whether the matrix B is singular. If it is singular, the iteration ends, otherwise proceed to the next step;

[0060] Step 6) Compare the corrected value with the specified tolerance. If it is less than the tolerance, the iteration ends. Otherwise, repeat steps 3) to 5) with the new approximate value.

[0061] The nonlinear equations based on spatial resection are solved by analogy with the collinear equations of spatial resection. Let Formula (1) can be transformed into:

[0062]

[0063] The correction factor for the unknown is dω, dκ, dx0, dy0, df0, dk1, dk2, dZ;

[0064] The error equation is:

[0065]

[0066] The constant term is: l x =x′-(x); l y =y′-(y); l z =0-(z); and form a matrix L, where (x), (y), (z) are the approximate values ​​of the unknowns and are substituted into the coordinates of the image points obtained by formula (5);

[0067] The coefficients of the error equation are obtained by taking partial derivatives of the unknowns in formula (5) and forming a coefficient matrix B; the partial derivative coefficients a 11 -a 39 for:

[0068]

[0069] Coefficient a 21 -a 39 The calculation method of is similar and will not be repeated here.

[0070] Convert formula (6) into matrix form: V = BQ-L; According to the least squares principle, the expression of the correction number is: Q = (B T B) -1 B T L;

[0071] According to the number of unknowns, 4 or more star points are required to solve the unknowns; the calculation is repeated by gradually approaching the method, using the sum of the approximate value and the correction number as the new approximate value to obtain a new correction number until the correction number is less than a certain limit.

[0072] like Figure 5 As shown, in the embodiment of the present invention, in step S2, the construction of the objective function requires solving the nonlinear equations twice;

[0073] First, the projection coordinates found by the improved particle swarm algorithm and the corresponding star point coordinates form a nonlinear equation system to solve the unknown quantity. Second, the solved unknown quantity and the projection coordinates found by the improved particle swarm algorithm are substituted into the nonlinear equation system to obtain the numerical solution of the star point coordinates. If the projection coordinates are accurate, the star point coordinates are equal to the numerical solution, and the solution is correct. The final expression of the objective function is:

[0074]

[0075] Where n is the number of stars, the coordinates of the star point of the i-th star are (x', y'), and the corresponding numerical solution is (x i' ,y i' ).

[0076] In step S4, the star point observation vector is determined according to the projection coordinates found by the improved particle swarm algorithm, and the formula is:

[0077]

[0078] The star point reference vector is determined after star map identification, and the formula is:

[0079]

[0080] ɑ i , β i is the right ascension and declination of star i in the celestial coordinate system after star map identification; the reference vector v i With the observation vector w i There is a corresponding transformation matrix C between IO , that is, the attitude matrix of the celestial coordinate system relative to the star sensor coordinate system, v i =C IO w i ; C IO The spacecraft attitude can be determined by combining the installation matrix of the star sensor relative to the spacecraft; based on the data of multiple stars, the QUEST algorithm can be used to calculate C IO .

[0081] In the embodiment of the present invention, in order to effectively describe the calibration results and solution accuracy, the evaluation is performed from the perspective of attitude solution;

[0082] According to the above method of determining the error parameters of the star sensor and the attitude angle of the spacecraft, it is necessary to obtain the projection coordinates of the star point, such as Figure 1 Therefore, the accuracy of attitude solution can replace the accuracy of star sensor error parameter calibration, and directly using the projection coordinates of star points to calculate the star sensor attitude can reduce the steps of error compensation and then attitude solution, thereby reducing calculation errors.

[0083] Referring to the statistical results of the satellite angular distance error, the attitude angle is expressed in Euler angles, and the evaluation formula is:

[0084]

[0085] Where Φ′, ψ′, and θ′ are the calculated Euler angles; Φ, ψ, and θ are the actual Euler angles; and Deta is the star sensor measurement accuracy (unit: ").

[0086] The technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above-mentioned embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0087] The above-described embodiments merely illustrate several implementations of the present invention, and while their descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the patent for this invention shall be determined by the appended claims.

Claims

1. The on-orbit calibration and attitude calculation method of star sensors based on the improved particle swarm optimization algorithm is characterized by: The method is implemented by the following steps: Step 1: Expose the star sensor. The photosensitive detector presents the star point on the focal plane, extracts the star point information, and establishes a star sensor error model. The star point information includes: star point coordinates and celestial coordinates determined by star map recognition; Step 2: Find the projection coordinates of the star points based on the improved particle swarm algorithm; The improved particle swarm algorithm is based on the multi-swarm collaborative particle swarm algorithm and adds a perturbation strategy. If the global optimal position obtained by the current optimization search is not updated in H consecutive iterations, the original search space is narrowed according to the obtained global optimal solution, and the particle position and speed are re-randomized to force the swarm particles to jump out of the local minimum. H is a natural number greater than 1. According to the star point coordinates described in step 1, and according to the constructed objective function value, the projection coordinates of the star point on the ideal plane are found within the allowable range; Step 3: Solve the nonlinear equations; Substituting the star point coordinates and the corresponding projected coordinates into the nonlinear equations in the star sensor error model described in step 1, solving the unknowns, and determining the error parameters of the star sensor's principal point, principal distance, distortion, focal plane tilt, and focal plane rotation; Step 4: Obtain an observation vector based on the projection coordinates, obtain a reference vector based on the celestial coordinates obtained in step 1, use the QUEST algorithm to obtain the star sensor attitude angle, and determine the spacecraft attitude in combination with the installation matrix.

