CN104407321B - Quantum ranging-based estimation method and equipment for relative orbits of formation flying satellites - Google Patents

Abstract

The invention discloses quantum ranging-based estimation method and equipment for relative orbits of formation flying satellites. Quantum ranging equipment is disclosed and comprises a spontaneous parametric down-conversion unit, a polarization beam splitter, four reflectors, two emitters, two photon receivers, two photon detectors and a TAC-MCA (time-amplitude converter-multi-channel analyzer) system. With the quantum ranging equipment, relative distances among a main satellite and auxiliary satellites are measured in a triangular quantum ranging method. An extended Kalman filter is adopted to solve the SSF relative orbit estimation problem. Through measurement of two delay time, two delay time expressions are constructed, a reference path is counteracted by the summation, errors, caused by the reference path, are eliminated, the defects that the reference path between two-point quantum ranging is hard to be measured accurately, and the physical property of the reference path might be changed to bring errors are overcome, and accordingly the relative orbits of the formation flying satellites are more accurately estimated.

Description

The Satellite Formation Flying relative orbit method of estimation found range based on quantum and its equipment

Technical field

The present invention relates to Satellite Orbit Determination and quantum positioning field, and in particular to the formation flying satellites found range based on quantum Track estimates that methods described is satellite and intersatellite range finding and satellites formation in the satellite formation flying (SFF) in space The orbit determination of flight provides and more accurately services.

Background technology

Satellite formation flying, is also called distributed satellites, cooperates to complete by the grapefruit satellite of two or more Some space tasks, it is capable of the unique geometry of effectively utilizes formation flight, so as to be supplied to our more those tradition The information that single satellite cannot be observed.SFF is introduced by National Aeronautics and Space Administration (NASA) in the mid-90.Compared to biography Single satellite of system, it spends few, and with short production cycle, performance is relatively reliable, low to the dependency degree on ground.But due to the shadow of perturbative force Ring, satellite not always as it is desirable that orbit.In order to construct a firm SFF geometry, satellite it Between relative distance will must measure at the moment, the result of measurement is used for safeguarding the satellite constellation structure of a needs.

Traditional distance-finding method is the relative distance that distributed satellites are estimated using GPS.Experiment shows the phase by GPS Cm ranks can be reached to range accuracy.However, in addition to the expensive cost of GPS system, when the track height of formation flying satellites When degree is higher than GPS constellation, this method will be unable to be suitable for.Improved ranging technology employs a kind of satellite-carried wireless electric unit, it With simple structure and the characteristics of lower cost, the shortcoming of GPS is compensate for.However, this radio unit is defended distributed Between star relatively far apart under conditions of can not effectively play a role.Afterwards people have also been proposed a kind of spaceborne laser ranging side Method is measuring the relative distance between satellite.In view of the stability of laser, and though this method satellite relative distance how far In the case of it is all pratical and feasible.This method uniquely have the disadvantage estimate distance accuracy with GPS in same yardstick, All it is merely able to reach cm ranks.

Quantum range finding is by using a kind of distance-finding method for tangling pulse.Compared to the traditional M arteries and veins with same band Punching, using M the distance-finding method of pulse is tangled, and precision can be made to improve one in principleThe factor, reaches conventional measurement away from side The method precision to be provided.

The content of the invention

For the deficiencies in the prior art, the present invention is intended to provide a kind of Satellite Formation Flying relative orbit found range based on quantum is estimated Meter method and its equipment, by being found range based on triangle quantum, are obtained main satellite and guide and protect the relative distance of star, and combine satellite The state equation of the Dynamic Model of relative motion track, is the track of SSF with extended BHF approach device (EKF) Estimation problem provides a kind of solution.

To achieve these goals, the present invention is adopted the following technical scheme that：

A kind of quantum distance-measuring equipment includes following several parts：

Converting unit under Spontaneous Parametric, is entangled photon pairs for converted photons signal；

Polarization beam splitter, for can reflective vertical polarized light and refraction horizontal polarization light；

Four sides reflecting mirror, for reflecting entangled photons；

Emitter, for transmitting entangled photons target satellite is reached；

Photon receiver, for receiving the photon from target satellite；

Photon detector, for exciting as photoimpact and recording the time of advent of photon by photon signal；

In addition, the quantum distance-measuring equipment also includes the multichannel analyzer system of time amplitude converter one and angle idol rib Mirror.

