CN106679675B - A kind of final Approach phase autonomous navigation method of Mars based on relative measurement information - Google Patents
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Abstract
The final Approach phase autonomous navigation method of a kind of Mars based on relative measurement information disclosed by the invention, belongs to field of deep space exploration.The present invention is to realize the final Approach phase independent navigation of Mars, establishes final approach and around kinetic model;In conjunction with the Doppler range rate measurement information of X-ray pulsar arrival time difference information and Mars orbiter, orbital vehicle, based on nonlinear filtering algorithm, Combined estimator is carried out to the state of proximity detector and Mars orbiter, orbital vehicle, it is absolutely navigated using two kinds of relative measurement information realizations of X-ray pulsar arrival time difference information and the Doppler range rate measurement information of Mars orbiter, orbital vehicle, improves the final Approach phase independent navigation precision of Mars and inlet point precision of state estimation.It has the advantages that and avoids introducing planet ephemeris error, reduce pulsar parameter uncertainty to the adverse effect of navigation performance;Reduce observations of pulsar time long caused state emission problem;The synchronous navigation performance for improving two detectors;Improve Navigation precision and convergence rate.
Description
Technical field
The present invention relates to a kind of final Approach phase autonomous navigation methods of Mars, belong to field of deep space exploration.
Background technique
Accuracy technology (within the scope of landing precision 100m), which can satisfy detector and land, has scientific research in martian surface
The preset location of value or safe landing have obtained extensive concern in mission requirements such as complex topographic territories in recent years.Into
The landing precision of decline landing (EDL) system is influenced by four principal elements, comprising: into the delivering error at interface, into boundary
The cognition in face is uncertain, environmental uncertainty and detector self performance (transfer ability etc.).It is new that atmosphere enters guidance etc.
The utilization of technology can eliminate adverse effect caused by inlet point delivering error and environmental uncertainty to a certain extent, visit
Under the premise of survey device proper property is certain, the position of inlet point and speed cognition uncertainty have weight to final landing precision
It influences.The navigation performance of the final Approach phase of Mars directly determines precision of state estimation of the detector at inlet point, to rear
Navigation, the guidance in continuous EDL stage are most important, and influence the final landing error of detector.Therefore, the final Approach phase of Mars is led
It navigates and is of great significance to the target for improving inlet point precision of state estimation and realization task accuracy.
In previous mars exploration task, detector carries out track using the tracking measurement and control network on ground mostly in Approach phase
It determines, but there are many limitations such as signal decaying, communication delay for this navigation mode.As what Future direction required constantly mentions
Rise, high-precision, independent of ground autonomous navigation technology be deep space exploration technology development trend.NASA (NASA)
The concept of spark arrester netting is successively proposed with European Space Agency (ESA), it is contemplated that the trunk network being made of orbiter, orbital vehicle is established near Mars
Network provides navigator fix and Communication of Support Services for proximity detector, lander and rover.However to based on orbiter, orbital vehicle
For radionavigation, the position and speed error of orbiter, orbital vehicle is the significant error source during proximity detector absolutely navigates, and
Under two-body dynamics environment, not can guarantee the complete of entire autonomous navigation system merely with tracking observation information between the stars such as ranging can
It sees.
X-ray pulsar belongs to the neutron star of high speed rotation, and magnetic pole wave beam is constantly radiated in rotary course, when wave beam is swept
It crosses when being mounted on ground or spaceborne detecting devices, detecting devices can receive continuous pulse signal, because it has
Extremely stable periodicity, X-ray pulsar provide a kind of new feasible way for Spacecraft Autonomous Navigation.In recent years, one
New autonomous navigation method of the kind based on X-ray pulsar relies on its high independence and robustness, obtains extensive concern.Successively
There is scholar to propose the independent navigation for carrying out Mars probes using X-ray pulsar;Utilize X-ray pulsar combination Doppler
The information that tests the speed improves detector and enters precision of state estimation etc..However, navigating using the absolute measurements of pulsar
During, state inevitably introduces planet ephemeris error when converting.Meanwhile the intrinsic parameter of X-ray pulsar (away from
From, azimuth etc.) navigation results can also be had an impact.
Summary of the invention
The final Approach phase autonomous navigation method of a kind of Mars based on relative measurement information disclosed by the invention, to be solved
Technical problem is to improve the precision of the final Approach phase independent navigation of Mars.
