CN116256004A - Star sensor on-orbit calibration and attitude resolving method based on improved particle swarm algorithm - Google Patents
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Abstract
An on-orbit calibration and attitude resolving method of a star sensor based on an improved particle swarm algorithm relates to the field of optical sensors, and solves the problem that the measurement accuracy of the star sensor is reduced because the influence of focal plane inclination and rotation errors is not considered in the calibration process of the existing star sensor. Then, a particle swarm algorithm is utilized to find star point projection coordinates, two groups of coordinates are utilized to calibrate influence factors including principal points, principal distance, focal plane inclination, rotation, distortion and the like, and the attitude angle of the star sensor is determined according to the projection coordinates, so that the calibration and attitude calculation of the star sensor are realized. The method solves a nonlinear equation set and improves a particle swarm algorithm based on space back intersection. By using the method of the invention, the on-orbit calibration of the star sensor can be carried out, and the measurement precision of the star sensor can be improved.
Description
Technical Field
The invention relates to the field of optical sensors, in particular to an on-orbit calibration and attitude resolving method of a star sensor based on an improved particle swarm algorithm.
Background
Under the drive of demand traction and technology, the spacecraft has a development trend of high precision. The star sensor is used as the instrument with the highest current absolute attitude determination precision, and plays an important role in an attitude measurement and control system of the spacecraft. The star sensor takes a star as a reference system and takes a star sky as a working object, and before formal use, the optical parameters of the star sensor need to be calibrated on the ground, but in an actual flight task, the internal parameters of the star sensor change greatly relative to the ground during the calibration due to vibration and impact during the transmission and abrasion during long-term working in a severe space environment, so that the observation precision and reliability of the star sensor are ensured, and the star sensor needs to be calibrated on the track.
The key to calibrating the star sensor is to find a higher accuracy reference. Two existing method types (attitude dependent and attitude independent) are used for on-orbit calibration of the star sensor. In the attitude-related method, the star sensor is calibrated by using external attitude information, accurate attitude parameters are required to be known, and if the external attitude parameters have errors, the errors are reserved in a final calibration result. In the attitude independent method, parameters of a star sensor are estimated based on the principle of constant star angular distance. At present, the research focuses on factors such as principal points, principal distances, distortion and the like, and the influence of focal plane inclination and rotation errors is not considered.
Aiming at the defects of the existing method, an on-orbit calibration and attitude resolving method of a star sensor based on an improved particle swarm algorithm is provided. In the calibration process, error factors of image plane inclination and rotation are considered, so that the method is more in line with the actual engineering situation, and is beneficial to improving the measurement accuracy of the star sensor.
Disclosure of Invention
The invention provides an on-orbit calibration and attitude resolving method for a star sensor based on an improved particle swarm algorithm, which aims to solve the problem that the measurement accuracy of the star sensor is reduced because the influence of focal plane inclination and rotation errors is not considered in the calibration process of the existing star sensor, so as to realize accurate on-orbit calibration of the star sensor and improve the measurement accuracy of the star sensor.
The method for on-orbit calibration and attitude calculation of the star sensor based on the improved particle swarm algorithm is realized by the following steps:
exposing a star sensor, enabling a star point to be displayed on a focal plane by a light sensing detector, extracting star point information, and establishing a star sensor error model; the star point information includes: star point coordinates and celestial coordinates determined through star map identification;
searching projection coordinates of star points based on an improved particle swarm algorithm;
the improved particle swarm algorithm is based on a multi-group cooperative particle swarm algorithm, and a disturbance strategy is added; setting that the global optimal position obtained by current optimization is not updated in continuous H iterations, reducing the original search space according to the obtained global optimal solution, randomizing the particle position and speed again, and forcing population particles to jump out of local minima; h is a natural number greater than 1;
searching the projection coordinates of the star point in an ideal plane within an allowable range according to the star point coordinates in the step one and the construction objective function value;
solving a nonlinear equation set;
substituting the star point coordinates and the corresponding projection coordinates into a nonlinear equation set in the star sensor error model in the first step, solving the unknown quantity, and determining error parameters of principal points, principal distances, distortion, focal plane inclination and focal plane rotation of the star sensor;
and step four, obtaining an observation vector according to the projection coordinates, obtaining a reference vector according to the celestial coordinates obtained in the step one, obtaining a star sensor attitude angle by using a QUEST algorithm, and determining the attitude of the spacecraft by combining an installation matrix.