A kind of Satellite Formation Flying relative orbit method of estimation found range based on quantum according to above-mentioned quantum distance-measuring equipment, is formed into columns The main satellite O of satellite and two guide and protect star A and B composition triangular structure, and methods described comprises the steps：

Step 1, guides and protect star A converting unit processes under its Spontaneous Parametric and produces the not conllinear entangled photons in the direction of propagation Right, the entangled photon pairs include unused photon and signal photon；Unused photon and signal photon simultaneously from guiding and protecting star A, The light path of unused photon is A → B → O → B → A, and the light path of signal photon is A → O → A, finally measure two-way photon it Between reaching time-difference；

Step 2, similarly, guides and protect star B converting unit process generation directions of propagation under its Spontaneous Parametric not conllinear After entangled photon pairs, unused photon and signal photon set out simultaneously, wherein the light path of unused photon is B → O → A → O → B, The light path of signal photon is B → A → B, finally measures the reaching time-difference of two-way photon；

Step 3, according to the reaching time-difference that step 1 and step 2 draw, calculates main satellite O and guides and protect the relative of star B Distance | OB |；

Step 4, sets up based on the coordinate system of relative motion, the barycenter of satellite O based on zero, and y-axis is earth centroid The direction of point coordinates origin, around the tangential direction of earth movements track, z-axis direction can be sat satellite O by the right hand based on x-axis Mark system determines；

Then, the dynamic model for guiding and protecting star B relative to main satellite O can be represented with following state vector：

In above formula, r and v represents respectively the position and speed for guiding and protecting star B relative to main satellite O；Major-minor satellite is not taken the photograph The impact of power, the earth-circling track of main satellite O is approximately round, meanwhile, main satellite O and guide and protect the distance between star B Much smaller than main satellite O around Earth's orbit major semiaxis；Now, the dynamic model for guiding and protecting the relatively main satellite O tracks of star B can be with Described with following Hill equations：

In above formula,Relative acceleration is represented respectively, and n is the angular velocity of main satellite O；

Show that the state equation of relative orbit is as follows according to dynamic model described above and Hill equations：

Here, A represents sytem matrix, t express times, and n is the angular velocity of main satellite O, and G is system noise matrix, and W is to be System noise；

Step 5, by a spaceborne photographing unit measurement on main satellite O the elevations angle of the star B relative to main satellite O positions is guided and protected And azimuth, just can obtain measurement vector as follows：

Z=[r θ φ]^T；

Wherein, r is that main satellite O is drawn in step 3 and the relative distance of star B is guided and protected, the relatively main satellite O positions of satellite B supplemented by θ The elevation angle put, the azimuth of the relatively main satellite O of satellite B supplemented by φ；

Then, further obtain measuring equation and be：

Wherein, [v_r v_θ v_φ]^TIt is measurement noise；

Step 6, obtains as follows with regard to the measurement Jacobean matrixes of Kalman filter：

In above formula,

Step 7, with Kalman filter, completes the estimation of track.

It should be noted that the step 1 is specifically included：

Step 1.1, signal photon after the inside light path that a two-face mirror by set by guiding and protecting star A is oriented to, Main satellite O is sent to by an emitter for guiding and protecting star A, the relative position of the two-face mirror is fixed；Then by main satellite O On angle idol prismatic reflection return to and guide and protect star A, collected by a photon receiver for guiding and protecting star A, inside identical After light path, recorded by a photon detector in the presence of polarization beam splitter, and be converted to corresponding photoimpact；

Step 1.2, while signal photon is sent to main satellite O, unused photon is anti-by the other two sides for guiding and protecting star A Another emitter that star A is guided and protected after the inside light path for penetrating mirror guiding is sent to up to star B is guided and protected, and is reached via guiding and protecting star B and being sent to Main satellite O, and be reflected back finally along former road and guide and protect star A, the relative position of the other two-face mirror is fixed；By phase After same inside light path, recorded and turned by another photon detector guided and protected on star A in the presence of polarization beam splitter It is changed to corresponding photoimpact；

Step 1.3, the two-way photoimpact obtained in step 1.1 and 1.2 is sent into the time amplitude conversion for guiding and protecting star A In device-multichannel analyzer system, time amplitude converter is first passed around, export a pulse for being proportional to reaching time-difference； Then the pulse is received and processed by multichannel analyser, when analyzing the arrival of the photon beam received by two photon detectors Between, and draw reaching time-difference.

