JPH0228084B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a method for determining the attitude of an artificial satellite based on stellar identification.

To improve the accuracy of satellite attitude control,
It is thought that it will be necessary to realize a system that determines the attitude of an artificial satellite using a stellar sensor.

By the way, this type of attitude determination method that has been developed conventionally uses the observed value of the stellar direction unit vector and the cataloged star corresponding to the observed star as known, and then uses an attitude estimation filter to find the optimal estimated value of the attitude. , using this as an initial value, the attitude was calculated sequentially based on the inertial sensor data.

However, in the conventional method described above, the problem remains as to how to determine the catalog star corresponding to the observed star (ie, the method of star identification), as is well known. Therefore, it has been difficult to realize a practical system.

Furthermore, when using a filter to obtain the optimal estimated value of the attitude, a memory is required to store the satellite observation data, and it takes a long time to obtain the estimation result, which requires an enormous amount of calculation. There were drawbacks such as:

This invention relates to a method for determining the attitude of an artificial satellite that will be necessary to realize a high-precision three-axis attitude control satellite that is expected to be developed in the future. Equipped with an attitude determination calculator that is equipped with a function to calculate relative attitude changes based on inertial sensor data, and is configured to prevent system malfunctions due to incorrect star identification The aim is to provide a method for determining the attitude of artificial satellites.

An embodiment of the present invention will be described in detail below with reference to the drawings.

FIG. 1 is a diagram showing the concept of the attitude determination method according to the present invention. In the figure, 1 is a star sensor, 2 is an inertial sensor, 3 is a star vector calculation device, 4 is a database, 5 is a subcatalog editing device, 6 is a star identification processing device, 7 is an attitude displacement calculation device, and 8 is an initial attitude value. An update device, 9 an attitude calculation device, and 10 an attitude determination computer.

In such a configuration, by inputting the stellar coordinates (y _i , z _i ) within the sensor field of view observed by the stellar sensor 1, where i is the number of the observed star, the stellar vector calculation device 3 calculates the coordinates relative to the satellite axis coordinates. Calculate the unit vector $ _i (t ₀ ) in the stellar direction. The subcatalog editing device 5 inputs the star catalog in the database 4 and edits the subcatalog $ _j ^a (j is the catalog star number). At this time, posture information is required, and in the first processing, for example, a predicted value of the posture set in advance in the database is used.
The identification processing device 6 receives the above $ _i (t) and $ _i ^a and determines the catalog star $ _ij ^a corresponding to the observed star $ _i (t). The attitude displacement calculation device 7 inputs the angular velocity ω _l (t) (where l = 1, 2, 3) around the satellite axis measured by the inertial sensor 2, and calculates it from the star observation time t ₀ to the time t (for example, t=t ₀ +
Calculate the change in attitude of the satellite [ΔC _B ] up to T). The attitude initial value updating device 8 receives the above ($ _i (t), $ _ij ^a ) and [ΔC _B ] _T as input and calculates the attitude at time t=(t ₀ +T). Using this as an initial value, the attitude calculation device 9 receives the inertial sensor data as input, and sequentially calculates and outputs the attitude. Thereafter, the star sensor data is read again and the above operation is repeated to update the attitude initial value every T time. Further, in the processing after time t=t ₀ +T, the configuration is such that the posture calculated by the posture calculation device 9 is fed back to the sub-catalog editing device 5 to provide posture information. The attitude determination computer 10 configured in this way updates the initial value of the attitude at every time T based on the fixed star identification, and uses this as an initial value to determine the attitude within time T at high frequency using inertial sensor data as input. It realizes a system that makes decisions and outputs them.

The details of each device constituting the attitude determination computer 10 will be described below with reference to FIGS. 2, 3, and 4.

