CN102426017A - Star-sensor-based method for determining attitude of carrier relative to geographical coordinate system - Google Patents

Abstract

The invention provides a star-sensor-based method for determining the attitude of a carrier relative to a geographical coordinate system. The invention belongs to the technical field of attitude measuring. First, according to a chronometer and a Greenwich sidereal time formula, or through GPS timing, a spring equinox Greenwich time angle of a measured time is obtained; a transformation matrix Cwi from an equatorial inertial coordinate system i to a WGS-84 coordinate system w is obtained by calculation; the geographical coordinate of the carrier is obtained by using external information or a locating apparatus, and a transformation matrix Ctw from the system w to a geographical coordinate system t is obtained by calculation; then a transformation matrix Csi from the system i to a star sensor coordinate system s is obtained by the star sensor; with the three attitude matrices, the attitude matrix Csb of the carrier geographical coordinate system b relative to the system t is obtained by calculation. The attitude matrix Csb is the installation constant matrix of the star sensor. According to the invention, the spring equinox Greenwich time angle is obtained based on the timing apparatus, and real-time calculation of the attitude information of the carrier relative to the geographical coordinate system is realized by computerized programs.

Description

A kind ofly confirm the method for carrier with respect to the geographic coordinate system attitude based on star sensor

(1) technical field

The present invention relates to a kind ofly confirm the method for carrier, belong to the attitude measurement technical field with respect to the geographic coordinate system attitude based on star sensor.

(2) background technology

The attitude parameter of carrier is the important parameter in the navigational system, mostly adopts inertial navigation system to obtain the attitude of carrier on the main body.The advantage that maturation, precision are high though inertial navigation system possesses skills, the data output rating is high; But shortcoming such as exist complex equipments, cost an arm and a leg; And along with accumulated time, drifting problem can occur, thereby often need the auxiliary correction drift of other navigate mode.

Star sensor is a kind ofly to confirm the high-precision attitude sensor of carrier with respect to equator inertial coordinates system absolute space attitude with fixed star as observed object, has the precision height, does not receive electromagnetic interference (EMI), advantages such as good concealment, high, the not free drift of reliability.The equator inertial coordinates system is X _iAxle points to Υ in the first point of Aries, Z _iAxle points to the geocentric inertial coordinate system of celestial north pole, and what star sensor directly recorded is exactly the absolute attitude with respect to this inertial space.If expectation confirms that based on star sensor carrier with respect to the geographic coordinate system attitude, also need confirm carrier positions, and utilizes precision interval clock to confirm the Greenwich hour angle (GHA in the first point of Aries _Υ).The attitude measurement result that this covering device obtains also can assist the drift correction of accomplishing in inertial navigation initial alignment and the carrier flight course gyro.

The time keeping instrument manufacturing is relatively easy, cost is low, precision is high, and the cesium-beam atomic clock of China's development did not differ from 1 second in 1,500 ten thousand, and the most accurate 300,000,000 years errors of atomic clock in the world were less than 1 second.Astronomical sight data and fitting formula precision of calculation results are also far above the engineering actual demand of navigating.Chronometer time mainly obtains through the time service at national time service center, or utilizes GPS receiver timing function, records clock correction and obtains accurate timing, obtains Greenwich apparent time (GAST) at last, also is GHA _Υ

Obtain the geographic position of carrier, can utilize inertial navigation system, or satellite navigation system, or based on the remote measurement of ground survey station, or resolve according to the carrier dynamics of orbits, or method such as reckoning.Satellite navigation system comprises the Beidou satellite navigation system of GPS of USA, China, the GLONASS of Russia, the Galileo satellite navigation system in Europe; Handle through receiving transmitting of the satellite line data of going forward side by side; Thereby try to achieve the geographic position of carrier; Below be example narration with navigational route type GPS receiver, said method is applicable to other locating terminal or method.