It should be noted that the step 2 is specifically included：

Step 2.1, signal photon after the inside light path that a two-face mirror by set by guiding and protecting star B is oriented to, It is sent to by an emitter for guiding and protecting star B and guides and protect star A, the angle idol prismatic reflection then guided and protected on star A is returned to guides and protect star B, The relative position of the two-face mirror is fixed；By in identical after being collected by a photon receiver for guiding and protecting star B Portion's light path, corresponding light is recorded and is converted in the presence of polarization beam splitter by the photon detector guided and protected on star B Electric pulse；

Step 2.2, while signal photon is sent to and guides and protect star A, unused photon is reflected by the other two sides for guiding and protecting star B Another emitter of star B is guided and protected after the inside light path that mirror is oriented to be sent to up to main satellite O, be sent to up to auxiliary via main satellite O Satellite A, and be reflected back finally along former road and guide and protect star B, the relative position of the other two-face mirror is fixed；Return to and guide and protect star After B, by identical inside light path, another photon detector institute guided and protected on star B in the presence of polarization beam splitter Record and be converted to corresponding photoimpact；

Step 2.3, the two-way photoimpact in step 2.1 and 2.2 is sent into and guides and protect the time amplitude converter of star B-many In Multiple Channel Analysis instrument system, time amplitude converter is first passed around, export a pulse for being proportional to reaching time-difference；Then should Pulse is received and processed by multichannel analyser, analyzes the time of advent of the photon beam received by two photon detectors.

It should be noted that main satellite O and guiding and protecting the calculating process of relative distance | OB | between star B in the step 3 Specifically include：

1) state of signal photon and unused photon is described with following formula：

|Ψ>It is the state vector in Hilbert space,It is respectively relative to the upper of signal photon and unused photon Speed-up time, d is differentiating operator, and footnote s and i represent respectively signal photon and unused photon, ω_pExpression pumping light frequency, Ω= ω_s-ω_p/ 2=ω_p/2-ω_i, ω_iAnd ω_sIt is respectively the frequency of unused photon and signal photon, coefficient c depends on pump light Intensity and susceptibility, F (Ω) is the spectrum amplitude of signal photon and unused photon radiation；

2) the second order Glauber correlation functions of the time of advent are defined as follows：

Wherein, (r_s, t_s) and (r_i, t_i) represent space-time on two points, r_iThe reference path of known unused photon is represented, r_sRepresent unknown signal photon path, t_sAnd t_iRespectively time of advent of signal photon and unused photon；Simultaneouslyt′_jRepresent propagation time of the photon in nonlinear crystal；

In the case of smoothly, G⁽²⁾(t_s, r_s；t_i, r_i) depending on time difference t for reaching_i-t_s, for lower turn of Spontaneous Parametric Process is changed, is had

Wherein, L is the length of nonlinear crystal, and the nonlinear crystal is as the basic material for producing Entangled State photon Material, D is the inverse of the group velocity difference of entangled photon pairs；Then, the second order Glauber correlation functions of the time of advent may be calculated

Obvious, can obtain：

Wherein, τ_cIt is reaching time-difference, that is to say expression formula G⁽²⁾(τ) symmetrical centre, and determined by multichannel analyser It is fixed；

3) fromCan release, the time delay Δ t in step 1 between two paths of signals₁With step 2 The time delay Δ t of middle two paths of signals₂：

τ_c1For the reaching time-difference measured in step 1, τ_c2It is the reaching time-difference measured in step 2；

4) can be respectively according to the time of advent of two-way photon in the time of advent of two-way photon in step 1 and step 2 Obtain following equation：

2 (| AB |+| OB |-| OA |)=c Δ t₁；

2 (| OA |+| OB |-| AB |)=c Δ t₂；

3) and 4) 5) it is according to obtaining main satellite O and guide and protect relative distance | the OB | between star B：

The beneficial effects of the present invention is：The measurement that the present invention passes through time delay twice, triangle quantum distance-finding method Two expression formulas with regard to time delay of construction, summation is offset reference path, the error that reference path brings is eliminated, so as to solve The reference path of 2 quantum telemetrys under practical situation of having determined is difficult accurately to be measured may with the physical characteristics of reference path Change so as to the defect of error brought so that the estimation of Satellite Formation Flying relative orbit is more accurate.

Description of the drawings

Fig. 1 is quantum distance-measuring equipment structural representation；

Fig. 2 is 2 quantum satellite ranging schematic diagrams；

Fig. 3 is the photon path schematic diagram of triangle quantum range finding；

Fig. 4 is the coordinate system schematic diagram of the relative motion of satellite.

Specific embodiment

Below with reference to accompanying drawing, the invention will be further described, it should be noted that the present embodiment is with this technology side Premised on case, detailed implementation steps and specific operating process are provided, but protection scope of the present invention is not limited to this enforcement Example.

As shown in figure 1, each satellite is equipped with quantum distance-measuring equipment.This quantum distance-measuring equipment includes following several portions Point：

Converting unit under Spontaneous Parametric, converted photons signal is entangled photon pairs；

One polarization beam splitter (PBS), PBS being capable of reflective vertical polarized light and refraction horizontal polarization light.

