CN100442015C - Astronomical/doppler combined navigation method for spacecraft - Google Patents

Abstract

The invention combines independent astronavigation with Doppler method. Method combines direct sensing horizon with indirect sensing horizon is adopted in astronavigation. One-way Doppler is adopted in Doppler method. Using method of Unscented Kalman filtering carries out united filtering, estimating position of spacecraft and speed guidance message. The invention can be in use for determining navigation parameters of earth satellite, manned spacecraft accurately in applications of observation over the ground, communication, and positioning navigation etc.

Description

A kind of astronomical/doppler combined navigation method for spacecraft

Technical field

The present invention relates to a kind of air navigation aid of spacecraft, can be used for accurately determining of earth satellite such as earth observation, communication, location navigation and manned spacecraft navigational parameter.

Background technology

At present, earth satellite, manned spacecraft mainly rely on land station's investigating method (Doppler's method) to position navigation.Since be subjected to the restriction of geographical conditions, the centering low orbit spacecraft, but the track segmental arc of domestic land station observing and controlling is very short, is difficult to realize the location navigation of whole rail; There are problems such as long delay, angle measurement accuracy be low again in remote spacecraft.Side by side plane system is also destroyed and is disturbed, the possibility of the information transmission generation interrupt choking effect on spacecraft and ground.In order to ensure the security and the reliability of spacecraft flight, each spacefaring nation is all in the various Autonomous Navigation Technigue for Spacecrafts that do not rely on terrestrial radio observing and controlling of develop actively, with the autonomous operation that improves spacecraft, autonomous management with in the rail viability.

At present the autonomous navigation method of spacecraft comprises and utilizes magnetometer, radar, GPS, inter-satellite link and astronomical navigation method.Wherein preceding two kinds of methods are more suitable for being used for the spacecraft of low orbit (LEO).Though GPS and inter-satellite link can carry out real-time navigation and reach higher precision, spacecraft must rely on other spacecrafts measurement information is provided, and in a sense, they can not a kind of at last autonomous air navigation aid fully.

Celestial navigation is a kind of autonomous positioning navigation method fully that celestial body (earth, the sun, other planets and the fixed star) azimuth information of utilizing heavenly body sensor to record is carried out the spacecraft position calculation.Because it has and only need utilize existing spacecraft attitude sensing unit star sensor and horizon instrument, and does not need additionally to increase other hardware device, and attitude and positional information can be provided simultaneously; Be not only applicable to low orbit satellite and be applicable to advantages such as high rail satellite and deep space probe, and enjoy favor, paid close attention to widely.But because the angular observation information between celestial body and spacecraft is only used in celestial navigation, be subjected to the restriction of heavenly body sensor precision, navigation accuracy is not really high.And, can't accurately set up the state model of navigational system because spacecraft autonomous astronomical navigation system model exists ascertainment error and stochastic error.Therefore can cause the navigation information precision exported not high, even the situation of filter divergence may occur.

To sum up, Doppler's method existence that earth satellite and manned spacecraft are commonly used at present is not autonomous, but the observing and controlling track is short, and is not suitable for long shortcoming apart from observing and controlling, and celestial navigation is subjected to the restriction of heavenly body sensor precision and system model, and navigation accuracy is not high.

Summary of the invention

The technical problem to be solved in the present invention is: overcome the deficiency of existing method, earth satellite, the manned spacecraft celestial self-navigation method of a kind of precision height, good reliability is provided.

The technical solution adopted for the present invention to solve the technical problems is: at earth satellite and manned spacecraft, adopt astronomical navigation method and one way Doppler method to obtain the position and the speed parameter of spacecraft respectively, wherein the method that directly responsive and indirect sensitivity combines is adopted in celestial navigation, then adopt the Unscented group of Kalman filters to carry out associating filtering to the position of the spacecraft that obtains with astronomical navigation method and speed parameter with the position and the speed parameter of the spacecraft of Doppler's method acquisition, obtain the position and the speed parameter of spacecraft, spacecraft is navigated according to the position and the speed parameter of the described spacecraft that obtains by associating filtering.

