CN114646312A - Astronomical analysis positioning method based on starlight refraction information - Google Patents
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Abstract
The invention relates to an astronomical analysis positioning method based on starlight refraction information, and belongs to the field of astronomical autonomous navigation. Firstly, two groups of starlight refraction information supporting a direct positioning method are obtained, then an auxiliary vector is constructed, a positioning model of double starlight refraction information is established by utilizing the geometric relation among an aircraft position vector, the starlight refraction vector and the auxiliary vector, two space linear equations are combined to construct a linear equation set, and finally the analysis and the calculation of the absolute position of the aircraft are completed by combining measured data.
Description
Technical Field
The invention belongs to the field of astronomical autonomous navigation, relates to an astronomical analytic positioning method of starlight refraction, in particular to a method for realizing the analytic positioning of an aircraft based on double-starlight refraction information, and is suitable for the direct calculation of the absolute position of the aircraft in an inertial coordinate system.
Background
The absolute navigation systems which are most commonly used at present comprise an inertial navigation system, a satellite positioning system, a database system, and a geomagnetic navigation system and an astronomical navigation system which depend on the information of the earth and the celestial body. The astronomical navigation realizes positioning navigation by measuring the vector direction of a natural celestial body relative to a spacecraft, has the advantages of high measurement precision, no error accumulation along with time, autonomy and the like, and becomes an autonomous navigation means which is particularly concerned. Particularly, the method for acquiring celestial body refraction sight line vector information based on visible light/infrared light observed by the star sensor enables the theoretical precision of the autonomous positioning precision to reach a hundred-meter level due to the high measurement precision of the angular-second level of the star sensor, and is an astronomical navigation method with great potential at present.
The autonomous navigation based on star light refraction information of the star sensor can be summarized into an astronomical navigation method of sensitive horizon. The sensitive horizon mode is mainly divided into two types, namely (1) a direct horizon sensitive positioning method of a combined horizon instrument and (2) an indirect horizon sensitive positioning method of a pure star sensor. The direct horizon sensitive positioning method (1) provides the horizon direction by means of the measurement information of a horizon instrument, and performs integrated navigation in combination with navigation information such as an inertial navigation system and the like, the method is simple and easy to implement, but the measurement precision of the horizon instrument is 1-2 orders of magnitude lower than that of a star sensor, and the theoretical positioning precision is mostly kilometer orders of magnitude and is not high due to the mismatching of the precision among the sensors; the indirect sensitive horizon method (2) is based on the principle that the fixed star light penetrates through the atmosphere at the edge of the earth and refracts towards the earth center, the sensitive refraction star light of the high-precision CCD fixed star sensor is fully utilized to obtain refraction information, horizon information is indirectly provided by combining with a star light atmospheric refraction model, and then the position of the aircraft is estimated by combining with information such as a motion equation, inertial navigation and the like and adopting a filtering algorithm.
One main direction of the indirect horizon-sensitive positioning method based on starlight refraction is improvement of a starlight-sensitive observation model, and a new measurement model taking refraction angle and refraction vector area array imaging coordinates as quantity measurement appears in recent years; the single star sensor realizes the star refraction navigation scheme; in addition, an astronomical direct positioning scheme based on starlight refraction indirect sensitivity is also provided, a nonlinear equation of refraction information and a user three-dimensional position is constructed, and a least square differential correction method is used for replacing nonlinear filtering to directly solve a nonlinear measurement equation set to obtain aircraft position information.
However, the main disadvantages of the existing star refraction indirect sensitive horizontal positioning method are as follows: the observability of the observation information based on the refraction information by adopting a filtering algorithm is not high, the filtering result with stable precision can be obtained only by long-time continuous observation (about 1.5 hours), the precision convergence is slow, the defects which are difficult to overcome aiming at the practical engineering application of the fast moving aircraft are defects, the refraction information is difficult to continuously obtain in the engineering practice, and the requirement of real-time flight cannot be met even if the precision convergence is slow (the time for obtaining the stable filtering precision is long); the astronomical direct positioning method not only needs to obtain at least three pieces of refraction information, but also adopts iterative calculation, the star light observation condition meeting the requirements can be realized with larger difficulty, and the calculated amount is slightly larger. Meeting these conditions is difficult for fast moving spacecraft, and a method with less calculation and less number of refraction stars needs to be sought.