Confirm that based on star sensor key link is exactly to try to achieve the transition matrix that the equator inertial coordinate is tied to terrestrial coordinate system in the serial link of carrier with respect to the geographic coordinate system attitude.The earth itself is exactly a big turntable, and carrier rotates with the earth, sees equator inertial coordinates system X from the relative motion angle _iAxle Υ in the first point of Aries pointed rotates GHA along the relative earth of celestial equator to east orientation west _ΥCan obtain by accurate timing, as shown in Figure 1, according to GHA _ΥJust can calculate the transition matrix that the equator inertial coordinate is tied to terrestrial coordinate system.GHA _ΥAlso can obtain, the Greenwich apparent time GAST of a zero hour in week is provided in the gps navigation message by GPS _w, utilize this information can obtain the GAST of this any time in week.

Find through the document retrieval; Chinese invention patent application number 201010215336.1, title: based on the alignment methods of CCD star sensor, this patent has related to utilizes timing to obtain the transition matrix that the equator inertial coordinate is tied to terrestrial coordinate system; But what this method was used is look-up table; Tabling look-up by hand means and can not realize full automation, and describes also perfectly inadequately about concrete embodiment, has restricted through engineering approaches.The equator inertial coordinate that this patent provides is tied to the computing method of the transition matrix of terrestrial coordinate system; Do not need manually to import any parameter; Utilize correlation formula and accurate timing to obtain the transition matrix that the equator inertial coordinate is tied to terrestrial coordinate system with realizing real-time robotization; Cooperate the output of star sensor, GPS equipment again, thereby obtain the attitude of carrier with respect to geographic coordinate system.

(3) summary of the invention

1. purpose: the purpose of this invention is to provide and a kind ofly confirm the method for carrier with respect to the geographic coordinate system attitude based on star sensor; It has made full use of star sensor, the high-precision characteristics of time keeping instrument; Utilize the extraneous carrier positions information of measuring; Obtain the attitude information of carrier automatically real-time, make things convenient for practical applications with respect to geographic coordinate system.

2. technical scheme: the objective of the invention is to realize through following technical scheme:

The present invention provides a kind of and confirms the method for carrier with respect to the geographic coordinate system attitude based on star sensor, and it comprises the steps:

Step 1: rely on accurate timing and GST (Greenwich sidereal time) exact formulas, or directly utilize GPS time service and text to resolve mode, obtain to measure GHA constantly _Υ, as shown in Figure 1, inertial coordinates system i is tied to the transition matrix C that WGS-84 coordinate system w is thereby ask for from the equator _Wi

Step 2:, ask for the transition matrix C that is tied to geographic coordinate system t system from w by the accurate geographic coordinate of external information or location survey equipment acquisition carrier _Tw

Step 3: rely on star sensor, obtain to be tied to the transition matrix C of star sensor coordinate system s system from i _Si

Step 4: after above-mentioned three steps provide attitude information, resolve and obtain the attitude matrix of carrier coordinate system b system with respect to geographic coordinate system t system

C wherein _SbBe the installation matrix of star sensor, at the experiment indoor measurement, be regarded as known constant matrix, i system, w system, t system, b are the spatial relation synoptic diagram, referring to Fig. 2.

Wherein, the high precision transition matrix C in the step 1 based on accurate timing technology _WiThe Electronic Data Processing method, be core technology of the present invention.The main development around 2 topmost formula used derivation, and first is earth rotation angle ERA (Earth Rotation Angle), represent with θ,

θ＝2π(0.7790572732640+1.00273781191135448T _u)

In the formula, T _u=(UT1 Julian date-2451545.0), promptly the Julian date of current epoch of observation and J2000.0 standard epoch at interval.

Second formula then is the solution formula of Greenwich apparent time GAST

$\mathrm{GAST}=0.14506+\mathrm{\θ}+4611.5739966t$

$+1.39667721t^2-0.00009344{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="HDA0000105042420000021.png,HDA0000105042420000022.png"\; state="\{\{state\}\}">t</figure-callout>}}^3+0.00001882t^4$

$+\mathrm{\&Delta;\&psi;}\cos {\mathrm{\&epsiv;}}_A-{\mathrm{\&Sigma;}}_k{C}_k^{\&prime;}\sin {\mathrm{\&alpha;}}_k-{0.00000087}^{\&prime;\&prime;}t\sin \mathrm{\&Omega;}$

Wherein, parametric t is the Julian century number of terrestrial time TT, and other parameter meaning is seen detailed description in (five).GAST is the Greenwich hour angle GHA in this first point of Aries constantly _Υ

Export during the high-precision real of Electronic Data Processing programming timing link; Need to guarantee the pin-point accuracy property of the related whole parameters of formula; The reckoning value of deviation delta TT between universal time UT1 and the terrestrial time TT; Can obtain from USNO (United States Naval Observatory, USNO-US Naval Observatory) website.