Specifically may further comprise the steps:

(1) foundation is based on the spacecraft state equation of dynamics of orbits;

(2) set up respectively with starlight refraction apparent altitude h _aWith starlight angular distance α be the measurement equation of measurement amount;

(3) setting up with the Doppler shift is the measurement equation of measurement amount;

(4) above state equation and three measurement equations are carried out discretize;

(5) reflect apparent altitude h respectively with starlight with state equation _aFor the measurement equation of measurement amount with starlight angular distance α is two subfilters of measurement equation composition of measurement amount, and forms first senior filter with Unscented Kalman filtering algorithm associating filtering;

(6) form second senior filter with state equation and the measurement equation that with the Doppler shift is the measurement amount;

(7) with the Unscented Kalman filtering algorithm described first senior filter and second senior filter are carried out associating filtering, and the output navigation information.

Described step (2) culminant star anaclasis apparent altitude h _aWith true altitude h _gBetween relation as follows:

h _a＝R _e(μ _g-1)+μ _gh _g (1)

Wherein, R _eBe earth radius; μ _gBe height h _gThe refractive index at place.

Doppler shift measurement amount in the described step (3) adopts one way Doppler method to realize: a receiver is installed on spacecraft, is used to receive land station or TDRS emitted radio signal.

Two subfilters in the described step (5), two partial estimation value X that in filtering, obtain _i(k) (i=1,2) and evaluated error P _i(k) merge by following formula in senior filter (k=1,2), obtains the global state estimated value and overall estimated error mean squares difference battle array is respectively:

${\hat{X}}_g\left(k\right)=P_g\left(k\right)[P_1^{-1}\left(k\right)X_1\left(k\right)+P_2^{-1}\left(k\right)X_2\left(k\right)],---\left(2\right)$

$P_g\left(k\right)={[P_1^{-1}\left(k\right)+P_2^{-1}\left(k\right)]}^{-1},---\left(3\right)$

Then overall estimated result is fed back to two subfilters, as the k estimated value of two subfilters constantly:

${\hat{X}}_i\left(k\right)={\hat{X}}_g\left(k\right)---\left(4\right)$

$Q_i^{-1}\left(k\right)={\mathrm{\β}}_i{Q}_g^{-1}\left(k\right)---\left(5\right)$

$P_i^{-1}\left(k\right)={\mathrm{\β}}_i{P}_g^{-1}\left(k\right)---\left(6\right)$

β ₁+β ₂＝1(i＝1，2?0≤β _i≤1) (7)

Wherein, Q (k)=E[w (k) w (k) ^T] be the covariance matrix of state model noise.β _iBe the information distribution factor.

The system of selection of the described information distribution factor is: satisfy information conservation formula β ₁+ β ₂=1 (i=1,2 0≤β _i≤ 1) be directly proportional with the filtering accuracy of local filter under the prerequisite, employing makes based on the algorithm of the dynamic assignment information factor of the norm of evaluated error matrix P

${\mathrm{\β}}_i\left(k\right)=\frac{{\left({\left|\right|P_i(k-1)\left|\right|}_F\right)}^{-1}}{\underset{i=1}{\overset{2}{\mathrm{\Σ}}}{\left({\left|\right|P_i(k-1)\left|\right|}_F\right)}^{-1}}---\left(8\right)$

In the formula, ‖ ‖ _FBe the Frobenius norm, promptly for any matrix A, ${\left|\right|A\left|\right|}_F=\sqrt{\mathrm{\Σdiag}(A^T\·A)}.$ The method that described astronomical navigation method adopts direct gentle sensitively indirect responsive Horizon to combine.Principle of the present invention is: the state equation of autonomous astronomical navigation system:

X ^&(t)＝f(X，t)+w(t) (9)

In the formula, state vector X=[x y z v _xv _yv _z] ^T, x, y, z, v _x, v _y, v _zBe respectively position and the speed of satellite in X, Y, three directions of Z; The state model noise $w={[w_x,w_y,w_z,w_{v_x},w_{v_y},w_{v_z}]}^T$

As shown in Figure 2, the starlight refraction apparent altitude h that star sensor measures is indirectly adopted in the observed quantity of indirect responsive Horizon _a, the starlight angular distance α that the observed quantity of direct responsive Horizon adopts star sensor and infrared horizon to record.Measurement equation is respectively:

$z_1=h_a=\sqrt{r^2-u^2}+u\tan \left(R\right)-R_e-a+v_1---\left(10\right)$

$z_2=\mathrm{\α}=\arccos (-\frac{r_s\·s}{r_s})+v_2---\left(11\right)$

Wherein, μ is a refractive index; R is refraction angle (rad); R _eBe earth radius; v ₁, v ₂Be the Gaussian measurement noise; r _sIt is the position vector of spacecraft in the geocentric inertial coordinate system; S is the unit vector of nautical star starlight direction.

Doppler shift when the radio signal of the fixed frequency by measuring land station's emission arrives spacecraft can obtain the relative velocity ρ between spacecraft and land station ^﹠amp;, its measurement equation is

$Z_3\left(t\right)=h_3[X\left(t\right),t]+V_3\left(t\right)=\frac{1}{\mathrm{\ρ}}(r-R)(v-w_e\×R)+v_3---\left(12\right)$

In the formula, r and R are respectively spacecraft and the land station position vector in the Earth central inertial spherical coordinate system; V is the speed of spacecraft; w _eBe earth's spin vector; v ₃Be the Gaussian measurement noise.

Form first subfilter with state equation (9) and measurement equation (10), state equation (9) and measurement equation (11) are formed second subfilter.

Carry out associating filtering with the Unscented Kalman filtering algorithm.When not reflecting star and occur, second subfilter time of carrying out to be upgraded and measure upgrade, first subfilter time of only carrying out upgrades; When observing the refraction star, two subfilters are carried out the time renewal and measure upgrading simultaneously.

Through the filter process of discretize concurrent operation, two partial estimation value X that obtain _i(k) (i=1,2) and evaluated error P _i(k) merge in first senior filter (k=1,2), obtains after the overall estimated value overall estimated result being fed back to two subfilters, as the estimated value of the k moment two subfilters.

First and second senior filters are merged with said method equally, and soon it is considered as two subfilters in the said method, merges again.

The cardinal rule that the information distribution factor is selected is to be directly proportional with the filtering accuracy of local filter under the prerequisite that satisfies the information conservation formula, in order to make the autonomous astronomical navigation system have stronger adaptive ability and fault-tolerant ability, use is based on the algorithm of the dynamic assignment information factor of the norm of evaluated error matrix P.

The present invention's advantage compared with prior art is: the present invention will be directly gentle sensitively starlight reflect indirect responsive Horizon and combine, this astronomical navigation method has higher relatively accuracy of observation, and the observation information of real-time continuous can be provided.One way Doppler's method need not transmitted radio signal, reduced the complicacy of equipment, and the independence and the reliability of system have been improved, both are combined, and the bank of filters that designs four Unscented group of Kalman filters one-tenth is carried out associating filtering, can walk abreast and finish the information fusion of four information sources, effectively improve accuracy of navigation systems and reliability, realize that the full arc section of earth satellite and manned spacecraft is accurately located.

Description of drawings

Fig. 1 is the process flow diagram of a kind of embodiment of the present invention.

Fig. 2 carries out the process flow diagram of filtering for the present invention adopts the Unscented group of Kalman filters

Fig. 3 is the astronomical navigation method that the present invention adopts---the combine observed quantity synoptic diagram of method of directly responsive and indirect responsive Horizon.