Two emitters, for transmitting entangled photons target satellite is reached；

Four sides reflecting mirror, is designated as M1, M2, M3 and M4, for reflecting two beam entangled photons, the relative position of wherein M1 and M3 Put, the relative position of M2 and M4 is all fixed, the position of M1 and M3 enables incident illumination to reach one after two secondary reflections The position of individual emitter, M2 and M4 enables incident illumination that another emitter is reached after two secondary reflections；

Two photon receivers, for receiving the photon from target satellite；

Two photon detectors D1 and D2, by photon signal the time of advent of photon is excited as photoimpact and records；

Time amplitude converter (TAC) -- multichannel analyser (MCA) system.These part collaborative works, record respectively As signal photon and the time of advent of unused photon, and produce a consistent photon related to the second order of photon pair and arrive Up to time difference distribution curve.

In addition each satellite also carries an angle idol prism for reflecting the transmission photon between two satellites.

Hereinafter the principle of 2 quantum range findings is illustrated first, as shown in Figure 2：

Step 1, obtains the entangled photon pairs as range finding medium.It should be noted that produce this entangled photon pairs is Spaceborne self start type parameter down conversion unit on main satellite.

Step 2, obtains the two-way photoimpact that photon conversion is obtained, and specifically includes following content：

The entangled photon pairs produced in step 1 are separated into the signal in different light paths footpath after a polarization beam splitter Photon and unused photon.

It should be noted that generally, the state of both photons can be described with following equation

|Ψ>It is the state vector in Hilbert space,It is respectively relative to the upper of signal photon and unused photon Speed-up time, d is differentiating operator, and footnote s and i represent respectively signal photon and unused photon, ω_pExpression pumping light frequency, Ω= ω_s-ω_p/ 2=ω_p/2-ω_i, ω_iAnd ω_sIt is respectively the frequency of unused photon and signal photon, coefficient c depends on pump light Intensity and susceptibility, F (Ω) is the spectrum amplitude of signal photon and unused photon radiation；

The propagation path (reference path, it is necessary in its length of satellite launch pre-test) of unused photon is not busy on main satellite After astigmatism by the detector D1 on main satellite behind path by reference to being received, the corresponding photoimpact being converted into.Meanwhile, Signal photon is sent to up to guiding and protecting star by the emitter on main satellite, is guided and protected after star reflects, by the reception on main satellite Device is received, and is monitored by detector D2, likewise, being converted into corresponding photoimpact.

Step 3, calculates reaching time-difference (TDOA) τ：The two-way photoimpact obtained in step 2, after being fed to TAC, Output one is proportional to the pulse for reaching time difference.The pulse is received and processed by MCA, in this way, obtains two spies Survey scattergram of the device for the coincidence measurement result of reaching time-difference τ.

It should be noted that this scattergram is consistent with the second order Glauber correlation functions of entangled photon pairs, Glauber phases Close function generally to can be defined as follows

In above formula, (r_s, t_s) and (r_i, t_i) represent space-time on two points, r_iRepresent the reference arm of known unused photon Footpath, r_sRepresent unknown signal photon path, t_sAnd t_iRespectively time of advent of signal photon and unused photon；SimultaneouslyT ' j represent propagation time of the photon in nonlinear crystal.

In the case of smoothly, G⁽²⁾(t_s, r_s；t_i, r_i) depend on reaching time-difference t_i-t_s, for the Spontaneous Parametric of II types Lower transformation process (changing under the Spontaneous Parametric under I type frequency nondegenerates), has

Here L is the length of nonlinear crystal, and nonlinear crystal is used as the stock for producing Entangled State photon；D is to entangle Twine the inverse of the group velocity difference of photon pair.Then, correlation function may be calculated

Obvious, can obtain

Here r_iRepresent the reference path of known unused photon, r_sRepresent unknown signal photon path.τ_cWhen being to reach Between it is poor, that is to say expression formula G⁽²⁾(τ) symmetrical centre, and determined by MCA.DL is given by the parameter of nonlinear crystal.

It is t the time required to assuming propagation of the unused photon in reference path₁, signal photon propagation time is t₂, then just The distance between two satellites d can be extrapolated：

t₁Known (spaceborne unused light path is to determine in satellite launch pre-test on main satellite), Δ t can be by formula (5) obtain

With reference to formula 6 and formula 7, the distance between two required satellites d can be expressed as

Based on the principle of 2 quantum range findings, defended using a kind of formation found range based on quantum of the quantum distance-measuring equipment Star relative orbit method of estimation specifically includes following steps：

Due in the case of most SFF, at least two are guided and protected star around main satellite.It is special due to this Position relationship, obtain a triangle geometrically be just very easy to, the method to be found range using geometric triangulation shape is provided Condition.

