CN107144283A - A kind of high considerable degree optical pulsar hybrid navigation method for deep space probe - Google Patents
A kind of high considerable degree optical pulsar hybrid navigation method for deep space probe Download PDFInfo
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Abstract
The present invention is disclosed the invention provides a kind of high considerable degree optical pulsar hybrid navigation method for deep space probe, and it is included：Step 1：Observations of pulsar equation is mixed with optical observation equation, mixing observational equation is set up；Step 2：Using many body gravity models of deep space probe, inertial position and speed using detector set up detector's status equation as quantity of state；Step 3：Construct EKF and optimal estimation calculating is carried out to the state of detector, obtain Position And Velocity under accurate detector inertial system.The method of the present invention overcomes the problem of inertial navigation accumulated error is big, solve the problem of pulsar navigation ornamental is weak, it greatly strengthen the ornamental of navigation system, greatly reduce the convergence time of navigation system, and navigation accuracy is effectively raised, it can be directly used for the autonomous control of deep space probe.
Description
Technical field
The present invention relates to deep space probe air navigation aid, and in particular to a kind of high considerable degree optics for deep space probe
Pulsar hybrid navigation method, it comprehensively utilizes the angular observation information and pulsar of the celestial body apart from observation information, in terms of
Calculate the main precision navigation information of deep space probe.
Background technology
Ground based radio navigation limited ability in the distribution of tracking telemetry and command station, device the factor such as distance constraint, it is difficult to for deep spy
Survey device and affordable high-precision real-time navigation information is provided.Traditional inertial navigation is not suitable for making due to error accumulation effect
For main navigation means.The Optical autonomous navigation of single goal is simultaneously non-fully considerable, and it is difficult to be generalized to whole mission phase in addition.
X-ray pulsar navigation technology has that independence is strong, anti-interference is good, can support the spies such as the full mission phase of deep space probe
Point.But the X-ray signal of pulsar is very weak, more feasible sensor scheme is only capable of tracking 1~2 navigation pulsar simultaneously,
The orbit information of detector can only be determined using Dynamic orbit determination method.Due to only having 1 vector, system is caused locally can not
See.
The content of the invention
It is an object of the invention to provide a kind of air navigation aid, it has high ornamental, can be used for survey of deep space.
In order to achieve the above object, mixed the invention provides a kind of high considerable degree optical pulsar for deep space probe
Air navigation aid is closed, this method comprises the following steps：
Step 1：During deep space probe is close to big celestial body, introduce to the optical observation amount of neighbouring celestial body as supplement,
Observations of pulsar equation is mixed with optical observation equation, mixing observational equation is set up；
Step 2：Using many body gravity models of deep space probe, inertial position and speed using detector are built as quantity of state
Vertical detector's status equation；
Step 3：According to the observational equation of step 1 and the state equation of step 2, construction EKF is to detector
State carry out optimal estimation calculating, obtain Position And Velocity under accurate detector inertial system；Wherein, EKF
Equation be：
K (k)=P (k, k-1) HT(k) [H (k) P (k, k-1) HT(k)+R(k)]-1
P (k, k-1)=Φ (k, k-1) P (k-1) ΦT(k, k-1)+Q (k-1)
Wherein, initial value isP (0,0)=Var { x (0) }=Px(0), in formula,Known state model
Covariance matrix E [w (k) w (k) of noiseT]=Q, covariance matrix E [v (k) v (k) of measurement model noiseT]=R, w represent system
Model error, v represents measurement noise, and k represents current step number, and x represents quantity of state, and μ represents gravitational constant, and X represents discrete state
Amount, T represents discrete periodic, and I represents unit matrix, and Z represents discrete observation amount, and t represents the time..
Above-mentioned is used for the high considerable degree optical pulsar hybrid navigation method of deep space probe, wherein, described pulse
Star observational equation is：
In formula, ΔΦiThe observation phase difference of pulse signal,For the unit direction vector of pulse direction of visual lines, λ is navigation
The distance propagated in pulse signal a cycle, Δ Ni is pulse period complete cycle difference, Δ x be spacecraft and sun barycenter it
Between distance, i represents pulsar sequence number.