Embodiment

As shown in Figure 1, specific implementation method of the present invention is as follows:

1, foundation is based on the spacecraft state equation of dynamics of orbits.

Initialized location, speed are set up dynamics of orbits model (system state equation) by following equation

$\left\{\begin{array}{c}\frac{\mathrm{dx}}{\mathrm{dt}}=v_x\\ \frac{\mathrm{dy}}{\mathrm{dt}}=v_y\\ \frac{\mathrm{dz}}{\mathrm{dt}}=v_z\\ \frac{{\mathrm{dv}}_x}{\mathrm{dt}}=-\mathrm{\μ}\frac{x}{r^3}[1-J_2\left(\frac{R_e}{r}\right)(7.5\frac{z^2}{r^2}-1.5)]+{\mathrm{\ΔF}}_x\\ \frac{{\mathrm{dv}}_y}{\mathrm{dt}}=-\mathrm{\μ}\frac{y}{r^3}[1-J_2\left(\frac{R_e}{r}\right)(7.5\frac{z^2}{r^2}-1.5)]+{\mathrm{\ΔF}}_y\\ \frac{{\mathrm{dv}}_z}{\mathrm{dt}}=-\mathrm{\μ}\frac{z}{r^3}[1-J_2\left(\frac{R_e}{r}\right)(7.5\frac{z^2}{r^2}-4.5)]+{\mathrm{\ΔF}}_z\end{array}\right.---\left(13\right)$

$r=\sqrt{x^2+y^2+z^2}$

Be abbreviated as

X ^&(t)＝f(X，t)+w(t) (14)

In the formula, state vector X=[x y z v _xv _yv _z] ^T, x, y, z, v _x, v _y, v _zBe respectively position and the speed of spacecraft in X, Y, three directions of Z; μ is a geocentric gravitational constant; R is the satellite position parameter vector; J ₂Be the terrestrial gravitation coefficient; Δ F _x, Δ F _y, Δ F _zBe the high-order perturbing term of perturbation of earths gravitational field and the influence of day, month perturbation and perturbative forces such as solar radiation pressure perturbation and atmospheric perturbation.

2, set up respectively with starlight refraction apparent altitude h _aWith starlight angular distance α be the measurement equation of measurement amount.

As shown in Figure 2, the starlight refraction apparent altitude h that star sensor measures is indirectly adopted in the observed quantity of indirect responsive Horizon navigation subsystem _a, the starlight angular distance α that the observed quantity of direct responsive Horizon navigation subsystem adopts star sensor and infrared horizon to record.Measurement equation is respectively:

$z_1=h_a=\sqrt{r^2-u^2}+u\tan \left(\mathrm{\δ}\right)-R_e-a+v_1---\left(15\right)$

$z_2=\mathrm{\α}=\arccos (-\frac{r\·s}{r})+v_2---\left(16\right)$

Wherein, μ is a refractive index; δ is refraction angle (rad); R _eBe earth radius; v ₁, v ₂Be the Gaussian measurement noise; r ₃It is the position vector of spacecraft in the geocentric inertial coordinate system; S is the unit vector of nautical star starlight direction.

3, setting up with the Doppler shift is the measurement equation of measurement amount.

Doppler shift when the radio signal of the fixed frequency by measuring land station's emission arrives spacecraft can obtain the relative velocity ρ between spacecraft and land station ^﹠amp;, its concrete principle is as follows

In the formula, c is the light velocity, f ₀Be the natural frequency of land station's emitted radio signal, the frequency of the radio signal that f ' receives for spaceborne receiver, δ f _AtmBe the time delay of atmospheric envelope to signal.δ f ₀The error that causes for drift by the signal source local frequency, because land station adopts the magnitude of this error of USO (UltraStable Oscillators) very little more at present, v _mMeasurement noise for instrument.

