CN114526726A - Star refraction navigation star-viewing scheme optimization design method based on observability analysis - Google Patents
Star refraction navigation star-viewing scheme optimization design method based on observability analysis Download PDFInfo
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Abstract
The invention discloses a starlight refraction navigation star-viewing scheme optimization design method based on observability analysis, which comprises the following steps: calculating the upper limit of the star viewing times according to the given star viewing time and the star sensor attitude adjustment preparation time; loading a pre-stored standard track of the aircraft, determining a search upper limit and a search lower limit of the start time of each satellite observation period based on the satellite observation times upper limit to obtain a search linear constraint, and generating the start time of each satellite observation period and a corresponding yaw angle during satellite observation according to the search linear constraint; and finally, constructing an objective function by taking the starting time of each satellite observation period and the corresponding yaw angle of the satellite observation period as optimization variables, operating an optimization algorithm, and determining the starting time of each satellite observation period and the corresponding yaw angle when the objective function reaches the maximum. The invention forms the star observation scheme by taking the observation performance of the refraction star as an optimization index by taking the start time of star observation and the yaw angle as optimization variables, and is beneficial to improving the navigation precision of starlight refraction.
Description
Technical Field
The invention belongs to the technical field of astronomical navigation, and particularly relates to a starlight refraction navigation star-viewing scheme optimization design method based on observability analysis.
Background
The aerospace cross-domain aircraft is an aircraft which is propelled by a rocket and navigates according to a free projectile track after being shut down. Because the aerospace cross-domain aircraft needs to strike a preset target accurately, a high-precision and high-reliability navigation technology becomes a key for supporting the aerospace cross-domain aircraft to achieve accurate guidance.
In order to realize high-precision autonomous navigation of aerospace cross-domain aircrafts, various navigation schemes have been intensively studied. The most basic scheme is to realize full-autonomous navigation based on inertial navigation. The inertial navigation technology is to utilize inertial devices such as an accelerometer, a gyroscope and the like to measure the visual acceleration, the angular velocity and other information of an aircraft, and output a real-time flight state after carrying out computer integral operation. However, even in expensive high-precision inertial navigation, navigation errors accumulate over time, and the errors cannot be corrected by a single navigation system, which leads to divergence of the navigation errors. Therefore, the navigation error must be corrected by an external auxiliary information source.
The inertial/starlight refraction combined navigation technology has become an important development direction of aerospace cross-domain aircraft navigation due to the unique advantages of high precision, full autonomy, high reliability and the like. The starlight refraction navigation is to measure refraction starlight information by using a high-precision star sensor and indirectly sensitively horizon through a mathematical model of starlight refraction in the atmosphere and an error compensation method, so that the high-precision positioning navigation of the aerospace cross-domain aircraft is realized [2 ]. In the inertial/starlight refraction combined navigation, the differences of navigation positioning precision can be caused by observing refraction star combinations in different directions. There is currently a great deal of work focused on the star-viewing solution, however, the methods already disclosed still need to be improved. The nature of the navigation positioning accuracy difference is that the observability of the system is different, namely the difference of the quantity measurement to the position estimation capability.
Disclosure of Invention
The invention aims to provide a starlight refraction navigation star-viewing scheme optimization design method based on observability analysis, and solves the problem.
In view of this, the present invention provides a method for optimizing a star-view scheme based on an observability analysis and star refraction navigation, comprising:
firstly, calculating the upper limit of the star viewing times according to the given star viewing time length and the star sensor attitude adjusting preparation time length;
then, loading a pre-stored aircraft standard track, determining a search upper limit and a search lower limit of the starting time of each satellite observation period based on the satellite observation times upper limit to obtain a search linear constraint, and generating the starting time of each satellite observation period and a corresponding yaw angle during satellite observation according to the search linear constraint;
and finally, constructing an objective function by taking the starting time of each satellite observation period and the corresponding yaw angle of the satellite observation period as optimization variables, operating an optimization algorithm, and determining the starting time of each satellite observation period and the corresponding yaw angle when the objective function reaches the maximum.