In the step 1, utilize GPS time service function and text to separate algorithm, then more simple, the Greenwich apparent time GAST of a zero hour in week is provided in the gps navigation message _w, Greenwich apparent time GAST=GAST that then should any time in week _w+ ω _Iet _Oe, t _OeBe that a zero hour in week is to measuring number second integral atomic time constantly.

3. advantage and effect: the present invention is based on star sensor and do not rely on the inertia measurement combination, confirm that in real time carrier is with respect to the geographic coordinate system attitude.It has made full use of that the time keeping instrument manufacturing is relatively easy, cost is low, precision is far above the characteristics of the attitude measurement instrument of most significant end, and has utilized the computing formula of true sidereal time to obtain GHA _Υ, attitude of carrier has been realized in real time output automatically.

(4) description of drawings

Fig. 1 Greenwich hour angle in first point of Aries synoptic diagram

Fig. 2 i system, w system, t system, b system, s are the spatial relation synoptic diagram

The attitude of the relative geographic coordinate system of Fig. 3 carrier is set up schematic flow sheet

Fig. 4 2006 annual GAST Error Simulation curve synoptic diagrams

Fig. 5 2011 annual GAST Error Simulation curve synoptic diagrams

Fig. 6 WGS-84 coordinate system w is tied to the Eulerian angle transformational relation synoptic diagram of geographic coordinate system t system

(5) embodiment

In order to understand technical scheme of the present invention better, embodiment of the present invention is further described below in conjunction with accompanying drawing:

It is as shown in Figure 3 that the attitude of the method for the invention is set up process flow diagram.This attitude measurement method may further comprise the steps:

Step 1: calculate the transition matrix C that equator inertial coordinates system i is tied to the WGS-84 coordinate system _Wi

Calculate attitude transition matrix C _WiKey be exactly that to find the solution GAST be GHA _ΥThe practical implementation step is following:

(1) asks earth rotation angle θ

Utilize the output of GPS timing type receiver to obtain universal time UT1, can calculate important parameter---earth rotation angle ERA (Earth Rotation Angle), represent with θ,

θ＝2π(0.7790572732640+1.00273781191135448T _u)(1)

Wherein, T _u=(UT1 Julian date-2451545.0), promptly the Julian date of current epoch of observation and J2000.0 standard epoch at interval.

(2) UT1 is scaled terrestrial time TT

TT＝UT1+ΔTT (2)

Wherein, Δ TT can obtain from USNO (UnitedStatesNavalObservatory, USNO-US Naval Observatory) website, in the data file that a form is deltat.preds, provides.At present, this website has predicted 2019 to the value of Δ TT, and is as shown in table 1, and this form adopts certain form to be bound in the working procedure.

Table 1 is by the predicted value that got Δ TT to 2019

Date	ΔTT	Date	ΔTT	Date	ΔTT
						2011.00	66.265	2014.00	67.7	2017.00	69.0
2011.25	66.396	2014.25	67.8	2017.25	69.0
						2011.50	66.447	2014.50	68.0	2017.50	69.0
2011.75	66.456	2014.75	68.0	2017.75	70.0
						2012.00	66.8	2015.00	68.0	2018.00	70.0
2012.25	66.9	2015.25	68.0	2018.25	70.0
						2012.50	67.0	2015.50	68.0	2018.50	70.0
2012.75	67.1	2015.75	69.0	2018.75	70.0
						2013.00	67.3	2016.00	69.0	2019.00	70.0
2013.25	67.4	2016.25	69.0	2019.25	70.0
						2013.50	67.4	2016.50	69.0	2019.50	70.0
2013.75	67.6	2016.75	69.0	2019.75	71.0

Should explain because the complicacy of earth rotation, still do not have so far complete theoretical model can be for a long time accurate forecast Δ TT, for the influence of GAST how the prediction error of Δ TT needs study and evaluates and tests.