FIG. 2 is a diagram showing the relationship between stellar sensor coordinates (X _S , T _S , Z _S ) and satellite axis coordinates (X _B , Y _B , Z _S ). In this example, the number of installed star sensors 1 is 2.
It is said that

In the figure, (α ₁ , δ ₁ ) and (α ₂ , δ ₂ ) are the respective stellar sensors, and (α ₂ , δ ₂ ) are the (azimuth angle, elevation angle) of the optical axis direction X _S of the stellar sensor 1, respectively. In such a relationship, the coordinate transformation matrices [ _B C _S ] ₁ and [ _B C _S ] ₂ that provide the relationship between the stellar sensor coordinates and the satellite axis coordinates are given by the following equations.

[ _B C _S ] ₁ = A ₁₁ A ₁₂ A ₁₃ A ₂₁ A ₂₂ A ₂₃ A ₃₁ A ₃₂ A ₃₃ (1) Here, A ₁₁ = cosα ₁・cosδ ₁ A ₁₂ = −sinα ₁ A ₁₃ = −cosα ₁・sinδ ₁ A ₂₁ = sinα ₁・cosδ ₁ A ₂₂ = cosα ₁ A ₂₃ = −sinα ₁・sinδ ₁ A ₃₁ = sinδ ₁ A ₃₂ = 0 A ₃₃ = cosδ ₁ [ _B C _S ] = B ₁₁ B ₁₂ B ₁₃ B ₂₁ B ₂₂ B ₂₃ B ₃₁ B ₃₂ B ₃₃ (2) Here, B ₁₁ = −sinα ₂・cosδ ₂ B ₁₂ = cosα ₂ B ₁₃ = sinα ₂・sinδ ₂ B ₂₁ = cosα ₂・cosδ ₂ B ₂₂ =-sinα ₂ B ₂₃ =-cosα ₂・sinδ ₂ B ₃₁ = sinδ ₂ B ₃₂ = 0 B ₃₃ = cosδ ₂ Figure 3 shows the observation concept of the unit vector $ _i (t) in the star direction with respect to the satellite axis coordinate. It is a diagram.

In the figure, (y _i , z _i ) are stellar coordinates within the field of view of the stellar sensor, and are values observed by the stellar sensor 1. (α _l ,
δ _l ) is the (azimuth angle, elevation angle) of the star sensor number l (l=1, 2) in the optical axis direction.

In this relationship, the stellar vector calculation device 2 calculates the unit vector $ _i (t) in the stellar direction with respect to the satellite axis coordinate using the following equation.

$ _i (t) = [ _B C _S ] _l cosy _i・cosz _i siny _i・cosz _i sinz _i l=1, 2 i=1, 2, 3 (3) However, in this example, two star sensors A total of 3 out of the multiple observed values by 1, that is $
₁ (t), $ ₂ (t), and $ ₃ (t) are selected and used in the following processing.

On the other hand, the subcatalog editing device 5 uses the [ _B C _S ] _t given from the database 4 and the attitude calculation device 9 (however, only for the first processing, for example, [ _B C _I ] ₀ set in advance in the database). As input, edit the subcatalog $ _j ^a in the following way.

First, the unit vector in the optical axis direction of the stellar sensor 〓
_sl (t) is calculated using the following formula.

〓 _sl (t)=[ _S C _B ] _l [ _B C _I ] _t [1, 0, 0] ^T , l=1, 2 (4) Next, the stellar catalog ^a in database 4
Based on the following conditional expression, a star $ _j ^a that is predicted to exist within the field of view of the star sensor is selected.

$ _j ^a ∈ [ ^a | | cos ^-1 { ^a・〓 _sl } | <ε ₁ ] (5) However, ε ₁ is set to a constant value taking into account the size of the field of view of the stellar sensor.

The star identification processing device 6 uses $ given by the above equation (3).
The following identification process is performed using _i (t), i=1, 2, 3, and the stellar catalog value $ _j ^a given by equation (5).

First, calculate a ₁ = $ ₁ (t)・S ₂ (t) a ₂ = $ ₂ (t)・S ₃ (t) a ₃ = $ ₃ (t)・S ₁ (t) (6) .