Because ρ=r-R, so

Make Z ₃=[ρ ^﹠amp;], the measurement equation that then can get Doppler navigation system is

$Z_3\left(t\right)=h_3[X\left(t\right),t]+V_3\left(t\right)=\frac{1}{\mathrm{\ρ}}(r-R)(v-w_e\×R)+v_3---\left(18\right)$

In the formula, r and R are respectively spacecraft and the land station position vector in the Earth central inertial spherical coordinate system, and v is the speed of spacecraft, w _eBe earth's spin vector; v ₃Be comprehensive measurement noise.

4, above state equation and three measurement equations are carried out discretize.

X(k+1)＝F(X(k)，u(k)，k)+w(k)(19)

Z ₁(k)＝h ₁X(k)，k]+v ₁(k)(20)

Z ₂(k)＝h ₂[X(k)，k]+v ₂(k)(21)

Z ₃(k)＝h ₃[X(k)，k]+v ₃(k)(22)

In the formula, Z ₁(k) be refraction apparent altitude, Z ₂(k) be the starlight angular distance, Z ₃(k) be Doppler shift.The covariance matrix of state model noise is E[w (k) w (k) ^T]=Q (k), the covariance matrix of measurement noise are E[v ₁(k) v ₁(k) ^T]=R ₁(k), E[v ₂(k) v ₂(k) ^T]=R ₂(k), w, v ₁, v ₂And v ₃Uncorrelated mutually.

5, reflect apparent altitude h respectively with starlight with state equation _aFor the measurement equation of measurement amount with starlight angular distance α is two subfilters of measurement equation composition of measurement amount, and carries out information fusion with the Unscented Kalman filtering algorithm and form first senior filter.

Concrete steps are as follows:

A. use state equation (19) and measurement equation (20) to form first subfilter, state equation (19) and measurement equation (21) are formed second subfilter.

B. carry out associating filtering with adaptive genetic particle filtering algorithm.When not reflecting star and occur, second subfilter time of carrying out to be upgraded and measure upgrade, first subfilter time of only carrying out upgrades; When observing the refraction star, two subfilters are carried out the time renewal and measure upgrading simultaneously.

Two partial estimation value X that in filtering, obtain _i(k) (i=1,2) and evaluated error P _i(k) merge by following formula in senior filter (k=1,2), obtains global state estimated value and overall estimated error mean squares difference and be difference:

${\hat{X}}_g\left(k\right)=P_g\left(k\right)[P_1^{-1}\left(k\right)X_1\left(k\right)+P_2^{-1}\left(k\right)X_2\left(k\right)]---\left(23\right)$

$P_g\left(k\right)={[P_1^{-1}\left(k\right)+P_2^{-1}\left(k\right)]}^{-1}---\left(24\right)$

C. overall estimated result is fed back to two subfilters, as the estimated value of the k moment two subfilters

${\hat{X}}_i\left(k\right)={\hat{X}}_g\left(k\right)---\left(25\right)$

$Q_i^{-1}\left(k\right)={\mathrm{\β}}_i{Q}_g^{-1}\left(k\right)---\left(26\right)$

$P_i^{-1}\left(k\right)={\mathrm{\β}}_i{P}_g^{-1}\left(k\right)---\left(27\right)$

β ₁+β ₂＝1(i＝1，2 0≤β _i≤1)(28)

Wherein, β _iBe the information distribution factor.

D. the cardinal rule of information distribution factor selection is to be directly proportional with the filtering accuracy of local filter under the prerequisite that satisfies the information conservation formula, in order to make the autonomous astronomical navigation system have stronger adaptive ability and fault-tolerant ability, use is based on the algorithm of the dynamic assignment information factor of the norm of evaluated error matrix P.

