CN102749089B - Method for determining three-probe star sensor gesture - Google Patents

Abstract

The invention discloses a method for determining the three-probe star sensor gesture. A data processing module times two probe modules periodically, so that the defect that time difference between two imaging probe modules is increased after a star sensor is operated for a long time is made up, and the defect of poor gesture precision of a single imaging probe module star sensor rolling shaft is made up. Even if a certain imaging probe module becomes invalid, the other two imaging probes still can output the gesture on the basis of guaranteeing the gesture precision, and the data reliability is improved.

Description

A kind of defining method of three probe star sensor attitudes

Technical field

The present invention relates to space technology, is exactly a kind of defining method of three probe star sensor attitudes specifically.

Background technology

Star sensor be experience the radiation of fixed star and instrumented satellite relative to a kind of optical attitude sensor in this fixed star orientation.Because the subtended angle of fixed star is very little, and the direction of starlight in inertial coordinates system is accurately known, so the measuring accuracy of star sensor is very high, and an order of magnitude higher than sun sensor.But because starlight is very faint, so input is more difficult, its imaging needs to use highly sensitive imageing sensor, such as image dissector or charge-coupled image sensor (CCD, Charge Coupled Device).It aerial fixed star quantity is a lot, and its brings alternative target satellite more and apply advantage easily on the one hand, but also brings the difficulty identified the fixed star detected, thus needs to be equipped with the stronger spaceborne digital machine of data Storage and Processing ability.In order to reduce the impact of external stray light, usually before the camera lens of star sensor, add a light shield.From the directional light of fixed star after optical system in image planes battle array focal imaging, the center (its precision can reach rad) of star image can be determined by center of energy method.Obtain the direction of starlight vector in star sensor coordinate system further according to focusing geometric relationship, then obtain the measurement vector of starlight vector in satellite body coordinate system by star sensor installation Matrix Calculating.

Star sensor can sense many fixed stars (normally 6 etc. above fixed star) simultaneously, after importance in star map recognition as the fixed star of three-axis attitude measuring basis generally more than 3.Utilize many vectors to determine appearance method and can obtain the three-axis attitude of satellite relative to inertial space (celestial coordinate system).After the orbital tracking of given aircraft, try to achieve the attitude of aircraft relative to orbital coordinate system by coordinate conversion.

The attitude determination accuracy of star sensor is determined by the measuring accuracy of star place.But be contradiction between the measuring accuracy of star place and probe angle size, in order to improve the attitude accuracy of star sensor further, many devisers reduce the probe of star sensor.For single probe star sensor, the error of roll angle is generally 5-10 times of crab angle and angle of pitch error.Therefore, the precision that star sensor probe also can not bring up to the precision of roll angle crab angle and the angle of pitch is reduced.

And in the star sensor probe of little probe, trappable nautical star number ratio is less, causes the reduction of star sensor star detectivity, is unfavorable for the dynamic property of importance in star map recognition and aircraft; Can not ensure can photograph enough nautical stars in each moment probe simultaneously.The star detectivity of star sensor can be limited like this and cause the decline of attitude determination accuracy.For the problem of star sensor measuring accuracy and star detectivity under solution spacecraft height dynamic flying condition, three star sensor schemes of popping one's head in can be adopted.

Summary of the invention

The object of the present invention is to provide a kind of defining method of three probe star sensor attitudes.The object of the present invention is achieved like this: method step is as follows:

Step one: read respectively

First obtains the attitude Q popped one's head in ₁with the t time of exposure ₁;

Second obtains the attitude Q popped one's head in ₂with the t time of exposure ₂;

3rd obtains the attitude Q popped one's head in ₃with the t time of exposure ₃;

Get t ₁, t ₂and t ₃maximal value;

If t ₁maximum; Calculate Δ t ₂=t ₁-t ₂, Δ t ₃=t ₁-t ₃;

Step 2: utilize Q ₂, Δ ₂with formula (11)

$\left[\begin{array}{c}{q}_{10}^{\′}\\ q_{11}^{\′}\\ q_{12}^{\′}\\ q_{13}^{\′}\end{array}\right]=\left[\begin{array}{c}{q}_{10}\\ q_{11}\\ q_{12}\\ q_{13}\end{array}\right]+\left[\begin{array}{c}{\stackrel{\·}{q}}_{10}\\ {\stackrel{\·}{q}}_{11}\\ {\stackrel{\·}{q}}_{12}\\ {\stackrel{\·}{q}}_{13}\end{array}\right]\×(t_1^{\′}-t_1)---\left(11\right)$

Calculate second and obtain probe at t ₁moment attitude Q ' ₂, utilize Q ₃, Δ t ₃calculate the 3rd with formula (11) and obtain probe at t ₁moment attitude Q ' ₃;

Step 3: utilize Q ₁calculate first and obtain probe at t ₁the optical axis in moment points to S ₁, utilize Q ' ₂calculate second and obtain probe at t ₁the optical axis in moment points to S ' ₂, utilize Q ' ₃calculate the 3rd and obtain probe at t ₁the optical axis in moment points to S ' ₃;

Step 4: the image space coordinate V that the first acquisition probe optical axis points to ₁be (0,0,1), utilize

Formula (5) $U_r=\left[\begin{array}{c}{U}_{\mathrm{rx}}\\ U_{\mathrm{ry}}\\ U_{\mathrm{rz}}\end{array}\right],$ $V_r=\left[\begin{array}{c}{V}_{\mathrm{rx}}\\ V_{\mathrm{ry}}\\ V_{\mathrm{rz}}\end{array}\right],$ $W_r=\left[\begin{array}{c}{W}_{\mathrm{rx}}\\ W_{\mathrm{ry}}\\ W_{\mathrm{rz}}\end{array}\right]---\left(5\right)$