Above-mentioned is used for the high considerable degree optical pulsar hybrid navigation method of deep space probe, wherein, described optics
Observational equation is：
Wherein, p, 1 is coordinate of the photocentre of target celestial body in camera image plane, and unit is millimeter, RcIFor camera coordinates
It is the pose transformation matrix of relative inertness coordinate system, x, y, z is position of the detector under Mars J2000 inertial coodinate systems.
Above-mentioned is used for the high considerable degree optical pulsar hybrid navigation method of deep space probe, wherein, RcIIt is to utilize phase
The posture for the body coordinate system relative inertness coordinate system that machine coordinate system opposing body Conversion Matrix of Coordinate and star sensor are determined
Transition matrix is determined.
Above-mentioned is used for the high considerable degree optical pulsar hybrid navigation method of deep space probe, wherein, described mixing
Observational equation：
Z=h (X)+v；Wherein, z represents p, l, △ φi；V is measurement noise.
Above-mentioned is used for the high considerable degree optical pulsar hybrid navigation method of deep space probe, wherein, in step 2, visit
Surveying device state equation is：
Wherein, state variable The position vector of detector is represented,Represent the speed arrow of detector
Amount；W is system model error, ax ay azFor projection of the solar gravitation perturbation under Mars inertial system, x, y, z is that detector exists
Position under Mars J2000 inertial coodinate systems,Wherein, centered on GM celestial body gravitational constant；R is flight
Position vector of the device in inertial system；P is perturbative force.
Above-mentioned is used for the high considerable degree optical pulsar hybrid navigation method of deep space probe, wherein, r calculation formula
It is as follows：
Wherein, rpFor the position vector of the relatively large celestial body barycenter of detector；μM、μS、μE、μJBe followed successively by big celestial body, the sun,
The gravitational constant of ball, Jupiter；rMp,rSp,rEp,rJpIt is followed successively by the position vector of big celestial body, the sun, the earth, Jupiter to detector；
rMS,rME,rMJFor position vector between two days bodies, drawn by the DE405 ephemeris in U.S. jet laboratory (JPL), subscript M is represented
Big celestial body, under
Mark S represents the sun, and subscript E represents the earth, and subscript J represents Jupiter.
Above-mentioned is used for the high considerable degree optical pulsar hybrid navigation method of deep space probe, wherein, in step 3, structure
The method for making EKF is included：
Step 3.1, state equation discretization first to step 2, and surroundingLinearisation,Nearby expand into two
Rank Taylor series；
Step 3.2, by the observational equation discretization of step one, andLinearisation nearby.
Above-mentioned is used for the high considerable degree optical pulsar hybrid navigation method of deep space probe, wherein, step 3.1 is handled
Second order Taylor series afterwards are：
Above-mentioned is used for the high considerable degree optical pulsar hybrid navigation method of deep space probe, wherein, step 3.2 is handled
Equation afterwards is：
The method that the present invention is provided overcomes the problem of inertial navigation accumulated error is big, solves pulsar navigation ornamental
Weak the problem of, the ornamental of navigation system is greatly strengthen, greatly reduce the convergence time of navigation system, and effectively improve
Navigation accuracy, can be directly used for the autonomous control of deep space probe.
Brief description of the drawings
Fig. 1 is hybrid measurement scheme schematic diagram of the present invention；
Fig. 2 is implementation result figure of the invention.
Embodiment
Technical scheme is described further below in conjunction with drawings and examples.
As shown in figure 1, be the optical pulsar hybrid measurement scheme schematic diagram of the present invention, wherein, SSB refers to solar system matter
(Solar System Barycenter, it is the coordinate origin in figure to the heart, and the r of deep space probe is that the relative point is calculated
), pulsar 1 and pulsar 2 are used for the observations of pulsar for nearly celestial body (such as Mars), and deep space probe is close to big celestial body
When, introduce and supplement is used as to the optical observation amount of neighbouring celestial body.
