CN109489689B - Satellite vector measurement error on-orbit estimation method based on alpha-beta filtering - Google Patents

Satellite vector measurement error on-orbit estimation method based on alpha-beta filtering Download PDF

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CN109489689B
CN109489689B CN201811384313.6A CN201811384313A CN109489689B CN 109489689 B CN109489689 B CN 109489689B CN 201811384313 A CN201811384313 A CN 201811384313A CN 109489689 B CN109489689 B CN 109489689B
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attitude
star
vector
alpha
quaternion
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CN109489689A (en
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李新鹏
马英超
吴永康
胡雄超
孙朔冬
黄厦
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Shanghai Aerospace Control Technology Institute
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Abstract

The invention discloses an on-orbit estimation method for star vector measurement errors based on alpha-beta filtering, which comprises the following steps: s1, calculating the attitude quaternion by the observation star vector and the reference star vector of the attitude determination star by adopting an equal weight method
Figure DDA0001872614100000011
S2, processing the attitude quaternion by adopting an alpha-beta filter
Figure DDA0001872614100000012
Obtaining a reference attitude quaternion
Figure DDA0001872614100000013
S3, quaternion from the reference attitude
Figure DDA0001872614100000014
Calculating a reference attitude matrix A; and S4, calculating the error of the observation star vector according to the reference attitude matrix A. The method can calculate the star vector weight in real time, optimize the attitude estimation algorithm and improve the attitude measurement precision.