The present invention is achieved through the following technical solutions:
The final Approach phase autonomous navigation method of a kind of Mars based on relative measurement information disclosed by the invention, to realize fire
The final Approach phase independent navigation of star establishes final approach and around kinetic model;In conjunction with X-ray pulsar arrival time difference
The Doppler range rate measurement information of information and Mars orbiter, orbital vehicle is based on nonlinear filtering algorithm, to proximity detector and Mars orbiter, orbital vehicle
State carry out Combined estimator, utilize the Doppler range rate measurement of X-ray pulsar arrival time difference information and Mars orbiter, orbital vehicle letter
It ceases two kinds of relative measurement information realizations absolutely to navigate, the precision for improving the final Approach phase independent navigation of Mars is estimated with into dotted state
Count precision.
The final Approach phase autonomous navigation method of a kind of Mars based on relative measurement information disclosed by the invention, including it is as follows
Step:
Step 1: establishing Mars and finally approach and around kinetic model.
The final Approach phase of Mars and circular section navigation system kinetic model are established under Mars centered inertial coordinate system.Ten
Two-dimensional state vector includes the fire that the position and speed vector sum of the Mars proximity detector indicated with subscript s is indicated with subscript o
The position and speed vector of star orbital logos and utensils, is denoted as
Wherein rs=[rx,s ry,s rz,s]T,vs=[vx,s vy,s vz,s]T;
Wherein ro=[rx,o ry,o rz,o]T,vo=[vx,o vy,o vz,o]T。
Using J2Two-body kinetics equation under disturbance carries out state recursion as system dynamics model, that is, completes to establish
Mars is finally approached and around kinetic model, is denoted as
Wherein f (x)=[fT(xs) fT(xo)]T,
μ is Mars gravitational constant, RMFor Mars mean radius, J2For the second order band spherical harmonic coefficient of Mars, riFor vector ri's
Mould, w are set as irrelevant process noise, it then follows statistical property shown in formula (3).
E (w)=0, E (wwT)=Q (3)
Q is process noise covariance matrix.
It is preferred that establishing the final Approach phase of Mars under J2000 Mars centered inertial coordinate system and around section navigation system power
Learn model.
Step 2: establishing Mars and finally approach and around independent navigation measurement model.
Mars finally approaches and includes X-ray pulsar arrival time difference information measurement around independent navigation measurement model
Model and doppler velocity measurement model based on Mars orbiter, orbital vehicle.
For single detector, after receiving X-ray pulse, it is carried out with solar system mass center nominal contour
Comparison can be obtained the difference TOA that pulse reaches solar system mass center and pulse reaches the detector time, be denoted as Δ ti, it is configured to,
In formula, niFor the unit direction vector for being directed toward i-th pulsar in the solar system, b is solar system mass center with respect to the sun
The position vector at center, rbPosition vector for detector relative to solar system mass center, b and rbFor the amplitude of corresponding vector, D0i
It is i-th distance of the pulsar with respect to solar system mass center, μsFor solar gravitation constant, c is the light velocity, and m is used pulsar
Number.
Since measurement equation (4) building is under solar system geocentric coordinate system, and motion dynamics equations (2) are established in Mars
Centered inertial coordinate system needs to carry out coordinate conversion.During conversion, ephemeris error will be unavoidably introduced.Meanwhile arteries and veins
Rushing star itself, there is also the uncertainties of intrinsic parameter, such as D0iAnd niUncertainty, can to measurement equation (4) forecast result
It causes a deviation.
To avoid introducing ephemeris error during conversion, and reduce the uncertain to leading of the intrinsic parameter of pulsar
Error caused by result of navigating assembles X-ray detector, two space flight simultaneously on two spacecrafts of proximity detector and orbiter, orbital vehicle
X-ray detector on device locks same X-ray pulsar every time and is observed simultaneously return pulse signal simultaneously, can obtain
The pulsar can be obtained pulse and be arrived to the pulse arrival time of two detectors by information exchange and related algorithm respectively
Up to the difference information DTOA of time, it is denoted as Δ dti.Shown in simplified single order DTOA measurement equation such as formula (5),
cΔdti=ni·(rs-ro)=ni·Δr (5)
Wherein relative position vector of the Δ r between detector and orbiter, orbital vehicle.The difference information DTOA of pulse arrival time with
The product of light velocity c reflects projector distance of two detector Relative position vectors on observed pulsar direction vector.It is logical
Differential mode is crossed, can be avoided and introduce planet ephemeris error, and the intrinsic parameter uncertainty of pulsar can be effectively reduced to navigation
The adverse effect of performance.