Disclosure of Invention
Technical problem to be solved
The development trend of autonomy and intellectualization has increasingly pressed the demand of the aircraft for autonomous navigation capability. An astronomical autonomous navigation method for detecting light refraction information of stars by using a star sensor is widely concerned due to good theoretical precision. At present, the starlight refraction navigation mostly adopts a combined filtering method taking a refraction angle, a refraction apparent height and a refraction starlight image plane imaging point coordinate as observation information.
The method for adopting a combined filtering mode aiming at starlight refraction has the main problems that: the star sensors of the aircraft are limited in number and only can output refraction angle, refraction apparent height and sight line information, so that the combined orbit dynamics model mostly adopts a combined navigation mode to complete positioning calculation, and the defects of poor observability and slow precision convergence exist.
Aiming at the astronomical direct positioning method based on starlight refraction, the main problems are as follows: the method constructs a nonlinear equation containing the aircraft position vector through the geometric relationship between refracted starlight and the aircraft, solves a nonlinear measurement equation set by numerical methods such as a least square differential correction method and the like under the condition of obtaining enough measurement information, at least three groups and more than three groups of refraction information are needed for directly calculating the absolute position information of the aircraft, high requirements are required for the number of airborne sensors and observation capacity, the technical realization difficulty is high, and the positioning accuracy is low.
In conclusion, the invention provides a novel direct positioning method based on indirect sensitivity horizon starting from the direct positioning capability of the double star sensor. According to the novel method, under the condition that two pieces of refracted star light information are observed only by means of the star sensor, the analytic positioning model of the three-dimensional position of the user is reestablished, analytic calculation of the three-dimensional absolute position of the aircraft based on the double-star light refraction information can be achieved, the requirement on the number of the refracted star information is lowered, the calculated amount is greatly reduced, the obtained analytic positioning result can be further used as absolute position observation information of an astronomical/inertia combined navigation system, system errors are corrected, the observability and the convergence speed of combined filtering are improved, and the method has good engineering realizability and application value.
Technical scheme
An astronomical resolution positioning method based on starlight refraction information is characterized by comprising the following steps:
step 1: the method comprises the following steps of acquiring starlight refraction information by utilizing a starlight refraction area near the atmospheric layer of the sensitive earth edge of a star sensor, wherein the starlight refraction information comprises the following steps: refracting starlight unit vector mu 'under inertial coordinate system'kUnit vector mu of original starlight corresponding to refracted starlight in inertial coordinate systemkAngle of refraction RkAnd a refractive apparent height htk；
Step 2: constructing an auxiliary vector r under an inertial system by using the measurement information in the step 1upkFor providing horizon information, using step 1 measurement information muk′、μkAnd htkAuxiliary vector r under the structural inertia system iupkThe following were used:
wherein R iseThe auxiliary vector r is the radius of the earthupkThe requirement is that the auxiliary vector and the original starlight unit vector lie in the space plane formed by the refracted starlight vector, the original starlight vector and the geocenter
Orthogonal;
thus, under the form of edge transmission of the earth atmosphere, the unit vector of the original starlight
The space coordinate point T under the inertial system is tangent to the spherical atmosphere, and the tangent point T under the inertial systemkVector formed by connecting with center of earth O
Exactly, the auxiliary vector is used for determining a space tangent point T corresponding to the refraction apparent height on the starlight transmission pathkThree-dimensional coordinates (x) in inertial framek,yk,zk) The coordinates provide the horizon information as an important basis for completing the positioning;
and step 3: combining the starlight refraction vector measured in the step 1 with the space tangent point T constructed in the step 2kA straight line L can be uniquely determined in spacekThe direction of the straight line and a refracted star light vector mu'kSame and passing through the spatial midpoint TkStraight line LkThe spatial equation of (a) is:
the line passes through the observation points according to the starlight transmission path, so that each point on the line is an aircraftThe potential location of (a). (s)xk,syk,szk) Denotes a refracted starlight unit vector μ 'denoted by reference numeral k'kThe component under the inertial system, the aircraft position vector r ═ (x, y, z);
and 4, step 4: simultaneously acquiring a second group of starlight refraction information according to the step 1-3, and constructing an equation of a second space straight line L;
