CN107024211B - A kind of deep space probe angle measurement/differential speed measuring/difference ranges Combinated navigation method - Google Patents
A kind of deep space probe angle measurement/differential speed measuring/difference ranges Combinated navigation method Download PDFInfo
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Abstract
The present invention relates to a kind of deep space probe angle measurement/differential speed measuring/difference ranges Combinated navigation methods.The state model of spacecraft is established according to dynamics of orbits first, it is utilized respectively angle measurement sensor again and obtains starlight angular distance measurement, pulse arrival time measurement is obtained using X-ray pulsar detector, astronomical doppler velocity measurement is obtained using spectrometer, establishes starlight angular distance measurement model, differential pulse arrival time measurement model and difference astronomy doppler velocity measurement model respectively according to these measurements later.The position and speed of UKF filtering estimation spacecraft is used after discretization.The invention belongs to Spacecraft Autonomous Navigation field, estimated accuracy of the present invention is high, has important practical significance to Spacecraft Autonomous Navigation.
Description
Technical field
The invention belongs to Spacecraft Autonomous Navigation fields, are related to a kind of based on starlight angular distance, differential pulse arrival time, difference
Divide the celestial self-navigation method of the measurements such as astronomical doppler velocity.
Background technique
China's plan emits a Mars probes in the year two thousand twenty, therefore mars exploration will attract more and more concerns.
For deep space exploration task, navigation accuracy has an important influence the success or failure of task.Mainly pass through ground observing and controlling at present
It stands and provides navigation information for spacecraft.With the increase of distance between spacecraft and the earth, signal is carried out by ground control station
The round trip time delay of transmission will be increasing.In addition, day, which insults, will cause signal interruption.Therefore, it is necessary to improve the certainly leading of spacecraft
Boat ability.
The autonomous navigation method that can be used for deep space probe mainly has astronomical angle measurement air navigation aid, X-ray pulsar ranging
Air navigation aid and astronomical Doppler range rate measurement air navigation aid.Astronomical angle measurement air navigation aid passes through measurement spacecraft and nearly celestial body and navigation
Angle between fixed star obtains the location information of spacecraft.But the navigation accuracy of this method is with spacecraft and nearly celestial body
Between distance increase and decline.X-ray pulsar range-finding navigation can provide high-precision location information, and navigation accuracy not by
The influence of position between spacecraft and celestial body.But since the signal of X-ray pulsar is fainter, it usually needs by longer
The epoch of time folds to obtain measurement.In addition, pulsar turning error and satellite atomic clock clock deviation will affect navigation essence
Degree.Astronomical Doppler range rate measurement navigation obtains spacecraft by measurement spectrum frequency displacement as caused by radial motion between spacecraft and fixed star
Velocity information.But this method can not provide location information, and the dynamic change of stellar spectrum will affect its navigation essence
Degree.
Summary of the invention
The present invention proposes a kind of deep space probe angle measurement/differential speed measuring/difference ranges Combinated navigation method, utilizes starlight angle
Absolute location information is provided away from measurement, is missed using time difference X-ray pulsar pulse arrival time measurement attenuation systems
The influence of difference, provides relative position information, weakens stellar spectrum dynamic using time difference astronomy doppler velocity measurement and becomes
The influence of change, provides velocity information.Three kinds of measurements are filtered by UKF and are combined, provide high-precision lead for deep space probe
Boat information.
The technical solution adopted by the present invention to solve the technical problems are as follows: the state of spacecraft is established according to dynamics of orbits
Model, obtains starlight angular distance measurement using angle measurement sensor, obtains pulse arrival time amount using X-ray pulsar detector
Measurement obtains astronomical doppler velocity measurement using spectrometer, establishes starlight angular distance respectively according to these measurements and measure mould
Type, differential pulse arrival time measurement model and difference astronomy doppler velocity measurement model.Estimated after discretization using UKF filtering
Count the position and speed of spacecraft.
