CN113688355A - Orbit measurement method of surrounding planet detector - Google Patents

Orbit measurement method of surrounding planet detector Download PDF

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CN113688355A
CN113688355A CN202111013731.6A CN202111013731A CN113688355A CN 113688355 A CN113688355 A CN 113688355A CN 202111013731 A CN202111013731 A CN 202111013731A CN 113688355 A CN113688355 A CN 113688355A
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叶楠
杨永安
王家松
王帆
陈俊收
李军锋
贺克山
叶修松
任凯强
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Abstract

The invention discloses a track measuring method of a surrounding planet detector, which is implemented by the following steps; performing finite-order Taylor expansion on the two one-way distance differences of the start and the end of the integration at the one-way distance vector at the integration end moment to obtain the geometric component of average speed measurement; and calculating to obtain a total average speed measurement value by combining the relativistic component of average speed measurement. When the planet position is calculated, the speed integral is used for replacing direct calculation for many times, the interpolation error of a star table is avoided, the distance difference is used as a function of a distance vector and a change vector, the requirement of storing and calculating the effective digit can be met only by double-precision floating point numbers, the calculation complexity caused by using four-precision floating point numbers is avoided, and the calculation precision and the efficiency are effectively considered.

Description

Orbit measurement method of surrounding planet detector
Technical Field
The invention belongs to the technical field of spacecraft orbit measurement, and relates to an orbit measurement method of a surrounding planet detector.
Background
The main orbit measurement means of the deep space planet detection is high-precision Doppler data, the Doppler data is used for carrying out precise orbit determination and positioning on a target, and theoretical modeling needs to be carried out on velocity measurement in advance to obtain a theoretical value which is more than one order of magnitude higher than the measurement precision. At present, the Doppler velocity measurement precision of the X frequency band can reach 0.1mm/s, and the corresponding theoretical velocity measurement precision can meet the requirement only when reaching more than 0.01 mm/s. The conventional method firstly calculates the distance between the detector and the measuring station and then obtains a theoretical speed measurement value through distance difference. When the distance is calculated, the positions of the detector and the measuring station need to be calculated, and the error of the star table interpolation planet position is about 0.1mm and cannot be eliminated through difference. When the distance difference is used for calculating the theoretical speed measurement, four-precision floating point numbers are needed to avoid truncation errors, and the storage and calculation speed is slow.
Disclosure of Invention
The invention aims to provide a track measuring method surrounding a planet detector, which solves the problems of large error and low calculation speed in the prior art.
The technical scheme adopted by the invention is that the orbit measurement method of the surrounding planet detector is implemented according to the following steps:
step 1, calculating a unidirectional downlink vector at the integral ending moment;
step 2, calculating a unidirectional uplink vector at the integral ending moment;
step 3, calculating a unidirectional downlink vector at the integration starting moment;
step 4, calculating a unidirectional uplink vector at the integration starting moment;
step 5, calculating the unidirectional uplink and downlink distance difference of the integration starting time and the integration ending time;
step 6, calculating the geometric component of Doppler velocity measurement;
step 7, calculating relativistic component of average speed measurement;
and 8, calculating the total average speed measurement.
The present invention is also characterized in that,
step 1, according to the condition of surrounding planets, calculating a unidirectional downlink vector of a detector as follows:
r23(tend)＝(rP+rsat)-(rE+rsta) (1)
in the formula (1), r23Is a unidirectional down vector, t, from the detector to the ground stationendIndicates the integration end time, rEIs a position vector of the geocentric under a solar system centroid celestial sphere reference system (BCRS), rstaFor measuring the position vector of the station under the Earth's center celestial sphere reference system, rPIs the position vector of the planet centroid under BCRS, rsatA position vector of the detector under a planet mass center celestial sphere reference system is determined; the celestial sphere reference systems only have translation of the origin of the coordinate system and do not relate to rotation of the orbital plane and the main direction;
when calculating the unidirectional downlink, taking the receiving time as an initial value, carrying out optical line time superposition to solve the forwarding time of the detector and the unidirectional distance value rho23＝||r23An | transformation less than 1% is considered as iterative convergence.