Next, take one star $ ₁ ^a from the subcatalog, and use the preset constant ε ₂ to calculate $ ₁ ^a , $ _j-1 ^a − for the remaining j−1 stars in the subcatalog. It is tested whether there is even one combination that satisfies a _i >cosε ₂ , i=1, 2, 3 (7). If even one pair exists, that star $ ₁ ^a
is left as an identification candidate. Also, if no pair exists, that star is removed from the subcatalog. Repeat this operation for all stars in the subcatalog. If ε ₂ is set to a sufficiently small value, the set of catalog stars corresponding to a ₁ , a ₂ , a ₃ in the subcatalog $ _1j ^a・$ _2j ^a , $ _2j ^a・$ _3j ^a , $ _3j ^a・$ _1j ^a
remains. Therefore, the catalog value of $ ₁ is $ _1j ^a ,
The catalog value of $ ₂ is $ _2j ^a , and the catalog star of $ ₃ is $
_3j ^a , and the identification is completed.

Figure 4 shows the star observation time t ₀ by star sensor 1.
Assuming that t ₀ =0, the relative relationship between the attitude of the artificial satellite at time (n-1)τ and time nτ is shown. However, τ
is the sampling time of stellar observation. In the figure, (〓 _Bo-1 ,〓 _Bo-1 ,〓 _Bo-1 ) is time (n-1)
Unit vector in the satellite axis direction at τ, (〓 _Bo , 〓 _B
o , 〓 _Bo ) is the unit vector in the satellite axis direction at time nτ, (ΔΨ _o , Δφ _o , Δθ _o ) is the Euler angle,
(ω _1o-1 , ω _2o-1 , ω _3o-1 ) and (ω _1o , ω _2o , ω _3o ) are rotational angular velocities around the satellite axis, respectively.

In such a relationship, the posture displacement calculation device 7
calculates the change in posture [ΔC _B ] from time t ₀ to time t=nτ using the following formula.

[ΔC _B ] = C ₁₁ C ₁₂ C _{13 C 21} C ₂₂ C ₂₃ C ₃₁ C ₃₂ C ₃₃ ……(8) Here, C ₁₁ = Δρ ₁ ² _{−Δρ 2 2} ^−Δρ ₃ ² +Δρ ₄ ² C ₁₂ = 2(-Δρ ₄ Δρ ₃ +Δρ ₁ Δρ ₂ ) C ₁₃ =2(Δρ ₄ Δρ ₂ +Δρ ₁ Δρ ₂ ) C ₂₁ =2(Δρ ₄ Δρ ₃ +Δρ ₁ Δρ ₂ ) C ₂₂ =−Δρ ₁ ² +Δρ ₂ ² +Δρ ₃ ² +Δρ ₄ ² C ₂₃ = 2 (−Δρ ₄ Δρ ₁ +Δρ ₂ Δρ ₃ ) C ₃₁ = 2 (−Δρ ₄ Δρ ₂ +Δρ ₁ Δρ ₃ ) C ₃₂ = 2 (Δρ ₄ Δρ ₁ +Δρ ₂ Δρ ₃ ) C ₃₃ = δ ₁ ² 2-2 2 δ ₃ ² + δ ₄ ^{2 2} However, δ ₁ δ ₂ δ ² δ ₃ Δ δ ₄ ｜ ｜ 〓 _O = ΔQ ₄ -ΔQ ₂ ΔQ 2 ΔQ ₃ ΔQ 4 ΔQ ₁ ΔQ 1 ΔQ 1 ΔQ ₁ ΔQ ₁ ΔQ ₁ ΔQ ₁ ΔQ ₂ −Δq ₂ Δq ₁ Δq ₄ Δq ₃ −Δq ₁ −Δq _{2 −Δq} 3 Δq 4 Δρ ₁ Δρ ₂ Δρ ₃ Δρ ₄ 〓 _｜ ｜ ｜ ｜ 〓 _o-1 (9) Δq ₁ ＝sinΔθn／2cosΔφn／2sinΔΨn／
2−cosΔθn／2sinΔφn／2cosΔΨn／2 Δq ₂ =−sinΔθn／2cosΔφn／2cosΔΨn
/2-cosΔθn/2sinΔφn/2sinΔΨn/2 Δq ₃ = sinΔθn/2cosΔφn/2cosΔΨn/
2-cosΔθn/2cosΔφn/2sinΔΨn/2 Δq ₄ =cosΔθn/2cosΔφn/2cosΔΨn/
2−sinΔθn／2sinΔφn／2sinΔΨn／2(10) The unknown quantity here is the Euler angle (Δφ,
Δθ, ΔΨ) _o , but the initial value Δφ ₀ at time t=0
=Δθ ₀ =ΔΨ ₀ =0, rotational angular velocity around the satellite axis measured by inertial sensor 2 ω _uo (u=1, 2, 3)
is read with a period τ and calculated using the following formula.