The image space coordinate V of probe optical axis sensing is obtained second ₂(0,0,1) is transformed into the image space coordinate V ' under the first acquisition probe co-ordinate system ₂, utilize formula (5)

$U_r=\left[\begin{array}{c}{U}_{\mathrm{rx}}\\ U_{\mathrm{ry}}\\ U_{\mathrm{rz}}\end{array}\right],$ $V_r=\left[\begin{array}{c}{V}_{\mathrm{rx}}\\ V_{\mathrm{ry}}\\ V_{\mathrm{rz}}\end{array}\right],$ $W_r=\left[\begin{array}{c}{W}_{\mathrm{rx}}\\ W_{\mathrm{ry}}\\ W_{\mathrm{rz}}\end{array}\right]---\left(5\right)$

The image space coordinate V of probe optical axis sensing is obtained the 3rd ₃(0,0,1) is transformed into the image space coordinate V ' under the first acquisition probe co-ordinate system ₃;

Step 5: utilize V ₁, V ' ₂, V ' ₃and S ₁, S ' ₂, S ' ₃, utilize formula (8)

$\left\{\begin{array}{c}{C}_{\mathrm{nb}}{F}_b=C_{\mathrm{nr}}{F}_r\\ F_b=C_{\mathrm{br}}{F}_r\\ C_{\mathrm{br}}=C_{\mathrm{nb}}^{-1}{C}_{\mathrm{nr}}=C_{\mathrm{nb}}^T{C}_{\mathrm{nr}}\end{array}\right.---\left(8\right)$

Calculate the attitude Q of three probes, and output time t ₁with attitude Q;

If t ₂maximum;

Calculate Δ t ₁=t ₂-t ₁, Δ t ₃=t ₂-t ₃;

Step 6: utilize Q ₁, Δ t ₁with formula (11)

$\left[\begin{array}{c}{q}_{10}^{\′}\\ q_{11}^{\′}\\ q_{12}^{\′}\\ q_{13}^{\′}\end{array}\right]=\left[\begin{array}{c}{q}_{10}\\ q_{11}\\ q_{12}\\ q_{13}\end{array}\right]+\left[\begin{array}{c}{\stackrel{\·}{q}}_{10}\\ {\stackrel{\·}{q}}_{11}\\ {\stackrel{\·}{q}}_{12}\\ {\stackrel{\·}{q}}_{13}\end{array}\right]\×(t_1^{\′}-t_1)---\left(11\right)$

Calculate first and obtain probe at t ₂moment attitude Q ' ₁, utilize Q ₃, Δ t ₃with formula (11)

Calculate the 3rd and obtain probe at t ₂moment attitude Q ' ₃;

Step 7: utilize Q ' ₁calculate first and obtain probe at t ₂the optical axis in moment points to S ' ₁, utilize Q ₂calculate second and obtain probe at t ₂the optical axis in moment points to S ₂, utilize Q ' ₃calculate the 3rd and obtain probe at t ₂the optical axis in moment points to S ' ₃

Step 8: the image space coordinate V that the first acquisition probe optical axis points to ₁be (0,0,1), utilize formula (5) to obtain the image space coordinate V of probe optical axis sensing second ₂(0,0,1) is transformed into the image space coordinate V ' under the first acquisition probe co-ordinate system ₂, utilize formula (5) to obtain the image space coordinate V of probe optical axis sensing the 3rd ₃(0,0,1) is transformed into the image space coordinate V ' under the first acquisition probe co-ordinate system ₃;

Utilize V ₁, V ' ₂, V ' ₃and S ' ₁, S ₂, S ' ₃, utilize formula (8) to calculate the attitude Q of three probes, and output time t ₂with attitude Q;

If t ₃maximum;

Calculate Δ t ₁=t ₃-t ₁, Δ t ₂=t ₃-t ₂

Utilize Q ₁, Δ t ₁calculate first with formula (11) and obtain probe at t ₃moment attitude Q ' ₁, utilize Q ₂, Δ t ₂calculate second with formula (11) and obtain probe at t ₃moment attitude Q ' ₂

Utilize Q ' ₁calculate first and obtain probe at t ₃the optical axis in moment points to S ' ₁, utilize Q ' ₂calculate second and obtain probe at t ₃the optical axis in moment points to S ' ₂, utilize Q ₃calculate the 3rd and obtain probe at t ₃the optical axis in moment points to S ₃

The image space coordinate V that first acquisition probe optical axis points to ₁be (0,0,1), utilize formula (5) to obtain the image space coordinate V of probe optical axis sensing second ₂(0,0,1) is transformed into the image space coordinate V ' under the first acquisition probe co-ordinate system ₂, utilize formula (5) to obtain the image space coordinate V of probe optical axis sensing the 3rd ₃(0,0,1) is transformed into the image space coordinate V ' under the first acquisition probe co-ordinate system ₃

Step 9: utilize V ₁, V ' ₂, V ' ₃and S ' ₁, S ' ₂, S ₃, utilize formula (8) to calculate the attitude Q of three probes, and output time t ₃with attitude Q.

The defining method of a kind of three probe star sensor attitudes of the present invention, data processing module fixed cycle ground is calibrated to two probe modules, after compensate for star sensor long-play, the shortcoming of mistiming increase between two imaging probe modules; Compensate for the shortcoming of single imaging probe module star sensor axis of rolling attitude accuracy difference; Even if certain imaging probe module actual effect, on the basis ensureing attitude accuracy, another two imaging probe modules still can export attitude, improve data reliability.

