JPS6050284B2 - How to measure the attitude of a spinning satellite - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a simple and highly accurate method for measuring the attitude of a spinning satellite.

As a conventional method for measuring the attitude of a spin satellite, a method has been known in which data obtained from a sun sensor, a sun sensor, and a sun sensor are statistically processed using the weighted least squares method.

FIGS. 1 and 2 are diagrams for explaining an example of the principle. In FIG. 1, P represents a spinning satellite, E represents the earth, and S represents the sun. Let the unit vectors in the PE direction and the PS direction be VE and Vs, respectively. The angles φE and φ formed by the unit vector s in the spin axis direction and VE and V are angles measured by the earth sensor and the sun sensor, respectively, and are hereinafter referred to as cone angles. VBI, V, can be known from satellite orbit information and astronomical information. φB, φ
Once s is measured, S can be found as a unit vector with the same direction as the branch line 5 or 50 of the two cones with half apex angles φE and φ, with VE and Vs as axes, as shown in Figure 2. I can do it. Since either 5 or 52 does not indicate the true attitude, it is necessary to determine the true attitude.

This is done as follows. Generally, the attitude of a spinning satellite is stable and does not change over a short period of time. Therefore,
Among the satellites 5, 50, the one showing the true attitude is stable over time, but the other can be easily determined because it moves relatively quickly as the satellite orbits the earth. Next, a conventional method for statistically processing data of a plurality of φE and φs will be described below. FIG. 3 shows a method of displaying a vector indicating the spin axis direction. γ is the direction of the vernal equinox, Z is the direction of the earth's north pole, and the direction of s is the right ascension α. and declination δ. Expressed as Now, as a state vector, X = (α0, δ0, Δ
φE, Δφs)", where ΔφE and ΔφS are the misalignments of the earth sensor and the sun sensor, and ()" means transposition.
In this case, in order to estimate X, the following successive correction method is used. That is, an appropriate V is given as an initial value, and a differential correction ΔX is added as follows. ΔX=
(HTWH)-゛HTW(Θ-Θ) ・・・・・・(1
) Here, each symbol shall be defined as follows.

Θ: Assuming that φB and φs are measured N times, they are φIE! 1｜φE29'゜゜9φEN, φ51｜φS
29″.

9φSN) θ=(φEl9φE29l9φEN9
Step vector defined as φSl9φS29=9φSN)T.

Valley: value of θ calculated from the estimated pose value H: A ×4 matrix obtained by partially differentiating e with respect to X, that is, W:
2Nx2N diagonal matrix.

The diagonal elements are φE, (1 = 1, 2,..., N) and φ
The weight is Si (1=1, 2,...,N), and it is taken as the reciprocal of the variance. The correction given by equation (1) is generally performed multiple times and repeated until the correction value becomes sufficiently small.

The above is a typical example of a conventional known method.

This method has the following drawbacks. (1) Since many operations such as matrix operations and partial differential calculations are required, the scale of the calculation program becomes large. (2) Since sequential calculations including matrix inversion and matrix multiplication are repeated until convergence, calculation time becomes long.

(3) The calculation process is not physically easy to understand.
Therefore, the present invention aims to improve the above-mentioned drawbacks of the prior art, and its purpose is to simplify data processing in posture measurement and to measure posture in a short time using a simple program.

The feature of the present invention is obtained by an earth sensor mounted on a spin satellite.

The angle between the spin axis and the direction of the earth as seen from the spinning satellite is the half-vertex angle, and the direction of the earth as seen from the spinning satellite is the axis of symmetry. When a plurality of cones are obtained during a certain period of time and there are a plurality of lines of intersection of these cones with a curved surface or a plane, a point Se is found such that the distances from these lines of intersection are equal to each other. A method for measuring the attitude of a spin satellite includes finding a temporal trajectory, obtaining an estimated value of the point Se, and setting this as the spin axis direction S. This will be explained in detail below with reference to the drawings. In the present invention, a known earth sensor such as an attitude detector is used.

That is, the so-called cone angle φE shown in FIG. 1 is detected by a known method. For reference, FIG. 4 shows an example of the detection method. That is, two infrared telescopes T1 and T2 are mounted at an installation angle of δ from a plane perpendicular to the spin axis S of the satellite. Now, as the telescope scans the Earth as it spins, the angle at which it scans the Earth is φ, as shown in Figure 4.
1, φ2. At this time, the angle φ between S and the unit vector VO in the earth direction. is given by the following formula. The unit vector VIll: in the earth direction changes direction as the satellite orbits the earth, and rotates in 360 directions while the satellite goes around the earth.