Specifically includes the following steps:
1. establishing the System State Model based on dynamics of orbits
It in the sports immunology of Mars Approach phase is using the sun as center celestial body to be taken the photograph Three-Body Model by spacecraft, by other
Disturbance is considered as process noise.Kinetic model at solar core inertial coodinate system (J2000.0) is writeable are as follows:
Wherein | | | | indicate 2 norms of vector, | | | |3Indicate | | | | cube, r and v be spacecraft relatively too
The position and speed of sun.μsAnd μmIt is the gravitational constant of the sun and Mars, r respectivelymIt is position vector of the Mars with respect to the sun, rsm
=r-rmIt is position vector of the spacecraft with respect to Mars.W is process noise caused by various disturbances.State mould can be obtained by above formula
Type is as follows:
Wherein quantity of state X=[r, v]TThe position for being spacecraft under sun inertial coodinate system and speed,For quantity of state X
Derivative,For moment t'sF (X (t), t) is mission nonlinear continuous state transfer function, and w is process noise, w
(t) w for being moment t.
2. judging whether there is pulse arrival time measurement
Due to pulse signal need observation cycle it is longer, solid with starlight angular distance measurement and astronomy doppler velocity measurement
Amount is compared, and the sampling period of pulse arrival time measurement is longer.Therefore, with starlight angular distance measurement and astronomical doppler velocity
The sampling period of measurement is as filtering cycle.When filtered time instant does not have pulse arrival time measurement, to by state model
And the system model that starlight angular distance measurement model, difference astronomy doppler velocity measurement model are constituted is used to by UKF filtering
Posteriority state estimation and posteriori error covariance of the spacecraft with respect to the sun under property system.When filtered time instant has pulse arrival time
When measurement, to by state model and starlight angular distance measurement model, difference astronomy doppler velocity measurement model, differential pulse to
The system model constituted up to measuring time value model is estimated by the posteriority state that UKF filters the opposite sun of spacecraft under acquisition inertial system
Meter and posteriori error covariance.
3. establishing the measurement model of starlight angular distance
The starlight angular distance between spacecraft and phobos, Deimos and its background fixed star is obtained using angle measurement sensor, with this
A little starlight angular distances establish measurement model as measurement:
Wherein αp1And αp2It is the starlight angular distance between spacecraft and phobos and two background fixed stars, α respectivelyd1And αd2Respectively
It is the starlight angular distance between spacecraft and Deimos and two background fixed stars, rsp、rsdIt is phobos, Deimos respectively relative to boat
The position vector of its device, s1、s2It is the direction vector of two fixed stars under inertial system, r respectivelyp、rdIt is phobos, Deimos respectively
Position vector relative to the sun.
Using these starlight angular distances as measurement Z1=[αp1,αp2,αd1,αd2]T, starlight angular distance measurement model can be established
Expression formula:
Z1=[αp1,αp2,αd1,αd2]T=h1[X(t),t]+v1(t) (4)
Wherein h1() indicates the non-linear continuous measurement function of starlight angular distance, v1(t) amount of t moment starlight angular distance is indicated
Survey noise.
4. establishing the measurement model of difference astronomy doppler velocity
Solar spectrum frequency displacement is obtained using spectrometer, and radial velocity of the spacecraft with respect to the sun is obtained according to frequency displacement, with
This establishes measurement model as measurement:
Wherein vrIndicate radial velocity measurement of the spacecraft with respect to the sun, vrtIndicate radial speed of the spacecraft with respect to the sun
Spend true value, υpIndicate the disturbance term as caused by solar spectrum frequency fluctuation, υmIndicate that astronomical doppler velocity measures noise.
Establish the measurement model of difference astronomy doppler velocity:
Wherein vr(t) and vrIt (t-1) is the radial velocity measurement of t moment and t-1 moment spacecraft with respect to the sun respectively,
vrt(t) and vrtIt (t-1) is the radial velocity true value of t moment and t-1 moment spacecraft with respect to the sun, υ respectivelyp(t) and υp(t-
It 1) is disturbance term caused by t moment and t-1 moment solar spectrum frequency fluctuation, υ respectivelym(t) and υm(t-1) be respectively t moment and
The measurement noise at t-1 moment, △ υp(t)=υp(t)-υpIt (t-1) is υ after differencepResidual error, △ υm(t)=υm(t)-υm(t-1)
It is υ after differencemResidual error.
