CN105372691B - The Long baselines satellites formation GNSS relative positioning methods that a kind of fuzziness is fixed - Google Patents
The Long baselines satellites formation GNSS relative positioning methods that a kind of fuzziness is fixed Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/42—Determining position
- G01S19/51—Relative positioning
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/40—Correcting position, velocity or attitude
- G01S19/41—Differential correction, e.g. DGPS [differential GPS]
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/42—Determining position
- G01S19/43—Determining position using carrier phase measurements, e.g. kinematic positioning; using long or short baseline interferometry
- G01S19/44—Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method
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Abstract
The Long baselines satellites formation GNSS relative positioning methods that a kind of fuzziness is fixed, it is therefore an objective to improve the precision that fuzziness fixes success rate and relative positioning result.Technical scheme is first to collect and pre-process input data, determines the absolute outline track of Satellite Formation Flying；Then the geometric distance and clock correction in difference observation data are eliminated, the single poor phase ambiguity float-solution of estimation and single poor ionosphere delay parameter, the wide lane ambiguity float-solution of double difference and covariance matrix are obtained using double difference conversion, the fixed wide lane integer ambiguity of double difference and the narrow lane integer ambiguity of double difference, finally export the relative positioning result that fuzziness is fixed.The problem of using accuracy of observation relatively low pseudo-code is strongly depend on present invention, avoiding the fuzziness fixation caused by the power processing such as pseudo-code, phase in conventional method M W combinations, improve the precision that Long baselines satellites formation GNSS relative positionings fuzziness fixes success rate and final relative positioning result, calculate stable, improve the reliability of relative positioning result.
Description
Technical field
The present invention relates to a kind of relative positioning method of aerospace measurement field medium-long baselines satellites formation, specifically one
Plant and employ GPS GNSS (Global Navigation Satellite System) measurement means and mould
The Long baselines satellites formation relative positioning method of paste degree fixed policy.
Background technology
Spaceborne GNSS uses star-star tracking mode, by installing GNSS receiver on the satellite of formation flight, using load
Wave phase difference GNSS technologies, eliminate or slacken the influence of some common errors, can provide millimetre-sized positioning precision.
Spaceborne GNSS has the advantages that round-the-clock, continuity, high accuracy, space-time covering are wide, determines to form into columns in high precision using spaceborne GNSS
The relative position of satellite has been successfully applied to the tasks such as distributed radar interference, terrestrial gravitation field measurement.
The key of Long baselines satellites formation GNSS high accuracy relative positionings is that the high success rate of phase ambiguity is fixed, GNSS
Double difference phase ambiguity has integer characteristic, if fuzziness is accurately fixed, the fuzziness parameter in double difference observation model
It can be eliminated, now phase observations data can be converted into high-precision relative distance, high-precision relative positioning can be achieved.In length
During baseline GNSS fuzzinesses are fixed, mainly influence in the ionosphere delay in GNSS signal communication process, ionosphere delay
Major part can be eliminated by difference processing, but ionosphere delay remaining after difference with the change of distance between Satellite Formation Flying it is big and
Become larger.When analyzing GNSS fuzziness fixed effects, it is reference typically with carrier phase wavelength X (20cm or so), works as star
Between distance when reaching tens kilometers even up to a hundred kilometers, remaining ionosphere delay can reach several decimeters of amounts for arriving rice after difference
Level, exceeds well over λ/4, and now its influence fixed to Phase integer ambiguity can not be ignored.According to the literature, at present on length
Baseline satellites formation GNSS relative positioning fuzzinesses are fixed, and mainly have following methods：A kind of method is Bernese softwares in early stage
Ground survey station between Kuan Xianghezhai lanes combined method is used in Long baselines GPS relative positionings, referring to Dach R etc. in 2007
" the Bernese GPS Software write:Version 5.0”.This method is first by M-W (Melbourne-W ü bbena)
Combination, eliminates the influence of geometric distance, ionosphere and clock correction, solves wide lane integer ambiguity, and then construction only has electric eliminating absciss layer
The double difference model of carrier phase observation solves narrow lane ambiguity.The shortcoming of the method is the power group such as pseudo-code, phase during M-W is combined
Closing causes wide lane integer ambiguity fixation to be strongly depend on the relatively low pseudo-code observation data of accuracy of observation, and success rate is limited, and
Once wide lane ambiguity can not be fixed, narrow lane ambiguity can be caused can not also to fix, reduce GNSS positioning precisions.It is another
Method is the sequential EKF filtering methods that Kroes R are used in GRACE double star relative positionings, referring to Kroes R in 2006
Thesis for the doctorate " Precise relative positioning of formation flying spacecraft using
GPS”.This method, come ionosphere delay random sequence remaining after approximate representation difference, is adopted with single order Gauss-Markov model
With sequential EKF filtering methods, ionosphere delay is added to as variable in filter state parameter to be estimated, in the relative rail of estimation
Ionosphere delay parameter is estimated while road parameter, the estimation and calibration of ionosphere delay is realized.The advantage of this method is energy
Enough online recurrence estimation double difference integer ambiguities, have the disadvantage if some integer ambiguity fixed error, can influence other nearby
The fixation of integer ambiguity, causes positioning precision to deteriorate, and even can cause filtering divergence when serious, leads to not output accurate
True relative positioning result.