Step 2, according to the situation of surrounding the planet, calculating a unidirectional uplink vector of the detector as follows:
r12(tend)＝(rE+rsta)-(rP+rsat) (2)
in the formula (2), the parameter tend，rE,rsta,rP,rsatDefinition is in accordance with step 1, r12A unidirectional uplink vector of a detector from a ground station is obtained;
when unidirectional uplink is calculated, the forwarding time of the detector is taken as an initial value, optical line time superposition is carried out to solve the sending time of the ground station signal, and the unidirectional distance value rho12＝||r12An | transformation less than 1% is considered as iterative convergence.
Integration start time t in step 3start＝tend-TcAnd calculating a unidirectional downlink vector as follows:
Figure BDA0003239146920000031
in the formula (3), the parameter rE，rsta，rP，rsatThe definition corresponds to step 1, where the term Δ is the amount of change of the corresponding vector in an integration period, where the change in the position of the station Δ rstaThe change of the position of the detector delta r is obtained by the coordinate conversion at different momentsstaVariation of the earth and planet position Δ r obtained by orbital integrationPAnd Δ rEObtaining by interpolation of planet ephemeris;
Δr23＝(ΔrP+Δrsat)-(ΔrE+Δrsta) The one-way down vector difference is the integration end and start time.
And 4, calculating a unidirectional uplink vector at the integration starting moment according to the step 2 and the step 3:
r12(tstart)＝r12(tend)+Δr12 (4)
in the formula (4), Δ r12The one-way up vector difference is the integration end and start time.
And 5, performing difference on the two one-way distances of the start and the end of integration, performing Taylor expansion on the difference value at the one-way distance vector r at the integration end moment, and eliminating a high-order term:
Figure BDA0003239146920000032
substituting the results of the formula (1) in the step 1 and the formula (3) in the step 3 into the formula (5) to obtain the distance difference | | | r of the single downward row23(tend)||-||r23(tstart)||；
Substituting the results of the formula (2) in the step 2 and the formula (4) in the step 4 into the formula (5) to obtain the distance difference | | | r of the unidirectional uplink12(tend)||-||r12(tstart)||。
Step 6, adding the uplink and downlink distance differences obtained in the step 5, and dividing the sum by the integral interval to obtain the geometric component of the Doppler velocity measurement
Figure BDA0003239146920000033
Figure BDA0003239146920000034
In the formula (6), the subscript 12 is a unidirectional upward row, and the subscript 23 is a unidirectional downward row.
Step 7, calculating the relativistic component of average speed measurement according to the relativistic time delay of the influence of the planet gravitation in the sun and the solar system
Figure BDA0003239146920000041
Figure BDA0003239146920000042
In equation (7), rlt represents the path elongation due to the relativistic effect, the subscript 12 represents the unidirectional upstream, and the subscript 23 represents the unidirectional downstream.
Step 8, adding the geometric component of the Doppler velocity measurement obtained in the step 6 and the relativistic component of the average velocity measurement obtained in the step 7 to obtain the final average Doppler velocity measurement
Figure BDA0003239146920000043
Figure BDA0003239146920000044
The invention has the beneficial effects that: aiming at the characteristic that the position of the deep space probe surrounding the planet is constrained by the planet attractive force, the invention uses the speed integral to replace the direct use of the star table to calculate the absolute position of the planet, thereby avoiding the interpolation error of the star table, uses the Taylor expansion comprising the position and the variation vector to calculate the distance difference, only needs two precision floating point numbers to meet the requirement of effective storage digit, avoids the calculation complexity caused by four precision floating point numbers, and effectively considers both the calculation precision and the efficiency.