X-ray pulsar arrival time difference information DTOA measurement model is expressed as,
yX=hX(x)=[Δ dt1 Δdt2 … Δdtm]T+νX (6)
In formula, νXFor measurement error, it is believed that Gaussian distributed.
Meanwhile passing through the Radio Measurement and communication of detector and the Mars orbiter, orbital vehicle for being equipped with wireless set, energy
Doppler range rate measurement information Δ F is accessed,
Wherein, Δ F is Doppler frequency shift, and M is frequency forward rate, fTFor tranmitting frequency, Tc=ts-teWhen to measure accumulative
Between be spaced, tsFor start time, teFor end time, Δ r=| Δ r | it is the instantaneous distance of detector and orbiter, orbital vehicle.
If assuming fTFor constant value, add up time of measuring TcIt is very short, Doppler range rate measurement information Δ F instantaneous distance change rate table
Show,
Wherein Δ v is the relative velocity vector of detector and orbiter, orbital vehicle.
Doppler velocity measurement model based on Mars orbiter, orbital vehicle can be expressed as,
yR=hR(x)=Δ F+ νR (9)
In formula, vRFor measurement error, it is believed that Gaussian distributed.
Formula (6) and formula (9) construct Mars jointly and finally approach and around independent navigation measurement model.
Radio Measurement and communication band preferably use UHF waveband or X-band.
Step 3: being based on nonlinear filtering algorithm, resolve detector real-time navigation status information, further increase Mars most
The precision of terminating proximal segment independent navigation.
It is finally approached according to Mars and around kinetic model (2) and measurement model formula (6) and formula (9), is filtered by navigation
Wave calculating can estimate the state of detector and orbiter, orbital vehicle.Since Mars finally approaches and around kinetic model (2)
And measurement model formula (9) present it is non-linear, therefore it is preferred that use nonlinear filter, such as Extended Kalman filter EKF, no mark card
Kalman Filtering UKF etc. improves Navigation precision and convergence rate.Final output detector and orbiter, orbital vehicle status information, utilize phase
Absolutely navigation is realized to metrical information, further increases the precision of the final Approach phase independent navigation of Mars.
The utility model has the advantages that
1, the final Approach phase autonomous navigation method of a kind of Mars based on relative measurement information disclosed by the invention, using X
Ray pulse star arrival time difference information DTOA can be avoided and introduce planet ephemeris error, and pulsar ginseng can be effectively reduced
The uncertain adverse effect to navigation performance of number.
2, the final Approach phase autonomous navigation method of a kind of Mars based on relative measurement information disclosed by the invention, using base
In the radio Doppler range rate measurement information of orbiter, orbital vehicle, data updating rate height is observed, there is directly test the speed information, and measurement accuracy
Height, state emission problem caused by can reduce due to observations of pulsar time length.
3, the final Approach phase autonomous navigation method of a kind of Mars based on relative measurement information disclosed by the invention, combines and estimates
The status information of proximity detector and Mars orbiter, orbital vehicle is counted, effective orbit keeping device orbit determination accuracy reduces orbiter, orbital vehicle fiducial error
On radionavigational influence, the navigation performance for improving two detectors can be synchronized.
4, a kind of final Approach phase autonomous navigation method of Mars based on relative measurement information disclosed by the invention, use are non-
Linear filter can be improved Navigation precision and convergence rate.
Detailed description of the invention
Fig. 1 is the flow chart of the final Approach phase independent navigation of Mars based on relative measurement information.
Fig. 2 is the final Approach phase independent navigation error result of Mars based on relative measurement information, wherein (a) is close to spy
Survey device position estimation error figure, (b) be proximity detector speed estimation error figure, (c) be orbiter, orbital vehicle position estimation error figure,
It (d) is orbiter, orbital vehicle speed estimation error figure.
Specific embodiment
Objects and advantages in order to better illustrate the present invention with reference to the accompanying drawing do further summary of the invention with example
Explanation.