Order

${\mathrm{\β}}_i\left(k\right)=\frac{{\left({\left|\right|P_i(k-1)\left|\right|}_F\right)}^{-1}}{\underset{i=1}{\overset{2}{\mathrm{\Σ}}}{\left({\left|\right|P_i(k-1)\left|\right|}_F\right)}^{-1}}---\left(29\right)$

In the formula, ‖ ‖ _FBe the Frobenius norm, promptly for any matrix A, ${\left|\right|A\left|\right|}_F=\sqrt{\mathrm{\Σdiag}(A^T\·A)}$

6, form second senior filter with state equation and the measurement equation that with the Doppler shift is the measurement amount.First and second senior filters are merged with said method equally, and soon it is considered as two subfilters in the said method, merges once more with the algorithm in the step 5.

7, outgoing position, velocity information.

Carry out Computer Simulation according to above-mentioned steps 1～6, set up the dynamics of orbits equation, measurement equation utilizes the Unscented Kalman filtering can finish position, velocity estimation to earth satellite.Output state vector X=[x y z v _xv _yv _z] ^TEstimated value $\hat{X}={\left[\begin{array}{cccccc}\hat{x}& \hat{y}& \hat{z}& {\hat{v}}_x& {\hat{v}}_y& {\hat{v}}_z\end{array}\right]}^T,$ Wherein

Be respectively to position and the speed x of spacecraft in X, Y, three directions of Z, y, z, v _x, v _y, v _zEstimation; And output estimation variance matrix $P={[p_x,p_y,p_z,p_{v_x},p_{v_y},p_{v_z}]}^T,$ Wherein

Be respectively the estimation error variance of spacecraft in X, Y, three direction positions of Z and speed.

The content that is not described in detail in the instructions of the present invention belongs to this area professional and technical personnel's known prior art.

Claims (3)

1, a kind of astronomical/doppler combined navigation method for spacecraft, it is characterized in that: at earth satellite and manned spacecraft, adopt astronomical navigation method and one way Doppler method to obtain the position and the speed parameter of spacecraft respectively, wherein the method that directly responsive and indirect sensitivity combines is adopted in celestial navigation, then adopt the Unscented group of Kalman filters to carry out associating filtering to the position of the spacecraft that obtains with astronomical navigation method and speed parameter with the position and the speed parameter of the spacecraft of Doppler's method acquisition, obtain the position and the speed parameter of spacecraft, position and speed parameter according to the described spacecraft that obtains by associating filtering navigate to spacecraft, and its concrete steps are as follows:

(1) foundation is based on the spacecraft state equation of dynamics of orbits;

(2) set up respectively with starlight refraction apparent altitude h _aWith starlight angular distance α be the measurement equation of measurement amount;

(3) setting up with the Doppler shift is the measurement equation of measurement amount;

(4) above state equation and three measurement equations are carried out discretize;

(5) reflect apparent altitude h respectively with starlight with state equation _aFor the measurement equation of measurement amount with starlight angular distance α is two subfilters of measurement equation composition of measurement amount, and forms first senior filter with Unscented Kalman filtering algorithm associating filtering;

(6) form second senior filter with state equation and the measurement equation that with the Doppler shift is the measurement amount;

(7) with the Unscented Kalman filtering algorithm described first senior filter and second senior filter are carried out associating filtering, and the output navigation information.

2, astronomical/doppler combined navigation method for spacecraft according to claim 1 is characterized in that: described step (2) culminant star anaclasis apparent altitude h _aWith true altitude h _gBetween relation as follows:

h _a＝R _e(μ _g-1)+μ _gh _g，

Wherein, R _eBe earth radius; μ _gBe height h _gThe refractive index at place,

Promptly obtain starlight refraction apparent altitude h by this relational expression _a

3, astronomical/doppler combined navigation method for spacecraft according to claim 1, it is characterized in that: the method that described astronomical navigation method adopts direct gentle sensitively indirect responsive Horizon to combine, after the first senior filter information fusion, form time senior filter with second senior filter of Doppler navigation again, carry out secondary information and merge.

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