Further, the generating of the starting time of each satellite observation period and the corresponding yaw angle of the satellite observation time includes: and extracting all the moments of each satellite observation time interval and the position vectors and the speed vectors in the geocentric inertial coordinate system corresponding to the moments.
Further, the operation optimization algorithm further includes: and determining the numbers of the refracted star stars and the unit direction vectors of the refracted star lights at all the moments of each star observation period.
Further, the operation optimization algorithm further includes: and determining the star signs of the refracted stars and the unit direction vectors of the refracted starlights imaged on the star sensor image plane at all times of each star observation period.
Further, the operation optimization algorithm further includes: and calculating the snow-charging information matrix of all the star viewing moments in each star viewing period.
Another objective of the present invention is to provide a star refraction navigation star-viewing scheme optimization design system based on observability analysis, which is characterized by comprising:
the processing unit is used for calculating the upper limit of the star viewing times according to the given star viewing time length and the star sensor posture adjusting preparation time length;
the generating unit is used for loading a pre-stored aircraft standard track, determining a search upper limit and a search lower limit of the starting time of each satellite observation time interval based on the satellite observation frequency upper limit to obtain a search linear constraint, and generating the starting time of each satellite observation time interval and a corresponding yaw angle during satellite observation according to the search linear constraint;
and the determining unit is used for constructing an objective function by taking the starting time of each satellite observation period and the corresponding yaw angle of the satellite observation period as optimization variables, operating an optimization algorithm and determining the starting time of each satellite observation period and the corresponding yaw angle when the objective function reaches the maximum.
Further, the generating unit comprises an obtaining module, configured to extract position vectors and velocity vectors in all time instants of each satellite observation period and the geocentric inertial coordinate system corresponding to the time instants.
Further, the determining unit further includes a first calculating module, configured to determine the refracted star number and the refracted star light unit direction vector at all times of each star observation period.
Furthermore, the determining unit further comprises a second calculating module, which is used for determining the refracted star number and the refracted star light unit direction vector imaged on the star sensor image plane at all times of each star observing time period.
Further, the determining unit further comprises a third calculating module for calculating the snow-charging information matrix of all the star-viewing moments in each star-viewing time interval.
The invention achieves the following significant beneficial effects:
the realization is simple, include: firstly, calculating the upper limit of the star viewing times according to the given star viewing time length and the star sensor attitude adjusting preparation time length; then, loading a pre-stored aircraft standard track, determining a search upper limit and a search lower limit of the starting time of each satellite observation period based on the satellite observation times upper limit to obtain a search linear constraint, and generating the starting time of each satellite observation period and a corresponding yaw angle during satellite observation according to the search linear constraint; and finally, constructing an objective function by taking the starting time of each satellite observation period and the corresponding yaw angle of the satellite observation period as optimization variables, operating an optimization algorithm, and determining the starting time of each satellite observation period and the corresponding yaw angle when the objective function reaches the maximum. The invention forms the star observation scheme taking the observation performance of the refraction star as the optimization index by taking the start time of the star observation and the yaw angle as the optimization variables, is applied to the optimization design of the star observation scheme in the inertia/starlight refraction combined navigation, and is beneficial to improving the navigation precision of starlight refraction.
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FIG. 1 is a flow chart of the star refraction navigation star-viewing scheme optimization design method based on observability analysis.
Detailed Description
The advantages and features of the present invention will become more fully apparent from the following description and appended claims, taken in conjunction with the accompanying drawings and detailed description of specific embodiments of the invention. It is to be noted that the drawings are in a very simplified form and are not to scale, which is intended merely for convenience and clarity in describing embodiments of the invention.
It should be noted that, for clarity of description of the present invention, various embodiments are specifically described to further illustrate different implementations of the present invention, wherein the embodiments are illustrative and not exhaustive. In addition, for simplicity of description, the contents mentioned in the previous embodiments are often omitted in the following embodiments, and therefore, the contents not mentioned in the following embodiments may be referred to the previous embodiments accordingly.