and 5: according to the two groups of starlight refraction information measured in the step 1-4, two constructed space straight lines have a unique intersection point in the space, and the intersection point is the potential absolute position of the aircraft; according to the geometrical relationship of the aircraft position vector, the starlight refraction vector and the auxiliary vector in the space, a linear equation set with the aircraft position information as an unknown number is constructed by combining two space linear equations, and then the absolute position of the aircraft is obtained by analytic solution:
wherein m and n represent symbols for observing two groups of refracted starlight,(s)xk,syk,szk) Denotes a refracted starlight unit vector μ 'denoted by reference numeral k'kThe component under the inertial system, the aircraft position vector r ═ (x, y, z); for convenient calculation, a group of parameters a, b and c are set according to the starlight refraction information measured in the step 1 in the following form:
substituting the parameters, solving a linear equation system to obtain the absolute position of the aircraft and obtaining a group of analytic solutions, wherein the analytic solutions are as follows:
the further technical scheme of the invention is as follows: the detailed steps of step 1 include:
(11) star sensor for refracted starlight emitted by star kCapturing the image in a CCD area array to obtain a unit vector of refracted starlight under a sensor coordinate system, namely an s system
(12) Obtaining the original star starlight corresponding to the refraction starlight vector under the inertial system i system according to the refraction star identification matching
(13) Calculating and obtaining refraction angle R between vectors according to an included angle cosine formulakCombining with the conventional atmosphere refraction model empirical formula ht＝-21.74089877-6.4413257005lnR+69.21177057R0.9805Calculating to obtain the refractive apparent height htk。
The further technical scheme of the invention is as follows: in the step 4, the second group of starlight refraction information can be in a form that a single star sensor observes two refraction stars simultaneously, or in a form that two airborne star sensors respectively observe one refraction star.
Advantageous effects
The invention provides an astronomical analytic positioning method based on starlight refraction information, which overcomes the defects that the existing astronomical direct positioning method based on starlight refraction needs iterative calculation and the number of refracted starlights is not less than three, has high requirement, and aims at the defects of poor observability and slow precision convergence of a starlight refraction astronomical filtering positioning method, and realizes analytic solution of the absolute position of an aircraft by using two groups of starlight refraction information, thereby having higher solving speed and higher positioning precision.
The invention can improve the pure astronomical positioning accuracy, is easy to realize, needs less refraction information (two groups) than the conventional pure astronomical direct positioning method (at least three groups and more than three groups), greatly reduces the calculated amount of the analytic method compared with the iterative calculation/filtering calculation of the conventional astronomical positioning, greatly reduces the required observation time, reduces the requirement on sensor configuration and the calculation difficulty, and can reach 10 in the orbit period on average in the condition of consistent simulation parameters-10Is higher than conventionalA pure astronomical direct positioning method; under the ideal condition that the measurement error of the star sensor is 3' (1 sigma), the positioning accuracy of the method reaches 150m (1 sigma), and is superior to the positioning accuracy of 300m (1 sigma) of the conventional pure astronomical direct positioning algorithm.
TABLE 1 two pure astronomical direct positioning methods based on star sensor precision comparison
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, wherein like reference numerals are used to designate like parts throughout.
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a schematic diagram of the refraction principle of starlight in the form of edge transmission in the earth atmosphere;
FIG. 3 is a schematic diagram of a dual-star light refraction direct positioning model according to the present invention;
FIG. 4 is a comparison graph of theoretical positioning accuracy of two methods: (a) a conventional method; (b) the invention is provided;
FIG. 5 is a plot of the positioning error of the present invention under a typical error source: (a) the X direction; (b) a Y direction; (c) a Z direction; (d) and (4) positioning errors.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention provides an astronomical analytic positioning method based on starlight refraction information, the implementation process is shown in figure 1, firstly, two groups of starlight refraction information supporting a direct positioning method are obtained, then auxiliary vectors are constructed, a positioning model of double starlight refraction information is established by utilizing the geometric relation among aircraft position vectors, starlight refraction vectors and the auxiliary vectors, two space linear equations are simultaneously established to construct a linear equation set, and finally, the analytic resolution of the absolute position of an aircraft is completed by combining measurement data.