Drawings
FIG. 1 is a schematic diagram of the average Doppler velocity measurement of the present invention;
FIG. 2 is a schematic diagram of the distance vector and the variation vector of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The orbit measurement method of the invention surrounding the planet detector is implemented according to the following steps as shown in figure 1:
step 1, calculating a unidirectional downlink vector at the integral ending moment;
according to the condition of surrounding planets, calculating a unidirectional descending vector of the detector as follows:
r23(tend)＝(rP+rsat)-(rE+rsta) (1)
in the formula (1), r23Is a unidirectional down vector, t, from the detector to the ground stationendIndicates the integration end time, rEIs a position vector of the geocentric under a solar system centroid celestial sphere reference system (BCRS), rstaFor measuring the position vector of the station under the Earth's center celestial sphere reference system, rPIs the position vector of the planet centroid under BCRS, rsatA position vector of the detector under a planet mass center celestial sphere reference system is determined; the celestial sphere reference systems only have translation of the origin of the coordinate system and do not relate to rotation of the orbital plane and the main direction;
when calculating the unidirectional downlink, taking the receiving time as an initial value, carrying out optical line time superposition to solve the forwarding time of the detector and the unidirectional distance value rho23＝||r23An | transformation less than 1% is considered as iterative convergence.
Step 2, calculating a unidirectional uplink vector at the integral ending moment;
according to the condition of surrounding planets, calculating the unidirectional ascending vector of the detector as follows:
r12(tend)＝(rE+rsta)-(rP+rsat) (2)
in the formula (2), the parameter tend，rE,rsta,rP,rsatDefinition is in accordance with step 1, r12A unidirectional uplink vector of a detector from a ground station is obtained;
when unidirectional uplink is calculated, the forwarding time of the detector is taken as an initial value, optical line time superposition is carried out to solve the sending time of the ground station signal, and the unidirectional distance value rho12＝||r12An | transformation less than 1% is considered as iterative convergence.
Step 3, calculating a unidirectional downlink vector at the integration starting moment;
integration start time tstart＝tend-TcAnd calculating a unidirectional downlink vector as follows:
Figure BDA0003239146920000051
in the formula (3), the parameter rE，rsta，rP，rsatThe definition is consistent with step 1, as shown in FIG. 2, where the term Δ is the amount of change in the corresponding vector during an integration period, where the change in the position of the station Δ r isstaObtained by converting coordinates at different times, and the position change delta r of the detectorstaVariation of the earth and planet position Δ r obtained by orbital integrationPAnd Δ rEObtaining by interpolation of planet ephemeris; at this time,. DELTA.r23＝(ΔrP+Δrsat)-(ΔrE+Δrsta) The one-way down vector difference is the integration end and start time. The error of the star table interpolation calculation planet position is about 0.1mm and cannot be eliminated through difference; the change deltar of the earth and planet position is calculated by proposing that the velocity of the central celestial body at the integration intermediate moment BCRS is multiplied by the integration time at an integration time of 1 secondPAnd Δ rEAnd errors introduced by star table interpolation are avoided.
Step 4, calculating a unidirectional uplink vector at the integration starting moment;
according to the step 2 and the step 3, calculating a unidirectional uplink vector at the integration starting moment:
r12(tstart)＝r12(tend)+Δr12 (4)
in the formula (4), Δ r12The one-way up vector difference is the integration end and start time.
Step 5, calculating the unidirectional uplink and downlink distance difference of the integration starting time and the integration ending time;
and 5, performing difference on the two one-way distances of the start and the end of integration, performing Taylor expansion on the difference value at the one-way distance vector r at the integration end moment, and eliminating a high-order term:
Figure BDA0003239146920000061
substituting the results of the formula (1) in the step 1 and the formula (3) in the step 3 into the formula (5) to obtain the distance difference | | | r of the single downward row23(tend)||-||r23(tstart)||；
Substituting the results of the formula (2) in the step 2 and the formula (4) in the step 4 into the formula (5) to obtain the distance difference | | | r of the unidirectional uplink12(tend)||-||r12(tstart)||。
According to the invention, the Taylor expansion including the position and the change vector is used for calculating the distance difference, the requirement of effective storage digits can be met only by double-precision floating point numbers, the problems that the distance is too far, the storage digits are limited, the precision of a small number part is lost and the calculation complexity caused by using four-precision floating point numbers is avoided, and the calculation speed is improved.
