CN102865866B - Satellite attitude determination method and attitude determination error analytical method based on two star sensors - Google Patents

Satellite attitude determination method and attitude determination error analytical method based on two star sensors Download PDF

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Publication number
CN102865866B
CN102865866B CN201210404220.1A CN201210404220A CN102865866B CN 102865866 B CN102865866 B CN 102865866B CN 201210404220 A CN201210404220 A CN 201210404220A CN 102865866 B CN102865866 B CN 102865866B
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matrix
star
optical axis
star sensor
inertial
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CN201210404220.1A
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CN102865866A (en
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耿云海
侯志立
张春阳
李诚良
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哈尔滨工业大学
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Abstract

The invention relates to a satellite attitude determination method and an attitude determination error analytical method, in particular to a satellite attitude determination method and an attitude determination error analytical method based on two star sensors, and aims at solving the problems that the existing measuring error in the star sensor optical axis direction is large and presently no attitude determination error analytical method exists. The first scheme is that the components LA<i*> and LB<i*> of the optical axis vector of each star sensor in an inertial system are calculated according to measuring output of the two star sensors, the components LA<b> and LB<b> of the optical axis vector of each star sensor in a satellite body system are calculated according to an installation matrix of each star sensor, the gesture of the satellite body system relative to the inertial system is calculated, and a gesture matrix is subjected to unit orthogonalization processing. The second scheme is that an attitude determination error matrix C* in the satellite gesture matrix Cbi* and not subjected to unit orthogonalization is separated; the expression of the attitude determination error matrix C* is evaluated according to the star sensor installation matrixes; and a satellite attitude determination error matrix delta C subjected to unit orthogonalization is gained. The satellite attitude determination method and the attitude determination error analytical method are used for satellite attitude determination and attitude determination error analyzing.

Description

Based on double star sensor satellite attitude determination method and determine appearance error analysis method

Technical field

The present invention relates to a kind of satellite attitude determination method and the error analysis method of appearance is determined to this.

Background technology

In the attitude of satellite sensor of various species, the metrical information of star sensor is the most accurate, along with the mankind are to the further exploration of space, to satellite determine appearance and control accuracy proposes higher requirement, therefore, the use of star sensor in Satellite Attitude Determination System gets more and more.Star sensor can provide the quick surving coordinate system of star relative to the three-axis attitude of inertial system, but, in the three-axis measurement information that star sensor provides, measuring error around the quick optical axis direction of star is often very large, measuring error around the quick optical axis direction of star is the several times in other direction, therefore how is undertaken combining by two or three star sensors and determines appearance to improve accuracy of attitude determination be highly significant; In addition, how oppositely releasing the quick precision of required star according to accuracy of attitude determination is to make the configuration of measuring sensor be determined by mission requirements completely.

To sum up, in the three-axis measurement information that existing star sensor provides, the measuring error around the quick optical axis direction of star is large and do not determine the analytical approach of appearance error to this at present.

Summary of the invention

The present invention is that to solve the existing measuring error around the quick optical axis direction of star large and this is not determined to the problem of the analytical approach of appearance error at present, and then provides a kind of satellite attitude determination method based on double star sensor and determine appearance error analysis method.

The present invention solves the problems of the technologies described above the technical scheme taked to be:

Technical scheme one: the described satellite attitude determination method based on double star sensor is realized by following steps:

Step one, to export according to the measurement of two star sensors and calculate the component of respective optical axis vector in inertial system with and utilize the optical axis vector that calculates to carry out multiplication cross at the component of inertial system to obtain another vector its detailed process is as follows:

Optical axis vector the component of inertial system and optical axis vector long-pending as follows at the component of inertial system:

L A i * = C iA * L A A , L B i * = C iB * L B B , L C i * = L A i * &times; L B i * - - - ( 1 )