Optical pulsar of the present invention mixes high considerable deep space air navigation aid, and its step is as follows：
Step one：During detector is close to big celestial body, introduces to the optical observation amount of neighbouring celestial body as supplement, set up
Mix observational equation；
Observations of pulsar equation is mixed with optical observation equation.Burst length model can typically be expressed as pulse signal
Total phase to the function of time.Total phase of burst length model can be expressed as a fractional part plus a complete cycle
Number, i.e.,
Φ (t)=Ψ (T)+N (t)
In formula, Φ (t) is total phase, and Ψ (T) is fractional part, and N (t) is integer part.Integer multiples are small plus observation
Number fractional phase just directly reflects detector to the distance of reference frame.
Δ ρ represents the distance component along pulsar direction of visual lines spacecraft (deep space probe) and sun barycenter, i tables in formula
Show pulsar sequence number, λiBy the distance propagated in the navigation pulse signal a cycle of i-th of pulsar,For observation arteries and veins
Rush arrival time and forecast the difference of pulse arrival time, △ ΦiThe observation phase difference of pulse signal, Δ NiFor pulse period complete cycle
Difference,For the unit direction vector of pulse direction of visual lines, Δ x is the distance between spacecraft and sun barycenter (equivalent to Fig. 1
In r, it is but consistent with state quantity symbol X for convenience here, so having used Δ x).It is rewritten into matrix form：
The direct observed quantity of optical navigation camera is the picpointed coordinate of Mars central point, is not considering electromagnetism and light distortion
In the case of, it is considered to by the use of the goal pels coordinate given by camera as observed quantity, it can be expressed as：
Wherein p, l are coordinate of the photocentre of target celestial body in camera image plane, and unit is millimeter, and RcI is camera coordinates
It is the pose transformation matrix of relative inertness coordinate system, RcI can utilize camera coordinates system opposing body's Conversion Matrix of Coordinate Rcb
The pose transformation matrix RbI of the body coordinate system relative inertness coordinate system determined with star sensor determines that x, y, z exists for detector
Position under Mars J2000 inertial coodinate systems.
The mixing observational equation that can determine system with reference to equation (1) and (2) is:
Z=h (X)+v.
Wherein z is p, l, △ φi, v is measurement noise, and X represents quantity of state.
Step 2：Using many body gravity models of deep space probe, inertial position and speed using detector are built as quantity of state
Vertical detector's status equation.
The motion of deep space probe is by center gravitation (Section 1 on the right of following formula equal sign) and each perturbative force synergy
Result.Its stress is as follows：
In formula centered on GM celestial body gravitational constant；R is position vector of the aircraft in inertial system, and R represents its mould
(scalar)；P be perturbative force for the deep space probe close to big celestial body, detector can be set up by gravitation body greatly centered on celestial body
The equation of motion.Consider big celestial body gravitation, solar gravitation, terrestrial gravitation, Jupiter gravitation herein, due to apart from big celestial body farther out,
Therefore other Perturbation Effects such as big celestial body gravitation aspherical can not be considered, kinetics equation is set up as follows：
In formula, rpFor the position vector of the relatively large celestial body barycenter of detector；μM、μS、μE、μJBe followed successively by big celestial body, the sun,
The gravitational constant of ball, Jupiter；rMp,rSp,rEp,rJpIt is followed successively by the position vector of big celestial body, the sun, the earth, Jupiter to detector；
rMS,rME,rMJFor position vector between two days bodies, drawn by JPL DE405 ephemeris, subscript M represents big celestial body, subscript S is represented
The sun, subscript E represents the earth, and subscript J represents Jupiter.
The Position And Velocity vector of selection detector is used as state variableObtained according to dynamics of orbits model
It is to system state equation
W is system model error, a in formulax ay azPerturbed projection under Mars inertial system for solar gravitation, x, y, z
It is meant that position of the detector under Mars J2000 inertial coodinate systems.