Accompanying drawing explanation

Fig. 1 is three probe star sensor Attitude Calculation process flow diagrams;

Fig. 2 is three probe star sensor schematic diagrams;

Fig. 3 calculates three-axis attitude graph of errors for adopting probe 1 star chart;

Fig. 4 is three probe star sensor test results.

Embodiment

Below in conjunction with accompanying drawing citing, the present invention will be further described.

Embodiment 1:

Composition graphs 1, Fig. 2, the defining method of a kind of three probe star sensor attitudes of the present invention, step is as follows:

Method step is as follows:

Step one: read respectively

First obtains the attitude Q popped one's head in ₁with the t time of exposure ₁;

Second obtains the attitude Q popped one's head in ₂with the t time of exposure ₂;

3rd obtains the attitude Q popped one's head in ₃with the t time of exposure ₃;

Get t ₁, t ₂and t ₃maximal value;

If t ₁maximum; Calculate Δ t ₂=t ₁-t ₂, Δ t ₃=t ₁-t ₃;

Step 2: utilize Q ₂, Δ t ₂with formula (11)

$\left[\begin{array}{c}{q}_{10}^{\′}\\ q_{11}^{\′}\\ q_{12}^{\′}\\ q_{13}^{\′}\end{array}\right]=\left[\begin{array}{c}{q}_{10}\\ q_{11}\\ q_{12}\\ q_{13}\end{array}\right]+\left[\begin{array}{c}{\stackrel{\·}{q}}_{10}\\ {\stackrel{\·}{q}}_{11}\\ {\stackrel{\·}{q}}_{12}\\ {\stackrel{\·}{q}}_{13}\end{array}\right]\×(t_1^{\′}-t_1)---\left(11\right)$

Calculate second and obtain probe at t ₁moment attitude Q ' ₂, utilize Q ₃, Δ t ₃calculate the 3rd with formula (11) and obtain probe at t ₁moment attitude Q ' ₃;

Step 3: utilize Q ₁calculate first and obtain probe at t ₁the optical axis in moment points to S ₁, utilize Q ' ₂calculate second and obtain probe at t ₁the optical axis in moment points to S ' ₂, utilize Q ' ₃calculate the 3rd and obtain probe at t ₁the optical axis in moment points to S ' ₃;

Step 4: the image space coordinate V that the first acquisition probe optical axis points to ₁be (0,0,1), utilize formula (5)

$U_r=\left[\begin{array}{c}{U}_{\mathrm{rx}}\\ U_{\mathrm{ry}}\\ U_{\mathrm{rz}}\end{array}\right],$ $V_r=\left[\begin{array}{c}{V}_{\mathrm{rx}}\\ V_{\mathrm{ry}}\\ V_{\mathrm{rz}}\end{array}\right],$ $W_r=\left[\begin{array}{c}{W}_{\mathrm{rx}}\\ W_{\mathrm{ry}}\\ W_{\mathrm{rz}}\end{array}\right]---\left(1\right)$

The image space coordinate V of probe optical axis sensing is obtained second ₂(0,0,1) is transformed into the image space coordinate V ' under the first acquisition probe co-ordinate system ₂, utilize formula (5)

$U_r=\left[\begin{array}{c}{U}_{\mathrm{rx}}\\ U_{\mathrm{ry}}\\ U_{\mathrm{rz}}\end{array}\right],$ $V_r=\left[\begin{array}{c}{V}_{\mathrm{rx}}\\ V_{\mathrm{ry}}\\ V_{\mathrm{rz}}\end{array}\right],$ $W_r=\left[\begin{array}{c}{W}_{\mathrm{rx}}\\ W_{\mathrm{ry}}\\ W_{\mathrm{rz}}\end{array}\right]---\left(5\right)$

The image space coordinate V of probe optical axis sensing is obtained the 3rd ₃(0,0,1) is transformed into the image space coordinate V ' under the first acquisition probe co-ordinate system ₃;

Step 5: utilize V ₁, V ' ₂, V ' ₃and S ₁, S ' ₂, S ' ₃, utilize formula (8)

$\left\{\begin{array}{c}{C}_{\mathrm{nb}}{F}_b=C_{\mathrm{nr}}{F}_r\\ F_b=C_{\mathrm{br}}{F}_r\\ C_{\mathrm{br}}=C_{\mathrm{nb}}^{-1}{C}_{\mathrm{nr}}=C_{\mathrm{nb}}^T{C}_{\mathrm{nr}}\end{array}\right.---\left(8\right)$

Calculate the attitude Q of three probes, and output time t ₁with attitude Q;

If t ₂maximum;

Calculate Δ t ₁=t ₂-t ₁, Δ t ₃=t ₂-t ₃;

Step 6: utilize Q ₁, Δ t ₁with formula (11)

$\left[\begin{array}{c}{q}_{10}^{\′}\\ q_{11}^{\′}\\ q_{12}^{\′}\\ q_{13}^{\′}\end{array}\right]=\left[\begin{array}{c}{q}_{10}\\ q_{11}\\ q_{12}\\ q_{13}\end{array}\right]+\left[\begin{array}{c}{\stackrel{\·}{q}}_{10}\\ {\stackrel{\·}{q}}_{11}\\ {\stackrel{\·}{q}}_{12}\\ {\stackrel{\·}{q}}_{13}\end{array}\right]\×(t_1^{\′}-t_1)---\left(11\right)$

Calculate first and obtain probe at t ₂moment attitude Q ' ₁, utilize Q ₃, Δ t ₃calculate the 3rd with formula (11) and obtain probe at t ₂moment attitude Q ' ₃;