Satellite based on note satellite O, satellite A and satellite B is and guides and protect star, need measurement be main satellite O and guide and protect star B it Between relative distance.

S1, measure unused photon by satellite A to satellite B, then by satellite B to satellite O, and the time of backtracking with Signal photon directly reaches satellite O, and the time difference between the time of backtracking by satellite A.

As shown in figure 3, outer space light path complete in step 1 is a, b, c in figure, now converting unit under Spontaneous Parametric Use barium metaborate (BBO) crystal of I types.

As shown in figure 1, step S1 to implement process as follows：First, conversion is single under Spontaneous Parametric in satellite A First process produces entangled photon pairs, and wherein signal photon is by an inside light path being oriented to by M1 and M3 reflecting mirrors respectively Afterwards, and by an emitter satellite O is sent to, the angle idol prismatic reflection that signal photon is installed on satellite O returns to satellite A, Then it is collected by a photon receiver, and by one by the molecular identical inner light path of M1 and M3 mirrors, Recorded by photon detector D1 in the presence of polarization beam splitter.Now, the outer space light path of signal photon can be denoted as A →O→A。

In addition, while signal photon is sent to satellite O, the inside light path that unused photon is oriented to by M2 and M4 reflecting mirrors Satellite B is delivered to by another emitter behind footpath, via satellite B satellite O is delivered to, and satellite is reflected back finally along former road A, the identical inner light path for being collected and being oriented to by reflecting mirror M2 and M4 by another photon receiver, in polarization beam splitting Recorded by the photon detector D2 on satellite A in the presence of device.Similar, the outer space light path of unused photon can be write For A → B → O → B → A.

The time of advent of the photon beam that last TAC-MCA systematic analysiss are received by detector D1 and detector D2, calculate Second-order qs-correlation function of the photon to the time of advent, that is, G₁ ⁽²⁾(τ)。

Following equation can be obtained according to the time of advent

2 (| AB |+| OB |-| OA |)=c Δ t₁ (9)

Here, the time delay Δ t between two paths of signals₁Can obtain from the equation (7) of top：

Here, τ_c1It is reaching time-difference, DL is the parameter of given nonlinear crystal.

S2, measure unused photon and sent to satellite O by satellite B, then by satellite O to satellite A, and the time of backtracking with Signal photon directly reaches satellite A, and the time difference between the time of backtracking by satellite B.

Outer space light path complete in step S2 is d, f, the e in Fig. 3.

This time by satellite A, converting unit process produces entangled photon pairs under Spontaneous Parametric.The same top of this step Process described by step S1 is similar.Can be described as B → A → B, the light path of unused photon as the path of signal photon Footpath is B → O → A → O → B.

Similar, following equation can be obtained

2 (| OA |+| OB |-| AB |)=c Δ t₂(11)

In above formula, Δ t₂It is the time delay of two paths of signals, τ_c2Reaching time-difference, i.e. G₂ ⁽²⁾(τ) centrosymmetry point, Nonlinear crystal on satellite B is with satellite A being consistent.Therefore, it is identical during DL is with formula (10).

S3, with reference to formula (9), (10), (11) and (12), | OB | of satellite O and satellite B can be expressed as：

In above formula, τ_c1And τ_c2Precision it is identical with the precision in formula (5), so, the range accuracy of | OB | can be arrived Up to 100 μm of level.

Based on the relative distance that above-mentioned quantum distance-finding method draws, the relative orbit of SFF is estimated, concrete grammar is such as Under：

As shown in figure 4, the coordinate system based on relative motion, the barycenter of satellite O based on zero, y-axis is earth centroid The direction of point coordinates origin, around the tangential direction of earth movements track, z-axis direction can be sat satellite O by the right hand based on x-axis Mark system determines.

Then, the dynamic model for guiding and protecting star B relative to main satellite O can be represented with following state vector：

In above formula, r and v represents respectively the position and speed for guiding and protecting star B relative to main satellite O.Assume major-minor satellite not Affected by perturbative force, the earth-circling track of main satellite O is approximately round, meanwhile, main satellite O and guide and protect between star B away from From also much smaller than main satellite O around Earth's orbit major semiaxis.Now, the dynamic model of the relatively main satellite O tracks of star B is guided and protected Can be described with following Hill equations (or Clohessy-Wiltshire equations)

In above formula,Relative acceleration is represented respectively, and n is the angular velocity of main satellite.

The state equation of the relative orbit represented according to equation (14), equation (15) is as follows：

Here, A represents sytem matrix, t express times, and n is the angular velocity of main satellite O, and G is system noise matrix, and W is to be System noise.