At present USNO has provided by the accurate measured value to the Δ TT in September, 2011, and lists by the predicted value to Δ TT in 2019, can find out according to existing accurate data, and the maximum error of the predicted value of the Δ TT that this website provides is within ± 1s.Carry out the error computing based on formula (1) to (9), all Mondaies of getting 2006 years, 2011 years respectively are as testDate, and any universal time of this day of picked at random is constantly as the test duration point.Only analyze the error percentage that GAST is caused, be regarded as stochastic error to the prediction error of Δ TT.When Δ TT exists between [1s; 1s] between error the time, (like Fig. 4, Fig. 5) can find out that the maximum error of GAST in 2006 is less than 0.000003 through simulation curve "; the maximum error of GAST in 2011 is less than 0.000004 ", the standard deviation sigma of 52 test points in 2006 _GAST2006=0.00000014 ", the standard deviation sigma of 52 test points in 2011 _GAST2011=0.00000024 ", for requirement of engineering precision, can ignore fully, so the predicted value of the Δ TT that employing USNO provides has very strong feasibility.Can and bind in the form write-in program in this website data download,, need not change any data, realize that automatic real-time is resolved attitude of carrier completely up to 2019.

(3) calculate Greenwich mean sidereal time (GMST) GMST

GMST＝0.14506+θ+4611.5739966t

+1.39667721t ²-0.00009344t ³+0.00001882t ⁴(3)

In the formula, t is the Julian century number of terrestrial time TT,

T=(TT-2001 TT in 1.5 days on the 1st January) (unit: day)/36525 (4)

(4) calculate equation of the equinoxes EECT

$\mathrm{EECT}=\mathrm{\&Delta;\&psi;}\cos {\mathrm{\&epsiv;}}_A-\underset{i=1}{\overset{33}{\mathrm{\&Sigma;}}}(C_{i1}\sin {\mathrm{\&alpha;}}_i+C_{i2}\cos {\mathrm{\&alpha;}}_i)-{0.00000087}^{\&prime;\&prime;}t\sin \mathrm{\&Omega;}---\left(5\right)$

Thereafter two is the additive term of equation of the equinoxes, and compare influence with first less, the present invention is directed to practical applications, only utilizes first precision enough.For improving program operation speed, simplify the computing formula of equation of the equinoxes,

EECT＝Δψcosε _A(6)

1. ask nutation of longitude Δ ψ

$\mathrm{\&Delta;\&psi;}={\mathrm{\&Delta;\&psi;}}_p+\underset{i=1}{\overset{77}{\mathrm{\&Sigma;}}}[(A_{\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="HDA0000105042420000021.png,HDA0000105042420000022.png"\; state="\{\{state\}\}">i</figure-callout>}1}+A_{i2})\sin {\mathrm{\&alpha;}}_i+A_{\mathrm{<figure-callout\; id="3"\; label="i"\; filenames="HDA0000105042420000021.png,HDA0000105042420000022.png"\; state="\{\{state\}\}">i</figure-callout>}3}\cos {\mathrm{\&alpha;}}_i]---\left(7\right)$

In the formula,

Δψ _p＝-0.135microarc?sec?ond

${\mathrm{\&alpha;}}_i=\underset{j=1}{\overset{5}{\mathrm{\&Sigma;}}}{n}_{\mathrm{ij}}{F}_j=n_{i1}{\mathrm{<figure-callout\; id="1"\; label="F"\; filenames="HDA0000105042420000021.png,HDA0000105042420000022.png"\; state="\{\{state\}\}">F</figure-callout>}}_1+n_{i2}{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="HDA0000105042420000021.png,HDA0000105042420000022.png"\; state="\{\{state\}\}">F</figure-callout>}}_2+n_{i3}{\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="HDA0000105042420000021.png,HDA0000105042420000022.png"\; state="\{\{state\}\}">F</figure-callout>}}_3+n_{i4}{F}_4+n_{i5}{F}_5.(i=1,...,77)$

In the formula, n _IjBe integer, can in IAU 2000B nutation model, find; F _j(F ₁, F ₂, F ₃, F ₄, F ₅) be respectively the mean anomaly l of the moon, the mean anomaly l of the sun, the flat some angular distance F that rises of the moon, life average angle D, anabibazon mean longitude Ω:

F ₁＝l＝134.96340251°+1717915923.2178″t，

F ₂＝l′＝357.52910918°+129596581.048″t，

F ₃＝F＝93.27209062°+1739527262.847″t，

F ₄＝D＝297.85019547°+1602961601.2090″t，

F ₅＝Ω＝125.04455501°-6962890.5431″t；

A _I1, A _I2, A _I3Can in IAU 2000B nutation model, find.

