CN101915926B - Method for confirming one-way distance in satellite laser ranging (SLR) - Google Patents

Abstract

The invention relates to a method for confirming one-way distance in satellite laser ranging (SLR), which comprises the following steps of: acquiring SLR data by utilizing an SLR telescope; and calculating relatively accurate uplink or downlink distance in laser ranging by utilizing a measurement value. Particularly, when a track is confirmed by using single-station ranging and angle measurement, a complete vector having accurate length (ranging value) and accurate direction value in space is needed, and the calculating method of the invention is quite applicable. In short, the method for calculating the one-way distance is more explicit in physical significance and clearer in space geometry.

Description

Definite method of one-way distance in a kind of satellite laser ranging (SLR)

Technical field

The present invention relates to definite method of one-way distance in a kind of satellite laser ranging (SLR).

Background technology

In year surplus satellite laser ranging (SLR) (Satellite Laser Ranging is called for short SLR) work has carried out 40, the SLR technology is to utilize Laser Measurement to find range the two-way time between ground and satellite.SLR only single measurement just can calculate absolute distance, has measuring accuracy and waits technical characterstic with find range from basic haveing nothing to do, and distance accuracy is brought up to present inferior centimeter order by initial meter level, develops to the millimeter class precision at present.Along with the continuous accumulation of SLR observational data, the SLR technology has obtained using widely in geodynamics and geodesy field.Measure how much analytical expression between survey station and the satellite about how utilizing measured value to set up; Utilize the laser ranging data to confirm in the works of satellite orbit in some elaborations; All enumerated two kinds of laser ranging models, promptly instantaneous laser ranging is separated laser ranging (being also referred to as the two-way laser range finding) with the band light time.Wherein, being defined as of instantaneous laser ranging:

$\mathrm{\ρ}=\frac{1}{2}c(t_3-t_1)---\left(1\right)$

Wherein, c is the light velocity, t ₃, t ₁Represent that respectively survey station receives and launch the moment of laser, constantly with central authorities

Be illustrated in this moment satellite and survey station between geometric distance be ρ.It is a notional distance, rather than the measuring distance of the point-to-point transmission that interrelates through the light signal in the space.Obviously, because survey station moves x time t with earth rotation ₁With the t time of reception ₃Survey station is arranged in 2 different points of space, and satellite is more residing when they and satellite reflection laser constitutes two light, i.e. so-called " up light " and " descending light " (seeing shown in Figure 1).And c (t ₃-t ₁) in fact represented up smooth row distance ρ _UWith Bottom Runby ρ _DSum.Because the distance of survey station and satellite is not the linear function of time, use

$\mathrm{\ρ}=\frac{1}{2}({\mathrm{\ρ}}_D+{\mathrm{\ρ}}_U)=\frac{1}{2}c(t_3-t_1)---\left(2\right)$

Promptly use, the mean value of Bottom Runby sum representes central authorities'

corresponding distance constantly, has deviation in theory.

When using the laser measurement satellite distance, the research station is at first at t ₁To the satellites transmits laser signal, be called upward signal constantly.This signal after the laser reflector on satellite reflection again by this research station at t ₃Receive.Return the signal of research station by satellite reflection and claim downgoing signal.The Top Runby of laser signal and the mean value of Bottom Runby are as theoretical value, and the moment t of downgoing signal is received in the research station ₃(perhaps transmit uplink signal t constantly ₁) as the markers of observed quantity.The laser ranging of this mode is called the laser ranging of being with the light time to separate.For the laser ranging of " band light time separate ", though considered the Top Runby and the Bottom Runby of light respectively, and provided by satellite motion model r (t) and survey station motion model R (t) and obtain concrete calculated value through iterative.Concrete computing method are following:

Provide the explanation of using each amount in the calculating earlier:

t ₁-laser is from survey station RP x time;

t ₂-laser arrives the moment of satellite;

t ₃-return laser beam arrives the moment of survey station RP;

The C-light velocity;

Δ T _UΔ T between the-up light time _U=t ₂-t ₁

Δ T _DΔ T between the-descending light time _D=t ₃-t ₂

R (the t)-position vector of satellite in reference frame;

R (the t)-position vector of survey station RP in reference frame.