While the invention is amenable to various modifications and alternative forms, specifics thereof have been shown by way of example in the drawings and will be described in detail. It should be understood that the inventors do not intend to limit the invention to the particular embodiments described, but intend to protect all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the claims. The same meta-module part number may be used throughout the drawings to represent the same or similar parts.
Referring to fig. 1, a method for optimizing a star-view scheme based on an observability analysis and star refraction navigation includes:
step S101, calculating the upper limit of the star viewing times according to the given star viewing time and the star sensor attitude adjusting preparation time;
step S102, loading a pre-stored aircraft standard track, determining a search upper limit and a search lower limit of the starting time of each satellite observation time interval based on the satellite observation frequency upper limit to obtain a search linear constraint, and generating the starting time of each satellite observation time interval and a corresponding yaw angle during satellite observation according to the search linear constraint;
and S103, constructing an objective function by taking the starting time of each satellite observation period and the corresponding yaw angle of the satellite observation period as optimization variables, operating an optimization algorithm, and determining the starting time of each satellite observation period and the corresponding yaw angle when the objective function reaches the maximum.
According to an aspect of an embodiment of the invention, the duration Δ t is based on a given observation satellite durationobsAnd star sensor attitude adjustment preparation time delta tattiCalculating the upper limit k of the number of satellite views
In the formula (I), the compound is shown in the specification,
is shown to take only
The integer part of (1); t is the observable star duration, i.e., the flight duration of the aircraft at the suitable star-viewing altitude. If k < 3, decrease Δ tobsK is more than or equal to 3; if k is more than or equal to 3, the star number n can be [3 k ]]Selected from integers within the range.
According to one aspect of the embodiment of the invention, a pre-stored standard trajectory of the aircraft is loaded, and the upper search limit, the lower search limit and the constraint of the starting time of each satellite observation period are determined. The optimization variable of the optimization algorithm is the start time t of each observation period1，t2，...，tnYaw angle alpha corresponding to the time of viewing the star1，α2，...，αnWherein the upper search limit for the start time is set to:
[T-Δtobs-(n-1)(Δtatti+Δtobs)：T-Δtobs-(n-2)(Δtatti+Δtobs)，...，T-Δtobs]
search lower bound is set to
[0，Δtobs+Δtatti，...，(n-1)(Δtobs+Δtatti)]
The linear constraint of the search is
According to one aspect of the embodiments of the present invention, an optimization algorithm is run to find the start time and corresponding yaw angle of each satellite observation period when the objective function is maximized. The optimization process is as follows:
1) generating a set of star observation start times t according to the constraints10，t20，...，tn0And yaw angle alpha10，α20，...，αn0. And extracting all the moments of the star observation time interval and the position vector r and the velocity vector v in the geocentric inertial coordinate system corresponding to the moments.
2) And determining the observable refraction star in the star observation period. Taking the ith time in the star observation period as an example, the position vector of the aircraft at the moment is assumed to be riIf the unit direction vector of the fixed star in the inertia generating system is e, the starlight vector-e of the jth fixed starjAnd the aircraft position vector riAngle of (theta)i，jCan be expressed as
θi，j＝arc cos(-ej·ri) (2)
The minimum and maximum included angles allowed by the aircraft and the starlight vector are respectively
In the formula, ρmin、ρmaxFor a predetermined minimum and maximum distance, where pmin＝20000m，ρmax＝50000m；ReIs the earth mean radius.
Determining thetamin＜θi，j＜θmaxWhether or not this is true. If yes, continuing the subsequent calculation process; if the satellite observation time interval does not exist, other fixed stars in the navigation star library are replaced, and the search upper limit, the search lower limit and the search constraint of the starting time of each satellite observation time interval are repeatedly determined.
In calculating thetai，jOn the basis of the formula, the refraction angle a can be solved by using the following formular
In the formula, h0Is a standard height; h is the height of the density scale; rho0Is h0Atmospheric density at altitude. k (. gamma.) can be calculated by the following formula
Where γ is the reciprocal of the wavelength of the light.