The concrete implementation steps are as follows:
step (1): obtaining starlight refraction information
The star refraction principle of the atmospheric edge transmission form is shown in figure 2, and at least two groups of refraction information are required for realizing the direct positioning of the star sensor based on the principle, and the method comprises the following steps: refracting starlight unit vector mu 'under inertial coordinate system'kUnit vector mu of original starlight corresponding to refracted starlight in inertial coordinate systemkAngle of refraction RkAnd a refractive apparent height htk. The star sensor is usually used as an attitude sensor to output attitude quaternion of an aircraft, and has the capability of outputting star light refraction information in the star light refraction working process of a star light refraction area near the atmospheric layer at the edge of the sensitive earth, and the detailed steps of the sensitive star light refraction information in the step (1) comprise:
(11) parallel starlight mu emitted by stellar kkThe light is refracted when passing through the atmosphere with the height of 25km to 50km from the earth surface, the refracted light is sensitive by the star sensor to form an image on a CCD (charge coupled device) area array, and the unit vector of the refracted star light under the coordinate system (s system) of the star sensor can be obtained through conversion according to the pixel point coordinates
(12) Obtaining refraction star light vectors under the inertial system i system according to the star map recognition algorithm and the refraction star recognition algorithm in a matching way
Corresponding original star starlight
And a coordinate conversion matrix M between the inertial system i and the star sensor system s, by which a refracted star light vector mu under the inertial system i can be obtainedk' (the inertial system superscript i is omitted in subsequent steps);
(13) obtaining the original starlight mu of the stellar k by observationkAnd refracting starlight mukCalculating and obtaining the refraction angle R between vectors according to the cosine formula of the included anglekThen combining the conventional atmosphere refraction model empirical formula
ht＝-21.74089877-6.4413257005lnR+69.21177057R0.9805
Into angle of refraction RkCalculating to obtain the corresponding refraction apparent height h of the starlight on the refraction pathtk。
Step (2): construction of auxiliary vectors to obtain horizon information
Vector information of the refracted starlight is obtained through measurement in the step (1), only one space free surface can be determined according to the vector information, and the free surface needs to be fixed through horizon information provided by an atmospheric refraction model. Using the information mu measured in step (1)k′、μkAnd htkAuxiliary vector r under the structural inertia system iupk：
Wherein R iseThe auxiliary vector r is the radius of the earth according to equation (1)upkLocated in the refracted starlight muk', original starlight mukAnd the refraction plane of the earth center and the unit vector mu of the original starlightkOrthogonal;
as shown in FIG. 3, the original starlight unit vector μ in the form of edge transmission in the earth's atmospherekThe space coordinate point T under the inertial system is tangent to the spherical atmosphere and tangent to the spherical atmospherekVector formed by connecting with center of earth O
And the auxiliary vector constructed in the step satisfies the following conditions:
thereby determining the space tangent point T corresponding to the refraction apparent height on the starlight transmission pathkThree-dimensional in inertial frameCoordinate (x)k,yk,zk)；
And (3): construction of a spatial rectilinear model
Constructing a space straight line at a position corresponding to the over-refraction apparent height according to a point line type, and measuring to obtain a starlight refraction vector mu in the step (1)k' providing the direction of the spatial straight line, the spatial tangent point T constructed in step (2)kProviding spatial coordinates whereby a straight line L can be uniquely determined in spacekStraight line LkThe spatial equation of (a) is:
the line passes through the observation points according to the starlight transmission path, so that each point on the line is a potential location of the aircraft. (s)xk,syk,szk) Denotes a refracted starlight unit vector μ 'denoted by reference numeral k'kThe component under the inertial system, the aircraft position vector r is (x, y, z).