Using difference astronomy doppler velocity as measurement Z2=[vr(t)-vr(t-1)] difference astronomy Doppler can, be established
The expression formula of velocity measurement model:
Z2=[vr(t)-vr(t-1)]=h2[X(t),X(t-1)]+v2(t) (7)
Wherein h2() indicates the non-linear continuous measurement function of difference astronomy doppler velocity, v2(t) indicate that t moment is poor
Divide the error in measurement of astronomical doppler velocity.With the posteriority state estimation at t-1 momentInstead of X (t-1), then difference arteries and veins
The expression formula being flushed to up to measuring time value model is writeable are as follows:
Z2=h2[X(t),t]+v2(t) (8)
5. establishing the measurement model of differential pulse arrival time
Pulse arrival time measurement is obtained using X-ray pulsar detector, using pulse arrival time as measurement
Establish measurement model:
Wherein tbIndicate that pulsar pulse reaches the time of solar system mass center, tSCIndicate that pulsar pulse reaches spacecraft
Time, rSIndicate that position vector of the spacecraft with respect to solar system mass center, c indicate that the light velocity, n indicate side of the pulsar under inertial system
To vector, D0Pulsar is indicated to the distance of solar system mass center, b indicates position vector of the solar system mass center with respect to the sun.
Establish the measurement model of differential pulse arrival time:
Wherein τ (t) indicates the differential pulse arrival time of t moment, tb(t) and tb(t-1) when respectively indicating t moment and t-1
Carve the time that pulsar pulse reaches solar system mass center, tSC(t) and tSC(t-1) t moment and t-1 moment pulsar are respectively indicated
The time of pulse arrival spacecraft.
Using differential pulse arrival time as measurement Z3=[τ (t)] can establish differential pulse arrival time measurement model
Expression formula:
Z3=[τ (t)]=h3[X(t),X(t-1)]+v3(t) (11)
Wherein h3() indicates the non-linear continuous measurement function of differential pulse arrival time, v3(t) t moment difference is indicated
The measurement noise of pulse arrival time.With the posteriority state estimation at t-1 momentInstead of X (t-1), then differential pulse arrives
Expression formula up to measuring time value model is writeable are as follows:
Z3=h3[X(t),t]+v3(t) (12)
6. carrying out discretization
When filtered time instant does not have pulse arrival time measurement, if the measurement Z of navigation system at this time12=[Z1,Z2]T,
Measure noise v12=[v1,v2]T, Navigation System Model are as follows:
Wherein h12() indicates the non-linear continuous measurement function of navigation system when no pulse arrival time measurement.It is right
Formula (13) carries out discretization:
Wherein XkAnd Z12kThe quantity of state of etching system and system when without pulse arrival time measurement when respectively indicating k
Measurement, F (Xk-1, k-1) be f (X (t), t) it is discrete after nonlinear state transfer function, H12(Xk, k) and it is h12[X (t), t] from
Non-linear measurement function after dispersion, WkAnd V12kRespectively indicate w (t) and v12(t) equivalent noise after discrete.
When filtered time instant has pulse arrival time measurement, if the measurement Z=[Z of navigation system at this time1,Z2,Z3]T,
Measure noise v=[v1,v2,v3]T, Navigation System Model are as follows:
Wherein h () indicates the non-linear continuous measurement function of navigation system when pulse arrival time measurement.To formula
(15) discretization is carried out:
Wherein ZkIndicate the measurement of etching system when k, H (Xk, k) be h [X (t), t] it is discrete after non-linear measurement function,
VkIndicate the equivalent noise after v (t) is discrete.
7. carrying out the position and speed estimation that UKF filtering obtains spacecraft
When filtered time instant does not have pulse arrival time measurement, UKF is passed through to the system model formula (14) after discretization
Be filtered obtain inertial system under spacecraft with respect to the sun posteriority state estimationAnd posteriori error association side
DifferenceWhereinRespectively position of the kth moment spacecraft with respect to the sun, speed Posterior estimator.When filtered time instant has arteries and veins
It is flushed to up to when time quantum measurement, acquisition is filtered by UKF to the system model formula (16) after discretizationAndIt willAndOutput, while these estimated values are returned into filter, for obtaining the output at k+1 moment.
The principle of the present invention is: obtaining observable Space Vehicle position information completely using starlight angular distance, but precision is not high.