Step 7: utilize Q ' ₁calculate first and obtain probe at t ₂the optical axis in moment points to S ' ₁, utilize Q ₂calculate second and obtain probe at t ₂the optical axis in moment points to S ₂, utilize Q ' ₃calculate the 3rd and obtain probe at t ₂the optical axis in moment points to S ' ₃

Step 8: the image space coordinate V that the first acquisition probe optical axis points to ₁be (0,0,1), utilize formula (5) to obtain the image space coordinate V of probe optical axis sensing second ₂(0,0,1) is transformed into the image space coordinate V ' under the first acquisition probe co-ordinate system ₂, utilize formula (5) to obtain the image space coordinate V of probe optical axis sensing the 3rd ₃(0,0,1) is transformed into the image space coordinate V ' under the first acquisition probe co-ordinate system ₃;

Utilize V ₁, V ' ₂, V ' ₃and S ' ₁, S ₂, S ' ₃, utilize formula (8) to calculate the attitude Q of three probes, and output time t ₂with attitude Q;

If t ₃maximum;

Calculate Δ t ₁=t ₃-t ₁, Δ t ₂=t ₃-t ₂

Utilize Q ₁, Δ t ₁calculate first with formula (11) and obtain probe at tX moment attitude Q ' ₁, utilize Q ₂, Δ t ₂calculate second with formula (11) and obtain probe at t ₃moment attitude Q ' ₂

Utilize Q ' ₁calculate first and obtain probe at t ₃the optical axis in moment points to S ' X, utilizes Q ' ₂calculate second and obtain probe at t ₃the optical axis in moment points to S ' ₂, utilize Q ₃calculate the 3rd and obtain probe at t ₃the optical axis in moment points to S ₃

The image space coordinate V that first acquisition probe optical axis points to ₁be (0,0,1), utilize formula (5) to obtain the image space coordinate V of probe optical axis sensing second ₂(0,0,1) is transformed into the image space coordinate V ' under the first acquisition probe co-ordinate system ₂, utilize formula (5) to obtain the image space coordinate V of probe optical axis sensing the 3rd ₃(0,0,1) is transformed into the image space coordinate V ' under the first acquisition probe co-ordinate system ₃

Step 9: utilize V ₁, V ' ₂, V ' ₃and S ' ₁, S ' ₂, S ₃, utilize formula (8) to calculate the attitude Q of three probes, and output time t ₃with attitude Q.

Embodiment 2:

Composition graphs 1, Fig. 2, three probe star sensor attitude determination principles:

Three unit vector X _n, Y _n, Z _n, and form a mutually orthogonal coordinate system, wherein: Y _nand Z _nmould | Y _n|=1 He | Z _n|=1, remember new coordinate system F _nfor

$F_n=\left[\begin{array}{c}{X}_n\\ Y_n\\ Z_n\end{array}\right]---\left(2\right)$

The body coordinate of spacecraft is F _b, georeferencing coordinate is F _r, their coordinate base is respectively

$F_b=\left[\begin{array}{c}{X}_b\\ Y_b\\ Z_b\end{array}\right],$ $F_r=\left[\begin{array}{c}{X}_r\\ Y_r\\ Z_r\end{array}\right]---\left(3\right)$

Wherein, X _b, Y _b, Z _bfor F _bunit vector, X _r, Y _r, Z _rfor F _runit vector.X _n, Y _n, Z _nthree vectors recorded, they and F _nand F _rbeing described as of coordinate system

$X_n=U_b^T{F}_b=U_r^T{F}_r$

$Y_n=V_b^T{F}_b=V_r^T{F}_r---\left(4\right)$

$Z_n=W_b^T{F}_b=W_r^T{F}_r$

Wherein, U _b, V _b, U _r, V _r, W _b, W _bbe respectively X _n, Y _n, Z _nat F _band F _rcoordinate array (direction cosine), being write as expansion is

$U_b=\left[\begin{array}{c}{U}_{\mathrm{bx}}\\ U_{\mathrm{by}}\\ U_{\mathrm{bz}}\end{array}\right],$ $V_b=\left[\begin{array}{c}{V}_{\mathrm{bx}}\\ V_{\mathrm{by}}\\ V_{\mathrm{bz}}\end{array}\right],$ $W_b=\left[\begin{array}{c}{W}_{\mathrm{bx}}\\ W_{\mathrm{by}}\\ W_{\mathrm{bz}}\end{array}\right]---\left(5\right)$

$U_r=\left[\begin{array}{c}{U}_{\mathrm{rx}}\\ U_{\mathrm{ry}}\\ U_{\mathrm{rz}}\end{array}\right],$ $V_r=\left[\begin{array}{c}{V}_{\mathrm{rx}}\\ V_{\mathrm{ry}}\\ V_{\mathrm{rz}}\end{array}\right],$ $W_r=\left[\begin{array}{c}{W}_{\mathrm{rx}}\\ W_{\mathrm{ry}}\\ W_{\mathrm{rz}}\end{array}\right]---\left(6\right)$

Due to three unit vector X _n, Y _n, Z _nit is mutually orthogonal,

Therefore,

$F_n=\left[\begin{array}{c}{X}_n\\ Y_n\\ Z_n\end{array}\right]=\left[\begin{array}{c}{U}_b\\ V_b\\ W_b\end{array}\right]F_b=C_{\mathrm{nb}}{F}_b---\left(7\right)$

C _nbfor F _nwith F _bbetween attitude matrix (direction cosine matrix).

In like manner,

$F_n=\left[\begin{array}{c}{X}_n\\ Y_n\\ Z_n\end{array}\right]=\left[\begin{array}{c}{U}_r\\ V_r\\ W_r\end{array}\right]F_r=C_{\mathrm{nr}}{F}_r---\left(8\right)$

C _nrfor F _nwith F _rbetween attitude matrix (direction cosine matrix).