The invention has the beneficial effects that:
1. in the calibration process, error factors of image plane inclination and rotation are considered, so that an error model is corrected, and the method is more in line with the actual engineering situation.
2. According to the shot star map initialization, the prior information and the external information are not relied on, the required data are less, and the actual on-orbit condition is met.
3. The star point coordinates are related to the projection positions of the star points on an ideal plane by using an optimization algorithm, so that the method can be suitable for the situation of larger measurement errors, and enriches the research of the on-orbit calibration and attitude resolving method of the star sensor.
Drawings
FIG. 1 is a flow chart of a star sensor on-orbit calibration and attitude solving method based on an improved particle swarm algorithm in an embodiment of the invention;
FIG. 2 is a schematic diagram of an on-orbit calibration and attitude solving method of a star sensor based on an improved particle swarm algorithm according to an embodiment of the invention;
FIG. 3 is a diagram of a star sensor error model in accordance with an embodiment of the present invention;
FIG. 4 is a schematic diagram showing a reduced search space of an improved particle swarm algorithm according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of a building objective function according to an embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the drawings and the specific embodiments.
Aiming at more complex error factors of focal plane inclination and rotation in a star sensor, the embodiment of the invention provides a method for realizing on-orbit calibration and attitude calculation of the star sensor based on an improved particle swarm algorithm, which comprises the following specific scheme.
Fig. 1 is a flowchart 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. As shown in fig. 1, the method includes four parts: the method comprises the steps of obtaining coordinates of star points, searching projection coordinates of the star points on an ideal plane by utilizing an improved particle swarm algorithm, determining star sensor errors and determining spacecraft attitude angles. The method comprises the following specific steps:
step S1, exposing a star sensor, enabling a light sensing detector to present star points on a focal plane, and extracting star point information through the star points, wherein the star point information comprises the following steps: star coordinates, i.e. the coordinates of a star in the focal plane; determining celestial coordinates after star map identification;
s2, adopting an improved particle swarm algorithm, and searching projection coordinates of star points on an ideal plane within an allowable range according to the objective function value according to the star point coordinates;
s3, substituting the star point coordinates and the corresponding projection coordinates into a nonlinear equation set established according to a geometric relation, solving an unknown quantity, and determining error parameters such as a principal point, a principal distance, distortion, focal plane rotation, focal plane inclination and the like of the star sensor;
and 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 by using a QUEST algorithm, and determining the spacecraft attitude angle by combining an installation matrix.
As shown in fig. 2, fig. 2 is a flow chart of a method for calibrating and resolving an on-orbit attitude of a star sensor based on an improved particle swarm algorithm according to an embodiment of the present invention. As shown in fig. 2, the value range of the improved particle swarm algorithm is determined according to the known star point coordinates, and initial projection coordinates are randomly generated in the value range; the star point coordinates and the projection coordinates of the star points form a nonlinear equation, the unknown quantity is solved, the numerical solution of the star point coordinates is obtained, and the numerical solution of the star point coordinates and the star point coordinates are subtracted to construct an objective function; the improved particle swarm algorithm searches the optimal projection coordinates in the value range according to the objective function value until the termination condition is met; and according to the observation vector determined by the projection coordinates and the reference vector after the star map is identified, carrying out gesture calculation by using a QUEST algorithm, and determining the gesture of the star sensor.