The pulse arrival time measurement obtained using the front and back moment obtains differential pulse arrival time by difference, weakens pulsar angle
The influence of location error and satellite atomic clock clock deviation to navigation accuracy, obtains high-precision location information.It is obtained using the front and back moment
The astronomical doppler velocity measurement obtained obtains difference astronomy doppler velocity by difference, weakens stellar spectrum dynamic change pair
The influence of navigation accuracy obtains high-precision velocity information.The state model that spacecraft is established according to dynamics of orbits, builds respectively
Vertical starlight angular distance measurement model, differential pulse arrival time measurement model and difference astronomy doppler velocity measurement model, it is discrete
It filters to obtain the high-precision position and speed of spacecraft using UKF after change.
The advantages of the present invention over the prior art are that: (1) it realizes and navigates to the high-precision independent of spacecraft.(2) sharp
High-precision location information is obtained with differential pulse arrival time.(3) it is obtained using difference astronomy doppler velocity high-precision
Velocity information.
Detailed description of the invention
Fig. 1 is deep space probe angle measurement/differential speed measuring/difference ranges Combinated navigation method flow chart in the present invention.
Fig. 2 is culminant star optic angle of the present invention away from measurement model schematic diagram.
Fig. 3 is X-ray pulsar range-finding navigation schematic illustration in the present invention.
Specific embodiment
Fig. 1 gives deep space probe angle measurement/differential speed measuring/difference ranges Combinated navigation method system flow chart.Here
By taking mars exploration Approach phase as an example, the specific implementation process that the present invention will be described in detail:
1. establishing the System State Model based on dynamics of orbits
It in the sports immunology of Mars Approach phase is using the sun as center celestial body to be taken the photograph Three-Body Model by spacecraft, by other
Disturbance is considered as process noise.Kinetic model at solar core inertial coodinate system (J2000.0) is writeable are as follows:
Wherein | | | | indicate 2 norms of vector, | | | |3Indicate | | | | cube, r and v be spacecraft relatively too
The position and speed of sun.μsAnd μmIt is the gravitational constant of the sun and Mars, r respectivelymIt is position vector of the Mars with respect to the sun, rsm
=r-rmIt is position vector of the spacecraft with respect to Mars.W is process noise caused by various disturbances.State mould can be obtained by above formula
Type is as follows:
Wherein quantity of state X=[r, v]TThe position for being spacecraft under sun inertial coodinate system and speed,For quantity of state X
Derivative,For moment t'sF (X (t), t) is mission nonlinear continuous state transfer function, and w is process noise, w (t)
For the w of moment t.
2. judging whether there is pulse arrival time measurement
Due to pulse signal need observation cycle it is longer, solid with starlight angular distance measurement and astronomy doppler velocity measurement
Amount is compared, and the sampling period of pulse arrival time measurement is longer.Therefore, with starlight angular distance measurement and astronomical doppler velocity
The sampling period of measurement is as filtering cycle.When filtered time instant does not have pulse arrival time measurement, to by state model
And the system model that starlight angular distance measurement model, difference astronomy doppler velocity measurement model are constituted is used to by UKF filtering
Posteriority state estimation and posteriori error covariance of the spacecraft with respect to the sun under property system.When filtered time instant has pulse arrival time
When measurement, to by state model and starlight angular distance measurement model, difference astronomy doppler velocity measurement model, differential pulse to
The system model constituted up to measuring time value model is estimated by the posteriority state that UKF filters the opposite sun of spacecraft under acquisition inertial system
Meter and posteriori error covariance.
3. establishing the measurement model of starlight angular distance
The starlight angular distance between spacecraft and phobos, Deimos and its background fixed star is obtained using angle measurement sensor, with this
A little starlight angular distances establish measurement model as measurement.Fig. 2 gives starlight angular distance measurement model schematic diagram.Wherein rsp、rsdPoint
It is not the position vector of phobos, Deimos relative to spacecraft, s1、s2It is the direction vector of two fixed stars under inertial system respectively,
rp、rdIt is the position vector of phobos, Deimos relative to the sun respectively.Starlight angular distance measurement model is writeable are as follows:
Wherein αp1And αp2It is the starlight angular distance between spacecraft and phobos and two background fixed stars, α respectivelyd1And αd2Respectively
It is the starlight angular distance between spacecraft and Deimos and two background fixed stars.Using these starlight angular distances as measurement Z1=[αp1,
αp2,αd1,αd2]T, the expression formula of starlight angular distance measurement model can be established:
Z1=[αp1,αp2,αd1,αd2]T=h1[X(t),t]+v1(t) (4)
Wherein h1() indicates the non-linear continuous measurement function of starlight angular distance, v1(t) amount of t moment starlight angular distance is indicated
Survey noise.