Then, the apparent height h is calculated by the formula (6)a
And determining whether the following equation is satisfied
20000≤ha≤50000 (7)
If yes, the fixed star is a refraction star which can be accurately observed, and the subsequent calculation process is continued; if the star period does not exist, replacing other fixed stars in the star base, and repeatedly determining the search upper limit, the search lower limit and the search restriction of the starting time of each star period. .
Refracted starlight unit direction vector e'jCan be expressed as
And repeatedly determining the upper limit, the lower limit and the constraint of the search of the starting time of each satellite observation period. The refracted star number and the refracted star light unit direction vector e 'are determined for each star viewing time'j。
According to an aspect of an embodiment of the invention, a refracted star that can be imaged on an image plane of the star sensor is determined.
The yaw angle beta can be expressed as
Wherein a is the side length of the image plane; f is the focal length of the star sensor. The yaw angle of each star observation is recorded as alpha, so that a transformation matrix from a starting inertial system to a star sensor coordinate system can be calculated
According to
And e ', a refracted starlight unit vector e ' in the star sensor coordinate system can be obtained 's
Thus, the pixel coordinate p of the refracted starlight can be expressed as
In the formula, nsIs a unit direction vector of the optical axis of the star sensor in the coordinate system of the star sensor. If the x and y axis coordinate value p in px、pyAnd if the refraction quantity is less than a, the refracted star light can be imaged on the star sensor image plane.
And repeatedly operating the optimization algorithm to find the starting time and the corresponding yaw angle of each satellite observation time interval when the objective function reaches the maximum. And determining the observable star signs of the refracted stars and the unit direction vector e' of the refracted stars in each star viewing moment.
According to an aspect of an embodiment of the invention, a fee snow information matrix F of the star viewing time is calculatedi。
The state transition matrix from the moment i-1 to the moment i is recorded as phii，t-1Then the time update of the snow-cost information matrix can be expressed as
In the formula, Fi-1The snow information matrix at the moment i-1; phii，i-1Can be referred to in reference [3 ]]。
Let σ (a)r) The angle measurement precision of the star sensor is obtained, and the measurement noise variance matrix of the refraction angle can be expressedIs composed of
R(ar)＝σ2(ar) (14)
The apparent height measurement noise variance matrix can be calculated by the following formula
R(ha)＝[rscos(ar+θij)]2R(ar) (15)
The observation matrix of the star moments can be expressed as
In the formula, rs＝|ri|。
Note Ri＝R(ha) The measurement update of the Fisher information matrix can be obtained by combining the equations (13), (15) and (16)
Iterative computation FiTo the last moment of the trajectory. Using Fi -1Diagonal element f of11、f22、f33Constructing an objective function
Searching the maximum value of the objective function and outputting the corresponding star observation starting time t1，t2，...，tn]maxAnd corresponding yaw angle [ alpha ]1，α2，...，αn]max。
According to one aspect of the embodiments of the present invention, a star observation scheme is generated: the viewing time periods are [ t ] respectively1 t1+Δtbos]、[t2t2+Δtobs]…[tn tn+Δtobs]The corresponding yaw angle is [ alpha ]1，α2，...，αn]max。
As a specific embodiment, the invention relates to a starlight refraction navigation star-viewing scheme optimization design method based on observability analysis, which comprises the following steps:
(1) gives the star viewing time length delta tobs60s and star sensor attitude setting preparation time delta tatti60 s. The star observation time length T is 500s, and the star observation time upper limit k is calculated according to the formula (1)
Since k is equal to or greater than 3, the star number n is set to 4.