In summary, the precision and reliability of Long baselines satellites formation GNSS relative positioning methods still await further changing
Enter.
The content of the invention
The technical problem to be solved in the present invention is：For being obscured in traditional Long baselines satellites formation GNSS relative positioning methods
The fixed not high problem of positioning precision being strongly depend on caused by pseudo-code of degree, proposes that the Long baselines that a kind of fuzziness is fixed are defended
Star formation GNSS relative positioning methods, by eliminating pseudo-code, phase differential weights in difference observation data after geometric distance, clock correction
Fuzziness is fixed in value combination, it is to avoid in conventional method M-W combination pseudo-code, phase by etc. power combine, improve fuzziness and be fixed into
The precision of power and relative positioning result.This method uses batch processing least square processing mode, calculates stable, overcomes sequential filter
The shortcoming that ripple processing method easily dissipates, improves relative positioning reliability.
Technical scheme comprises the following steps：
The first step, is collected and pretreatment input data.
1.1 collect observation data from satellite platform：GNSS observations data, satellite platform attitude data；Collect auxiliary from website
Help data：GNSS satellite precise ephemeris, clock correction and antenna phase center change PCV (Phase Center Variation) letters
Breath, earth gravitational field, earth rotation parameter, UTC (Coordinated Universal Time) time jump second data, JPL
(Jet Propulsion Laboratory) solar calendar, solar radiation flow, geomagnetic index；
The observation data of 1.2 pairs of collections are pre-processed：The GNSS outlier for observing data is rejected, and detecting phase
Cycle slip.Unruly-value rejecting and Cycle Slips Detection are shown in the monograph " Measurement that Zhengming Wang etc. were published in 2011
Section 7.2 of Data Modeling and Prameter Estimation " (measurement data is modeled and parameter Estimation).
Second step, determines the absolute outline track of Satellite Formation Flying.
Using the non-poor reduced-dynamic method (monograph published see Zhengming Wang etc. in 2011
" Measurement Data Modeling and Prameter Estimation " (measurement data model and parameter Estimation) the
7.3 sections) determine Satellite Formation Flying A, B absolute orbit position.Export Satellite Formation Flying A, B orbital mechanics model parameter yA0、yB0With
The absolute orbit position r at each moment tA(t)、rB(t), orbital position includes three cartesian components of x, y, z, and precision is several
Individual cm, is mainly used as the outline orbital position of follow-up higher precision relative positioning.
3rd step, eliminates the geometric distance and clock correction in difference observation data.