As shown in fig. 3, in the embodiment of the present invention, the error factors of the star sensor error model include a principal point (x 0 ，y 0 ) Main distance (f) 0 ) Distortion (k) 1 ，k 2 ) Focal plane tilt and focal plane rotation. The error of rotation and inclination of the focal plane can be represented by Euler angles between the two planes; in an ideal plane S a Build-up O a -X a Y a Z a Coordinate system, actual focal plane S b Build-up O b -X b Y b Z b And (5) a coordinate system. The error in focal plane rotation and focal plane tilt can be represented by the euler angle between the two planes: definition of the Z from the actual focal plane to the ideal focal plane b -X b -Y b Sequentially rotated angles of K, omega,
The corresponding conversion matrix is C, C 11 ～c 33 Corresponding to each term in matrix C; distortion includes radial distortion, decentered distortion, and thin prismatic distortion, where we choose radial second order distortion because the effect of radial distortion is greatest and higher order distortion may lead to numerical instability. According to the geometric relationship, the actual value and the theoretical value of the star point can be expressed by the formula (1), namely, the relationship between the star point coordinate A and the projection coordinate A' is as follows:
wherein x is I 、y I Is the theoretical coordinates of a star point in an ideal plane (star point projection coordinates), x ', y' are the star point coordinates, and x i 、y i For the coordinates of the star point in the focal plane after the distortion is removed, X, Y, Z is the coordinates of the star point in the ideal plane, x 0 、y 0 F is the theoretical main distance of the star sensor, which is the intersection point of the main optical axis and the ideal plane; f (f) 0 The drift amount of the focal plane principal point in the Z axis direction is used; k (k) 1 、k 2 Is an optical radial distortion coefficient.
In the embodiment of the present invention, the searching for star point projection coordinates based on the improved particle swarm algorithm includes:
the allowable range searched by the improved particle swarm algorithm is star point coordinates + -boundary value delta, and delta is specifically determined according to star sensor design precision 3 delta, star number n and focal length f:
the improved particle swarm algorithm is based on a multi-group cooperative particle swarm algorithm, and a strategy for adding disturbance factors is adopted; assuming that the global optimal position obtained by current optimization is not updated in continuous H iterations, reducing the original search space according to the obtained global optimal solution, and randomizing the position and speed of the particles again to force population particles to jump out of a local minimum value; h is a natural number greater than 1, called a perturbation factor;
as shown in fig. 4, the rule for reducing the original search space is: comparing the distance between the current global optimal position and the boundary, selecting one side with a relatively close distance, and taking the global optimal position as a center to determine a new value range;
the multi-group cooperative particle swarm algorithm divides the population into a master group and a plurality of slave groups in a master-slave mode, and utilizes the symbiotic relationship between the master group and the slave group to exchange and transfer information.
The multi-group cooperative particle swarm algorithm updates the speed and the position of the group particles by the formula:
wherein: v, x represent speed and position, subscript iS represents i particles in slave group S, superscript k, k+1 iS iteration number; w is the inertia coefficient, c 1 And c 2 R is the learning factor 1 And r 2 Is [0,1]The uniform random numbers in the range, pbest is the individual optimum value, and gbest is the global optimum value.
The main group particle updating speed and position formula of the multi-group cooperative particle swarm algorithm:
wherein M represents a master group, S represents a slave group, and the definition of the slave group is the same as that of the above formula; Φ is a migration factor, defined as:
in step S2, the step of improving the particle swarm algorithm is as follows:
step1: setting the size of algorithm parameters, and initializing the positions and speeds of particles of a master group and a slave group;
step2: evaluating the adaptive value of each particle in the master group and the slave group, and solving the global optimal value of each slave group and the global optimal position of the whole group;
step3: updating all the slave group particles by using the formula (2), and evaluating the adaptation value of each particle of the slave group;
step4: transmitting the global optimal position of the slave group to the master group, updating each particle of the master group according to the formula (3) and the formula (4), and evaluating the adaptation value of each particle of the master group;
step5: if k-kl > H, k is expressed as the current iteration step number of the main group, and kl is expressed as the initial iteration step 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, step6 is executed, otherwise Step7 is executed.
Step6: and comparing the distance between the global optimal position and the upper and lower boundaries in the search space, selecting a shorter distance, and resetting the search space and the particle speed of the main group.