Wherein with be respectively the component of optical axis vector under respective Department of Survey of star sensor A and star sensor B, two weight expressions are [0,0,1] t; the inertial system exported for star sensor A relative to the attitude matrix of star sensor A Department of Survey, for the inertial system of star sensor B output is relative to the attitude matrix of star sensor B Department of Survey, see shown in formula (2):

C iA * = C ib C bA C A * , C iB * = C ib C bB C B * - - - ( 2 )

C in formula bAfor the installation matrix of star sensor A, C bBfor the installation matrix of star sensor B, C ibfor actual inertial system is relative to the attitude matrix of body series; the inertial system exported for star sensor A relative to the attitude matrix of star sensor A Department of Survey, the inertial system exported for star sensor B is relative to the attitude matrix of star sensor B Department of Survey;

In formula be respectively the measurement noises matrix of the quick A of star and the quick B of star, the measurement noises matrix expression of the quick A of star and the quick B of star is respectively:

Wherein Δ θ a, for A sensor is in the measuring error of vertical optical axis direction separately, Δ θ b, for B sensor is in the measuring error of vertical optical axis direction separately, Δ ψ afor A sensor is around the measuring error of respective optical axis direction, Δ ψ bfor B sensor is around the measuring error of respective optical axis direction,

In above-mentioned (1), (2), (3) formula, represent containing subscript * and obtained, namely containing noise by the quick measurement of star; Substantial amount is not represented containing subscript *;

Step 2, by the quick installation matrix computations of each star separately optical axis vector at the component of body series and utilize carry out multiplication cross and obtain another vector its detailed process is as follows:

According to the quick installation Matrix C of star bA, C bBoptical axis vector can be obtained amass at the component of body series at the component of body series and optical axis vector:

L A b = C bA L A A , L B b = C bB L B B , L C b = L A b &times; L B b - - - ( 4 )

Wherein C bAfor the installation matrix of star sensor A, C bBfor the installation matrix of star sensor B; with be respectively the component of optical axis vector under respective Department of Survey of star sensor A and star sensor B;

Step 3, calculate satellite body system relative to the attitude of inertial system, and carry out unit orthogonalization process to this attitude matrix, detailed process is as follows:

Step 3 one: structural matrix: order L 3 &times; 3 b = L A b L B b L C b , L 3 &times; 3 i * = L A i * L B i * L C i * ,

Step 3 two: calculate the attitude matrix of satellite body system relative to inertial system, expression is

C bi * = L 3 &times; 3 b ( L 3 &times; 3 i * ) - 1 - - - ( 5 )

Step one is obtained to obtain with step 2 substitute into satellite body system relative in the attitude matrix of inertial system;

Step 3 three: utilize least square method to the attitude matrix in step 3 two carry out unit orthogonalization, expression is:

C bi 0 = 1 2 C bi * ( 3 E - ( C bi * ) T ( C bi * ) ) - - - ( 6 )

In formula, E is the unit matrix of 3 × 3, is substituted in formula (6) by formula (5).

Technical scheme two: the described attitude of satellite error analysis method based on double star sensor is realized by following steps:

Step one, the orthogonalized attitude of satellite matrix of unit will do not carried out in the appearance error battle array C* that determines be separated:

Relation according to each attitude matrix can obtain:

L 3 &times; 3 i * = L A i * L B i * L C i * = C ib L A b * L B b * L C b * - - - ( 7 )

Wherein, C ibfor inertial system relative to body attitude matrix, invert can try to achieve C by formula (7) bi, L A b * = C bA C A * L A A , L B b * = C bB C B * L B B , L C b * = L A b * &times; L B b * ;

Can expression formula be obtained by determining appearance result:

C bi * = L A b L B b L C b L A b * L B b * L C b * - 1 C bi - - - ( 8 )

Order C * = L A b L B b L C b L A b * L B b * L C b * - 1 - - - ( 9 )

Determine the attitude matrix that appearance obtains with true attitude matrix C bidiffer C *, C *be try to achieve determine appearance error matrix;