And (4): obtaining a second spatial line
Synchronously and simultaneously observing the horizon in other directions by using another star sensor carried on the aircraft, and calculating to obtain a second space straight line L according to the steps (1), (2) and (3)nAny point on the same straight line is the potential position of the aircraft;
and (5): calculating aircraft absolute position information
Obtaining two groups of starlight refraction information in different directions at the same time according to the step (1), and determining two space straight lines L according to the steps (2), (3) and (4)m、LnThe two spatial lines intersect at a point in space, which is the absolute position of the aircraft. And (3) constructing a linear equation system with the aircraft position information as an unknown quantity according to the geometrical relationship of the aircraft position vector, the starlight refraction vector and the auxiliary vector in the space, and solving to obtain the absolute position r of the aircraft.
The detailed steps of the step (5) comprise:
(51) according to the null presented in step (3)Inter-linear model, according to the principle of step (5), space linear Lm、LnThe system of equations (a) and (b) are combined to obtain a linear system of equations containing aircraft position information r:
see FIG. 3, where m and n denote indices for observing two groups of refracted starlight,(s)xm,sym,szm) Denotes a refracted starlight unit vector μ 'denoted by the reference numeral m'mThe component under the inertial system, the aircraft position vector r ═ (x, y, z);
(52) for convenient calculation, a group of parameters a, b and c are set according to the starlight refraction information measured in the step (1) in the following form:
(53) substituting the parameters set in the step (52) to solve a linear equation system of the formula (3) to obtain the absolute position of the aircraft:
in this example, it should be noted that:
the basic condition for realizing the astronomical analysis positioning method provided by the invention is that the number of the refraction stars can be observed to be two at the current observation time, and the condition can be satisfied in the form that a single star sensor simultaneously observes two refraction stars or in the form that two airborne star sensors are respectively used for observing one refraction star in the step (4).
The linear equation set (3) constructed in the step (51) comprises four mutually independent equations, the number of the equations is more than that of the unknowns, so that the analytical solution obtained in the steps (52) and (53) according to the embodiment of the invention is only one form, and the parameter configuration form in the step (52) is different from that in the solution, for example, c is equal to s in the formula (4)xn/synIn step (53)The solution (5) was obtained in a different expression form although the values were the same.
The simulation verification of the theoretical precision and the positioning precision under a typical error source of the astronomical analytic positioning method is completed according to the steps of the example:
[1] setting simulation parameters of the star sensor: focal length set to 0.098m, field of view set to 8 ° × 8 °; by Tycho
II, constructing a navigation star library by a star table according to certain screening conditions; the precision of the angle measurement of the optical axis of the star sensor is 3'.
[2] Track parameters: the initial flying speed is 7668m/s, the track height is 400km, the initial track long semi-axis is 6778.13km, the track inclination angle is 60 degrees, the eccentricity is 0, and the ascension of the ascending intersection point, the argument of the perigee and the true perigee are 0 degrees.
[3]And (3) simulation results: the simulation time length is set to be 5400s of one track period, the theoretical positioning accuracy result of the invention is compared and shown in figure 4, and the average time can reach 10 in the track period-10Of the order of magnitude, with a positioning accuracy of less than 10 at part of the time-8Magnitude; under the ideal condition of introducing a typical error source, namely a star sensor measuring error of 3' (1 sigma), the positioning accuracy of the invention reaches about 150m (1 sigma), and a variation curve of the calculated positioning error and the predicted covariance within the simulation time length of 400s is shown in figure 5. Wherein the gray curve with larger internal variation amplitude represents the calculated positioning error;
a black curve with relatively gentle peripheral changes represents the prediction mean square error;
[4] and (4) analyzing results: compared with the conventional pure astronomical direct positioning method based on starlight refraction, the method has the advantages that the theoretical positioning precision can be higher; under the condition that an error source is modeled as white noise, the positioning random error distribution of a simulation result is matched with the statistical prediction mean square error, the correctness of the positioning model and the error model is illustrated, the statistical prediction covariance is about 150m (1 sigma), and the positioning precision of the conventional pure astronomical direct positioning algorithm reaches 300m (1 sigma).
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications or substitutions can be easily made by those skilled in the art within the technical scope of the present disclosure.