3.1 single poor relative positionings.Method is：Poor list is same GNSS satellite, the same species observed two receivers
Type observation data make the difference, and form difference observation data, eliminate GNSS satellite clock correction using the poor observational equation of the list of t (1), protect
Receiver is stayed with respect to clock correction,
Wherein t represents the observation moment, and subscript j (1≤j≤M) represents jth GNSS satellite, and M is the sum of satellite；Subscript
1st, 2 GNSS signal frequency f is represented1、f2；Δ represents single poor；ΔP1 j(t) it is in moment t frequency f1Pseudo-code difference observation data；For in moment t frequency f2Pseudo-code difference observation data；For in moment t frequency f1Time-differenced phase observation number
According to；For in moment t frequency f2Time-differenced phase observation data；A, B represent two Satellite Formation Flyings；Defended to form into columns
Star A is in moment t frequency f1Pseudo-code observation data；It is Satellite Formation Flying A in moment t frequency f2Pseudo-code observation data；
It is Satellite Formation Flying A in moment t frequency f1Phase observations data；It is Satellite Formation Flying A in moment t frequency f2Phase observations number
According to；It is Satellite Formation Flying B in moment t frequency f1Pseudo-code observation data；It is Satellite Formation Flying B in moment t frequency f2Puppet
Code observation data；It is Satellite Formation Flying B in moment t frequency f1Phase observations data；It is Satellite Formation Flying B in moment t
Frequency f2Phase observations data；
It is all from the first step observing data by pretreated GNSS；It is Satellite Formation Flying A, B in moment t and GNSS satellite j
Between the poor geometric distance of list；C represents the light velocity, δ tABFor the relative clock correction between two GNSS receivers of Satellite Formation Flying A, B；For in the poor ionosphere delay of moment t list；For kth (1≤k≤nb, nbFor continuous tracking segmental arc sum) it is individual continuous
Track segmental arc f1The poor phase ambiguity of list of frequency；For k-th of continuous tracking segmental arc f2The poor phase ambiguity of list of frequency；
ε is observation error.
Ionosphere delay is eliminated using iono-free combinationThe poor observational equation (2) of electric eliminating absciss layer list is obtained,
Wherein " IF " represents iono-free combination；For the moment t poor pseudo-code iono-free combination data of list；For the moment t poor phase iono-free combination data of list；The corresponding poor phase of list of segmental arc is continuously tracked for k-th
Electric eliminating absciss layer fuzziness.Single poor geometric distanceIt can be calculated by following formula (3),
Wherein | | represent to calculate the length of trivector；rA(t)、rB(t) it is the absolute orbit of Satellite Formation Flying A, B in moment t
Position；Be GNSS satellite j in moment t position, obtained using the IGS interpolation of the precise ephemeris afterwards meters provided.
WillIn outline pointPlace's linearisation expansion, obtains formula (4),
Represent the direction of visual lines unit vector in moment t from satellite B to GNSS satellite j；For's
Outline point, Satellite Formation Flying A, B that its initial value is obtained using second step absolute orbit position, which are calculated, to be obtained；ΔrB(t) it is to defend
Star B t orbital position improvement,
ΔrB(t)=rAC(yB0+ΔyB,t)-rAC(yB0,t) (5)
Wherein rACRepresent orbital mechanics integral function, rAC(yB0, t) represent to orbital mechanics model parameter yB0Carry out
Orbital positions of the satellite B that Adams-Cowell Multi-step Integrations are obtained in moment t.Adams-Cowell Multistep Integrators (see《My god
Literary Gazette》" with the Adams-Cowell methods of once sum " that the 4th periodical of volume 33 in 1992 is carried), integration step takes 10 seconds；
yB0、ΔyBThe initial value and improvement of satellite B orbital mechanics model parameter vector are represented respectively, mainly include initial time rail
Road position and speed, solar light pressure coefficient, atmospheric drag coefficient and experience acceleration factor；yB0The track exported using second step
Mechanical model parameter；ΔyBObtained according to following formula (6) using least-squares estimation.
The poor observational equation (2) of the electric eliminating absciss layer list at multiple moment is organized into matrix form, single poor observation corrected value is obtained
Vectorial zSD,
zSD=HSD·xSD+eSD (6)
Wherein " SD " represents single poor；Single poor observation corrected value vector
[]TRepresenting matrix transposition；Design matrixRepresent partial derivative；Error vectorParameter vector to be estimatedNow wait to estimate ginseng
Number mainly includes：Receiver is with respect to clock correction δ tAB(t) (each observation moment 1), single poor phase electric eliminating absciss layer fuzziness
(each continuous tracking segmental arc 1) and orbital mechanics model parameter improve vectorial Δ yB, wherein vectorial Δ yBInclude preliminary orbit
Position and speed parameter (3 location coordinates components and 3 speed coordinate components, altogether 6 parameters to be estimated), solar light pressure coefficient
(1 parameter to be estimated), atmospheric drag coefficient (1 parameter to be estimated) and experience acceleration parameter (every 15 minutes 1 group of parameters to be estimated).