Figure 5 shows the earth direction unit vector ■ on the unit sphere. , is a diagram displaying the spin axis direction S and the locus of the cone. Fifth
In the figure, LO is the trajectory drawn by the tip of ■E while the satellite orbits the earth once, VEl, ■TE. 2, VTE. 3 indicates VE at times Tl, T2, and t3. Also, Cl,
C2 and C3 are intersection lines where cones with VEl9, E29, and VE3 as axes and cone angles φEl, φE2, and φE3 intersect with the unit sphere, respectively. Cone angle φ detected by earth sensor
. In a hypothetical case in which 1, φE2, and φE3 do not include errors, Cl, C2, and C3 intersect at one point, which coincides with the spin axis direction S.

In reality, Cl, C2, and C3 do not intersect at one point, but generally draw a spherical triangle because of errors caused by sensor misalignment, wobble, noise, and the like. Generally, the error of the sensor is a small value, and in this range (near the tip of the vector S), the spherical triangle described above is approximated by a triangle on a plane. In addition, in the example of Fig. 5, 3
Although we considered data at time, in general, data at time N, that is, t
=Tl, t2, t3, . . . , T, . . ., a data set of VIIll and φE at TN is obtained. This) (■El9φE1) (VE29φE2) (■
E39φE3) (VEi9φEi)
(■EN9φεN). In the present invention, as shown in FIG.
It is characterized by knowing the true posture using a polygon (obtained by approximating the tip of the vector S in No. 3 with a straight line).
FIG. 6 shows an approximate polygon obtained by C, (1=1,2,3,N). As mentioned above, the polygon becomes irregular due to noise contained in the sensor and is not necessarily a regular polygon. These are statistically processed to obtain an estimated point Se in the spin axis direction near the center of the polygon. At that time, the distance from Se to each straight line is 11 (1 = 1, 2, 3,...
, N) is the average value Vli/N of misalignment.
Gives an estimate of 1=1.

FIG. 7 shows an example in which the spin axis attitude changes slowly and Se changes as a function of time. Se here
indicates the tip of vector S. Regard each C, as a straight line (
Expressed in x, y) coordinates. Now x<! :． y to time t(
7) Assume that it can be approximated by an M-order function. That is, at time t, assuming that f is given, the coefficients P,,q,
(j=0,1,2,...,M) is determined.

Let the equation of C at time t1 be.

Now, let the coordinates of the position of Se at time T, be (X,,yO
Then, the distance h from (X,, yO to straight line C,
It is given by the following formula. is rewritten as

Let Z be the estimated value of h, and define the evaluation relationship L as follows. Now, Pj, qj (j=0, 1
,2,...,M) and Z.

Since absolute value symbols exist in L, an iterative method is generally required to find the minimum point of L. As an example, N
Applying the ewtOn-RaphsOn method results in the following. As an initial value, a certain P,,q,(j=0,1,
2, .

(1=1,2,3,...,N) At this time, from the condition of minimum L, from this, (2M+1) unknowns P,, q, (
j=0,1,2,...,M), the following 0M+ for Z
1) Obtain equations.

I put it here like this:

P,,q, obtained by solving the simultaneous equations (6) are Xi,
For y, (1=1,2,3,...,N), h≧0 is not necessarily given, but the signs of A,, b,, Cl are changed so that h≧0, and the above is repeated. Set up simultaneous equations, P,, q
, , calculate Z.

This process is repeated, and convergence is considered when the improvement in the value of L becomes small. As explained above, according to the present invention, the attitude determination of the spin satellite 1 is reduced to solving the simultaneous equations given by equation (6), and usually equation (6) is a low-element equation. , the calculation time is extremely short, and the calculation program is also small-scale.

In addition, misalignment is expressed in a visually clear form as shown in Figure 6, and the size of misalignment, which was traditionally strictly required to be reduced, can be arbitrarily selected, and posture determination accuracy is improved. It has advantages such as not depending on the magnitude of misalignment at all.

[Brief explanation of the drawing]

Figure 1 is a diagram showing the relationship between the spin satellite's attitude and the directions of the Earth and the sun. Figure 2 is a diagram showing that the spin axis direction is determined as the intersection line of two cones. Figure 3 represents the attitude. Figure 4 is a diagram illustrating the known principle for detecting cone angle by an earth sensor.
5 is a diagram showing the intersection points of cones at a plurality of points in time for explaining the principle of the present invention; FIG. 6 is an enlarged view of the vicinity of the intersection points of the cones in FIG. 5 approximated by a plane; 7th
The figure is a diagram showing how the posture changes over time. E...Earth, S...Sun, S...
...Unit vector in the spin axis direction, ■.

Claims (1)

[Claims] 1. The angle between the spin axis and the earth direction as seen from the spin satellite, obtained by the earth sensor mounted on the spin satellite, is the half-apex angle, and the cone whose axis of symmetry is the earth direction as seen from the spin satellite is constant. When multiple cones are obtained over time and there are multiple lines of intersection of these cones with a curved surface or plane,
A temporal trajectory of a point S_e whose distances from these plurality of intersection lines are approximately equal to each other is found, an estimated value of the point S_e is found, and this is set as the spin axis direction S. A method for measuring the attitude of a spinning satellite.