Step 6, calculating the geometric component of Doppler velocity measurement;
adding the uplink and downlink distance differences obtained in the step 5, and dividing the sum by the integral interval to obtain the geometric component of the Doppler velocity measurement
Figure BDA0003239146920000071
Figure BDA0003239146920000072
In the formula (6), the subscript 12 is a unidirectional upward row, and the subscript 23 is a unidirectional downward row.
Step 7, calculating relativistic component of average speed measurement;
calculating the relativistic component of average speed measurement according to the relativistic time delay of the influence of the planetary gravitation in the sun and the solar system
Figure BDA0003239146920000073
Figure BDA0003239146920000074
In equation (7), rlt represents the path elongation due to the relativistic effect, the subscript 12 represents the unidirectional upstream, and the subscript 23 represents the unidirectional downstream.
Step 8, calculating the total average speed measurement;
adding the geometric component of the Doppler velocity measurement obtained in the step 6 and the relativistic component of the average velocity measurement obtained in the step 7 to obtain the final average Doppler velocity measurement
Figure BDA0003239146920000075
Figure BDA0003239146920000076
The invention relates to an orbit measurement method of a surrounding planet detector, which solves each self-variation vector by decomposing a distance vector into four parts including a unidirectional downlink vector at an integral ending moment, a unidirectional uplink vector at the integral ending moment, a unidirectional downlink vector at an integral starting moment and a unidirectional uplink vector at the integral starting moment, further obtains a total variation vector, and uses speed integral to replace direct calculation of planet positions for many times, thereby avoiding interpolation errors of a star table. The finite-order Taylor expansion is carried out on the distance difference at the one-way distance vector of the integral ending time to form an expression of the distance vector and the change vector, the expansion is used for calculating the one-way distance difference of the integral starting time and the integral ending time, the two-way distance sum difference is further calculated, the calculation of the distance difference only needs double-precision floating point numbers, the requirement of storing and calculating the effective digit can be met, and the calculation complexity caused by using four-precision floating point numbers is avoided; differentiating the two groups of distance sums to obtain an average speed measurement in an integration period; and obtaining a geometric component of velocity measurement, and combining a relativistic component of velocity measurement to obtain a final high-precision average Doppler velocity measurement result.

Claims (9)

1. A method for measuring a track around a satellite detector is characterized by comprising the following steps:
step 1, calculating a unidirectional downlink vector at the integral ending moment;
step 2, calculating a unidirectional uplink vector at the integral ending moment;
step 3, calculating a unidirectional downlink vector at the integration starting moment;
step 4, calculating a unidirectional uplink vector at the integration starting moment;
step 5, calculating the unidirectional uplink and downlink distance difference of the integration starting time and the integration ending time;
step 6, calculating the geometric component of Doppler velocity measurement;
step 7, calculating relativistic component of average speed measurement;
and 8, calculating the total average speed measurement.
2. The orbit measurement method of claim 1, wherein the step 1 is to calculate the unidirectional downward vector of the detector according to the situation of the circum-planet as follows:
r23(tend)＝(rP+rsat)-(rE+rsta) (1)
in the formula (1), r23Is a unidirectional down vector, t, from the detector to the ground stationendIndicates the integration end time, rEIs a position vector of the geocentric under a solar system centroid celestial sphere reference system (BCRS), rstaIs a position vector of a measuring station under a geocentric celestial sphere reference system, rPIs the position vector of the planet centroid under BCRS, rsatTo detectThe device is a position vector under a planet mass center celestial sphere reference system; the celestial sphere reference systems only have translation of the origin of the coordinate system and do not relate to rotation of the orbital plane and the main direction;
when calculating the unidirectional downlink, taking the receiving time as an initial value, carrying out optical line time superposition to solve the forwarding time of the detector and the unidirectional distance value rho23＝||r23An | transformation less than 1% is considered as iterative convergence.