2. ask mean obliquity ε _A

ε _A＝ε ₀-46.84024″t-0.00059″t ²+0.001813″t ³(8)

In the formula, ε ₀=84381.448 ", be ecliptic obliquity epoch, t is the Julian century number of terrestrial time TT, shown in formula (4).

(5) calculate Greenwich apparent time GAST

GAST＝GMST+EECT (9）

(6) inertial coordinates system i is tied to the transition matrix C that WGS-84 coordinate system w is from the equator in calculating _Wi

In the formula, if originally GAST adopts sidereal time unit hour (h), minute (m) and second (s) expression, also must be according to the order of h → ° (degree) → rad (radian), the unit's of being converted into radian is with the GHA of formula above the GAST substitution of Rad _ΥCarry out computing.

Perhaps, in can utilizing the application model of GPS, utilize the GPS Service of Timing can the more convenient GAST of resolving.The GAST of one zero hour in week is provided in the gps navigation message _w, GAST=GAST that then should any time in week _w+ ω _Iet _Oe, t _OeBe that a zero hour in week is to measuring the atom second of time number that adds up constantly.

Step 2:, ask for the transition matrix C that is tied to geographic coordinate system t system from w by the accurate geographic coordinate of external information or location survey equipment acquisition carrier _Tw

(λ φ), can adopt inertial navigation system to the latitude and longitude value of carrier present position, or GPS device measuring method, or adopts based on the remote measurement of ground survey station, or resolves according to the carrier dynamics of orbits, or method such as reckoning.The positioning result that is provided by GPS is the elements of a fix under the w system.As shown in Figure 6, be tied to the transition matrix C that t is from w so _TwBe expressed as,

$C_{\mathrm{tw}}=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos (90-\mathrm{\&phi;})& \sin (90-\mathrm{\&phi;})\\ 0& -\sin (90-\mathrm{\&phi;})& \cos (90-\mathrm{\&phi;})\end{array}\right]\left[\begin{array}{ccc}\cos (90+\mathrm{\&lambda;})& \sin (90+\mathrm{\&lambda;})& 0\\ -\sin (90+\mathrm{\&lambda;})& \cos (90+\mathrm{\&lambda;})& 0\\ 0& 0& 1\end{array}\right]---\left(11\right)$

$=\left[\begin{array}{ccc}-\sin \mathrm{\&lambda;}& \cos \mathrm{\&lambda;}& 0\\ -\sin \mathrm{\&phi;}\cos \mathrm{\&lambda;}& -\sin \mathrm{\&phi;}\sin \mathrm{\&lambda;}& \cos \mathrm{\&phi;}\\ \cos \mathrm{\&phi;}\cos \mathrm{\&lambda;}& \cos \mathrm{\&phi;}\sin \mathrm{\&lambda;}& \sin \mathrm{\&phi;}\end{array}\right]$

Step 3: rely on star sensor, obtain to be tied to the transition matrix C of carrier coordinate system b system from i _Bi

Step 4: behind the attitude information that above-mentioned three steps provide, resolve to such an extent that carrier coordinate system b is the attitude matrix C with respect to geographic coordinate system t system _Bt

C _si＝C _sbC _btC _twC _wi

$C_{\mathrm{bt}}=C_{\mathrm{sb}}^{-1}{C}_{\mathrm{si}}{C}_{\mathrm{wi}}^{-1}{C}_{\mathrm{tw}}^{-1}$

The C that obtains _BtBe the attitude matrix of carrier current time, perhaps further with C with respect to the equator inertial coordinates system _BtConvert hypercomplex number or Eulerian angle to.C _SbInstallation matrix for star sensor can obtain in the laboratory, is constant matrices.So far, obtained the attitude of carrier with respect to geographic coordinate system.This method does not need manually to import any supplementary, robotization in real time obtain attitude of carrier.