3.2 obtain x using the estimation of weighted least-squares methodSD,
Wherein single poor observation weight matrixσLRepresent phase observations precision, σPTable
Show pseudo-code accuracy of observation.
3.3 calculate single poor geometric distance.When orbital mechanics model parameter improves vectorial Δ yBAfter being estimated, satellite rail
Road position rB(t) r is integrated by orbital mechanicsAC(yB0+ΔyB, t) obtain, then by rB(t) substitute into formula (3) renewal and calculate single poor
Geometric distance
3.4 eliminate single poor geometric distance in difference observation dataWith clock correction δ tAB(t).The list that 3.3 are obtained is poor
Geometric distanceWith 3.2 obtained clock correction δ tAB(t) deducted from the observation data in formula (1), obtain multiple moment
The poor observational equation of list (8) after geometric distance and clock correction is deducted,
Due to the phase ambiguity in 3.2 single poor relative positioningsEstimation use only iono-free combination " floating-point
Real solution form ", is not fixed, therefore obtains formation relative orbit rB(t)-rA(t) 8.2 " fixed integer behind ratio of precision
Solution form " is much lower.Nevertheless, rB(t)-rA(t) precision has also reached several mm magnitudes, far smaller than phase wave length λ's
1/4, as eliminating, the wide lane ambiguity fixed precision of geometric distance, auxiliary is enough.
4th step, the single poor phase ambiguity float-solution of estimation and single poor ionosphere delay parameter.
4.1 set the ratio between pseudo-code weights and phase weights wP:wL.Because phase observations precision is far above pseudo-code, here type B error
Code weight wPWith phase weight wLThe ratio between wP:wL.Traditional M-W methods pseudo-code and phase combination such as can only be at the power (wP:wL=1:1)
, it is impossible to give full play of the characteristics of phase data accuracy of observation is far above pseudo-code, and w of the present inventionP:wLCan according to pseudo-code and
The accuracy of observation of phase data is freely set, and generally takes wP:wL=σL:σP, σLRepresent phase observations precision, σPRepresent pseudo-code observation
Precision, this is a main advantage of the present invention compared with conventional method.
4.2 using the single poor phase ambiguity float-solution of weighted least-squares method estimation and single poor ionosphere delay parameter.
In k-th of continuous tracking segmental arc, the poor observational equation of list (8) that multiple moment are deducted into geometric distance and clock correction is organized into matrix
Form,
zk=Hk·xk+ek (9)
Wherein single poor observation correction vectorError vector
Design matrixParameter vector to be estimatedNow parameter to be estimated is main
Including：Single poor ionosphere delay(each moment 1), the poor phase ambiguity parameter of 2 listsWith
For compensating and absorbing the influence that satellites formation difference ionosphere delay is brought under Long baselines situation.Obtain xkA weighting most young waiter in a wineshop or an inn
Multiply estimateFor,
Wherein observe weight matrixDiag () represents diagonal matrix.Output estimation
Obtain the poor phase ambiguity parameter of list of k-th of continuous tracking segmental arcWith single poor ionosphere delay parameter
5th step, the wide lane ambiguity float-solution of double difference and covariance matrix are obtained using double difference conversion.
5.1 kth (1≤the k≤n for obtaining the 4th stepb) the individual continuous poor phase ambiguity parameter of list for tracking segmental arcSubtract each other, obtain the corresponding poor wide lane ambiguity of listThen nbIndividual continuous tracking segmental arc
Corresponding Dan Chakuan lanes phase ambiguity is respectivelyDefine floating-point solution vectorAnd its association side
Poor matrixThe single poor wide lane ambiguity floating-point solution vector of constructionDue to
Single differential mode type does not introduce correlation, then independently of one another, variance is single poor wide lane ambiguityNow
5.2 according to the relation between double difference and single poor observational equation, construction double difference linear transformation operator TDD, obtain double difference wide
Lane ambiguity float-solution is,
Wherein
Calculated by formula (12) and obtain the wide lane ambiguity covariance matrix of double difference
6th step, the wide lane integer ambiguity of fixed double difference.