Contrast (6) and (7), and make F _band F _rbetween attitude matrix be C _br, have

$\left\{\begin{array}{c}{C}_{\mathrm{nb}}{F}_b=C_{\mathrm{nr}}{F}_r\\ F_b=C_{\mathrm{br}}{F}_r\\ C_{\mathrm{br}}=C_{\mathrm{nb}}^{-1}{C}_{\mathrm{nr}}=C_{\mathrm{nb}}^T{C}_{\mathrm{nr}}\end{array}\right.---\left(9\right)$

C _brbe required F _band F _rbetween attitude matrix, can F be obtained thus _bthree unit vector X _n, Y _n, Z _nat F _rin description, namely determine the attitude of aircraft three axle.Due to X _n, Y _n, Z _nmutually orthogonal, not parallel, therefore must exist.

If F _bfor aircraft body coordinate system, F _r=F _ofor orbital coordinate system, for the roll angle of x-y-z rotational order definition pitching angle theta and crab angle ψ are all the situation at little angle, F _bwith F _obetween attitude matrix C _bofor

Therefore formula (8) is utilized to obtain roll angle pitching angle theta and crab angle ψ.Need to illustrate, due to roll angle pitching angle theta and crab angle ψ are about decided to be low-angle, also normal with Δ θ, Δ ψ represent, are referred to as rolling, pitching, driftage deviation angle.

2. the fundamentals of successive deduction of attitude

Suppose t ₁the attitude quaternion of certain probe of moment star sensor is Q ₁, t ₁the angular velocity of moment star sensor is ω ₁, wherein Q ₁=q ₁₀× i+q ₁₁× j+q ₁₂× k+q ₁₃, so have

$\left[\begin{array}{c}{\stackrel{\·}{q}}_{10}\\ {\stackrel{\·}{q}}_{11}\\ {\stackrel{\·}{q}}_{12}\\ {\stackrel{\·}{q}}_{13}\end{array}\right]=\frac{1}{2}\left[\begin{array}{cccc}0& {\mathrm{\ω}}_{1x}& -{\mathrm{\ω}}_{1y}& {\mathrm{\ω}}_{1z}\\ -{\mathrm{\ω}}_{1z}& 0& {\mathrm{\ω}}_{1x}& {\mathrm{\ω}}_{1y}\\ {\mathrm{\ω}}_{1y}& -{\mathrm{\ω}}_{1x}& 0& {\mathrm{\ω}}_{1z}\\ -{\mathrm{\ω}}_{1x}& -{\mathrm{\ω}}_{1y}& -{\mathrm{\ω}}_{1z}& 0\end{array}\right]\left[\begin{array}{c}{q}_{10}\\ q_{11}\\ q_{12}\\ q_{13}\end{array}\right]---\left(11\right)$

T ' ₁(wherein t ' ₁> t ₁) attitude quaternion of moment this probe of star sensor is Q ' ₁(Q ' ₁=q ' ₁₀× i+q ' ₁₁× j+q ' ₁₂× k+q ' ₁₃) be:

$\left[\begin{array}{c}{q}_{10}^{\′}\\ q_{11}^{\′}\\ q_{12}^{\′}\\ q_{13}^{\′}\end{array}\right]=\left[\begin{array}{c}{q}_{10}\\ q_{11}\\ q_{12}\\ q_{13}\end{array}\right]+\left[\begin{array}{c}{\stackrel{\·}{q}}_{10}\\ {\stackrel{\·}{q}}_{11}\\ {\stackrel{\·}{q}}_{12}\\ {\stackrel{\·}{q}}_{13}\end{array}\right]\×(t_1^{\′}-t_1)---\left(12\right)$

Embodiment 3:

Experimental technique is as follows: as shown in Figure 2, three probe star sensors to outdoor, three probe star sensors are placed on the turntable of the earth, adjustment turntable, make three probes can observe enough fixed stars, random alignment celestial sphere region and geo-stationary when three probes are initial, and along with earth rotation rotation, carry out long-play.Star tracing mode is independently entered after three probe star sensor whole day ball identifications, for in same computation period, first three probe star sensors adopt the star chart of probe 1 to calculate attitude, then the star chart of three probes is adopted to adopt method of the present invention to calculate attitude, export and adopt the three-axis attitude measured value of probe 1 and adopt the star chart of three probes to adopt method of the present invention to calculate attitude, and export this two groups of three-axis attitude measured values, then the attitude calculated is sent to host computer by RS422, host computer is preserved after receiving attitude in real time, and calculate the difference (i.e. attitude error) of the attitude received and true attitude in real time, (Frame of about 1820 seconds is such as received) after receiving the attitude of some, MATLAB is adopted to show attitude error curve, and calculate three-axis attitude precision.As shown in Figure 3, as calculated, the three-axis attitude error only adopting the star chart of probe 1 to calculate is respectively: crab angle 1.1025 " (3 σ), the angle of pitch 1.0401 " (3 σ), roll angle 5.8576 " (3 σ).As shown in Figure 4, the three-axis attitude error adopting three star charts of popping one's head in adopt method of the present invention to calculate attitude is respectively: crab angle 0.4561 " (3 σ), the angle of pitch 0.3408 " (3 σ), roll angle 0.3659 " (3 σ).