The elevations angle and orientation of the star B relative to main satellite O positions is guided and protected by a spaceborne photographing unit measurement on main satellite O Angle (measurement progress can reach 0.01 ° of rank), just can obtain measurement vector as follows：

Z=[r θ φ]^T(17)

Wherein, r is that main satellite O is drawn in step S3 and the relative distance of star B is guided and protected, the relatively main satellite O of satellite B supplemented by θ The elevation angle of position, the azimuth of the relatively main satellite O of satellite B supplemented by φ；

Then, further obtain measuring equation and be：

Wherein, [v_r v_θ v_φ]^TIt is measurement noise.

Then obtain as follows with regard to the measurement Jacobean matrixes of Kalman filter (EKF)：

In above formula,

Finally, with EKF, the estimation of track is completed

For a person skilled in the art, technical scheme that can be according to more than and design, provide various corresponding Change and deform, and all these changes and deformation should be construed as being included within the protection domain of the claims in the present invention.

Claims (5)

1. a kind of Satellite Formation Flying relative orbit method of estimation found range based on quantum, the main satellite O of Satellite Formation Flying and two guide and protect Star A and B constitute triangular structure, it is characterised in that methods described comprises the steps：

Step 1, guides and protect star A converting unit processes under its Spontaneous Parametric and produces the not conllinear entangled photon pairs in the direction of propagation, The entangled photon pairs include unused photon and signal photon；Unused photon and signal photon are unused simultaneously from star A is guided and protected The light path of photon is A → B → O → B → A, and the light path of signal photon is A → O → A, is finally measured between two-way photon Reaching time-difference；

Step 2, similarly, guides and protect star B converting unit processes under its Spontaneous Parametric and produces that the direction of propagation is not conllinear tangles To rear, unused photon and signal photon set out photon simultaneously, wherein the light path of unused photon is B → O → A → O → B, signal The light path of photon is B → A → B, finally measures the reaching time-difference of two-way photon；

Step 3, the reaching time-difference measured according to step 1 and 2 calculates main satellite O and guides and protect relative distance | OB | of star B；

Step 4, sets up based on the coordinate system of relative motion, the barycenter of satellite O based on zero, and y-axis is that earth centroid is pointed to The direction of zero, around the tangential direction of earth movements track, z-axis direction can pass through right-handed coordinate system to satellite O based on x-axis It is determined that；

Then, the dynamic model for guiding and protecting star B relative to main satellite O can be represented with following state vector:

$X\left(t\right)={\left(\begin{array}{cc}r& v\end{array}\right)}^T={\left(\begin{array}{cccccc}x,& y,& z,& \stackrel{\·}{x},& \stackrel{\·}{y},& \stackrel{\·}{z}\end{array}\right)}^T;$

In above formula, r and v represents respectively the position and speed for guiding and protecting star B relative to main satellite O；Major-minor satellite does not receive perturbative force Impact, the earth-circling track of main satellite O is approximately round, meanwhile, main satellite O and to guide and protect the distance between star B also remote little In main satellite O around Earth's orbit major semiaxis；Now, the dynamic model for guiding and protecting the relatively main satellite O tracks of star B can be with such as Under Hill equations description：

$\stackrel{\·\·}{x}=-2n\stackrel{\·}{y}$

$\stackrel{\·\·}{y}=3n^{2}y+2n\stackrel{\·}{x}$

$\stackrel{\·\·}{z}=-n^{2}z;$

In above formula,Relative acceleration is represented respectively, and n is the angular velocity of main satellite O；

Show that the state equation of relative orbit is as follows according to dynamic model described above and Hill equations：

$\stackrel{\·}{X}\left(t\right)=AX\left(t\right)+GW=\left[\begin{array}{cccccc}0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& -2n& 0\\ 0& 0& 0& 2n& 3n^2& 0\\ 0& 0& 0& 0& 0& -n^2\end{array}\right]X\left(t\right)+GW;$

Here, A represents sytem matrix, t express times, and n is the angular velocity of main satellite O, and G is system noise matrix, and W is system noise Sound；

Step 5, by a spaceborne photographing unit measurement on main satellite O the elevations angle and side of the star B relative to main satellite O positions is guided and protected Parallactic angle, just can obtain measurement vector as follows：

Z=[r θ φ]^T；

Wherein, r is that main satellite O is drawn in step 3 and the relative distance of star B is guided and protected, the relatively main satellite O positions of satellite B supplemented by θ The elevation angle, the azimuth of the relatively main satellite O of satellite B supplemented by φ；