6.1 fix the wide lane integer ambiguity of double difference using integer least square method.The wide lane ambiguity of double difference that 5th step is obtained
Spend float-solutionAnd its covariance matrixAs input, the wide lane of double difference is fixed using integer least square method whole
All fuzzinesses, that is, search for integer space and obtain the wide lane integer ambiguity fixed solution of double difference
So that formula (13) reaches minimum,
Wherein cov-1Represent the inverse of covariance matrix；Min { } represents to minimize；ZnRepresent integer space.Using minimum
Two multiply the integer solution that de-correlation (LAMBDA) scans for obtaining the wide lane phase ambiguity of double difference, LAMBDA methods referring to
" the The LAMBDA method for integer ambiguity that Paul de Jonge etc. write in 1996
estimation:Implementation aspects " (LAMBDA methods estimate the realization of integer ambiguity).
6.2 examine the wide lane integer ambiguity of double difference to fix correctness.Calculate the suboptimum integral circumference ambiguity of LAMBDA methods output
Spend corresponding fuzziness residual error amount RSFuzziness residual error amount R corresponding with optimal integer ambiguityBThe ratio between, if RS/RB≤kS/B, then
The wide lane integer ambiguity fixed solution z of double differenceW,DDIt is used, turns the 7th step；If RS/RB＞ kS/B, then it is assumed that the wide lane complete cycle mould of double difference
Paste degree fixed solution zW,DDFixation is incorrect, and the wide lane ambiguity of double difference still uses its float-solutionEven
kS/B(k is taken for given threshold valueS/B=2.5), turn the 7th step.
7th step, the narrow lane integer ambiguity of fixed double difference.
The 7.1 wide lane integer ambiguity fixed solution z of the double difference for obtaining the 6th stepW,DDAs known quantity from double difference phase observation
Deducted in equation, double difference observation includes double difference pseudo-code and double difference phase, be again to difference on the basis of single poor observational equation
The poor observation data of the list of GNSS satellite make poor, and cancellation receiver is with respect to clock correction, i.e.,
Wherein ▽ Δs represent double difference；Subscript j, k represent jth, k GNSS satellite；Between expression GNSS satellite j, k
Double difference pseudo-code electric eliminating absciss layer observation, Represent the double difference between GNSS satellite j, k
Phase electric eliminating absciss layer observation, The wide lane ambiguity of double difference is represented respectively
Degree and the narrow lane ambiguity of double difference；The double difference geometric distance between GNSS satellite j, k is represented,
The double difference phase observation equation (14) at multiple moment is organized into matrix form, multiple moment double difference observation sides are obtained
Journey (15)
zDD=HDD·xDD+eDD (15)
Wherein " DD " represents double difference；zDDVector is corrected for double difference observation,
Design matrixError vectorParameter vector to be estimated
7.2 according to multiple moment double difference observational equations (15), and using the least square estimation method, estimation obtains narrow lane phase
Fuzziness floating-point solution vectorAnd its covariance matrix
7.3 fix the narrow lane integer ambiguity of double difference using integer least square method.By narrow lane phase ambiguity float-solutionAnd its covariance matrixAs input, the narrow lane integral circumference ambiguity of double difference is fixed using integer least square method
Degree, search integer space obtains the narrow lane integer ambiguity fixed solution of double differenceSo that formula (16)
Reach minimum,
7.4 examine the narrow lane integer ambiguity of double difference to fix correctness.Calculate the corresponding fuzziness of suboptimum integer ambiguity residual
Residual quantity RSFuzziness residual error amount R corresponding with optimal integer ambiguityBThe ratio between, if RS/RB≤kS/B(take kS/B=2.5), then double difference
Narrow lane integer ambiguity fixed solution zN,DDIt is used, turns the 8th step；If RS/RB＞ kS/B, then it is assumed that the narrow lane integer ambiguity of double difference
Fixed solution zN,DDFixation is incorrect, and the narrow lane ambiguity of double difference still uses its float-solutionEvenTurn the 8th
Step.