Step 2, determine appearance error matrix C according to the quick installation matrix computations of star *expression formula:

Step 2 one, by the quick installation matrix computations of each star, optical axis vector is at the component of body series separately, and the concrete expression of each component is as follows:

L A b = C bA 0 0 1 , L B b = C bB 0 0 1 , L C b = C bA 0 0 1 &times; C bB 0 0 1 - - - ( 10 )

By formula (10) known matrix L A b L B b L C b By Matrix C bA, C bB, C bCits 3rd row of each taking-up combine;

Step 2 two, contained the component of the quick optical axis vector of star at body series of measurement noises by the installation matrix computations that star is quick, its expression formula is as follows:

Order A = L A b L B b L C b , Will L A b * L B b * L C b * Be expressed as the form of A+ Δ A, wherein Δ A is and measuring error Δ θ a, Δ θ b, relevant item, Δ A is that Δ A expression formula is as follows in a small amount:

(12)

In formula, C ii-th row of representing matrix C, can obtain the expression formula that Δ A and A substitutes into formula (9)

C *=A(A+ΔA) -1????(13)

Because Δ A is in a small amount, second order is ignored and is carried out abbreviation and can obtain in a small amount:

C *=A(A+ΔA) -1=A(E+A -1ΔA) -1A -1=A(E-A -1ΔA)A -1=E-ΔAA -1????(14)

Will A = L A b L B b L C b The expression substituting into formula (14) can obtain C *=E-B 1+ B 2;

In formula (14)

B 1 = A 1 &Delta; &theta; A &Delta; &theta; B &Delta; &theta; A &Delta; &theta; B A 3 - 1 ,

In formula (15)

A 1 = C bA 1 C bB 1 C bA 1 &times; C bB 3 C bA 3 &times; C bB 1

A 2 = C bA 2 C bB 2 C bA 2 &times; C bB 3 C bA 3 &times; C bB 2 - - - ( 16 )

A 3 = C bA 3 C bB 3 C bA 3 &times; C bB 3

Step 3, ask for the Satellite Attitude Determination error matrix Δ C after unit orthogonalization:

Will bring into expression formula, can obtain C bi 0 = 1 2 C * ( 3 E - C * T C * ) C bi - - - ( 17 )

In formula (17) appearance error matrix is determined, order for what finally will ask for

&Delta;C = 1 2 C * ( 3 E - C * T C * ) - - - ( 18 )

Formula (18) is substituted into formula (14) can obtain

&Delta;C = E - ( B 1 - B 1 T ) 2 + ( B 2 - B 2 T ) 2 - - - ( 19 )

Wherein E is the unit matrix of 3 × 3,

Order by B 1expression formula in each matrix carry out piecemeal process, can obtain

B 1 = A 1 1 A 1 2 A 1 3 A 1 4 &Delta; &theta; A &Delta; &theta; B &Delta; &theta; A &Delta; &theta; B A inv 3 1 , A inv 3 2 , A inv 3 3 , - - - ( 20 )

= ( A 1 1 A inv 3 1 , + A 1 3 A inv 3 3 , ) &Delta; &theta; A + ( A 1 2 A inv 3 2 + A 1 4 A inv 3 3 , ) &Delta; &theta; B

In like manner, by B 2expression formula in each matrix carry out piecemeal process and can obtain B 2expression formula be:

In formula (20), (21), represent A inv3the i-th row; A 1, A 2, A 3directly can substitute in formula (20), (21) according to installation Matrix Formula (16).

The present invention has following beneficial effect:

Satellite attitude determination method based on double star sensor of the present invention can the effective quick measuring error around optical axis direction of filtering star, improves the accuracy of attitude determination that star is quick; Double star sensor attitude determination method of the present invention is not by the impact that satellite is motor-driven, and can be used in the attitude and heading reference system in attitude of satellite mobile process, usable range is wide;

The error analysis method of the attitude of satellite based on double star sensor of the present invention can analyze the accuracy of attitude determination of double star sensor accurately, the object that the measuring accuracy quick to required star according to accuracy of attitude determination claims can be realized, in addition, of the present inventionly determine appearance error analysis method and do not limit to and determine appearance with double star sensor.