According to star sensor principle of work, adopt the ratio of precision crab angle of roll angle and the low precision of the angle of pitch of a star sensor of popping one's head in, analyze theoretically, the relation of the ratio of precision crab angle of roll angle and about 5 times of the low precision of the angle of pitch, as can be seen from Figure 3, the three-axis attitude error only adopting the star chart of probe 1 to calculate is respectively: crab angle 1.1025 " (3 σ); the angle of pitch 1.0401 " (3 σ), " (3 σ), therefore the error of roll angle is approximately than low precision 5 times of relations of crab angle and the angle of pitch for roll angle 5.8576.And adopt three star charts of popping one's head in adopt method of the present invention to calculate the three-axis attitude of attitude, the roll angle that not direct three probes export, but adopt the crab angle of three probes and the angle of pitch to carry out information fusion, thus make up the shortcoming of single probe star sensor roll angle low precision, as can be seen from Figure 4, the output three-axis attitude of dual probe star sensor all meets 1 " attitude error.

Embodiment 4:

Be below a kind of embodiment of dual probe star sensor, the attitude quaternion adopting ESOQ2 algorithm can calculate three probes is respectively:

The attitude quaternion of probe 1: Q ₁=q ₀1 × i+q ₁₁× j+q ₂₁× k+q ₃₁;

The attitude quaternion of probe 2: Q ₂=q ₀₂× i+q ₁₂× j+q ₂₂× k+q ₃₂;

The attitude quaternion of probe 3: Q ₃=q ₀₃× i+q ₁₃× j+q ₂₃× k+q ₃₃.

Utilize $A\left(q\right)=\left[\begin{array}{ccc}{q}_1^2-q_2^2-q_3^2+q_4^2& 2(q_1{q}_2+q_3{q}_4)& 2(q_1{q}_3-q_2{q}_4)\\ 2(q_1{q}_2-q_3{q}_4)& -q_1^2+q_2^2-q_3^2+q_4^2& 2(q_2{q}_3+q_1{q}_4)\\ 2(q_1{q}_3+q_2{q}_4)& 2(q_2{q}_3-q_1{q}_4)& -q_1^2-q_2^2+q_3^2+q_4^2\end{array}\right]$

Can calculate the attitude matrix of three probes respectively, according to the attitude matrix of three probes, the optical axis calculating three probes is oriented to: the optical axis of probe 1 points to: S ₁=s ₀₁× i+s ₁₁× j+s ₂₁× k; The optical axis of probe 2 points to: S ₂=s ₀₂× i+s ₁₂× j+s ₂₂× k; The optical axis of probe 3 points to: S ₃=s ₀₃× i+s ₁₃× j+s ₂₃× k.The coordinate of three optical axis sensings under body image space coordinate system is all (0,0,1), suppose that the attitude polarity calculating three probe star sensors is consistent with the polarity of probe 1, the coordinate conversion of so popping one's head under 2 and probe 3 body image spaces, to the image space coordinate of probe 1, supposes probe 2 and pass between the coordinate system of 1 body image space of popping one's head in is R ₁₂, the pass between the coordinate system of probe 3 and probe 1 body image space is R ₁₃, the coordinate of 2 body image space coordinates under the coordinate system of probe 1 body image space of so popping one's head in is: U ₁₂=R ₁₂(0,0,1), the coordinate of 3 body image space coordinates under the coordinate system of probe 1 body image space of popping one's head in is: U ₁₃=R ₁₃(0,0,1), the coordinate of 1 body image space coordinate under the coordinate system of probe 1 body image space of popping one's head in is: U ₁=(0,0,1), utilizes U ₁₂, U ₁₃, U ₁and S ₁, S ₂and S ₃, utilize formula (8) just can calculate the attitude of three probe star sensors.

The features and advantages of the invention:

First: data processing module fixed cycle ground is calibrated to two probe modules, after compensate for star sensor long-play, the shortcoming of mistiming increase between two imaging probe modules;

Second: the shortcoming that compensate for single imaging probe module star sensor axis of rolling attitude accuracy difference;

3rd: even if certain imaging probe module actual effect, on the basis ensureing attitude accuracy, another two imaging probe modules still can export attitude, improve data reliability.

The main performance index of single probe module:

Probe: 20 ° × 20 °

Face battle array: 2048 × 20484

Detection magnitude: 5.5Mv

Data updating rate: 5Hz

The optical axis of three probes points to pairwise orthogonal.

In order to verify the precision of this three probes star sensor, and with star sensor the precision of the output attitude that certain is popped one's head in carried out outfield see star compare (due to this three pop one's head in star sensor output attitude polarity with probe 1 star sensor polarity consistent, therefore in experimentation, three probe attitudes of output compare with the attitude of probe 1).

Claims (1)

1. a defining method for three probe star sensor attitudes, is characterized in that: step is as follows:

Step one: read the attitude Q that first obtains probe respectively ₁with the t time of exposure ₁; Second obtains the attitude Q popped one's head in ₂with the t time of exposure ₂; 3rd obtains the attitude Q popped one's head in ₃with the t time of exposure ₃; Get t ₁, t ₂and t ₃maximal value; If t ₁maximum; Calculate Δ t ₂=t ₁-t ₂, Δ t ₃=t ₁-t ₃;

Step 2: utilize Q ₂, Δ t ₂calculate second with formula (1) and obtain probe at t ₁moment attitude Q ' ₂, utilize Q ₃, Δ t ₃calculate the 3rd with formula (1) and obtain probe at t ₁moment attitude Q ' ₃;

$\left[\begin{array}{c}{q}_{10}^{\′}\\ q_{11}^{\′}\\ q_{12}^{\′}\\ q_{13}^{\′}\end{array}\right]=\left[\begin{array}{c}{q}_{10}\\ q_{11}\\ q_{12}\\ q_{13}\end{array}\right]+\left[\begin{array}{c}{\stackrel{\·}{q}}_{10}\\ {\stackrel{\·}{q}}_{11}\\ {\stackrel{\·}{q}}_{12}\\ {\stackrel{\·}{q}}_{13}\end{array}\right]\×(t_1^{\′}-t_1)---\left(1\right)$