Step7: if the termination condition is met, returning to a global optimal value and an adaptive value of the main group; otherwise, returning to Step3.
In step S3, the nonlinear equation set is solved based on the space back convergence, and the steps are as follows:
step 1), acquiring known data: star coordinates and projection coordinates;
step 2), determining an initial value of the unknown number,
step 3), calculating the approximate value of the star point coordinates point by point according to the formula (5);
step 4), calculating coefficients and constant items of an error equation point by point, and solving the correction of the unknown number;
step 5), judging whether the matrix B is singular or not by using the sum of the approximate value and the correction of the unknown number as a new value of the unknown number, if so, ending the iteration, otherwise, carrying out the next step;
and 6) comparing the correction with a specified limit difference, if the correction is smaller than the limit difference, ending the iteration, otherwise, repeating the steps 3) to 5) with a new approximate value.
The nonlinear equation set is solved based on the space back intersection, and the space back intersection is analogizedWill be collinear equation, let
Equation (1) can be expressed as:
the correction of the unknown number is
dω，dκ,dx0，dy0，df0，dk1，dk2，dZ；
The error equation is:
the constant term is: l (L) x ＝x′-(x)；l y ＝y′-(y)；l z =0- (z); and forming a matrix L, wherein (x), (y) and (z) are the pixel coordinates obtained by substituting the approximate values of the unknowns into the formula (5);
the coefficients of the error equation are obtained by solving the bias derivative of the unknown number in the formula (5) and form a coefficient matrix B; coefficient of partial conductivity a 11 -a 39 The method comprises the following steps:
coefficient a 21 -a 39 The calculation method of (2) is similar and will not be described in detail herein.
Converting equation (6) into a matrix form: v=bq-L; according to the least square principle, the expression of the correction is obtained: q= (B) T B) -1 B T L；
According to the number of unknowns, 4 or more star points are needed to calculate the unknowns; the calculation is repeated by a gradual approach method by using the sum of the approximation value and the correction as a new approximation value, and a new correction value is obtained until the correction value is smaller than a certain limit value.
As shown in fig. 5, in the embodiment of the present invention, in step S2, the objective function needs to be constructed to solve the nonlinear equation set twice;
firstly, the projection coordinates searched by the improved particle swarm algorithm and the corresponding star point coordinates form a nonlinear equation set, and the unknown quantity is solved; substituting the calculated unknown quantity and the projection coordinates found by the improved particle swarm algorithm into a nonlinear equation set to obtain a numerical solution of star 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:
wherein n is a star number, the coordinates of the star point of the ith star are (x ', y'), and the corresponding numerical solution is (x) i' ,y i' )。
In step S4, the star point observation vector is determined according to the projection coordinates found by the improved particle swarm algorithm, where the formula is:
the star point reference vector is determined after being identified by a star map, and the formula is as follows:
ɑ i 、β i after identifying the star map, the right ascension and the right ascension of the star i under the celestial coordinate system; reference vector v i And observation vector w i With a corresponding conversion matrix C between IO I.e. the attitude matrix of the celestial coordinate system relative to the star sensor coordinate system, v i ＝C IO ·w i ；C IO The attitude of the spacecraft can be determined by combining the installation matrix of the star sensor relative to the spacecraft; based on the multiple star data, a QUEST algorithm can be usedMethod calculation C IO 。
In the embodiment of the invention, in order to effectively describe the calibration result and the resolving precision, the evaluation is carried out from the perspective of gesture resolving;
according to the method for determining the error parameters of the star sensor and the attitude angle of the spacecraft, the projection coordinates of the star point are required to be obtained, as shown in fig. 1. Therefore, the accuracy of the attitude solving can replace the accuracy of the star sensor error parameter calibration, the attitude of the star sensor is calculated directly by using the projection coordinates of the star points, the steps of attitude solving after error compensation can be reduced, and the calculation error is reduced.
Referring to star-to-range error statistical results, the attitude angle is represented by Euler angles, and the evaluation formula is as follows:
wherein phi ', theta' are calculated Euler angles; phi, phi and theta are actual Euler angles; deta is the star sensor measurement accuracy in (").