Embodiment 1:
A kind of final Approach phase autonomous navigation method of Mars based on relative measurement information disclosed in this example, including it is as follows
Step:
Step 1: establishing Mars and finally approach and around kinetic model.
The final Approach phase of Mars and circular section navigation system kinetic model are established in J2000 Mars centered inertial coordinate system
Under.Ten two-dimensional state vectors include that the position and speed vector sum of the Mars proximity detector indicated with subscript s is indicated with subscript o
Mars orbiter, orbital vehicle position and speed vector, be denoted as
Wherein rs=[rx,s ry,s rz,s]T,vs=[vx,s vy,s vz,s]T;
Wherein ro=[rx,o ry,o rz,o]T,vo=[vx,o vy,o vz,o]T。
Using J2Two-body kinetics equation under disturbance carries out state recursion as system dynamics model, that is, completes to establish
Mars is finally approached and around kinetic model, is denoted as
Wherein f (x)=[fT(xs) fT(xo)]T,
μ is Mars gravitational constant, RMFor Mars mean radius, J2For the second order band spherical harmonic coefficient of Mars, riFor vector ri's
Mould, w are set as irrelevant process noise, it then follows following statistical property
E (w)=0, E (wwT)=Q (3)
Q is process noise covariance matrix.
Step 2: establishing Mars and finally approach and around independent navigation measurement model.
Mars finally approaches and includes X-ray pulsar arrival time difference information measurement around independent navigation measurement model
Model and doppler velocity measurement model based on Mars orbiter, orbital vehicle.
For single detector, after receiving X-ray pulse, it is carried out with solar system mass center nominal contour
The difference TOA that pulse reaches solar system mass center and pulse reaches the detector time can be obtained in comparison.It is denoted as Δ ti, it is configured to,
In formula, niFor the unit direction vector for being directed toward i-th pulsar in the solar system, b is solar system mass center with respect to the sun
The position vector at center, rbPosition vector for detector relative to solar system mass center, b and rbFor the amplitude of corresponding vector, D0i
It is i-th distance of the pulsar with respect to solar system mass center, μsFor solar gravitation constant, c is the light velocity.
Since measurement equation (4) building is under solar system geocentric coordinate system, and motion dynamics equations (2) are established in Mars
Centered inertial coordinate system needs to carry out coordinate conversion.During conversion, ephemeris error will be unavoidably introduced.Meanwhile it surveying
Measuring model itself, there is also the uncertainties of the intrinsic parameter of pulse, such as D0iAnd niUncertainty, can be pre- to measurement equation (4)
Report result causes a deviation.
To avoid introducing ephemeris error during conversion, and reduce the uncertain to leading of the intrinsic parameter of pulsar
Error caused by result of navigating assembles X-ray detector, two space flight simultaneously on two spacecrafts of proximity detector and orbiter, orbital vehicle
X-ray detector on device locks same X-ray pulsar every time and is observed simultaneously return pulse signal simultaneously, can obtain
The pulsar can be obtained pulse and be arrived to the pulse arrival time of two detectors by information exchange and related algorithm respectively
Up to the difference information DTOA of time, it is denoted as Δ dti.Shown in simplified single order DTOA measurement equation such as formula (5),
cΔdti=ni·(rs-ro)=ni·Δr (5)
Wherein relative position vector of the Δ r between detector and orbiter, orbital vehicle.The difference information DTOA of pulse arrival time with
The product of light velocity c reflects projector distance of two detector Relative position vectors on observed pulsar direction vector.It is logical
Differential mode is crossed, can be avoided and introduce planet ephemeris error, and pulsar parameter uncertainty can be effectively reduced to navigation performance
Adverse effect.
X-ray pulsar arrival time difference information DTOA measurement model is expressed as,
yX=hX(x)=[Δ dt1 Δdt2]T+νX (6)
In formula, νXFor measurement error, it is believed that Gaussian distributed.
Meanwhile passing through the Radio Measurement and communication of detector and the Mars orbiter, orbital vehicle for being equipped with wireless set, energy
Doppler range rate measurement information Δ F is accessed,
Wherein, Δ F is Doppler frequency shift, and M is frequency forward rate, fTFor tranmitting frequency, Tc=ts-teWhen to measure accumulative
Between be spaced, tsFor start time, teFor end time, Δ r=| Δ r | it is the instantaneous distance of detector and orbiter, orbital vehicle.