4. establishing the measurement model of difference astronomy doppler velocity
Solar spectrum frequency displacement is obtained using spectrometer, and radial velocity of the spacecraft with respect to the sun is obtained according to frequency displacement, with
This establishes measurement model as measurement:
Wherein vrIndicate radial velocity measurement of the spacecraft with respect to the sun, vrtIndicate radial speed of the spacecraft with respect to the sun
Spend true value, υpIndicate the disturbance term as caused by solar spectrum frequency fluctuation, υmIndicate that astronomical doppler velocity measures noise.
Establish the measurement model of difference astronomy doppler velocity:
Wherein vr(t) and vrIt (t-1) is the radial velocity measurement of t moment and t-1 moment spacecraft with respect to the sun respectively,
vrt(t) and vrtIt (t-1) is the radial velocity true value of t moment and t-1 moment spacecraft with respect to the sun, υ respectivelyp(t) and υp(t-
It 1) is disturbance term caused by t moment and t-1 moment solar spectrum frequency fluctuation, υ respectivelym(t) and υm(t-1) be respectively t moment and
The measurement noise at t-1 moment, △ υp(t)=υp(t)-υpIt (t-1) is υ after differencepResidual error, △ υm(t)=υm(t)-υm(t-1)
It is υ after differencemResidual error.
Using difference astronomy doppler velocity as measurement Z2=[vr(t)-vr(t-1)] difference astronomy Doppler can, be established
The expression formula of velocity measurement model:
Z2=[vr(t)-vr(t-1)]=h2[X(t),X(t-1)]+v2(t) (7)
Wherein h2() indicates the non-linear continuous measurement function of difference astronomy doppler velocity, v2(t) indicate that t moment is poor
Divide the error in measurement of astronomical doppler velocity.With the posteriority state estimation at t-1 momentInstead of X (t-1), then difference arteries and veins
The expression formula being flushed to up to measuring time value model is writeable are as follows:
Z2=h2[X(t),t]+v2(t) (8)
5. establishing the measurement model of differential pulse arrival time
Fig. 3 gives X-ray pulsar range-finding navigation schematic illustration.Wherein tSCAnd tbRespectively indicate i-th pulsar
Pulse reaches the time of spacecraft and solar system mass center (SSB), and n is the direction vector of lower i-th pulsar of day heart inertial system, rS
Position vector for detector with respect to solar system mass center, is represented by rS=r-b, b are position vector of the SSB with respect to the sun, c table
Show the light velocity.As can be seen from Figure, c (tb-tSC) it is believed that rSProjection on n.Consider relativistic effect and geometric effect, time
Transformation model may be expressed as:
Wherein D0Pulsar is indicated to the distance of solar system mass center, equation the right first item is what geometric distance generated
Doppler delay, Section 2 indicate that X-ray reaches time delay caused by the solar system in parallel, usually first two are referred to as
Roemer delay, Section 3 indicate the time delay that bending of light generates under solar gravitation field action, and referred to as Shapiro prolongs
Late.
Establish the measurement model of differential pulse arrival time:
Wherein τ (t) indicates the differential pulse arrival time of t moment, tb(t) and tb(t-1) when respectively indicating t moment and t-1
Carve the time that pulsar pulse reaches solar system mass center, tSC(t) and tSC(t-1) t moment and t-1 moment pulsar are respectively indicated
The time of pulse arrival spacecraft.