Step 3：Optimal estimation is carried out to the state of detector using EKF (EKF), accurately visited
Survey Position And Velocity under device inertial system；
The new state equation and new observational equation being augmented more than, are extended the design of Kalman's optimal estimation algorithm：
For continuous system described above, the state equation discretization that first need to be set up step 2, and surroundLinearisation,
ExistNearby expand into second order Taylor series：
The mixing observational equation discretization that step one is set up, andNearby linearly turn to：
In formula, H represents 1 rank of series expansion.
Covariance matrix E [w (k) w (k) of known state plant noiseT]=Q, the covariance matrix E [v of measurement model noise
(k)v(k)T]=R, then EKF recurrence equation is：
K (k)=P (k, k-1) HT(k)[H(k)P(k,k-1)HT(k)+R(k)]-1
P (k, k-1)=Φ (k, k-1) P (k-1) ΦT(k,k-1)+Q(k-1)
Initial value isP (0,0)=Var { x (0) }=Px(0), in formula,
Choose an imaginary mars exploration task, when detector is close to Mars, to deep space optical guidance
(OpN), three kinds of air navigation aids of optical pulsar hybrid navigation method (OPHN) of single pulsar navigation (PN) and the present invention
Tested, as a result as shown in Figure 2.Use as we can clearly see from the figure after the present invention, the convergence time of navigation algorithm is by original
Carry out reducing for tens of hours in a few hours, while navigation accuracy is also carried by original more than 10 best kms for simple pulsar navigation
Height arrives thousands of rice.
From Observability Analysis, using the observation program of single goal, single goal optical navigation method (OpN) simultaneously can not
See, optical guidance precision finally dissipates gradually with the time；The ornamental of pulse star air navigation aid (PN) is with detector position
In right amount with the relation of observed pulsar vector and and change, therefore its ornamental is unstable.
In mathematical simulation, restrained during the navigation accuracy of pulse star air navigation aid, when and dissipate.Precision is distributed in several
Ten arrive hundreds of kms, and convergence process therein is also in or so tens of hours.And by the angular surveying of optical target and pulsar
Time measurement be combined after, the ornamental of hybrid navigation method is greatly improved.Using the navigation system of OPHN methods whole
Close to Mars process, single convergence is embodied, navigation accuracy just quickly converges to km magnitude after a few hours.Easily see
To OPHN, either convergence or precision are all substantially better than OpN and PN.
In summary, the present invention is when deep space probe is close to big celestial body, angle of the optical guidance sensor to the celestial body
Spend observed quantity and introduce navigation system, rebuild the observational equation mixed with pulsar distance observation, substantially increased and lead
The ornamental of boat system, so that between the convergence for substantially reducing navigation system is received, and improve the precision of navigation system.
Although present disclosure is discussed in detail by above preferred embodiment, but it should be appreciated that above-mentioned
Description is not considered as limitation of the present invention.After those skilled in the art have read the above, for the present invention's
A variety of modifications and substitutions all will be apparent.Therefore, protection scope of the present invention should be limited to the appended claims.
Claims (10)
1. a kind of high considerable degree optical pulsar hybrid navigation method for deep space probe, it is characterised in that this method bag
Include following steps：
Step 1：During deep space probe is close to big celestial body, introduce to the optical observation amount of neighbouring celestial body as supplement, by arteries and veins
Rush star observational equation to mix with optical observation equation, set up mixing observational equation；
Step 2：Using many body gravity models of deep space probe, the inertial position and speed using detector are set up and visited as quantity of state
Survey device state equation；
Step 3：According to the observational equation of step 1 and the state equation of step 2, shape of the construction EKF to detector
State carries out optimal estimation calculating, obtains Position And Velocity under accurate detector inertial system；Wherein, the side of EKF
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K (k)=P (k, k-1) HT(k) [H (k) P (k, k-1) HT(k)+R(k)]-1
P (k, k-1)=Φ (k, k-1) P (k-1) ΦT(k, k-1)+Q (k-1)
Wherein, initial value isP (0,0)=Var { x (0) }=Px(0), in formula,Known state model
Covariance matrix E [w (k) w (k) T]=Q of noise, covariance matrix E [v (k) v (k) of measurement model noiseT]=R, w represent system
Model error, v represents measurement noise, and k represents current step number, and x represents quantity of state, and μ represents gravitational constant, and X represents discrete state
Amount, T represents discrete periodic, and I represents unit matrix, and Z represents discrete observation amount, and t represents the time.