Can draw following light time equation by the simple geometric relation:

$\mathrm{\Δ}{T}_D=\frac{1}{c}|r(t_3-\mathrm{\Δ}{T}_D)-R\left(t_3\right)|---\left(3\right)$

Obviously, this equation can be found the solution with following iterative relation formula

$\mathrm{\Δ}{T}_D^{(n+1)}=\frac{1}{c}|r(t_3-\mathrm{\Δ}{T}_D^{\left(n\right)})-R\left(t_3\right)|---\left(4\right)$

Setting limit difference scope by present precision of laser ranging is 1ps=10 ^-12Sec obtains Δ T in this limit difference inner iteration _D, Δ T has been arranged _DAfterwards, utilize following formula to ask Δ T _U

$\mathrm{\Δ}{T}_U=\frac{1}{c}|r(t_3-\mathrm{\Δ}{T}_D)-R(t_3-\mathrm{\Δ}{T}_D-\mathrm{\Δ}{T}_U)|---\left(5\right)$

By following iterative relation formula, solve Δ T equally _U

$\mathrm{\Δ}{T}_U^{(n+1)}=\frac{1}{c}|r(t_3-\mathrm{\Δ}{T}_D)-R(t_3-\mathrm{\Δ}{T}_D-\mathrm{\Δ}{T}_U^{\left(n\right)})|---\left(6\right)$

The Δ T that resolves out with formula (3), (5) _UAnd Δ T _D, Top Runby is just arranged certainly

ρ _U＝cΔT _U，(7)

Bottom Runby ρ _D=c Δ T _D(8)

With

to indicate the central moments

the corresponding distance.The resulting distance value of this distance measurement mode is the calculated value of laser ranging, generally is used for data pre-service O-C residual error and handles.

Many to artificial satellite tracking observation means at present; By and large, if every kind of technology correspondence all is global observational data, and can obtain abundant high precision data; Utilize the observation orbit determination of monotechnics so, also can reach high-precision orbit determination result.But actual conditions are really not so; For example the SLR technology is exactly effectively a kind of technological means, also is that present distance accuracy is the highest, because the restriction of observation condition; Cause the SLR observational data less relatively, and need the data of at least three survey station simultaneous observations with SLR data orbit determination.In addition, single station short arc SLR data can not be used for orbit determination.When single station has range finding and angle measurement data simultaneously; Satellite different observation vectors constantly in the survey station coordinate system have been equivalent to directly obtain in principle; It is unchallenged utilizing these observation vectors to come orbit determination; And in this observation vector most critical amount, be exactly that survey station is to the accurate one-way distance of satellite.Here the one-way distance of mentioning, the deflection that is carved into satellite in the time of must following survey station any is strictly corresponding one by one.Obviously, the distance value of being mentioned in the two kinds of range findings in the front model does not meet the demands.Here the problem of being discussed is the laser ranging data pre-service to near-earth satellite, and generally, available laser ranging observed reading is (t ₃, t ₁), how to utilize these two observed readings accurately to obtain the moment t that laser reaches satellite ₂, just obtain Top Runby (one-way distance) ρ accurately _U=c (t ₂-t ₁) be exactly the problem that the present invention need solve.

Summary of the invention

The purpose of this invention is to provide a kind of definite method that has more one-way distance in the physical significance satellite laser ranging (SLR).

The computing method of one-way distance measured value of the present invention are following:

By Laser emission moment t ₁, utilize alternative manner to ask up light time Δ T _U

$\mathrm{\Δ}{T}_U=\frac{1}{c}|r(t_1+\mathrm{\Δ}{T}_U)-R\left(t_1\right)|---\left(10\right)$

Equally, use the t time of reception ₃, utilize alternative manner to ask descending light time Δ T _D

$\mathrm{\Δ}{T}_D=\frac{1}{c}|r(t_3-\mathrm{\Δ}{T}_D)-R\left(t_3\right)|---\left(11\right)$

Undoubtedly, Δ T _UWith Δ T _DValue depend on model r (t) and R (t), and respectively as the t of epoch time ₃And t ₁If the model that adopts has been represented truth really, three physical events that interrelate with light signal that in the space-time reference frame, take place so should satisfy following formula:

t ₃-t ₁＝ΔT _U+ΔT _D (12)

Actual conditions always have the value of not meeting, and show that model and actual conditions have deviation, promptly

Δt＝(t ₃-t ₁)-(ΔT _U+ΔT _D)≠0(13)

The present invention utilizes discrepancy Δ t to revise r just, in the data preprocessing process, earlier abnormality value removing is fallen, and works as in the observed reading after processing

(t ₃-t ₁)＞(ΔT _U+ΔT _D) (14)

The time, show that satellite position (model value) is near partially with respect to the survey station position, need a reduction Δ r, get

$\mathrm{\Δr}=0.618\frac{c[(t_3-t_1)-(\mathrm{\Δ}{T}_U+\mathrm{\Δ}{T}_D)]}{2}\left(\frac{r-R}{|r-R|}\right)---\left(15\right)$