The technical features of the above-described embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above-described embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The above examples illustrate only a few embodiments of the invention, which are described in detail and are not to be construed as limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention. Accordingly, the scope of protection of the present invention is to be determined by the appended claims.
Claims (9)
1. The star sensor on-orbit calibration and attitude resolving method based on the improved particle swarm algorithm is characterized by comprising the following steps: the method is realized by the following steps:
exposing a star sensor, enabling a star point to be displayed on a focal plane by a light sensing detector, extracting star point information, and establishing a star sensor error model; the star point information includes: star point coordinates and celestial coordinates determined through star map identification;
searching projection coordinates of star points based on an improved particle swarm algorithm;
the improved particle swarm algorithm is based on a multi-group cooperative particle swarm algorithm, and a disturbance strategy is added; setting that the global optimal position obtained by current optimization is not updated in continuous H iterations, reducing the original search space according to the obtained global optimal solution, randomizing the particle position and speed again, and forcing population particles to jump out of local minima; h is a natural number greater than 1;
searching the projection coordinates of the star point in an ideal plane within an allowable range according to the star point coordinates in the step one and the construction objective function value;
solving a nonlinear equation set;
substituting the star point coordinates and the corresponding projection coordinates into a nonlinear equation set in the star sensor error model in the first step, solving the unknown quantity, and determining error parameters of principal points, principal distances, distortion, focal plane inclination and focal plane rotation of the star sensor;
and step four, obtaining an observation vector according to the projection coordinates, obtaining a reference vector according to the celestial coordinates obtained in the step one, obtaining a star sensor attitude angle by using a QUEST algorithm, and determining the attitude of the spacecraft by combining an installation matrix.
2. The method for on-orbit calibration and attitude solving of a star sensor based on an improved particle swarm algorithm according to claim 1, wherein the method comprises the following steps: in the first step, error factors of the sensor error model comprise principal points, principal distances, distortion, focal plane inclination and focal plane rotation; the error in focal plane rotation and focal plane tilt is represented by the euler angle between the two planes;
defining the rotation angles from the actual focal plane to the ideal focal plane according to the Z-X-Y sequence as kappa and omega respectively、
The corresponding conversion matrix is C, and according to the geometric relationship, the actual value and the theoretical value of the star point are represented by the following nonlinear equation set, namely: the relation between the star point coordinates and the projection coordinates is as follows:
wherein x is I 、y I Is the projection coordinates of the star point, x 'and y' are the star point coordinates, x i 、y i For the coordinates of the star point in the focal plane after the distortion is removed, X, Y, Z is the coordinates of the star point in the ideal plane, x 0 、y 0 F is the theoretical main distance of the star sensor, which is the intersection point of the main optical axis and the ideal plane; f (f) 0 The drift amount of the focal plane principal point in the Z axis direction is used; k (k) 1 、k 2 Is an optical radial distortion coefficient.
3. The method for on-orbit calibration and attitude solving of a star sensor based on an improved particle swarm algorithm according to claim 1, wherein the method comprises the following steps: in the second step, the allowable range searched by the improved particle swarm algorithm is obtained by taking the star point coordinate as the center, and is expressed as a star point coordinate + -boundary value delta, wherein delta is specifically determined according to the design precision 3 delta of the star sensor, the star number n and the focal length f:
4. the method for on-orbit calibration and attitude solving of a star sensor based on an improved particle swarm algorithm according to claim 1, wherein the method comprises the following steps: in the second step, the step of improving the particle swarm algorithm is as follows:
step1: setting the improved particle swarm algorithm parameters, and initializing the positions and speeds of the particles of the master swarm and the slave swarm;
step2: evaluating the adaptive value of each particle in the master group and the slave group, and solving the global optimal value of each slave group and the global optimal position of the whole group;
step3: updating all the particles of the slave group by using a formula of the slave group in a multi-group cooperative particle swarm algorithm, and evaluating the adaptation value of each particle of the slave group;
step4: transmitting the global optimal position of the slave group to the master group, updating each particle of the master group according to a formula of the master group in a multi-group cooperative particle swarm algorithm, and then evaluating the adaptive value of each particle of the master group;
step5: setting k-kl > H, wherein k is the current iteration step number of the main group, and kl is the initial iteration step number when the main group is updated to the current global optimal position; step6 is executed if the global optimal position of the main group is not updated, otherwise Step7 is executed;
step6: comparing the distance between the global optimal position and the upper and lower boundaries in the search space, selecting a shorter distance, and resetting the search space and particle speed of the main group;
step7: if the termination condition is met, returning to a global optimal value and an adaptive value of the main group; otherwise, returning to Step3.