(2) Loading a standard track of the aircraft, wherein the optimization variable of the optimization algorithm is the starting time t of each satellite observation period1，t2，t3，t4And corresponding yaw angle alpha1，α2，α3，α4With the upper search limit set to [80, 200, 320, 440 ]]s, search lower bound set to [0, 120, 240, 360%]s
The linear constraint of which is
(3) And (3) running an optimization algorithm, wherein the optimization process of the optimization algorithm is to search for optimization variables meeting the constraint in the step (2) and solve the maximum value of the objective function. The optimization process comprises the following calculation steps:
1) and (3) generating a group of staring start time [ 4178298430 ] s and a yaw angle [ 1252748189 ] °accordingto the constraints in the step (2). Extracting position vectors r and velocity vectors v, e.g. of all instants of the observation period and their corresponding geocentric inertial frame representations
[1s 410901m -6534158m 761088m 31.7438m/s -1109m/s 7235m/s。
2) And determining the observable refraction star in the star observation period. Taking 4s in the star observation period as an example, the aircraft position vector r4＝[410994 6537445 782790]And m is selected. Loading sidereal rowbankExtracting all fixed star unit direction vectors e, and calculating the fixed star starlight-e with the number 20872087And r4Angle of (theta)4，2087
θ4，2087＝arccos(-e2087·r4)＝76.15° (20)
At this time, the minimum angle and the maximum angle are respectively
As can be seen from the above calculation process, θ4，2087Between the minimum included angle and the maximum included angle, the refraction angle a is solved by using the following formular
A can be obtained by calculationr＝216.89″。
Further calculating the apparent height
The apparent height satisfies 20000 m-haLess than or equal to 50000m, the particle fixed star is a refraction star which can be accurately observed. A refracted star light unit direction vector e 'of the refracted star'jIs calculated as follows
And repeating the step 2), and recording the star number and the unit direction vector e' of each refracted star at each star viewing moment.
3) A refracted star that can be imaged on the star sensor image plane is determined.
Noting the yaw angle of each observation satellite as α, the yaw angle β can be expressed as
In the formula, a is 1024 pixels; and f 3232.64 pixels. Further calculating coordinate transformation matrix
e′sIs a unit direction vector e 'of refracted star light expressed in a star sensor body coordinate system'sHas the following conversion relation with e
Judging whether the refracted star light energy is observed by the star sensor
Because the x and y axis coordinate value p in px、pyAnd the refracted star light can be imaged on the star sensor image plane when the refracted star light is smaller than a. And repeating the step 3), and recording the fixed star signs and the refraction starlight unit direction vectors e' of the observable refraction stars in each star observation time t.
4) Time update F for calculating a snow cost information matrixi/i-1
σ(ar) The angle measurement precision of the star sensor and the measurement noise variance matrix are calculated as follows
R(ha)＝[rscos(ar+θij)]2R(ar)＝7845m2 (33)
Calculate Hi
Computing matrix Fi
5) Repeating the steps 2) to 4), and iteratively calculating FiTo the last moment of the trajectory. Taking Fi -1Diagonal element f of11、f22、f33Calculating an objective function
6) And repeating the steps 1) to 5), searching the maximum value of the objective function, and outputting the corresponding start time [ 4178298430 ] s of the sightseeing star and the corresponding yaw angle [ 1252748189 ] °.
(5) Generating a star observation scheme: the star observation time periods are respectively [ 464 ] s, [ 178238 ] s and [ 298358 ] s [ 430490 ] s, and the corresponding yaw angle is [ 1252748189 ] °.
From the above description, it can be seen that the above-described embodiments of the present application achieve the following technical effects:
the realization is simple, include: firstly, calculating the upper limit of the star viewing times according to the given star viewing time length and the star sensor attitude adjusting preparation time length; then, loading a pre-stored aircraft standard track, determining a search upper limit and a search lower limit of the starting time of each satellite observation period based on the satellite observation times upper limit to obtain a search linear constraint, and generating the starting time of each satellite observation period and a corresponding yaw angle during satellite observation according to the search linear constraint; and finally, constructing an objective function by taking the starting time of each satellite observation period and the corresponding yaw angle of the satellite observation period as optimization variables, operating an optimization algorithm, and determining the starting time of each satellite observation period and the corresponding yaw angle when the objective function reaches the maximum. The invention forms the star observation scheme taking the observation performance of the refraction star as the optimization index by taking the start time of the star observation and the yaw angle as the optimization variables, is applied to the optimization design of the star observation scheme in the inertia/starlight refraction combined navigation, and is beneficial to improving the navigation precision of starlight refraction.