2. The method for on-orbit calibration and attitude calculation of a star sensor based on an improved particle swarm optimization algorithm according to claim 1, characterized in that: In step 1, the error factors of the sensor error model include principal point, principal distance, distortion, focal plane tilt and focal plane rotation; the errors of focal plane rotation and focal plane tilt are represented by the Euler angle between the two planes; The angles of rotation from the actual focal plane to the ideal focal plane in the order of ZXY are defined as κ, ω, The corresponding transformation matrix is ​​C. According to the geometric relationship, the actual value and theoretical value of the star point are expressed by the following nonlinear equations, that is, the relationship between the star point coordinates and the projection coordinates is: Where x I 、y I is the projection coordinate of the star point, x', y' are the coordinates of the star point, x i 、y i are the coordinates of the star point in the focal plane after distortion removal, X, Y, and Z are the coordinates of the star point in the ideal plane, x0 and y0 are the intersections of the principal optical axis and the ideal plane, f is the theoretical principal distance of the star sensor; f0 is the drift of the principal point of the focal plane in the Z-axis direction; k1 and k2 are the optical radial distortion coefficients.

3. The on-orbit star sensor calibration and attitude calculation method based on the improved particle swarm optimization algorithm according to claim 1 is characterized in that: In step 2, the allowable range of the improved particle swarm algorithm search is obtained with the star point coordinates as the center, and is expressed as the star point coordinates ± the boundary value Δ, where Δ is determined based on the design accuracy 3δ of the star sensor, the number of stars n, and the focal length f:

4. The method for on-orbit calibration and attitude calculation of a star sensor based on an improved particle swarm optimization algorithm according to claim 1, characterized in that: In step 2, the steps of improving the particle swarm algorithm are: Step 1: Set the parameters of the improved particle swarm algorithm and initialize the positions and velocities of the master and slave swarm particles; Step 2: Evaluate the fitness of each particle in the master group and the slave group, and solve the global optimal value of each slave group and the global optimal position of the entire population; Step 3: Use the formula of the slave group in the multi-swarm collaborative particle swarm algorithm to update all the slave group particles and evaluate the fitness value of each particle in the slave group; Step 4: The global optimal position of the slave group is passed to the master group, and each particle of the master group is updated according to the formula of the master group in the multi-group collaborative particle swarm algorithm, and then the fitness value of each particle of the master group is evaluated; Step 5: Set k-kl>H, where k is the current iteration number of the main group and kl is the initial iteration number when the main group is updated to the current global optimal position. If the global optimal position of the main group is not updated, execute Step 6, otherwise execute Step 7. Step 6: Compare the distances between the global optimal position and the upper and lower boundaries in the search space, select the shorter distance, and reset the search space and particle speed of the main group; Step 7: If the termination condition is met, return the global optimal value and fitness value of the main group; otherwise, return to step 3.

5. The method for on-orbit calibration and attitude calculation of a star sensor based on an improved particle swarm optimization algorithm according to claim 1, characterized in that: In step 2, the rule for narrowing the original search space is: compare the distance between the current global optimal position and the boundary, select the side with the shorter distance, and determine a new value range with the global optimal position as the center.

6. The method for on-orbit calibration and attitude calculation of a star sensor based on an improved particle swarm optimization algorithm according to claim 1, characterized in that: In step 2, constructing the objective function value requires solving the nonlinear equations twice; First, the projection coordinates found by the improved particle swarm algorithm and the corresponding star point coordinates constitute a nonlinear equation system to solve the unknown quantity; The second time, the calculated unknowns and the projection coordinates found by the improved particle swarm algorithm are substituted into the nonlinear equations to obtain the numerical solution of the star point coordinates. If the projection coordinates are accurate, the star point coordinates are equal to the numerical solution, and the solution is correct. The final expression of the objective function is: Where n is the number of stars, the coordinates of the star point of the i-th star are (x', y'), and the corresponding numerical solution is (x' i ,y' i ).

7. The method for on-orbit calibration and attitude calculation of a star sensor based on an improved particle swarm optimization algorithm according to claim 2, characterized in that: In step 3, the nonlinear equations are solved based on spatial resection. The specific process is as follows: Step 31. Obtain star point coordinates and projection coordinates; Step 3.2: Determine the initial value of the unknown number. Step 33: Calculate the approximate values ​​of the star point coordinates point by point; Step 3 and 4: Calculate the coefficients and constant terms of the error equation point by point to obtain the correction value of the unknown number; Step 35: Use the sum of the approximate value of the unknown and the correction number as the new value of the unknown, and determine whether the matrix is ​​singular. If it is singular, the iteration ends; otherwise, execute step 36; Step 36: Compare the correction number with the specified limit. If it is less than the limit, the iteration ends. Otherwise, use the new value obtained in step 35 and return to step 33 for calculation.

8. The method for on-orbit calibration and attitude calculation of a star sensor based on an improved particle swarm optimization algorithm according to claim 2, characterized in that: In step 4, the observation vector w is obtained according to the projection coordinates i , the specific formula is: The star point reference vector v i The formula is: In the formula, ɑ i , β i is the right ascension and declination of star i in the celestial coordinate system after star map identification; the reference vector v i With the observation vector w i There is a corresponding transformation matrix C between IO , that is: the attitude matrix of the celestial coordinate system relative to the star sensor coordinate system, v i =C IO w i ; C IO The spacecraft attitude is determined by combining the installation matrix of the star sensor relative to the spacecraft; the QUEST algorithm is used to calculate C based on multiple star data. IO .

9. The method for on-orbit calibration and attitude calculation of a star sensor based on an improved particle swarm optimization algorithm according to claim 1, characterized in that: It also includes evaluating the calibration results and solution accuracy through the angle of attitude solution; the evaluation formula is: Where Φ′, ψ′, and θ′ are the calculated Euler angles; Φ, ψ, and θ are the actual Euler angles; and Deta is the measurement accuracy of the star sensor.

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