5. The method for on-orbit calibration and attitude solving of a star sensor based on an improved particle swarm algorithm according to claim 1, wherein the method comprises the following steps: in the second step, the rule for reducing the original search space is as follows: and comparing the distance between the current global optimal position and the boundary, selecting one side with a smaller distance, and taking the global optimal position as the center to determine a new value range.
6. The method for on-orbit calibration and attitude solving of a star sensor based on an improved particle swarm algorithm according to claim 1, wherein the method comprises the following steps: in the second step, the objective function value is constructed by solving a nonlinear equation set twice;
firstly, the projection coordinates searched by the improved particle swarm algorithm and the corresponding star point coordinates form a nonlinear equation set, and the unknown quantity is solved;
substituting the calculated unknown quantity and the projection coordinates found by the improved particle swarm algorithm into a nonlinear equation set to obtain a numerical solution of star 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:
wherein n is a star number, the coordinates of the star point of the ith star are (x ', y'), and the corresponding numerical solution is (x) i' ,y i' )。
7. The method for on-orbit calibration and attitude solving of a star sensor based on an improved particle swarm algorithm according to claim 1, wherein the method comprises the following steps: in the third step, the nonlinear equation set is solved based on space back intersection, and the specific process is as follows:
step three, acquiring star point coordinates and projection coordinates;
step three, the initial value of the unknown quantity is determined,
thirdly, calculating an approximate value of coordinates of the star point by point;
thirdly, calculating coefficients and constant terms of an error equation point by point to obtain the correction of the unknown number;
step three, adopting the sum of the approximate value and the correction of the unknown number as a new value of the unknown number to judge whether the matrix is singular, and ending iteration if the matrix is singular; otherwise, executing the third step;
and step III, comparing the correction with a specified limit difference, if the correction is smaller than the limit difference, ending the iteration, otherwise, returning to the step III for calculation by adopting the new value obtained in the step III.
8. The method for on-orbit calibration and attitude solving of a star sensor based on an improved particle swarm algorithm according to claim 1, wherein the method comprises the following steps: in the fourth step, an observation vector w is obtained according to the projection coordinates i The specific formula is as follows:
the star point reference vector v i The formula of (2) is:
in the formula alpha i 、β i After identifying the star map, the right ascension and the right ascension of the star i under the celestial coordinate system; reference vector v i And observation vector w i With a corresponding conversion matrix C between IO The method comprises the following steps: attitude matrix of celestial coordinate system relative to star sensor coordinate system, v i ＝C IO ·w i ；C IO Determining the attitude of the spacecraft by combining the installation matrix of the star sensor relative to the spacecraft; based on the data of a plurality of stars, calculating C by adopting QUEST algorithm IO 。
9. The method for on-orbit calibration and attitude solving of a star sensor based on an improved particle swarm algorithm according to claim 1, wherein the method comprises the following steps: the method further comprises the step of evaluating a calibration result and resolving precision through an attitude resolving angle; the evaluation formula is:
wherein phi ', phi ' and theta ' are calculated Euler angles; phi, phi and theta are actual Euler angles; deta is the star sensor measurement accuracy.
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| CN116485043B (en) * | 2023-06-19 | 2023-09-01 | 中国人民解放军国防科技大学 | Homing multi-target optimization method for parafoil cluster system |
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