With new r through revising _New=r+ Δ r, (16) are updated to formula (10), (11), calculate the Δ T that makes new advances _UWith Δ T _D, again and observed reading (t ₃-t ₁) relatively, can obtain Δ r again with corrected value formula (15), so repeat down, in limit poor (1ps) scope of setting, reach $(t_3-t_1)-(\mathrm{\Δ}{T}_U+\mathrm{\Δ}{T}_D)\≅0.$

The Δ T that solve this moment _UWith Δ T _D, just should be to meet observation actual up light time and descending light time, also just can obtain Top Runby respectively certainly

ρ _U＝cΔT _U (17)

With Bottom Runby ρ _D=c Δ T _D(18)

Simultaneously can basis

ΔT _U＝t ₂-t ₁ (19)

Or Δ T _D=t ₃-t ₂(20)

Confirm to be positioned at Laser emission t constantly ₁Reach the t time of reception ₃Between laser pulse arrive the moment t of satellite ₂

Measured value Laser emission moment t according to land station's acquisition ₁And the echo t time of reception ₃, can derive the moment t that laser arrives satellite accurately ₂, and corresponding Top Runby ρ _UWith Bottom Runby ρ _DDescribe the motion r (t) of satellite with time t as the general markers of system, the expression formula of corresponding Top Runby and Bottom Runby then is:

${\mathrm{\ρ}}_U=\sqrt{{[r\left(t\right)-R(t-\mathrm{\Δ}{T}_U)]}^T[r\left(t\right)-R(t-\mathrm{\Δ}{T}_U)]}---\left(21\right)$

${\mathrm{\ρ}}_D=\sqrt{{[r\left(t\right)-R(t+\mathrm{\Δ}{T}_D)]}^T[r\left(t\right)-R(t+\mathrm{\Δ}{T}_D)]}---\left(22\right)$

Each variable symbol definition is as follows in the formula (21):

ρ _U: the laser ranging Top Runby

R (t): satellite is at time t position vector constantly

R (t-Δ T _U): laser ranging stands in (t-Δ T _U) constantly position vector

Each variable symbol definition is as follows in the formula (22):

ρ _D: the laser ranging Bottom Runby

R (t): satellite is at time t position vector constantly

R (t+ Δ T _D): laser ranging stands in (t+ Δ T _D) constantly position vector

As if above-mentioned two kinds of calculating are of equal value, in use more have positive effect with Top Runby.

Describe the orbital motion of satellite and the diurnal motion with earth rotation of ground survey station, in earth centroid inertial coordinate reference frame J2000.0, carry out.Because problem relates to the transmission of light signal; And need to calculate the passing time of light signal between the point of confirming; Here adopted the space-time framework of special relativity, thought that just light carries out with constant speed c in selected coordinate system, irrelevant with the movement velocity of light source.And the precision of modern surveying technology, having reached needs the general-relativistic effect of considering that gravitational field is propagated light, with call for Votes related effect of the present invention be gravitation time delay and gravitational deflection.Disposal route to the gravitation time delay is, light still is considered to be in the straight space and carries out with constant speed c, and the gravitation delay volume corrects as computable system and joins (distance value of mentioning among the present invention all representes to have done the correction of each item system) in the measured value.As for gravitational deflection, in the frame of reference that adopts, the light time error that the calculating light time uses linear light path directly to bring in separating can be ignored.

Utilize the range finding of single station, when angle measurement comes orbit determination, promptly need complete vector ρ in the space, it has precise length (distance measurement value) and accurate direction value, and computing method of the present invention are very suitable.With the one-way distance computing method that the present invention proposes, be clearer and more definite in the physical sense, also be more clearly on space geometry.

Description of drawings

Fig. 1 is survey station and the graph of a relation of satellite in laser ranging.

Embodiment

1. utilize the satellite laser ranging (SLR) telescope to obtain artificial satellite SLR data, promptly a series of (t ₃, t ₁) observed reading.

2. to observed reading (t ₃, t ₁) carrying out the data pre-service, the data pretreatment mode is following:

If t _iSatellite distance observed reading and calculated value constantly is respectively ρ _O(t _i), ρ _C(t _i), residual error does

Δρ _i＝ρ _O(t _i)-ρ _C(t _i)

At first use one with the fitting of a polynomial Δ ρ of time as independent variable _i(t), promptly

$\mathrm{\Δ}{\mathrm{\ρ}}_i\left(t\right)=a_0+a_1{t}_i+a_2{t}_i^2+...$

Can obtain undetermined coefficient a by least square method ₀, a ₁, a ₂Probability value

Residual error after the match

Then root-mean-square value is counted for the observation of this observation segmental arc for

N.