If assuming fTFor constant value, add up time of measuring TcIt is very short, Doppler range rate measurement information Δ F instantaneous distance change rate table
Show,
Wherein Δ v is the relative velocity vector of detector and orbiter, orbital vehicle.
Doppler velocity measurement model based on Mars orbiter, orbital vehicle can indicate are as follows:
yR=hR(x)=Δ F+ νR (9)
In formula, vRFor measurement error, it is believed that Gaussian distributed.
Formula (6) and formula (9) construct Mars jointly and finally approach and around independent navigation measurement model.
Step 3: being based on nonlinear filtering algorithm, resolve detector real-time navigation status information, further increase Mars most
The precision of terminating proximal segment independent navigation.
It is finally approached according to Mars and around kinetic model (2) and measurement model formula (6) and formula (9), is filtered by navigation
Wave calculating can estimate the state of detector and orbiter, orbital vehicle.Since Mars finally approaches and around kinetic model (2)
And measurement model formula (9) present it is non-linear, therefore it is preferred that use nonlinear filter --- Unscented kalman filtering UKF raising lead
Boat filtering accuracy and convergence rate.Final output detector and orbiter, orbital vehicle status information, it is absolute using relative measurement information realization
Navigation, further increases the precision of the final Approach phase independent navigation of Mars.
To navigation scheme progress simulating, verifying, the orbit parameter of proximity detector and orbiter, orbital vehicle is as shown in table 1.Close to spy
Survey device original state location error is 10km, and velocity error 10m/s, the original state location error of orbiter, orbital vehicle is 10m, speed
Error is 0.1m/s.Simulation time be before entering martian atmosphere from detector 12h to entering Mars atmosphere (away from martian surface height
Spend 125km).Close to during, when observations of pulsar a length of 10min;Doppler range rate measurement interval 1min;Radio distance-measuring is tested the speed
Precision is 1mm/s.
The orbital tracking of table 1 detector and orbiter, orbital vehicle
The final Approach phase autonomous navigation scheme performance of Mars based on relative measurement information is as shown in Fig. 2, figure
(a), (b), (c), (d) be respectively last 10 hours proximity detectors and Mars orbiter, orbital vehicle navigation position, speed
Evaluated error and the 3 σ limitss of error.The position of detector and speed estimation error are quick at any time it can be seen from simulation result
Convergence, can finally obtain high-precision state estimation information, the position of orbiter, orbital vehicle and velocity error can also restrain and maintain compared with
Good precision level.
The scope of the present invention is not only limited to embodiment, and embodiment is used to explain the present invention, it is all with of the invention identical
Change or modification under the conditions of principle and design is within protection scope disclosed by the invention.
Claims (4)
1. a kind of final Approach phase autonomous navigation method of Mars based on relative measurement information, it is characterised in that: including walking as follows
Suddenly,
Step 1: establishing Mars and finally approach and around kinetic model;
The final Approach phase of Mars and circular section navigation system kinetic model are established under Mars centered inertial coordinate system;Ten two dimensions
State vector includes the Mars rail that the position and speed vector sum of the Mars proximity detector indicated with subscript s is indicated with subscript o
The position and speed vector of logos and utensils, is denoted as
Wherein rs=[rx,s ry,s rz,s]T,vs=[vx,s vy,s vz,s]T;
Wherein ro=[rx,o ry,o rz,o]T,vo=[vx,o vy,o vz,o]T;
Using J2Two-body kinetics equation under disturbance carries out state recursion as system dynamics model, that is, completes to establish Mars
It is final to approach and around kinetic model, be denoted as
Wherein f (x)=[fT(xs) fT(xo)]T,
μ is Mars gravitational constant, RMFor Mars mean radius, J2For the second order band spherical harmonic coefficient of Mars, riFor vector riMould, w
It is set as irrelevant process noise, it then follows statistical property shown in formula (3);
E (w)=0, E (wwT)=Q (3)
Q is process noise covariance matrix;
Step 2: establishing Mars and finally approach and around independent navigation measurement model;
Mars finally approaches and includes X-ray pulsar arrival time difference information measurement model around independent navigation measurement model
With the doppler velocity measurement model based on Mars orbiter, orbital vehicle;
For single detector, after receiving X-ray pulse, it is carried out with solar system mass center nominal contour pair