Step 3: utilize Q ₁calculate first and obtain probe at t ₁the optical axis in moment points to S ₁, utilize Q ' ₂calculate second and obtain probe at t ₁the optical axis in moment points to S ' ₂, utilize Q ' ₃calculate the 3rd and obtain probe at t ₁the optical axis in moment points to S ' ₃;

Step 4: the image space coordinate V that the first acquisition probe optical axis points to ₁be (0,0,1), utilize formula (2) to obtain the image space coordinate V of probe optical axis sensing second ₂(0,0,1) is transformed into the image space coordinate V ' under the first acquisition probe co-ordinate system ₂, utilize formula (2) to obtain the image space coordinate V of probe optical axis sensing the 3rd ₃(0,0,1) is transformed into the image space coordinate V ' under the first acquisition probe co-ordinate system ₃;

$U_r=\left[\begin{array}{c}{U}_{\mathrm{rx}}\\ U_{\mathrm{ry}}\\ U_{\mathrm{rz}}\end{array}\right],V_r=\left[\begin{array}{c}{V}_{\mathrm{rx}}\\ V_{\mathrm{ry}}\\ V_{\mathrm{rz}}\end{array}\right],W_r=\left[\begin{array}{c}{W}_{\mathrm{rx}}\\ W_{\mathrm{ry}}\\ W_{\mathrm{rz}}\end{array}\right]---\left(2\right)$

Step 5: utilize V ₁, V ' ₂, V ' ₃and S ₁, S ' ₂, S ' ₃, utilize formula (3) to calculate the attitude Q of three probes, and output time t ₁with attitude Q; If t ₂maximum, calculate Δ t ₁=t ₂-t ₁, Δ t ₃=t ₂-t ₃;

$\left\{\begin{array}{c}{C}_{\mathrm{nb}}{F}_b=C_{\mathrm{nr}}{F}_r\\ F_b=C_{\mathrm{br}}{F}_r\\ C_{\mathrm{br}}=C_{\mathrm{nb}}^{-1}{C}_{\mathrm{nr}}=C_{\mathrm{nb}}^T{C}_{\mathrm{nr}}\end{array}\right.---\left(3\right)$

Step 6: utilize Q ₁, Δ t ₁calculate first with formula (1) and obtain probe at t ₂moment attitude Q ' ₁, utilize Q ₃, Δ t ₃calculate the 3rd with formula (1) and obtain probe at t ₂moment attitude Q ' ₃;

Step 7: utilize Q ' ₁calculate first and obtain probe at t ₂the optical axis in moment points to S ' ₁, utilize Q ₂calculate second and obtain probe at t ₂the optical axis in moment points to S ₂, utilize Q ' ₃calculate the 3rd and obtain probe at t ₂the optical axis in moment points to S ' ₃

Step 8: the image space coordinate V that the first acquisition probe optical axis points to ₁be (0,0,1), utilize formula (2) to obtain the image space coordinate V of probe optical axis sensing second ₂(0,0,1) is transformed into the image space coordinate V ' under the first acquisition probe co-ordinate system ₂, utilize formula (2) to obtain the image space coordinate V of probe optical axis sensing the 3rd ₃(0,0,1) is transformed into the image space coordinate V ' under the first acquisition probe co-ordinate system ₃;

Utilize V ₁, V ' ₂, V ' ₃and S ' ₁, S ₂, S ' ₃, utilize formula (3) to calculate the attitude Q of three probes, and output time t ₂with attitude Q;

If t ₃maximum;

Calculate Δ t ₁=t ₃-t ₁, Δ t ₂=t ₃-t ₂

Utilize Q ₁, Δ t ₁calculate first with formula (1) and obtain probe at t ₃moment attitude Q ' ₁, utilize Q ₂, Δ t ₂calculate second with formula (1) and obtain probe at t ₃moment attitude Q ' ₂

Utilize Q ' ₁calculate first and obtain probe at t ₃the optical axis in moment points to S ' ₁, utilize Q ' ₂calculate second and obtain probe at t ₃the optical axis in moment points to S ' ₂, utilize Q ₃calculate the 3rd and obtain probe at t ₃the optical axis in moment points to S ₃

The image space coordinate V that first acquisition probe optical axis points to ₁be (0,0,1), utilize formula (2) to obtain the image space coordinate V of probe optical axis sensing second ₂(0,0,1) is transformed into the image space coordinate V ' under the first acquisition probe co-ordinate system ₂, utilize formula (2) to obtain the image space coordinate V of probe optical axis sensing the 3rd ₃(0,0,1) is transformed into the image space coordinate V ' under the first acquisition probe co-ordinate system ₃

Step 9: utilize V ₁, V ' ₂, V ' ₃and S ' ₁, S ' ₂, S ₃, utilize formula (3) to calculate the attitude Q of three probes, and output time t ₃with attitude Q;

Wherein, three probe star sensor attitude determination method:

Three unit vector X _n, Y _n, Z _n, and form a mutually orthogonal coordinate system, wherein: Y _nand Z _nmould | Y _n|=1 He | Z _n|=1, remember new coordinate system F _nfor

$F_n=\left[\begin{array}{c}{X}_n\\ Y_n\\ Z_n\end{array}\right]---\left(4\right)$

The body coordinate of spacecraft is F _b, georeferencing coordinate is F _r, their coordinate base is respectively