Then, further obtain measuring equation and be：

$Z_k=\left[\begin{array}{c}\sqrt{x^2+y^2+z^2}\\ \arctan (x/y)\\ \arctan (z/\sqrt{x^2+y^2})\end{array}\right]+\left[\begin{array}{c}{v}_r\\ v_{\mathrm{\θ}}\\ v_{\mathrm{\φ}}\end{array}\right];$

Wherein, [v_r v_θ v_φ]^TIt is measurement noise；

Step 6, obtains as follows with regard to the measurement Jacobean matrixes of Kalman filter：

$H=\left[\begin{array}{cccccc}\frac{x}{\left|r\right|}& \frac{y}{\left|r\right|}& \frac{z}{\left|r\right|}& 0& 0& 0\\ \frac{y}{x^2+y^2}& \frac{-x}{x^2+y^2}& 0& 0& 0& 0\\ \frac{-xz}{|r{|}^2\sqrt{x^2+y^2}}& \frac{-yz}{|r{|}^2\sqrt{x^2+y^2}}& \frac{\sqrt{x^2+y^2}}{|r{|}^2}& 0& 0& 0\end{array}\right];$

In above formula,

Step 7, with Kalman filter, completes the estimation of track.

2. a kind of Satellite Formation Flying relative orbit method of estimation found range based on quantum according to claim 1, its feature exists In the step 1 is specifically included：

Step 1.1, signal photon after the inside light path that a two-face mirror by set by guiding and protecting star A is oriented to, by auxiliary One emitter of satellite A is sent to main satellite O, and the relative position of the two-face mirror is fixed；Then by main satellite O Angle idol prismatic reflection is returned to guides and protect star A, is collected by a photon receiver for guiding and protecting star A, by identical inside light path Behind footpath, recorded by a photon detector in the presence of polarization beam splitter, and be converted to corresponding photoimpact；

Step 1.2, while signal photon is sent to main satellite O, unused photon is by guiding and protecting the other two-face mirror of star A Another emitter that star A is guided and protected after the inside light path of guiding is sent to up to star B is guided and protected, and via star B is guided and protected Da Zhuwei is sent to Star O, and be reflected back finally along former road and guide and protect star A, the relative position of the other two-face mirror is fixed；By identical After internal light path, recorded and be converted to by another photon detector guided and protected on star A in the presence of polarization beam splitter Corresponding photoimpact；

Step 1.3, the two-way photoimpact obtained in step 1.1 and 1.2 is sent into and guides and protect the time amplitude converter of star A-many In Multiple Channel Analysis instrument system, time amplitude converter is first passed around, export a pulse for being proportional to reaching time-difference；Then should Pulse is received and processed by multichannel analyser, analyzes the time of advent of the photon beam received by two photon detectors, and Draw reaching time-difference.

3. according to claim 1 it is a kind of based on quantum find range Satellite Formation Flying relative orbit method of estimation, it is characterised in that The step 2 is specifically included：

Step 2.1, signal photon after the inside light path that a two-face mirror by set by guiding and protecting star B is oriented to, by auxiliary One emitter of satellite B is sent to guides and protect star A, and the angle idol prismatic reflection then guided and protected on star A is returned to guides and protect star B, described The relative position of two-face mirror is fixed；Pass through identical interior lights after being collected by a photon receiver for guiding and protecting star B Path, corresponding photoelectricity arteries and veins is recorded and is converted in the presence of polarization beam splitter by the photon detector guided and protected on star B Punching；

Step 2.2, while signal photon is sent to and guides and protect star A, unused photon is led by the other two-face mirror for guiding and protecting star B To inside light path after guided and protected another emitter of star B and be sent to up to main satellite O, be sent to up to guiding and protecting star via main satellite O A, and be reflected back finally along former road and guide and protect star B, the relative position of the other two-face mirror is fixed；Return to and guide and protect after star B, By identical inside light path, recorded by another photon detector guided and protected on star B in the presence of polarization beam splitter And be converted to corresponding photoimpact；

Step 2.3, the two-way photoimpact in step 2.1 and 2.2 is sent into the time amplitude converter-multichannel for guiding and protecting star B In analyzer system, time amplitude converter is first passed around, export a pulse for being proportional to reaching time-difference；Then the pulse Received and processed by multichannel analyser, analyze the time of advent of the photon beam received by two photon detectors.