8th step, the relative positioning result that output fuzziness is fixed.
The 8.1 narrow lane integer ambiguity fixed solutions of the double difference for obtaining the 7th stepAs known quantity again from double
Deducted in poor phase observations equation (14), obtain deducting the double difference observational equation (17) after fuzziness.
Double difference observational equation (17) after the deduction fuzziness at multiple moment is organized into matrix form, multiple moment are obtained
Deduct the double difference observational equation (18) after fuzziness
Wherein double difference observation correction is vectorial,
Design matrixParameter vector Δ y to be estimatedBVector is improved for orbital mechanics model parameter.
8.2 deduct the double difference observational equation (18) after fuzziness according to multiple moment, using the least square estimation method, estimate
Meter obtains orbital mechanics model parameter and improves vectorial Δ yB, satellite orbital position rB(t) r can be integrated by orbital mechanicsAC(yB0+
ΔyB, t) obtain, so as to export the formation relative orbit r after final fuzziness is fixedB(t)-rA(t).It is single poor relatively fixed with 3.1
Position is compared, and phase ambiguity is fixed in the form of Kuan Xianghezhai lanes in 8.2, therefore 8.2 obtain after final fuzziness fixation
Formation relative orbit precision it is more much higher than 3.1 " float-solution forms ".
The present invention has the following advantages that compared with prior art：
The present invention eliminates difference geometric distance and clock correction using relative positioning float-solution, passes through pseudo-code, phase differential weights group
Close to estimate single poor phase ambiguity and ionosphere delay parameter, and the wide lane ambiguity float-solution of double difference is obtained by double difference conversion
And its covariance matrix, and then realize that wide lane integer ambiguity is fixed using integer least square method, it is to avoid conventional method
Fuzziness in M-W combinations caused by the power processing such as pseudo-code, phase, which is fixed, is strongly depend on asking for the relatively low pseudo-code of accuracy of observation
Topic, improves the precision that Long baselines satellites formation GNSS relative positionings fuzziness fixes success rate and final relative positioning result.
The present invention uses batch processing least square processing mode, calculates stable, even if local segmental arc fuzziness is fixed wrong
Mistake also can't cause the algorithm of whole period not restrained, and overcome the shortcoming that Sequential filter processing method easily dissipates, carry
The reliability of high relative positioning result.
The method of the present invention has versatility, it is adaptable to the high accuracy of Long baselines satellites formation and other moving targets
GNSS relative positioning applications.
Brief description of the drawings
Fig. 1 is Long baselines satellites formation GNSS relative positioning fuzziness fixed solution flow charts of the invention；
Fig. 2 is the single poor ionosphere delay estimated result figure of GRACE formation of the invention.
Fig. 3 is the present invention and conventional method GRACE formation positioning precision comparison charts；
Embodiment
The present invention is described further below in conjunction with the accompanying drawings.By taking GRACE satellites formation GNSS relative positionings as an example, the volume
The km of interstellar distance 140 in team in January, 2006, belongs to typical Long baselines satellites formation, chooses on 2 1st, 2006
Totally 7 days in-orbit measured datas to 7 days.As shown in figure 1, the Long baselines satellites formation GNSS phases that a kind of fuzziness of the present invention is fixed
Localization method is comprised the following steps：
The first step, is collected and pretreatment input data.
Observation data are collected from satellite platform and collect assistance data (being shown in Table 1) from website.To 7 days GRACE satellites formations
GNSS observations data pre-processed, mark outlier and cycle slip, and by pretreated daily data in text form
Preserve, export pretreated GNSS observation data files (* .edt).
Table 1 observes data and auxiliary positioning input data
| Sequence number | Data type | Remarks |
| 1 | GNSS observes data | Passed above and below Rinex (* .yyo), GNSS receiver, star |
| 2 | Satellite platform attitude data | Passed above and below quaternary number (* .att), star |
| 3 | GNSS satellite ephemeris | Download Rinex (* .sp3), website |
| 4 | GNSS satellite clock correction | Download Rinex (* .clk), website |
| 5 | GNSS antenna PCV information | Download igs08.atx, website |
| 6 | Earth gravitational field | Download GGM02C, website |
| 7 | Earth rotation parameter | Download IERS 2000A, website |
| 8 | UTC time jump second | Download TAI-UTC, website |
| 9 | JPL solar calendars | Download DE405, website |
| 10 | Solar radiation flow | Daily 1 record, website is downloaded |
| 11 | Geomagnetic index | Every 3 hours 1 record, website is downloaded |
Second step, determines the absolute outline track of every Satellite Formation Flying.