$F_b=\left[\begin{array}{c}{X}_b\\ Y_b\\ Z_b\end{array}\right],F_r=\left[\begin{array}{c}{X}_r\\ Y_r\\ Z_r\end{array}\right]---\left(5\right)$

Wherein, X _b, Y _b, Z _bfor F _bunit vector, X _r, Y _r, Z _rfor F _runit vector,

X _n, Y _n, Z _nthree vectors recorded, they and F _band F _rbeing described as of coordinate system:

$X_n=U_b^T{F}_b=U_r^T{F}_r$

$Y_n=V_b^T{F}_b=V_r^T{F}_r---\left(6\right)$

$Z_n=W_b^T{F}_b=W_r^T{F}_r$

Wherein, U _b, V _b, U _r, V _r, W _b, W _bbe respectively X _n, Y _n, Z _nat F _band F _rcoordinate array, expansion is:

$U_b=\left[\begin{array}{c}{U}_{\mathrm{bx}}\\ U_{\mathrm{by}}\\ U_{\mathrm{bz}}\end{array}\right],V_b=\left[\begin{array}{c}{V}_{\mathrm{bx}}\\ V_{\mathrm{by}}\\ V_{\mathrm{bz}}\end{array}\right],W_b=\left[\begin{array}{c}{W}_{\mathrm{bx}}\\ W_{\mathrm{by}}\\ W_{\mathrm{bz}}\end{array}\right]---\left(7\right)$

$U_r=\left[\begin{array}{c}{U}_{\mathrm{rx}}\\ U_{\mathrm{ry}}\\ U_{\mathrm{rz}}\end{array}\right],V_r=\left[\begin{array}{c}{V}_{\mathrm{rx}}\\ V_{\mathrm{ry}}\\ V_{\mathrm{rz}}\end{array}\right],W_r=\left[\begin{array}{c}{W}_{\mathrm{rx}}\\ W_{\mathrm{ry}}\\ W_{\mathrm{rz}}\end{array}\right]---\left(8\right)$

Due to three unit vector X _n, Y _n, Z _nit is mutually orthogonal,

Therefore,

$F_n=\left[\begin{array}{c}{X}_n\\ Y_n\\ Z_n\end{array}\right]=\left[\begin{array}{c}{U}_b\\ V_b\\ W_b\end{array}\right]F_b=C_{\mathrm{nb}}{F}_b---\left(9\right)$

C _nbfor F _nwith F _bbetween attitude matrix,

In like manner,

$F_n=\left[\begin{array}{c}{X}_n\\ Y_n\\ Z_n\end{array}\right]=\left[\begin{array}{c}{U}_r\\ V_r\\ W_r\end{array}\right]F_r=C_{\mathrm{nr}}{F}_r---\left(10\right)$

C _nrfor F _nwith F _rbetween attitude matrix,

Contrast (8) and (9), and make F _band F _rbetween attitude matrix be C _br, have

$\left\{\begin{array}{c}{C}_{\mathrm{nb}}{F}_b=C_{\mathrm{nr}}{F}_r\\ F_b=C_{\mathrm{br}}{F}_r\\ C_{\mathrm{br}}=C_{\mathrm{nb}}^{-1}{C}_{\mathrm{nr}}=C_{\mathrm{nb}}^T{C}_{\mathrm{nr}}\end{array}\right.---\left(11\right)$

C _brbe required F _band F _rbetween attitude matrix, obtain F thus _bthree unit vector X _n, Y _n, Z _nat F _rin description, namely determine the attitude of aircraft three axle, due to X _n, Y _n, Z _nmutually orthogonal, not parallel, therefore must exist;

If F _bfor aircraft body coordinate system, F _r=F _ofor orbital coordinate system, for the roll angle of x-y-z rotational order definition pitching angle theta and crab angle ψ are all the situation at little angle, F _bwith F _obetween attitude matrix C _bofor

Therefore formula (9) is utilized to obtain roll angle pitching angle theta and crab angle ψ;

2. the fundamentals of successive deduction of attitude

If t ₁the attitude quaternion of certain probe of moment star sensor is Q ₁, t ₂the attitude quaternion of certain probe of moment star sensor is Q ₂, t ₃the attitude quaternion of certain probe of moment star sensor is Q ₃, t ₁the angular velocity of moment star sensor is ω ₁, wherein Q ₁=q ₁₀× i+q ₁₁× j+q ₁₂× k+q ₁₃, so have

$\left[\begin{array}{c}{\stackrel{\·}{q}}_{10}\\ {\stackrel{\·}{q}}_{11}\\ {\stackrel{\·}{q}}_{12}\\ {\stackrel{\·}{q}}_{13}\end{array}\right]=\frac{1}{2}\left[\begin{array}{cccc}0& {\mathrm{\ω}}_{1x}& -{\mathrm{\ω}}_{1y}& {\mathrm{\ω}}_{1z}\\ -{\mathrm{\ω}}_{1z}& 0& {\mathrm{\ω}}_{1x}& {\mathrm{\ω}}_{1y}\\ {\mathrm{\ω}}_{1y}& -{\mathrm{\ω}}_{1x}& 0& {\mathrm{\ω}}_{1z}\\ -{\mathrm{\ω}}_{1x}& -{\mathrm{\ω}}_{1y}& -{\mathrm{\ω}}_{1z}& 0\end{array}\right]\left[\begin{array}{c}{q}_{10}\\ q_{11}\\ q_{12}\\ q_{13}\end{array}\right]---\left(13\right)$

T ' ₁the attitude quaternion of moment this probe of star sensor is Q ' ₁=q ' ₁₀× i+q ' ₁₁× j+q ' ₁₂× k+q ' ₁₃, wherein, t ' ₁> t ₁.