2. it is used for the high considerable degree optical pulsar hybrid navigation method of deep space probe, its feature as claimed in claim 1
It is, described observations of pulsar equation is：
In formula, △ ΦiThe observation phase difference of pulse signal,For the unit direction vector of pulse direction of visual lines, λ is navigation pulse
The distance propagated in signal a cycle, Δ NiFor pulse period complete cycle difference, Δ x is between spacecraft and sun barycenter
Distance, i represents pulsar sequence number.
3. it is used for the high considerable degree optical pulsar hybrid navigation method of deep space probe, its feature as claimed in claim 2
It is, described optical observation equation is：
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Wherein, p, l are coordinate of the photocentre of target celestial body in camera image plane, and unit is millimeter, RcIFor camera coordinates system phase
To the pose transformation matrix of inertial coodinate system, x, y, z is position of the detector under Mars J2000 inertial coodinate systems.
4. it is used for the high considerable degree optical pulsar hybrid navigation method of deep space probe, its feature as claimed in claim 3
It is, RcIIt is that the body coordinate system determined using camera coordinates system opposing body Conversion Matrix of Coordinate and star sensor is used to relatively
Property coordinate system pose transformation matrix determine.
5. it is used for the high considerable degree optical pulsar hybrid navigation method of deep space probe, its feature as claimed in claim 3
It is, described mixing observational equation：
Z=h (X)+v；Wherein, z represents p, l, △ φi；V is measurement noise.
6. it is used for the high considerable degree optical pulsar hybrid navigation method of deep space probe, its feature as claimed in claim 1
It is, in step 2, detector's status equation is：
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<mfrac>
<mi>&mu;</mi>
<msup>
<mi>r</mi>
<mn>3</mn>
</msup>
</mfrac>
<mi>x</mi>
<mo>+</mo>
<msub>
<mi>a</mi>
<mi>x</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mfrac>
<mi>&mu;</mi>
<msup>
<mi>r</mi>
<mn>3</mn>
</msup>
</mfrac>
<mi>y</mi>
<mo>+</mo>
<msub>
<mi>a</mi>
<mi>y</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mfrac>
<mi>&mu;</mi>
<msup>
<mi>r</mi>
<mn>3</mn>
</msup>
</mfrac>
<mi>z</mi>
<mo>+</mo>
<msub>
<mi>a</mi>
<mi>z</mi>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>+</mo>
<mi>w</mi>
<mo>,</mo>
</mrow>
Wherein, state variable The position vector of detector is represented,Represent the velocity of detector；W is
System model error, axayazFor projection of the solar gravitation perturbation under Mars inertial system, x, y, z is detector in Mars J2000
Position under inertial coodinate system,Wherein, centered on GM celestial body gravitational constant；R is aircraft in inertia
Position vector in system；P is perturbative force.