Any other suitable modifications can be made according to the technical scheme and the conception of the invention. All such alternatives, modifications, and improvements as would be apparent to one skilled in the art are intended to be within the scope of the invention as defined by the appended claims.
Claims (10)
1. A starlight refraction navigation star-viewing scheme optimization design method based on observability analysis is characterized by comprising the following steps:
firstly, calculating the upper limit of the star viewing times according to the given star viewing time length and the star sensor attitude adjustment preparation time length;
then, loading a pre-stored aircraft standard track, determining a search upper limit and a search lower limit of the starting time of each satellite observation period based on the satellite observation times upper limit to obtain a search linear constraint, and generating the starting time of each satellite observation period and a corresponding yaw angle during satellite observation according to the search linear constraint;
and finally, constructing an objective function by taking the starting time of each satellite observation period and the corresponding yaw angle of the satellite observation period as optimization variables, operating an optimization algorithm, and determining the starting time of each satellite observation period and the corresponding yaw angle when the objective function reaches the maximum.
2. The observability analysis-based starlight refraction navigation star-viewing scheme optimization design method according to claim 1, wherein the generating of the starting time of each star-viewing period and the corresponding yaw angle of the star-viewing period comprises: and extracting all the moments of each satellite observation time interval and the position vectors and the speed vectors in the geocentric inertial coordinate system corresponding to the moments.
3. The observability analysis-based starlight refraction navigation star-viewing scheme optimization design method according to claim 1, wherein the operation optimization algorithm further comprises: and determining the numbers of the refracted stars and the unit direction vectors of the refracted stars at all the moments of each staring time period.
4. The observability analysis-based starlight refraction navigation star-viewing scheme optimization design method according to claim 1, wherein the operation optimization algorithm further comprises: and determining the star signs of the refracted stars and the unit direction vectors of the refracted starlights imaged on the star sensor image plane at all times of each star observation period.
5. The observability analysis-based starlight refraction navigation star-viewing scheme optimization design method according to claim 1, wherein the operation optimization algorithm further comprises: and calculating the snow-charging information matrix of all the star viewing moments in each star viewing period.
6. A starlight refraction navigation star-viewing scheme optimization design system based on observability analysis is characterized by comprising the following steps:
the processing unit is used for calculating the upper limit of the star viewing times according to the given star viewing time length and the star sensor posture adjusting preparation time length;
the generating unit is used for loading a pre-stored aircraft standard track, determining a search upper limit and a search lower limit of the starting time of each satellite observation time interval based on the satellite observation frequency upper limit to obtain a search linear constraint, and generating the starting time of each satellite observation time interval and a corresponding yaw angle during satellite observation according to the search linear constraint;
and the determining unit is used for constructing an objective function by taking the starting time of each satellite observation period and the corresponding yaw angle of the satellite observation period as optimization variables, operating an optimization algorithm and determining the starting time of each satellite observation period and the corresponding yaw angle when the objective function reaches the maximum.
7. The observability analysis-based starlight refraction navigation star-viewing scheme optimization design system according to claim 6, wherein the generation unit comprises an acquisition module for extracting position vectors and velocity vectors at all times of each star-viewing period and in the geocentric inertial coordinate system corresponding to the time.
8. The observability analysis-based star refraction navigation star viewing scheme optimization design system according to claim 6, wherein the determination unit further comprises a first calculation module for determining the refracted star number and the refracted star unit direction vector at all times of each star viewing period.
9. The observability-analysis-based star refraction navigation star viewing scheme optimization design system according to claim 6, wherein the determination unit further comprises a second calculation module for determining the refracted star and the refracted star unit direction vector imaged on the star sensor image plane at all times of each star viewing period.
10. The observability-analysis-based starlight refraction navigation star viewing scheme optimization design system according to claim 6, wherein the determination unit further comprises a third calculation module for calculating snow-charge information matrices of all star viewing moments for each star viewing period.
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