Δφ _o = 1/6 (d ₁ +2d ₂ +2d ₃ +d ₄ ) Δθ _o = 1/6 (η ₁ +2η ₂ +2η ₃ +η ₄ ) ΔΨ _o = 1/6 (f ₁ +2f ₂ +2f ₃ +f ₄ ) (11 ) However, d ₁ = τω _1o η ₁ = τω _2o f ₁ = τω _3o d ₂ = τ｛ω _1o cos(ω _2o τ/2) + ω _3o sin(ω _2o τ/2
)} η ₂ = τ{ω _1o tan (ω _1o τ/2) sin (ω _2o τ/2) +
ω _2o −ω _3o tan (ω _1o τ/2) cos (ω _2o τ/2)} f ₂ = τ{−ω _1o sin (ω _2o τ/2)/cos (ω _1o τ/2)
+ω _3o cos (ω _2o τ/2)/cos (ω _1o τ/2)} d ₃ = τ{ω _1o cos (η ₂ /2) + ω _3o sin (η ₂ /2)} η ₃ = τ{ω _1o tan (d ₂ /2) sin (η ₂ /2) + ω _2o −ω
_3o tan (d ₂ /2) cos (η ₂ /2)} f ₃ = τ{−ω _1o sin (η ₂ /2) / cos (d ₂ /2) + ω _3o c
os(η ₂ /2) / cos(d ₂ /2)} d ₄ =τ{ω _1o cosη ₃ +ω ₃ 〓sinη ₃ } η ₄ =τ{ω _1o tand ₃ sinη ₃ +ω _2o −ω _3o tand ₃ cosη ₃ } f ₄ = τ{−ω _1o sinη ₃ /cosd ₃ +ω _3o cosη ₃ /cosd ₃ } In addition, [Δρ ₁ , Δρ ₂ , Δρ ₃ , Δρ ₄ ] ^T ₀ = [0, 0, 0, 1] Set ^T ₀ (12).

The attitude initial value updating device 8 uses the outputs of the star identification processing device 6, that is, ($ ₁ , $ ₂ , $ ₃ ) and ($ _1j
^a , $ _2j ^a , $ _3j ^a ), first, at time t=0 (=
t ₀ ), that is, the satellite axis coordinates (X _B ,
The relationship [B C I ] _t=0 between Y _B , Z _B ) and the inertial space coordinates ( _{X I} , Y _I , _{Z I} ) as posture reference coordinates is calculated by the following formula.

[ _B C _I ] _t=0 = $ ₁ A $ ₂ $ ₃ [ $ _1j ^a , $ _2j ^a , $ _3j ^a ] (13) Next, using equations (13) and (8), time t= Calculate the attitude at nτ [ _B C _I ] _t=o 〓 using the following formula.

[ _B C _I ] _t=o = [〓C _B ] [ _B C _I ] _t=0 (14) The attitude calculation device 9 calculates the above equation (14) until the attitude initial value is updated again after T time. ) is used as the initial value, the attitude is calculated and output using the following formula.