The σ that utilization is obtained accepts or rejects the judgement that Δ ρ ' carries out exceptional value, uses 2.5 σ as criterion usually, if promptly | and Δ ρ ' _i|>=2.5 σ, think that then this observation data is an exceptional value, need to reject.

3. calculate the moment t that laser arrives satellite according to the method for the invention ₂The practical implementation process illustrates as follows: explanation for ease, suppose that the survey station position coordinates is at t ₁Be R (0,0,0) constantly, at t ₃Be R (1,0,0) constantly, satellite position coordinate (Model Calculation value) is at t ₂Be r (10000,5000,5000) constantly, unit is km, and light velocity c is defined as 300000km/s.Observed reading (t ₃-t ₁) be 0.081647936482s, obtain according to above-mentioned (10), (11) formula simultaneously

(t ₃-t ₁)-(Δ T _U+ Δ T _D)=0.000001s shows that then satellite position is relative and survey station is near partially, needs to correct the satellite position coordinate, promptly

$\mathrm{\Δr}=0.618\×0.15\×\frac{1}{12247.449}\left(\begin{array}{c}10000\\ 5000\\ 5000\end{array}\right)=\left(\begin{array}{c}0.075688922\\ 0.037844461\\ 0.037844461\end{array}\right),$

So it is new

Utilize new co-ordinates of satellite calculated value, recomputate Δ T _UWith Δ T _DValue, again with observed reading relatively, obtain new Δ r, again r is revised, up to Till.According to Δ T _U=t ₂-t ₁Can accurately obtain t ₂

With t ₂Constantly represent, then utilize following one-way distance computing formula, calculate laser ranging one-way distance value with markers t.

${\mathrm{\ρ}}_U=\sqrt{{[r\left(t\right)-R(t-\mathrm{\Δ}{T}_U)]}^T[r\left(t\right)-R(t-\mathrm{\Δ}{T}_U)]}$

${\mathrm{\ρ}}_D=\sqrt{{[r\left(t\right)-R(t+\mathrm{\Δ}{T}_D)]}^T[r\left(t\right)-R(t+\mathrm{\Δ}{T}_D)]}$

Claims (1)

1. definite method of one-way distance in the satellite laser ranging (SLR) is characterized in that being undertaken by following:

1) utilizes the satellite laser ranging (SLR) telescope to obtain artificial satellite SLR data, promptly obtain a series of (t ₃, t ₁) observed reading, t ₁Be the Laser emission moment, t ₃For receiving the moment of return laser beam;

2) to observed reading (t ₃, t ₁) carry out the data pre-service, processing mode is residual analysis commonly used, and that promptly utilizes satellite does residual analysis apart from observation data and orbit prediction calculated value, and the data that surpass 2.5 σ that residual error is bigger are rejected, and σ is a root-mean-square value;

3) utilize formula (15), (16), (17), (18), (19), (20) obtain the moment t that laser arrives satellite ₂

r _new＝r+Δr (16)

ρ _U＝cΔT _U (17)

ρ _D＝cΔT _D (18)

ΔT _U＝t ₂-t ₁ (19)

Or Δ T _D=t ₃-t ₂(20)

Wherein, each variable symbol defines as follows in the above-mentioned formula:

Δ r: the reduction of satellite position vector;

R: the position vector of satellite;

R: the position vector of laser ranging station;

r _New: the satellite position vector after the correction;

C: the light velocity;

t ₃: return laser beam is accepted constantly in the laser ranging process;

t ₂: laser arrives the moment of satellite in the laser ranging process;

t ₁: Laser emission is constantly in the laser ranging process;

ρ _U: laser Top Runby in the laser ranging process;

ρ _D: laser Bottom Runby in the laser ranging process;

Δ T _U: line time on the laser in the laser ranging process;

Δ T _D: laser downgoing time in the laser ranging process;

4) with t ₂Constantly represent, utilize following one-way distance computing formula to calculate laser ranging one-way distance value with markers t;

Wherein, each variable symbol defines as follows in above-mentioned two formula:

R (t): satellite is at time t position vector constantly;

ρ _U: laser Top Runby in the laser ranging process;

R (t-Δ T _U): laser ranging stands in (t-Δ T _U) constantly position vector;

ρ _D: laser Bottom Runby in the laser ranging process;

R (t+ Δ T _D): laser ranging stands in (t+ Δ T _D) constantly position vector.

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