Claims (3)
1. An astronomical resolution positioning method based on starlight refraction information is characterized by comprising the following steps:
step 1: the method comprises the following steps of acquiring starlight refraction information by utilizing a starlight refraction area near the atmospheric layer of the sensitive earth edge of a star sensor, wherein the starlight refraction information comprises the following steps: refracting starlight unit vector mu 'under inertial coordinate system'kUnit vector mu of original starlight corresponding to refracted starlight in inertial coordinate systemkAngle of refraction RkAnd a refractive apparent height htk；
Step 2: constructing an auxiliary vector r under an inertial system by using the measurement information in the step 1upkFor providing horizon information, using step 1 measurement information muk′、μkAnd htkAuxiliary vector r under the structural inertia system iupkThe following:
wherein R iseIs the radius of the earth, the auxiliary vector rupkThe requirement is that the auxiliary vector and the original starlight unit vector are located in the space plane formed by the refracted starlight vector, the original starlight vector and the earth center
Orthogonal;
therefore, under the earth atmosphere edge transmission form, the original starlight unit vector
Air under inertial systemThe position of the inter-coordinate point T is tangent to the spherical atmosphere and is tangent to the inertial system at a point TkVector formed by connecting with center of earth O
Exactly the auxiliary vector, so as to determine the space tangent point T corresponding to the refraction apparent height on the starlight transmission pathkThree-dimensional coordinates (x) in inertial framek,yk,zk) The coordinates provide important basis for the horizon information to complete the positioning;
and step 3: combining the starlight refraction vector measured in the step 1 with the space tangent point T constructed in the step 2kA straight line L can be uniquely determined in spacekThe direction of the straight line and the refracted star light vector mu'kSame and passing through the spatial midpoint TkStraight line LkThe spatial equation of (a) is:
the line passes through the observation points according to the starlight transmission path, so that each point on the line is a potential location of the aircraft. (s)xk,syk,szk) Denotes a refracted starlight unit vector μ 'denoted by k'kThe component under the inertial system, the aircraft position vector r ═ (x, y, z);
and 4, step 4: simultaneously acquiring a second group of starlight refraction information according to the steps 1-3, and constructing an equation of a second space straight line L;
and 5: according to the two groups of starlight refraction information measured in the step 1-4, two constructed space straight lines have a unique intersection point in the space, and the intersection point is the potential absolute position of the aircraft; according to the geometrical relationship of the aircraft position vector, the starlight refraction vector and the auxiliary vector in the space, a linear equation set with the aircraft position information as an unknown number is constructed by simultaneous two space linear equations, and then the absolute position of the aircraft is obtained by analytic solution:
wherein m and n represent symbols for observing two groups of refracted starlight,(s)xk,syk,szk) Denotes a refracted starlight unit vector μ 'denoted by reference numeral k'kThe component under the inertial system, the aircraft position vector r ═ (x, y, z); for convenient calculation, a group of parameters a, b and c are set according to the star light refraction information measured in the step 1 in the following form:
substituting the parameters, solving a linear equation system to obtain the absolute position of the aircraft and obtaining a group of analytic solutions, wherein the analytic solutions are as follows:
2. the astronomical resolution positioning method based on starlight refraction information according to claim 1, wherein: the detailed steps of step 1 include:
(11) the refracted starlight emitted by the star k is captured by the star sensor and imaged on the CCD area array to obtain the unit vector of the refracted starlight under the sensor coordinate system, namely the s system
(12) Obtaining the original star starlight corresponding to the refracted star light vector under the inertial system i system according to the refracted star identification matching
(13) Calculating to obtain the refraction angle R between vectors according to the cosine formula of the included anglekCombined with the empirical formula h of the conventional atmospheric refraction modelt＝-21.74089877-6.4413257005lnR+69.21177057R0.9805Calculating to obtain the refractive apparent height htk。
3. The astronomical resolution positioning method based on starlight refraction information according to claim 1, wherein: in the step 4, the second group of starlight refraction information can be in a form that a single star sensor simultaneously observes two refraction stars, or in a form that two airborne star sensors respectively observe one refraction star.
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