Accompanying drawing explanation

Fig. 1 is the FB(flow block) of the satellite attitude determination method based on double star sensor of the present invention, Fig. 2 is the FB(flow block) of the error analysis method of the attitude of satellite based on double star sensor of the present invention, Fig. 3 is that the concrete emulation of double star quick A, B is determined appearance result schematic diagram (wherein the first half is that the axis of rolling determines appearance error, center section is that pitch axis determines appearance error, and the latter half is that yaw axis determines appearance error); Fig. 4 is that appearance result schematic diagram (wherein the first half is that the axis of rolling determines appearance error, and center section is that pitch axis determines appearance error, and the latter half is that yaw axis determines appearance error) is determined in the concrete emulation of the quick A of single star.

Embodiment

Embodiment one: as shown in Figure 1, Figure 3 and Figure 4, the satellite attitude determination method based on double star sensor of present embodiment is realized by following steps:

Step one, to export according to the measurement of two star sensors and calculate the component of respective optical axis vector in inertial system with and utilize the optical axis vector that calculates to carry out multiplication cross at the component of inertial system to obtain another vector its detailed process is as follows:

Optical axis vector the component of inertial system and optical axis vector long-pending as follows at the component of inertial system:

L A i * = C iA * L A A , L B i * = C iB * L B B , L C i * = L A i * &times; L B i * - - - ( 1 )

Wherein with be respectively the component of optical axis vector under respective Department of Survey of star sensor A and star sensor B, two weight expressions are [0,0,1] t; the inertial system exported for star sensor A relative to the attitude matrix of star sensor A Department of Survey, for the inertial system of star sensor B output is relative to the attitude matrix of star sensor B Department of Survey, see shown in formula (2):

C iA * = C ib C bA C A * , C iB * = C ib C bB C B * - - - ( 2 )

C in formula bAfor the installation matrix of star sensor A, C bBfor the installation matrix of star sensor B, C ibfor actual inertial system is relative to the attitude matrix of body series; the inertial system exported for star sensor A relative to the attitude matrix of star sensor A Department of Survey, the inertial system exported for star sensor B is relative to the attitude matrix of star sensor B Department of Survey;

In formula be respectively the measurement noises matrix of the quick A of star and the quick B of star, the measurement noises matrix expression of the quick A of star and the quick B of star is respectively:

Wherein Δ θ a, for A sensor is in the measuring error of vertical optical axis direction separately, Δ θ b, for B sensor is in the measuring error of vertical optical axis direction separately, Δ ψ afor A sensor is around the measuring error of respective optical axis direction, Δ ψ bfor B sensor is around the measuring error of respective optical axis direction,

In above-mentioned (1), (2), (3) formula, represent containing subscript * and obtained, namely containing noise by the quick measurement of star; Substantial amount is not represented containing subscript *;

Step 2, by the quick installation matrix computations of each star separately optical axis vector at the component of body series and utilize carry out multiplication cross and obtain another vector its detailed process is as follows:

According to the quick installation Matrix C of star bA, C bBoptical axis vector can be obtained amass at the component of body series at the component of body series and optical axis vector:

L A b = C bA L A A , L B b = C bB L B B , L C b = L A b &times; L B b - - - ( 4 )

Wherein C bAfor the installation matrix of star sensor A, C bBfor the installation matrix of star sensor B; with be respectively the component of optical axis vector under respective Department of Survey of star sensor A and star sensor B;

Step 3, calculate satellite body system relative to the attitude of inertial system, and carry out unit orthogonalization process to this attitude matrix, detailed process is as follows:

Step 3 one: structural matrix: order L 3 &times; 3 b = L A b L B b L C b , L 3 &times; 3 i * = L A i * L B i * L C i * ,

Step 3 two: calculate the attitude matrix of satellite body system relative to inertial system, expression is

C bi * = L 3 &times; 3 b ( L 3 &times; 3 i * ) - 1 - - - ( 5 )

Step one is obtained to obtain with step 2 substitute into satellite body system relative in the attitude matrix of inertial system;

Step 3 three: utilize least square method to the attitude matrix in step 3 two carry out unit orthogonalization, expression is:

C bi 0 = 1 2 C bi * ( 3 E - ( C bi * ) T ( C bi * ) ) - - - ( 6 )

In formula, E is the unit matrix of 3 × 3, is substituted in formula (6) by formula (5).

Embodiment two: as shown in figs. 2 to 4, the attitude of satellite error analysis method based on double star sensor of present embodiment is realized by following steps:

Step one, the orthogonalized attitude of satellite matrix of unit will do not carried out in determine appearance error battle array C *be separated:

Relation according to each attitude matrix can obtain:

L 3 &times; 3 i * = L A i * L B i * L C i * = C ib L A b * L B b * L C b * - - - ( 7 )

Wherein, C ibfor inertial system relative to body attitude matrix, invert can try to achieve C by formula (7) bi, L A b * = C bA C A * L A A , L B b * = C bB C B * L B B , L C b * = L A b * &times; L B b * ;

Can expression formula be obtained by determining appearance result:

C bi * = L A b L B b L C b L A b * L B b * L C b * - 1 C bi - - - ( 8 )

Order C * = L A b L B b L C b L A b * L B b * L C b * - 1 - - - ( 9 )

Determine the attitude matrix that appearance obtains with true attitude matrix C bidiffer C *, C *be try to achieve determine appearance error matrix;

Step 2, determine appearance error matrix C according to the quick installation matrix computations of star *expression formula:

Step 2 one, by the quick installation matrix computations of each star, optical axis vector is at the component of body series separately, and the concrete expression of each component is as follows:

L A b = C bA 0 0 1 , L B b = C bB 0 0 1 , L C b = C bA 0 0 1 &times; C bB 0 0 1 - - - ( 10 )

By formula (10) known matrix L A b L B b L C b By Matrix C bA, C bB, C bCits 3rd row of each taking-up combine;

Step 2 two, contained the component of the quick optical axis vector of star at body series of measurement noises by the installation matrix computations that star is quick, its expression formula is as follows:

Order A = L A b L B b L C b , Will L A b * L B b * L C b * Be expressed as the form of A+ Δ A, wherein Δ A is and measuring error Δ θ a, Δ θ b, relevant item, Δ A is that Δ A expression formula is as follows in a small amount:

(12)

In formula, C ii-th row of representing matrix C, can obtain the expression formula that Δ A and A substitutes into formula (9)

C *=A(A+ΔA) -1????(13)

Because Δ A is in a small amount, second order is ignored and is carried out abbreviation and can obtain in a small amount:

C *=A(A+ΔA) -1=A(E+A -1ΔA) -1A -1=A(E-A -1ΔA)A -1=E-ΔAA -1????(14)

Will A = L A b L B b L C b The expression substituting into formula (14) can obtain C *=E-B 1+ B 2;

In formula (14)

B 1 = A 1 &Delta; &theta; A &Delta; &theta; B &Delta; &theta; A &Delta; &theta; B A 3 - 1 ,

In formula (15)

A 1 = C bA 1 C bB 1 C bA 1 &times; C bB 3 C bA 3 &times; C bB 1

A 2 = C bA 2 C bB 2 C bA 2 &times; C bB 3 C bA 3 &times; C bB 2 - - - ( 16 )

A 3 = C bA 3 C bB 3 C bA 3 &times; C bB 3

Step 3, ask for the Satellite Attitude Determination error matrix Δ C after unit orthogonalization:

Will bring into expression formula, can obtain C bi 0 = 1 2 C * ( 3 E - C * T C * ) C bi - - - ( 17 )

In formula (17) appearance error matrix is determined, order for what finally will ask for

&Delta;C = 1 2 C * ( 3 E - C * T C * ) - - - ( 18 )

Formula (18) is substituted into formula (14) can obtain

&Delta;C = E - ( B 1 - B 1 T ) 2 + ( B 2 - B 2 T ) 2 - - - ( 19 )

Wherein E is the unit matrix of 3 × 3,

Order by B 1expression formula in each matrix carry out piecemeal process, can obtain

B 1 = A 1 1 A 1 2 A 1 3 A 1 4 &Delta; &theta; A &Delta; &theta; B &Delta; &theta; A &Delta; &theta; B A inv 3 1 , A inv 3 2 , A inv 3 3 , - - - ( 20 )

= ( A 1 1 A inv 3 1 , + A 1 3 A inv 3 3 , ) &Delta; &theta; A + ( A 1 2 A inv 3 2 + A 1 4 A inv 3 3 , ) &Delta; &theta; B

In like manner, by B 2expression formula in each matrix carry out piecemeal process and can obtain B 2expression formula be:

In formula (20), (21), represent A inv3the i-th row; A 1, A 2, A 3directly can substitute in formula (20), (21) according to installation Matrix Formula (16).

As can be seen from the expression formula of Δ C, not containing Δ ψ in Δ C a, Δ ψ b, double star of the present invention quick attitude determination algorithm can eliminate the impact of the measuring error around optical axis direction completely as can be seen here;

If the statistical property of the quick measurement noises of star is known, can according to noise delta θ a, Δ θ b, statistical property, can in the hope of the standard deviation sigma of noise matrix Δ C Δ C, Δ C is antisymmetric matrix, and its off diagonal element correspond to quick three axles of double star and determines appearance error;

If the statistical property position of the quick measurement noises of star, but the noise upper bound is known, can get norm, can analyze the upper bound of determining appearance error equally to Δ C two ends.

Specific embodiment:

Adopt concrete parameter, implement the parameter designing process of variable structure control algorithm of the present invention, and control result:

This example provides the installation matrix of double star sensor to be respectively:

C bA = 0.2435 - 0.9427 0.2281 - 0.8238 - 0.3251 - 0.4643 0.5119 - 0.0749 - 0.8558 , C bB = - 0.2435 - 0.9427 0.2281 - 0.8238 0 . 3251 0.4643 - 0.5119 - 0.0749 - 0.8558

The quick three-axis measurement error of two stars is respectively:

" (3 σ), around optical axis direction: 35 " (3 σ) in vertical optical axis direction: 5.

Adopt Matlab/simulink software to emulate, simulation result is shown in accompanying drawing.

Result of calculation according to the error analysis method of the satellite attitude determination method based on double star sensor can calculate, the three-axis attitude determination accuracy standard difference σ that this double star is quick Δ Cvalue:

&sigma; &Delta;C = 1 1.3775 0.7146 1.3775 1 0.8231 0.7146 0.8231 1 &sigma;

In above formula, σ=5 are " for vertical optical axis direction noise criteria is poor.Contrast matrix σ Δ Cin element and the attitude angle representated by small angle tower matrix can to obtain three-axis measurement accuracy value as follows:

σ Δθ=0.7146×σ=3.57″=0.99×10 -3

σ Δψ=1.3775×σ=6.89″=1.91×10 -3

In formula, represent that the axis of rolling determines appearance error, σ Δ θfor pitch axis determines appearance error, σ Δ ψfor yaw axis determines appearance error.As can be seen from simulation result: error analysis result and simulation result meet.Simultaneously as can be seen from simulation result, double star sensor accuracy of attitude determination improves 5 times than single star sensor accuracy of attitude determination.