Using non-poor reduced-dynamic method, pretreated GNSS observations data file is handled, GRACE is exported
The outline orbital mechanics model parameter of A and GRACE B satellites and absolute orbit position.For the km of interstellar distance 140
GRACE forms into columns, in order that relative positioning reaches 1mm precision, now requires that absolute orbit Product Precision needs to be better than 10cm.Table 2
Give the GRACE satellites formations 2006 year 2 month absolute orbit product of 1 to 7 and science track comparison result, it is seen that three-dimensional
Trajectory accuracy has averagely reached 3.5cm or so, meets follow-up high-precision relative positioning needs.
The GRACE formation absolute orbit products of table 2 and science track comparison result
3rd step, eliminates the geometric distance and clock correction in difference observation data.
Single poor relative positioning is carried out, the orbital mechanics model parameter and track of the GRACE B satellites that second step is obtained is improved
Position, obtains single poor relative positioning float-solution.Calculate single poor geometric distance, eliminate in difference observation data single poor geometric distance and
Clock correction.Table 4 gives the GRACE satellites formations 2006 year 2 month list of 1 to 7 poor relative positioning float-solution precision, it is seen that it is put down
Equal precision has reached the 1/4 of 4mm or so, far smaller than phase wave length λ, as elimination geometric distance and the wide lane ambiguity of auxiliary
Spend fixed precision enough.
The KBR of the single poor relative positioning float-solution of the GRACE of table 4 formation checks precision
| Date | KBR compares standard deviation/mm |
| 2006-02-01 | 2.90 |
| 2006-02-02 | 3.70 |
| 2006-02-03 | 4.38 |
| 2006-02-04 | 4.59 |
| 2006-02-05 | 3.82 |
| 2006-02-06 | 4.23 |
| 2006-02-07 | 4.17 |
| Average value | 3.97 |
4th step, pseudo-code, phase differential weights value are combined, and single poor phase ambiguity floating-point is estimated using least square method
Solution and single poor ionosphere delay parameter.
The ratio between the pseudo-code weights and phase weights of GRACE satellites w is setP:wL=1:100, the deduction obtained to the 3rd step
The poor pseudo-code of list and phase observations equation after geometric distance and clock correction are solved using least square method, the single poor phase ambiguity of output
Spend float-solution and single poor ionosphere delay parameter estimated result.Fig. 2 gives the estimation knot that GRACE forms into columns single poor ionosphere delay
Really, it is seen that difference ionosphere delay has reached 3 meters or so, hence it is evident that more than the 1/4 of phase wave length λ, therefore for Long baselines situation
Lower satellites formation, ionosphere delay influence can not directly be eliminated by difference, and it can not be ignored to fuzziness fixed effect, must
Must be by increasing parameter compensation absorption.
5th step, the wide lane ambiguity float-solution of double difference and covariance matrix are obtained using double difference conversion.
The poor phase ambiguity float-solution of different frequency list that 4th step is obtained subtracts each other, and obtains single poor wide lane ambiguity floating-point
Solution, and according to double difference and it is single it is poor between relation, by double difference linear transformation, calculating obtain the wide lane ambiguity float-solution of double difference and
Covariance matrix.
6th step, the wide lane integer ambiguity of fixed double difference.
The wide lane ambiguity float-solution of double difference and its covariance matrix that 5th step is obtained are minimum using integer as input
Least square method fixes the wide lane integer ambiguity of double difference.Table 5 gives GRACE satellites formations 2006 year 2 month 1 to 7, the present invention
With the wide lane ambiguity success rate comparing result of traditional M-W methods, it is seen that it is relative that integer ambiguity of the invention fixes success rate
5% is improved in traditional M-W methods.