Using differential pulse arrival time as measurement Z3=[τ (t)] can establish differential pulse arrival time measurement model
Expression formula:
Z3=[τ (t)]=h3[X(t),X(t-1)]+v3(t) (11)
Wherein h3() indicates the non-linear continuous measurement function of differential pulse arrival time, v3(t) t moment difference is indicated
The measurement noise of pulse arrival time.With the posteriority state estimation at t-1 momentInstead of X (t-1), then differential pulse arrives
Expression formula up to measuring time value model is writeable are as follows:
Z3=h3[X(t),t]+v3(t) (12)
6. carrying out discretization
When filtered time instant does not have pulse arrival time measurement, if the measurement Z of navigation system at this time12=[Z1,Z2]T,
Measure noise v12=[v1,v2]T, Navigation System Model are as follows:
Wherein h12() indicates the non-linear continuous measurement function of navigation system when no pulse arrival time measurement.It is right
Formula (13) carries out discretization:
Wherein XkAnd Z12kThe quantity of state of etching system and system when without pulse arrival time measurement when respectively indicating k
Measurement, F (Xk-1, k-1) be f (X (t), t) it is discrete after nonlinear state transfer function, H12(Xk, k) and it is h12[X (t), t] from
Non-linear measurement function after dispersion, WkAnd V12kRespectively indicate w (t) and v12(t) equivalent noise after discrete.
When filtered time instant has pulse arrival time measurement, if the measurement Z=[Z of navigation system at this time1,Z2,Z3]T,
Measure noise v=[v1,v2,v3]T, Navigation System Model are as follows:
Wherein h () indicates the non-linear continuous measurement function of navigation system when pulse arrival time measurement.To formula
(15) discretization is carried out:
Wherein ZkIndicate the measurement of etching system when k, H (Xk, k) be h [X (t), t] it is discrete after non-linear measurement function,
VkIndicate the equivalent noise after v (t) is discrete.
7. carrying out the position and speed estimation that UKF filtering obtains spacecraft
System model after discretization is filtered by UKF, specific step is as follows.
A. init state amountWith State error variance battle array P0
In formula,It is the estimated value of the 0th moment (initial time) Space Vehicle position and speed, X0It is the 0th moment spacecraft
The true value of position and speed.
B. sigma sampled point is chosen
InA series of sampled points are nearby chosen, the mean value and covariance of these sample points are respectivelyWith
State variable is 6 × 1 dimensions, then choosing 13 sample pointsAnd its weight w0,w1…,w12It is as follows respectively:
Wherein τ indicates zooming parameter,Indicate the i-th row or column of sqrtm of making even.
C. it transmits sigma sampled point and obtains prior estimate and prior uncertainty covariance
The one-step prediction of each sampled pointAre as follows:
Merge allObtain prior state estimationAre as follows:
Prior uncertainty covarianceAre as follows:
In formula, QkFor k moment state model noise covariance battle array.
D. it measures and updates
According to measurement equation, each sampled point is calculatedPrediction measurementWhen filtered time instant does not have pulse arrival
When time quantum measures:
When filtered time instant has pulse arrival time measurement:
Merge allIt obtains prediction and measures YkAre as follows:
It calculates prediction and measures covariance Pyy,kAnd cross covariance Pxy,k:
Wherein RkThe measurement noise covariance battle array of etching system when for k.Calculate filtering gain KkAre as follows:
Calculate posteriority state estimation
Calculate posteriori error covariance
It willAndOutput, while these estimated values are returned into filter, for obtaining the output at k+1 moment.
The content that description in the present invention is not described in detail belongs to the prior art well known to professional and technical personnel in the field.