Here, if the update time t=nτ of the attitude initial value is set to f=0 again, the attitude of the satellite [〓 _B , 〓 _B ,
〓 _B 〕 _tk is 〓 _B , 〓 _B , 〓 _B 〓 _tk = 〓 _B C _I 〓 _tk 〓 _I , 〓 _I , 〓 _I 〕(15
) [ _B C _I ] _tk = [〓C _B ] [ _B C _I ] _tk-1 (16).

However, for [ _B C _I ] ₀ , the calculation result of equation (14) is used. [〓C _B ] reads inertial sensor data ω _l (l = 1, 2, 3) every time τ = t _k - t _k-1 , and according to equations (11) and (12),
Calculate Euler angles Δφ, Δθ, ΔΨ, substitute them into equation (10), calculate Euler parameters (Δρ ₁ , Δρ ₂ , Δρ ₃ , Δρ ₄ ) from equations (9) and (10), This is expressed by the formula (8
)
Substitute it into the right-hand side of and calculate [〓C _B ] sequentially.

As is clear from the above, the attitude determination method according to the present invention uses the attitude at the time of constancy observation obtained based on constancy identification, and the attitude during the star identification processing period obtained using inertial sensor data. The initial value of the posture is updated periodically by combining the changes in
Based on this, the attitude of the satellite can be determined sequentially. Therefore, a filter for posture estimation is not required. In addition, the output frequency of attitude determination is high. Also,
Using equations (6) and (7), the observed star can be uniquely identified regardless of the magnitude of the error in the attitude information. It has the following advantages.

Note that this example shows a method of directly using stars in the subcatalog to process equation (7), but in order to reduce the number of vector calculations (inner products) using equation (7), the observed values and stars in the subcatalog ^Among _{the stars of _ _} ^_ _{_ _ _} ^_ _{_} Even if the core catalog is edited and formula (7) is applied to the stars in this core catalog, the effects of the present invention will not be hindered in any way.

[Brief explanation of drawings]

Fig. 1 is a diagram showing the configuration concept of the attitude determination system according to the present invention, Fig. 2 is a conceptual diagram showing the installation of a stellar sensor, Fig. 3 is a diagram showing a mathematical model for star observation, and Fig. 4 is a diagram showing the sequential attitude determination system. It is a diagram explaining the relationship between the previous stage attitude and the current attitude in the process of change calculation, 1 is a stellar sensor, 2 is an inertial sensor, 3 is a stellar vector calculation device, 4 is a database, 5 is a sub-catalog editing device, 6 is a star identification processing device, 7 is an attitude displacement calculation device, 8 is an attitude initial value updating device,
9 is an attitude calculation device, and 10 is an attitude determination computer.

Claims (1)

[Claims] 1. A stellar sensor that measures the coordinates of stars within the field of view, a stellar vector calculation device that uses the output signal from the stellar sensor as input to calculate a unit vector in the stellar direction with respect to the satellite axis coordinates, and a stellar catalog and attitude determination result. a subcatalog editing device that reads the predicted attitude values used in the step before obtaining them from a database and edits a catalog of stars predicted to be within the field of view of the stellar sensor; and the above-mentioned stellar vector calculation device and subcatalog editing device. An identification processing device that uses the output signal as input to identify the catalog star corresponding to the observed star, an inertial sensor that measures the angular velocity around the satellite axis, and an inertial sensor that uses the output signal from the inertial sensor as input to identify the star from the star observation time using the star sensor an attitude displacement calculation device that calculates a change in the attitude of the artificial satellite up to the point in time; an attitude initial value update device that calculates an initial attitude value by inputting output signals of the identification processing device and the attitude displacement calculation device; An attitude determination computer comprising an initial value updating device and an attitude calculation device that calculates the attitude of an artificial satellite using inertial sensor data as input, and configured to feed back an output signal of the attitude calculation device to the subcatalog editing device. An attitude determination method for an artificial satellite, characterized in that the above-mentioned artificial satellite is equipped with the above-mentioned satellite, and outputs an attitude determination value and an attitude change rate of the artificial satellite.