Description

Satellite vector measurement error on-orbit estimation method based on alpha-beta filtering
Technical Field
The invention particularly relates to an on-orbit estimation method for star vector measurement errors based on alpha-beta filtering.
Background
The star sensor-gyroscope combined navigation is a mainstream scheme of a satellite platform with higher requirement on the current attitude measurement precision, and as a sensor with the highest attitude measurement precision at present, the attitude measurement precision of the star sensor directly influences the attitude control precision of the satellite platform. The attitude measurement precision is the most important assessment index of the star sensor.
Astronomical navigation sensors represented by star sensors are mostly used for estimating the attitude of an aircraft based on the Wahba problem. Minimum loss function of star sensor measurement attitude:
Figure BDA0001872614080000011
in the formula: n is the number of stars involved in the attitude estimation,
Figure BDA0001872614080000012
is an observation star vector under a star sensor measurement coordinate system;
Figure BDA0001872614080000013
is a reference star vector under a celestial coordinate system, aiIs the weight of the star vector.
The research literature finds that doctor Shuter proposes that the weight a of a star vector is determined by the error of an observed star vectori. Suppose the error of the attitude determination star i is sigmaiThen the weight aiThe calculation process of (2) is as follows:
Figure BDA0001872614080000014
Figure BDA0001872614080000015
there is no complete method for evaluating the error magnitude of the star vector in an on-orbit manner in the published literature, and most domestic star sensors adopt a method with equal weight in attitude calculation:
Figure BDA0001872614080000016
in the formula: and n is the star number participating in attitude calculation. And estimating the attitude by using the equal weight value, averaging the error of the star vector, and if the error of the star vector can be estimated in an orbit, and the weight of the star vector with smaller error in the attitude calculation process is improved, the attitude measurement precision of the star sensor can be improved under the condition of the same measurement information.
Disclosure of Invention
The invention aims to provide an alpha-beta filtering-based star vector measurement error on-orbit estimation method, which can calculate star vector weights in real time, optimize an attitude estimation algorithm and improve attitude measurement precision.
In order to achieve the purpose, the invention is realized by the following technical scheme:
an on-orbit estimation method for star vector measurement errors based on alpha-beta filtering is characterized by comprising the following steps:
s1, according to the observation star vector and the reference star vector of the attitude determination star, the weight a of the star vector in the attitude estimation algorithm such as QUESTiEqual method for calculating attitude quaternion
Figure BDA0001872614080000021
Wherein
Figure BDA0001872614080000022
q0Is a marked part, and is characterized in that,
Figure BDA0001872614080000023
is a sagittal portion;
s2, processing the attitude quaternion by adopting an alpha-beta filter
Figure BDA0001872614080000024
Obtaining a reference attitude quaternion
Figure BDA0001872614080000025
S3, quaternion from the reference attitude
Figure BDA00018726140800000216
Calculating a reference attitude matrix A, wherein the attitude matrix describes a conversion relation from an inertial coordinate system to a star sensor measurement coordinate system;
and S4, calculating the error of the observation star vector according to the reference attitude matrix A.
The filter equation adopted in step S2 is:
Figure BDA0001872614080000026
Figure BDA0001872614080000027
the prediction equation:
Figure BDA0001872614080000028
Figure BDA0001872614080000029
in the formula:
Figure BDA00018726140800000210
an estimate of the position at time k;
Figure BDA00018726140800000211
an estimate of the velocity at time k;
Figure BDA00018726140800000212
a predicted estimate for time k;
Figure BDA00018726140800000213
the predicted speed at the moment k;
z (k) is the measurement position at time k; t is a sampling period; alpha, beta is the system gain, alpha
Referred to as position gain, β as velocity gain;
the measured value Z (k) is an attitude quaternion
Figure BDA00018726140800000214
Sagittal portion of
Figure BDA00018726140800000215
The step S3 specifically includes:
Figure BDA0001872614080000031
q0is a marked part, and is characterized in that,
Figure BDA0001872614080000032
computing references for vector components
An attitude matrix A:
Figure BDA0001872614080000033
the step S4 specifically includes:
calculating the error sigma of the ith star vectori: by
Figure BDA0001872614080000034
1,2, n, n is the star number participating in attitude calculation;
Figure BDA0001872614080000035
is an observation star vector under a star sensor measurement coordinate system,
Figure BDA0001872614080000036
is a reference star vector under a celestial coordinate system.
Compared with the prior art, the invention has the following advantages:
the prior art can not estimate the vector error of the observation star in real time on line, and the attitude estimation precision is lower under the condition of the same star point mass center positioning error; the alpha-beta filter has small calculated amount and can estimate the star vector error in real time on orbit; compared with a method for directly adopting the measured value and the star base reference value to carry out difference estimation error, the method adopts the filtering value to calculate the reference attitude matrix to estimate the star vector error, and the reliability of the error value is higher; the alpha-beta filter has strong tracking capability and can effectively inhibit the influence of low-frequency errors.
Drawings
FIG. 1 is a flow chart of an on-orbit estimation method of star vector measurement error based on alpha-beta filtering according to the present invention;
fig. 2 is a flowchart of step S2;
FIG. 3 is a comparison of the attitude triaxial attitude statistical errors calculated by the equal weight and unequal weight solutions.
Detailed Description
The present invention will now be further described by way of the following detailed description of a preferred embodiment thereof, taken in conjunction with the accompanying drawings.
As shown in fig. 1, an on-orbit estimation method for star vector measurement error based on α - β filtering includes the following steps:
s1, according to the observation star vector and the reference star vector of the attitude determination star, the weight a of the star vector in the attitude estimation algorithm such as QUESTiEqual method for calculating attitude quaternion
Figure BDA0001872614080000037
Wherein
Figure BDA0001872614080000038
q0Is a marked part, and is characterized in that,
Figure BDA0001872614080000039
is a sagittal portion;
s2, processing the attitude quaternion by adopting an alpha-beta filter
Figure BDA0001872614080000041
Obtaining a reference attitude quaternion
Figure BDA0001872614080000042
S3, quaternion from the reference attitude
Figure BDA0001872614080000043
Calculating a reference attitude matrix A, wherein the attitude matrix describes a conversion relation from an inertial coordinate system to a star sensor measurement coordinate system;
and S4, calculating the error of the observation star vector according to the reference attitude matrix A.
As shown in fig. 2, the filtering equation used in step S2 is:
Figure BDA0001872614080000044
Figure BDA0001872614080000045
the prediction equation:
Figure BDA0001872614080000046
Figure BDA0001872614080000047
in the formula:
Figure BDA0001872614080000048
an estimate of the position at time k;
Figure BDA0001872614080000049
an estimate of the velocity at time k;
Figure BDA00018726140800000410
a predicted estimate for time k;
Figure BDA00018726140800000411
the predicted speed at the moment k;
z (k) is the measurement position at time k; t is a sampling period; alpha and beta are system gains, alpha is called position gain, and beta is called speed gain;
the measured value Z (k) is an attitude quaternion
Figure BDA00018726140800000412
Sagittal portion of
Figure BDA00018726140800000413
The step S3 specifically includes:
Figure BDA00018726140800000414
computing a reference attitude matrix A
Figure BDA00018726140800000415
The step S4 specifically includes:
calculating the error sigma of the ith star vectori: by
Figure BDA00018726140800000416
N, n is the number of stars participating in attitude calculation, and the error sigma of the ith star vector is calculatedi；
Figure BDA00018726140800000417
Is an observation star vector under a star sensor measurement coordinate system,
Figure BDA00018726140800000418
is a reference star vector under a celestial coordinate system.
As shown in fig. 3, the verification result based on the data of the outlay star can be obtained: the weight calculation is distributed based on the star vector error, and the three-axis attitude measurement precision is improved compared with the weight calculation distributed based on the attitude determination star number.
In conclusion, the satellite vector measurement error on-orbit estimation method based on alpha-beta filtering calculates the satellite vector weight in real time, optimizes the attitude estimation algorithm and improves the attitude measurement precision.
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.