Claims (1)
1. a kind of deep space probe angle measurement/differential speed measuring/difference ranges Combinated navigation method, it is characterised in that: dynamic according to track
Mechanics establishes the state model of spacecraft, obtains starlight angular distance measurement using angle measurement sensor, is detected using X-ray pulsar
Device obtains pulse arrival time measurement, astronomical doppler velocity measurement is obtained using spectrometer, according to these measurements point
Starlight angular distance measurement model, differential pulse arrival time measurement model and difference astronomy doppler velocity measurement model are not established；
The position and speed of UKF filtering estimation spacecraft is used after discretization；Specifically includes the following steps:
1. establishing the System State Model based on dynamics of orbits
In the sports immunology of Mars Approach phase it is using the sun as center celestial body to be taken the photograph Three-Body Model by spacecraft, other is disturbed
It is considered as process noise；Kinetic model under solar core inertial coodinate system is writeable are as follows:
Wherein | | | | indicate 2 norms of vector, | | | |3Indicate | | | | cube, r and v are position of the spacecraft with respect to the sun
It sets and speed；μsAnd μmIt is the gravitational constant of the sun and Mars, r respectivelymIt is position vector of the Mars with respect to the sun, rsm=r-rm
It is position vector of the spacecraft with respect to Mars；W is process noise caused by various disturbances；State model can be obtained by above formula such as
Under:
Wherein quantity of state X=[r, v]TThe position for being spacecraft under sun inertial coodinate system and speed,For leading for quantity of state X
Number,For moment t'sF (X (t), t) is mission nonlinear continuous state transfer function, and w is process noise, and w (t) is
The w of moment t；
2. judging whether there is pulse arrival time measurement
Since the observation cycle that pulse signal needs is longer, Gu with starlight angular distance measurement and astronomical doppler velocity measurement phase
Than the sampling period of pulse arrival time measurement is longer；Therefore, it is measured with starlight angular distance measurement and astronomical doppler velocity
The sampling period of amount is as filtering cycle；When filtered time instant does not have pulse arrival time measurement, to by state model and star
Optic angle is filtered by UKF away from the system model that measurement model, difference astronomy doppler velocity measurement model are constituted and obtains inertial system
Posteriority state estimation and posteriori error covariance of the lower spacecraft with respect to the sun；When filtered time instant has pulse arrival time measurement
When amount, when to being reached by state model and starlight angular distance measurement model, difference astronomy doppler velocity measurement model, differential pulse
Between measurement model constitute system model by UKF filtering obtain inertial system under spacecraft relatively the sun posteriority state estimation with
And posteriori error covariance；
3. establishing the measurement model of starlight angular distance
The starlight angular distance between spacecraft and phobos, Deimos and its background fixed star is obtained using angle measurement sensor, with these stars
Optic angle is away from establishing measurement model as measurement:
Wherein αp1And αp2It is the starlight angular distance between spacecraft and phobos and two background fixed stars, α respectivelyd1And αd2It is boat respectively
Starlight angular distance between its device and Deimos and two background fixed stars, rsp、rsdIt is phobos, Deimos respectively relative to spacecraft
Position vector, s1、s2It is the direction vector of two fixed stars under inertial system, r respectivelyp、rdIt is that phobos, Deimos are opposite respectively
In the position vector of the sun；
Using these starlight angular distances as measurement Z1=[αp1,αp2,αd1,αd2]T, the expression of starlight angular distance measurement model can be established
Formula:
Z1=[αp1,αp2,αd1,αd2]T=h1[X(t),t]+v1(t) (4)
Wherein h1() indicates the non-linear continuous measurement function of starlight angular distance, v1(t) indicate that the measurement of t moment starlight angular distance is made an uproar
Sound；
4. establishing the measurement model of difference astronomy doppler velocity
Solar spectrum frequency displacement is obtained using spectrometer, and radial velocity of the spacecraft with respect to the sun is obtained according to frequency displacement, is made with this
Measurement model is established for measurement:
Wherein vrIndicate radial velocity measurement of the spacecraft with respect to the sun, vrtIndicate that spacecraft is true with respect to the radial velocity of the sun
Real value, υpIndicate the disturbance term as caused by solar spectrum frequency fluctuation, υmIndicate that astronomical doppler velocity measures noise；
Establish the measurement model of difference astronomy doppler velocity:
Wherein vr(t) and vrIt (t-1) is the radial velocity measurement of t moment and t-1 moment spacecraft with respect to the sun, v respectivelyrt(t)
And vrtIt (t-1) is the radial velocity true value of t moment and t-1 moment spacecraft with respect to the sun, υ respectivelyp(t) and υp(t-1) divide
It is not disturbance term caused by t moment and t-1 moment solar spectrum frequency fluctuation, υm(t) and υmIt (t-1) is t moment and t-1 respectively
The measurement noise at moment, Δ υp(t)=υp(t)-υpIt (t-1) is υ after differencepResidual error, Δ υm(t)=υm(t)-υm(t-1) it is
υ after differencemResidual error；
Using difference astronomy doppler velocity as measurement Z2=[vr(t)-vr(t-1)] difference astronomy doppler velocity can, be established
The expression formula of measurement model:
Z2=[vr(t)-vr(t-1)]=h2[X(t),X(t-1)]+v2(t) (7)
Wherein h2() indicates the non-linear continuous measurement function of difference astronomy doppler velocity, v2(t) t moment difference day is indicated
The error in measurement of literary doppler velocity；With the posteriority state estimation at t-1 momentInstead of X (t-1), then differential pulse arrives
Expression formula up to measuring time value model is writeable are as follows:
Z2=h2[X(t),t]+v2(t) (8)
5. establishing the measurement model of differential pulse arrival time
Pulse arrival time measurement is obtained using X-ray pulsar detector, is established using pulse arrival time as measurement
Measurement model:
Wherein tbIndicate that pulsar pulse reaches the time of solar system mass center, tSCIndicate pulsar pulse reach spacecraft when
Between, rSIndicate that position vector of the spacecraft with respect to solar system mass center, c indicate that the light velocity, n indicate direction of the pulsar under inertial system
Vector, D0Pulsar is indicated to the distance of solar system mass center, b indicates position vector of the solar system mass center with respect to the sun；
Establish the measurement model of differential pulse arrival time:
Wherein τ (t) indicates the differential pulse arrival time of t moment, tb(t) and tb(t-1) t moment and t-1 moment arteries and veins are respectively indicated
Rush the time that star pulse reaches solar system mass center, tSC(t) and tSC(t-1) t moment and t-1 moment pulsar pulse are respectively indicated
Reach the time of spacecraft；
Using differential pulse arrival time as measurement Z3=[τ (t)], can establish the table of differential pulse arrival time measurement model
Up to formula:
Z3=[τ (t)]=h3[X(t),X(t-1)]+v3(t) (11)
Wherein h3() indicates the non-linear continuous measurement function of differential pulse arrival time, v3(t) t moment differential pulse is indicated
The measurement noise of arrival time；With the posteriority state estimation at t-1 momentInstead of X (t-1), then when differential pulse reaches
Between measurement model expression formula it is writeable are as follows:
Z3=h3[X(t),t]+v3(t) (12)
6. carrying out discretization
When filtered time instant does not have pulse arrival time measurement, if the measurement Z of navigation system at this time12=[Z1,Z2]T, measure
Noise v12=[v1,v2]T, Navigation System Model are as follows:
Wherein h12() indicates the non-linear continuous measurement function of navigation system when no pulse arrival time measurement；To formula into
Row discretization:
Wherein XkAnd Z12kWhen respectively indicating k the quantity of state of etching system and when without pulse arrival time measurement system measurement
Amount, F (Xk-1, k-1) be f (X (t), t) it is discrete after nonlinear state transfer function, H12(Xk, k) and it is h12[X (t), t] discretization
Non-linear measurement function afterwards, WkAnd V12kRespectively indicate w (t) and v12(t) equivalent noise after discrete；
When filtered time instant has pulse arrival time measurement, if the measurement Z=[Z of navigation system at this time1,Z2,Z3]T, measure
Noise v=[v1,v2,v3]T, Navigation System Model are as follows:
Wherein h () indicates the non-linear continuous measurement function of navigation system when pulse arrival time measurement；Formula is carried out
Discretization:
Wherein ZkIndicate the measurement of etching system when k, H (Xk, k) be h [X (t), t] it is discrete after non-linear measurement function, VkTable
Show the equivalent noise after v (t) is discrete；
7. carrying out the position and speed estimation that UKF filtering obtains spacecraft
When filtered time instant does not have pulse arrival time measurement, the system model formula after discretization is filtered by UKF
Posteriority state estimation of the spacecraft with respect to the sun under acquisition inertial systemAnd posteriori error covarianceIts
InRespectively position of the kth moment spacecraft with respect to the sun, speed Posterior estimator；When filtered time instant has pulse arrival
Between measurement when, acquisition is filtered by UKF to the system model formula after discretizationAndIt willAndOutput, together
When by these estimated values return filter, for obtaining the output at k+1 moment.
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