4. a kind of Satellite Formation Flying relative orbit method of estimation found range based on quantum according to claim 1, its feature exists In the calculating process of main satellite O and relative distance | the OB | for guiding and protecting star B is specifically included in the step 3：

1) state of signal photon and unused photon is described with following formula：

|Ψ>It is the state vector in Hilbert space,J=i, s are respectively relative to signal photon and the rising of unused photon is calculated Symbol, d is differentiating operator, and footnote s and i represent respectively signal photon and unused photon, ω_pRepresent pumping light frequency, Ω=ω_s- ω_p/ 2=ω_p/2-ω_i, ω_iAnd ω_sIt is respectively the frequency of unused photon and signal photon, coefficient c depends on the intensity of pump light And susceptibility, F (Ω) is the spectrum amplitude of signal photon and unused photon radiation；

2) the second order Glauber correlation functions of the time of advent are defined as follows：

$\begin{array}{c}{G}^{\left(2\right)}\left(t_s,r_s;t_i,r_i\right)\\ =<E^{(-)}\left(t_s,r_s\right)E^{(-)}\left(t_i,r_i\right)E^{(+)}\left(t_i,r_i\right)E^{(+)}\left(t_s,r_s\right)>\\ =|\&Integral;d\mathrm{\&Omega;}F\left(\mathrm{\&Omega;}\right)e^{-i\mathrm{\&Omega;}\left(t_i^{\&prime;}-t_s^{\&prime;}\right)}{|}^2\end{array};$

Wherein, (r_s,t_s) and (r_i,t_i) represent space-time on two points, r_iRepresent the reference path of known unused photon, r_sTable Show unknown signal photon path, t_sAnd t_iRespectively time of advent of signal photon and unused photon；Simultaneouslyj =s, i, t '_jRepresent propagation time of the photon in nonlinear crystal；

In the case of smoothly, G⁽²⁾(t_s,r_s；t_i,r_i) depending on time difference t for reaching_i-t_s, it is converted under Spontaneous Parametric Journey, has

$F\left(\mathrm{\&Omega;}\right)=e^{\frac{-i\mathrm{\&Omega;}DL}{2}}\sin c\left(\frac{\mathrm{\&Omega;}DL}{2}\right);$

Wherein, L is the length of nonlinear crystal, and the nonlinear crystal is that, used as the stock for producing Entangled State photon, D is The inverse of the group velocity difference of entangled photon pairs；Then, the second order Glauber correlation functions of the time of advent may be calculated

$G^{\left(2\right)}\left(\mathrm{\&tau;}\right)=|\&Integral;d\mathrm{\&Omega;}\sin c\left(\frac{\mathrm{\&Omega;}DL}{2}\right)e^{-i\mathrm{\&Omega;}\&lsqb;\mathrm{\&tau;}+\frac{DL}{2}-(\frac{r_s}{c}-\frac{r_i}{c})\&rsqb;}{|}^2;$

Obvious, can obtain：

$r_s-r_i=c({\mathrm{\&tau;}}_c+\frac{DL}{2});$

Wherein, τ_cIt is reaching time-difference, that is to say expression formula G⁽²⁾(τ) symmetrical centre, and determined by multichannel analyser；

3) fromCan release, the time delay Δ t in step 1 between two paths of signals₁With in step 2 two The time delay Δ t of road signal₂：

${\mathrm{\&Delta;t}}_1={\mathrm{\&tau;}}_{c1}+\frac{DL}{2};$

${\mathrm{\&Delta;t}}_2={\mathrm{\&tau;}}_{c2}+\frac{DL}{2};$

τ_c1For the reaching time-difference measured in step 1, τ_c2It is the reaching time-difference measured in step 2；

4) can be respectively obtained according to the time of advent of two-way photon in the time of advent of two-way photon in step 1 and step 2 Following equation：

2 (| AB |+| OB |-| OA |)=c Δ t₁；

2 (| OA |+| OB |-| AB |)=c Δ t₂；

5) according to obtaining 3) and 4) relative distance | OB | and be:

$\left|OB\right|=\frac{1}{4}c({\mathrm{\&Delta;t}}_1+{\mathrm{\&Delta;t}}_2)=\frac{1}{4}c({\mathrm{\&tau;}}_{c1}+{\mathrm{\&tau;}}_{c2}+DL).$

5. a kind of quantum distance-measuring equipment, estimates for being based on the Satellite Formation Flying relative orbit that quantum is found range as claimed in claim 1 Method, it is characterised in that including following several parts：

Converting unit under Spontaneous Parametric, is entangled photon pairs for converted photons signal；

Polarization beam splitter, for can reflective vertical polarized light and refraction horizontal polarization light；

Four sides reflecting mirror, for reflecting entangled photons；

Emitter, for transmitting entangled photons target satellite is reached；

Photon receiver, for receiving the photon from target satellite；

Photon detector, for exciting as photoimpact and recording the time of advent of photon by photon signal；

In addition, the quantum distance-measuring equipment also includes time amplitude converter -- multichannel analyzer system and angle idol prism.