Claims (2)

1. An alpha-beta filtering-based star vector measurement error on-orbit estimation method is characterized by comprising the following steps of:
s1, according to the observation star vector and the reference star vector of the attitude determination star, the weight a of the star vector in the attitude estimation algorithm such as QUESTiEqual method for calculating attitude quaternion
Figure FDA0002589383170000011
Wherein
Figure FDA0002589383170000012
q0Is a marked part, and is characterized in that,
Figure FDA0002589383170000013
is a sagittal portion;
s2, processing the attitude quaternion by adopting an alpha-beta filter
Figure FDA0002589383170000014
Obtaining a reference attitude quaternion
Figure FDA0002589383170000015
S3, quaternion from the reference attitude
Figure FDA0002589383170000016
Calculating a reference attitude matrix A, wherein the attitude matrix describes a conversion relation from an inertial coordinate system to a star sensor measurement coordinate system;
s4, calculating the error of the observation star vector according to the reference attitude matrix A;
the filter equation adopted in step S2 is:
Figure FDA0002589383170000017
Figure FDA0002589383170000018
the prediction equation:
Figure FDA0002589383170000019
Figure FDA00025893831700000110
in the formula:
Figure FDA00025893831700000111
an estimate of the position at time k;
Figure FDA00025893831700000112
an estimate of the velocity at time k;
Figure FDA00025893831700000113
a predicted estimate for time k;
Figure FDA00025893831700000114
the predicted speed at the moment k;
z (k) is the measurement position at time k; t is a sampling period; alpha and beta are system gains, alpha is called position gain, and beta is called speed gain;
the measured value Z (k) is an attitude quaternion
Figure FDA00025893831700000115
Sagittal portion of
Figure FDA00025893831700000116
The step S3 specifically includes:
Figure FDA00025893831700000117
q0is a marked part, and is characterized in that,
Figure FDA00025893831700000118
computing a reference attitude matrix a for the vector:
Figure FDA00025893831700000119
2. the α - β filtering-based on-orbit estimation method for star vector measurement error as claimed in claim 1, wherein said step S4 specifically includes:
calculating the error sigma of the ith star vectori: by
Figure FDA0002589383170000021
1,2, n, n is the star number participating in attitude calculation;
Figure FDA0002589383170000022
is an observation star vector under a star sensor measurement coordinate system,
Figure FDA0002589383170000023
is a reference star vector under a celestial coordinate system.
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CN105300384A (en) * 2015-04-03 2016-02-03 东南大学 Interactive filtering method for satellite attitude determination
CN107246883A (en) * 2017-08-07 2017-10-13 上海航天控制技术研究所 A kind of Rotating Platform for High Precision Star Sensor installs the in-orbit real-time calibration method of matrix
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