Than the difference TOA that pulse reaches solar system mass center and pulse reaches the detector time can be obtained, be denoted as Δ ti, it is configured to,
In formula, njFor the unit direction vector for being directed toward jth pulsar in the solar system, b is solar system mass center with respect to solar core
Position vector, rbPosition vector for detector relative to solar system mass center, b and rbFor the amplitude of corresponding vector, D0jIt is jth
Distance of the pulsar with respect to solar system mass center, μsFor solar gravitation constant, c is the light velocity, m for used pulsar number;
To avoid introducing ephemeris error during conversion, and reduces the uncertain of the intrinsic parameter of pulsar and navigation is tied
Error caused by fruit assembles X-ray detector simultaneously on two spacecrafts of proximity detector and orbiter, orbital vehicle, on two spacecrafts
X-ray detector lock every time same X-ray pulsar be observed and simultaneously return pulse signal, the arteries and veins can be obtained
Star is rushed respectively to the pulse arrival time of two detectors, by information exchange and related algorithm, when can obtain pulse arrival
Between difference information DTOA, be denoted as Δ dti;Shown in simplified single order DTOA measurement equation such as formula (5),
cΔdtj=nj·(rs-ro)=nj·Δr (5)
Wherein relative position vector of the Δ r between detector and orbiter, orbital vehicle;The difference information DTOA and light velocity c of pulse arrival time
Product reflect projector distance of two detector Relative position vectors on observed pulsar direction vector;Pass through difference
Mode can be avoided and introduce planet ephemeris error, and the intrinsic parameter uncertainty of pulsar can be effectively reduced to navigation performance
Adverse effect;
X-ray pulsar arrival time difference information DTOA measurement model is expressed as,
yX=hX(x)=[Δ dt1 Δdt2 … Δdtm]T+νX (6)
In formula, νXFor measurement error, it is believed that Gaussian distributed;
Meanwhile by the Radio Measurement and communication of detector and the Mars orbiter, orbital vehicle for being equipped with wireless set, can obtain
To Doppler range rate measurement information Δ F,
Wherein, Δ F is Doppler frequency shift, and M is frequency forward rate, fTFor tranmitting frequency, Tc=ts-teBetween the measurement cumulative time
Every tsFor start time, teFor end time, Δ r=| Δ r | it is the instantaneous distance of detector and orbiter, orbital vehicle;
If assuming fTFor constant value, add up time of measuring TcVery short, Doppler range rate measurement information Δ F is indicated with instantaneous distance change rate,
Wherein Δ v is the relative velocity vector of detector and orbiter, orbital vehicle;
Doppler velocity measurement model based on Mars orbiter, orbital vehicle is expressed as,
yR=hR(x)=Δ F+ νR (9)
In formula, vRFor measurement error, it is believed that Gaussian distributed;
Formula (6) and formula (9) construct Mars jointly and finally approach and around independent navigation measurement model;
Step 3: being based on nonlinear filtering algorithm, resolve detector real-time navigation status information, further increase Mars most terminating
The precision of proximal segment independent navigation;
It is finally approached according to Mars and around kinetic model (2) and formula (6) and formula (9), being calculated by Navigation can be right
The state of detector and orbiter, orbital vehicle is estimated;It is finally approached due to Mars and is presented around kinetic model (2) and formula (9)
It is non-linear, therefore nonlinear filter is used to improve Navigation precision and convergence rate;Final output detector and orbiter, orbital vehicle shape
State information is absolutely navigated using relative measurement information realization, further increases the precision of the final Approach phase independent navigation of Mars.
2. a kind of final Approach phase autonomous navigation method of Mars based on relative measurement information as described in claim 1, special
Sign is: Radio Measurement and communication band use UHF waveband or X-band in step 2.
3. a kind of final Approach phase autonomous navigation method of Mars based on relative measurement information as claimed in claim 1 or 2,
Be characterized in that: nonlinear filter uses method for Extended Kalman filter EKF or Unscented kalman filtering UKF in step 3.
4. a kind of final Approach phase autonomous navigation method of Mars based on relative measurement information as claimed in claim 1 or 2,
It is characterized in that: establishing the final Approach phase of Mars in step 1 under J2000 Mars centered inertial coordinate system and around section navigation system
Kinetic model.
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