7. it is used for the high considerable degree optical pulsar hybrid navigation method of deep space probe, its feature as claimed in claim 6
It is, r calculation formula is as follows：
<mrow>
<msub>
<mover>
<mi>r</mi>
<mo>&CenterDot;&CenterDot;</mo>
</mover>
<mi>p</mi>
</msub>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>&mu;</mi>
<mi>M</mi>
</msub>
<mfrac>
<msub>
<mi>r</mi>
<mrow>
<mi>M</mi>
<mi>p</mi>
</mrow>
</msub>
<msubsup>
<mi>r</mi>
<mrow>
<mi>M</mi>
<mi>p</mi>
</mrow>
<mn>3</mn>
</msubsup>
</mfrac>
<mo>-</mo>
<msub>
<mi>&mu;</mi>
<mi>S</mi>
</msub>
<mo>&lsqb;</mo>
<mfrac>
<msub>
<mi>r</mi>
<mrow>
<mi>S</mi>
<mi>p</mi>
</mrow>
</msub>
<msubsup>
<mi>r</mi>
<mrow>
<mi>S</mi>
<mi>p</mi>
</mrow>
<mn>3</mn>
</msubsup>
</mfrac>
<mo>+</mo>
<mfrac>
<msub>
<mi>r</mi>
<mrow>
<mi>M</mi>
<mi>S</mi>
</mrow>
</msub>
<msubsup>
<mi>r</mi>
<mrow>
<mi>M</mi>
<mi>S</mi>
</mrow>
<mn>3</mn>
</msubsup>
</mfrac>
<mo>&rsqb;</mo>
<mo>-</mo>
<msub>
<mi>&mu;</mi>
<mi>E</mi>
</msub>
<mo>&lsqb;</mo>
<mfrac>
<msub>
<mi>r</mi>
<mrow>
<mi>E</mi>
<mi>p</mi>
</mrow>
</msub>
<msubsup>
<mi>r</mi>
<mrow>
<mi>E</mi>
<mi>p</mi>
</mrow>
<mn>3</mn>
</msubsup>
</mfrac>
<mo>+</mo>
<mfrac>
<msub>
<mi>r</mi>
<mrow>
<mi>M</mi>
<mi>E</mi>
</mrow>
</msub>
<msubsup>
<mi>r</mi>
<mrow>
<mi>M</mi>
<mi>E</mi>
</mrow>
<mn>3</mn>
</msubsup>
</mfrac>
<mo>&rsqb;</mo>
<mo>-</mo>
<msub>
<mi>&mu;</mi>
<mi>J</mi>
</msub>
<mo>&lsqb;</mo>
<mfrac>
<msub>
<mi>r</mi>
<mrow>
<mi>J</mi>
<mi>p</mi>
</mrow>
</msub>
<msubsup>
<mi>r</mi>
<mrow>
<mi>J</mi>
<mi>p</mi>
</mrow>
<mn>3</mn>
</msubsup>
</mfrac>
<mo>+</mo>
<mfrac>
<msub>
<mi>r</mi>
<mrow>
<mi>M</mi>
<mi>J</mi>
</mrow>
</msub>
<msubsup>
<mi>r</mi>
<mrow>
<mi>M</mi>
<mi>J</mi>
</mrow>
<mn>3</mn>
</msubsup>
</mfrac>
<mo>&rsqb;</mo>
<mo>,</mo>
</mrow>
Wherein, rpFor the position vector of the relatively large celestial body barycenter of detector；μM、μS、μE、μJBe followed successively by big celestial body, the sun, the earth,
The gravitational constant of Jupiter；rMp,rSp,rEp,rJpIt is followed successively by the position vector of big celestial body, the sun, the earth, Jupiter to detector；rMS,
rME,rMJFor position vector between two days bodies, drawn by JPL DE405 ephemeris, subscript M represents big celestial body, subscript S is represented too
Sun, subscript E represents the earth, and subscript J represents Jupiter.
8. it is used for the high considerable degree optical pulsar hybrid navigation method of deep space probe, its feature as claimed in claim 1
It is, in step 3, the method for construction EKF is included：
Step 3.1, state equation discretization first to step 2, and surroundingLinearisation,Nearby expand into second order safe
Strangle series；
Step 3.2, by the observational equation discretization of step one, andLinearisation nearby.
9. it is used for the high considerable degree optical pulsar hybrid navigation method of deep space probe, its feature as claimed in claim 8
It is, the second order Taylor series after step 3.1 processing are：
10. it is used for the high considerable degree optical pulsar hybrid navigation method of deep space probe, its feature as claimed in claim 8
It is, the equation after step 3.2 processing is：
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