3. The orbit measurement method of claim 2, wherein the step 2 is to calculate the unidirectional upward vector of the detector according to the condition of the circum-planet as follows:
r12(tend)＝(rE+rsta)-(rP+rsat) (2)
in the formula (2), the parameter tend，rE,rsta,rP,rsatDefinition is in accordance with step 1, r12A unidirectional uplink vector of a detector from a ground station is obtained;
when unidirectional uplink is calculated, the forwarding time of the detector is taken as an initial value, optical line time superposition is carried out to solve the sending time of the ground station signal, and the unidirectional distance value rho12＝||r12An | transformation less than 1% is considered as iterative convergence.
4. The method according to claim 3, wherein the integration start time t in step 3 isstart＝tend-TcAnd calculating a unidirectional downlink vector as follows:
Figure FDA0003239146910000021
in the formula (3), the parameter rE，rsta，rP，rsatThe definition is consistent with step 1, wherein the term delta is the variation of the corresponding vector in an integration period, wherein the change of the position of the measuring station delta rstaObtained by converting coordinates at different moments, and the position of the detector changesChange of arstaVariation of the earth and planet position Δ r obtained by orbital integrationPAnd Δ rEObtaining by interpolation of planet ephemeris; at this time,. DELTA.r23＝(ΔrP+Δrsat)-(ΔrE+Δrsta) The one-way down vector difference is the integration end and start time.
5. The orbit measurement method of claim 4, wherein the step 4 is to calculate the unidirectional ascending vector at the start of integration according to the steps 2 and 3:
r12(tstart)＝r12(tend)+Δr12 (4)
in the formula (4), Δ r12The one-way up vector difference is the integration end and start time.
6. A method as claimed in claim 5, wherein step 5 comprises subtracting the two single direction distances at the start and end of the integration, Taylor expanding the difference at the single direction distance vector r at the end of the integration, and eliminating higher order terms:
Figure FDA0003239146910000031
substituting the results of the formula (1) in the step 1 and the formula (3) in the step 3 into the formula (5) to obtain the unidirectional descending distance difference | | | r23(tend)||-||r23(tstart)||；
Substituting the results of the formula (2) in the step 2 and the formula (4) in the step 4 into the formula (5) to obtain the distance difference | | | r of the unidirectional ascending12(tend)||-||r12(tstart)||。
7. The method as claimed in claim 6, wherein the step 6 adds the difference between the up and down distances obtained in step 5 and divides the sum by the integration interval to obtain the geometry of Doppler velocity measurementComponent(s) of
Figure FDA0003239146910000032
Figure FDA0003239146910000033
In the formula (6), the subscript 12 is a unidirectional upward row, and the subscript 23 is a unidirectional downward row.
8. The method according to claim 7, wherein the step 7 is to calculate the relativistic component of the average velocity measurement according to the relativistic time delay of the influence of the planetary attraction in the sun and the solar system
Figure FDA0003239146910000034
Figure FDA0003239146910000035
In equation (7), rlt represents the path elongation due to the relativistic effect, subscript 12 represents the unidirectional upstream, and subscript 23 represents the unidirectional downstream.
9. The method as claimed in claim 8, wherein the step 8 adds the geometric component of the doppler velocity measurement obtained in the step 6 and the relativistic component of the average velocity measurement obtained in the step 7 to obtain the final average doppler velocity measurement
Figure FDA0003239146910000036
Figure FDA0003239146910000037
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CN102495715A (en) * 2011-11-28 2012-06-13 北京航天飞行控制中心 Deep space Doppler speed measurement calculating method defined by double-precision floating point
CN106643744A (en) * 2016-12-29 2017-05-10 武汉大学 Remote moon surface landing device precise positioning method based on four-stroke tracking mode

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Application publication date: 20211123