Claims (2)

1. confirm the method for carrier with respect to the geographic coordinate system attitude based on star sensor for one kind, it is characterized in that: these method concrete steps are following:

Step 1: rely on accurate timing and GST (Greenwich sidereal time) exact formulas; Or directly utilize GPS time service and text to resolve mode; Obtain to measure Greenwich hour angle in the first point of Aries constantly, inertial coordinates system i is tied to the transition matrix C that WGS-84 coordinate system w is thereby ask for from the equator _Wi

Step 2:, ask for the transition matrix C that is tied to geographic coordinate system t system from w by the accurate geographic coordinate of external information or location survey equipment acquisition carrier _Tw

Step 3: rely on star sensor, obtain to be tied to the transition matrix C of star sensor coordinate system s system from i _Si

Step 4: after above-mentioned three steps provide attitude information, resolve to such an extent that carrier coordinate system b is the attitude matrix with respect to t system

C wherein _SbInstallation matrix for star sensor.

2. according to claim 1ly a kind ofly confirm the method for carrier with respect to the geographic coordinate system attitude based on star sensor; It is characterized in that: with the earth of rotation as a big turntable; The parameter that robotization zooming program utilizes IERS (International Earth Rotation and reference frame service) website and USNO (United States Naval Observatory, USNO-US Naval Observatory) website to provide is through timing and time system conversion; Obtain Greenwich apparent time GAST, promptly the first point of Aries Greenwich hour angle GHA _Υ, the solution formula general type of Greenwich apparent time GAST is:

$\mathrm{GAST}={0.14506}^{\&prime;\&prime;}+\mathrm{\&theta;}+{4611.5739966}^{\&prime;\&prime;}t+{1.39667721}^{\&prime;\&prime;}{t}^2$

$-{0.00009344}^{\&prime;\&prime;}{t}^3+{0.00001882}^{\&prime;\&prime;}{t}^4+\mathrm{\&Delta;\&psi;}\cos {\mathrm{\&epsiv;}}_A$

$-{\mathrm{\&Sigma;}}_k{C}_k^{\&prime;}\sin {\mathrm{\&alpha;}}_k-{0.00000087}^{\&prime;\&prime;}t\sin \mathrm{\&Omega;}$

In the equation of the equinoxes additive term

; The item that adds up is got 33, and then concrete form is:

$\mathrm{GAST}={0.14506}^{\&prime;\&prime;}+\mathrm{\&theta;}+{4611.5739966}^{\&prime;\&prime;}t+{1.39667721}^{\&prime;\&prime;}{t}^2$

$-{0.00009344}^{\&prime;\&prime;}{t}^3+{0.00001882}^{\&prime;\&prime;}{t}^4+\mathrm{\&Delta;\&psi;}\cos {\mathrm{\&epsiv;}}_A$

$-\underset{i=1}{\overset{33}{\mathrm{\&Sigma;}}}(C_{i1}\sin {\mathrm{\&alpha;}}_i+C_{i2}\cos {\mathrm{\&alpha;}}_i)-{0.00000087}^{\&prime;\&prime;}t\sin \mathrm{\&Omega;}$

To the low situation of practical applications accuracy requirement, is to improve Electronic Data Processing program computing velocity, an equation of the equinoxes additive term desirable item number still less that adds up, or can directly omit the equation of the equinoxes additive term, then reduced form is:

GAST＝0.14506″+θ+4611.5739966″t+1.39667721″t ²

-0.00009344″t ³+0.00001882″t ⁴+Δψcosε _A

Parametric t is the Julian century number of terrestrial time TT, and θ is the earth rotation angle, is two common-used formula forms of θ as follows:

θ＝2π(UT1Julian?day?fraction+0.779057273264+0.00273781191135448T _u)

θ＝2π(0.7790572732640+1.00273781191135448T _u)

Perhaps, utilize GPS time service function and text to separate algorithm and obtain GAST, then more simple, the Greenwich apparent time GAST of a zero hour in week is provided in the gps navigation message _w, Greenwich apparent time GAST=GAST that then should any time in week _w+ ω _Iet _Oe, t _OeBe that a zero hour in week is to measuring number second integral atomic time constantly;

Obtain being tied to the real-time transition matrix C of w system at last from i _Wi, accomplish C _WiAccurately resolve in real time.

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