Claims (1)

1., based on a satellite attitude determination method for double star sensor, it is characterized in that what described satellite attitude determination method was realized by following steps:
Step one, to export according to the measurement of two star sensors and calculate the component of respective optical axis vector in inertial system with and utilize the optical axis vector that calculates to carry out multiplication cross at the component of inertial system to obtain another vector its detailed process is as follows:
Optical axis vector the component of inertial system and optical axis vector long-pending as follows at the component of inertial system:
L A i * = C iA * L A A , L B i * = C iB * L B B , L C i * = L A i * &times; L B i * - - - ( 1 )
Wherein with be respectively the component of optical axis vector under respective Department of Survey of star sensor A and star sensor B, two weight expressions are [0,0,1] t; the inertial system exported for star sensor A relative to the attitude matrix of star sensor A Department of Survey, for the inertial system of star sensor B output is relative to the attitude matrix of star sensor B Department of Survey, see shown in formula (2):
C iA * = C ib C bA C A * , C iB * = C ib C bB C B * - - - ( 2 )
C in formula bAfor the installation matrix of star sensor A, C bBfor the installation matrix of star sensor B, C ibfor actual inertial system is relative to the attitude matrix of body series; the inertial system exported for star sensor A relative to the attitude matrix of star sensor A Department of Survey, the inertial system exported for star sensor B is relative to the attitude matrix of star sensor B Department of Survey;
In formula be respectively the measurement noises matrix of the quick A of star and the quick B of star, the measurement noises matrix expression of the quick A of star and the quick B of star is respectively:
Wherein Δ θ a, for A sensor is in the measuring error of vertical optical axis direction separately, Δ θ b, for B sensor is in the measuring error of vertical optical axis direction separately, Δ ψ afor A sensor is around the measuring error of respective optical axis direction, Δ ψ bfor B sensor is around the measuring error of respective optical axis direction,
In above-mentioned (1), (2), (3) formula, represent containing subscript * and obtained, namely containing noise by the quick measurement of star; Substantial amount is not represented containing subscript *;
Step 2, by the quick installation matrix computations of each star separately optical axis vector at the component of body series and utilize carry out multiplication cross and obtain another vector its detailed process is as follows:
According to the quick installation Matrix C of star bA, C bBoptical axis vector can be obtained amass at the component of body series at the component of body series and optical axis vector:
L A b = C bA L A A , L B b = C bB L B B , L C b = L A b &times; L B b - - - ( 4 )
Wherein C bAfor the installation matrix of star sensor A, C bBfor the installation matrix of star sensor B; with be respectively the component of optical axis vector under respective Department of Survey of star sensor A and star sensor B;
Step 3, calculate satellite body system relative to the attitude of inertial system, and carry out unit orthogonalization process to this attitude matrix, detailed process is as follows:
Step 3 one, structural matrix: order L 3 &times; 3 b = L A b L B b L C b , L 3 &times; 3 i * = L A i * L B i * L C i * ,
Step 3 two, calculate satellite body system relative to the attitude matrix of inertial system, expression is
C bi * = L 3 &times; 3 b ( L 3 &times; 3 i * ) - 1 - - - ( 5 )
Step one is obtained to obtain with step 2 substitute into satellite body system relative in the attitude matrix of inertial system;
Step 3 three, utilize least square method to the attitude matrix in step 3 two carry out unit orthogonalization, expression is:
C bi 0 = 1 2 C bi / ( 3 E - ( C bi * ) T ( C bi * ) ) - - - ( 6 )
In formula, E is the unit matrix of 3 × 3, is substituted in formula (6) by formula (5).
CN201210404220.1A 2012-10-22 2012-10-22 Satellite attitude determination method and attitude determination error analytical method based on two star sensors CN102865866B (en)

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CN104406583B (en) * 2014-12-05 2017-02-22 中国人民解放军63680部队 Combined defining method for carrier attitude of double-star sensor
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