The wide lane ambiguity success rate of GRACE formation of the present invention of table 5 and conventional method are contrasted
7th step, the narrow lane integer ambiguity of fixed double difference.
The wide lane integer ambiguity fixed solution of double difference that 6th step is obtained is as known quantity from double difference phase observation equation
It is middle to deduct, narrow lane phase ambiguity floating-point solution vector and its covariance matrix are obtained using the least square estimation method estimation, adopted
The narrow lane integer ambiguity of double difference is fixed with integer least square method.
8th step, the relative positioning result that output fuzziness is fixed.
The narrow lane integer ambiguity fixed solution of double difference that 7th step is obtained is as known quantity from double difference phase observation equation
Deduct, using the least square estimation method, estimation obtains orbital mechanics model parameter and improves vector, defeated after orbit integration
Go out the formation relative orbit after final fuzziness is fixed.Fig. 3 gives the GRACE formation relative positionings of the present invention and conventional method
KBR comparison results, it is seen that the present invention is also effectively improved relative positioning while integer ambiguity fixation success rate is improved
As a result precision, KBR compares standard deviation and is significantly reduced, and average result is reduced to 0.78mm by the 0.91mm of conventional method,
Positioning precision is significantly improved, and many days result of calculation is relatively stablized.
Claims (4)
1. the Long baselines satellites formation GNSS relative positioning methods that a kind of fuzziness is fixed, it is characterised in that comprise the following steps：
The first step, is collected and pretreatment input data：
1.1 collect observation data from satellite platform：GNSS observations data, satellite platform attitude data；Supplementary number is collected from website
According to：GNSS satellite precise ephemeris, clock correction and antenna PCV information, earth gravitational field, earth rotation parameter, UTC time jump second number
According to, JPL solar calendars, solar radiation flow, geomagnetic index；
The observation data of 1.2 pairs of collections are pre-processed：The GNSS outlier for observing data is rejected, and detecting phase week
Jump；
Second step, determines Satellite Formation Flying A, B absolute orbit position, output Satellite Formation Flying A, B orbital mechanics model parameter yA0、
yB0With each moment t absolute orbit position rA(t)、rB(t), orbital position includes three cartesian components of x, y, z；
3rd step, eliminates the geometric distance and clock correction in difference observation data：
3.1 single poor relative positionings, method is：Poor list is that same GNSS satellite, the same kind of two receivers observation are seen
Survey data to make the difference, form difference observation data, GNSS satellite clock correction is eliminated using the poor observational equation of the list of t (1), reservation connects
Receipts machine with respect to clock correction,
Wherein t represents the observation moment, and subscript j represents jth GNSS satellite, 1≤j≤M, and M is the sum of satellite；Subscript 1,2 tables
Show GNSS signal frequency f1、f2；Δ represents single poor；ΔP1 j(t) it is in moment t frequency f1Pseudo-code difference observation data；
For in moment t frequency f2Pseudo-code difference observation data；For in moment t frequency f1Time-differenced phase observation data；For in moment t frequency f2Phase data difference observation data；A, B represent two Satellite Formation Flyings；Defended to form into columns
Star A is in moment t frequency f1Pseudo-code observation data；It is Satellite Formation Flying A in moment t frequency f2Pseudo-code observation data；It is Satellite Formation Flying A in moment t frequency f1Phase observations data；It is Satellite Formation Flying A in moment t frequency f2Phase
Position observation data；It is Satellite Formation Flying B in moment t frequency f1Pseudo-code observation data；It is Satellite Formation Flying B in moment t
Frequency f2Pseudo-code observation data；It is Satellite Formation Flying B in moment t frequency f1Phase observations data；Defended to form into columns
Star B is in moment t frequency f2Phase observations data； It is all from the first step observing data by pretreated GNSS；For Satellite Formation Flying A, B when
Carve the poor geometric distance of list between t and GNSS satellite j；C represents the light velocity, δ tABFor between two GNSS receivers of Satellite Formation Flying A, B
Relative clock correction；For in the poor ionosphere delay of moment t list；For k-th of continuous tracking segmental arc f1The list of frequency is poor
Phase ambiguity, 1≤k≤nb, nbFor continuous tracking segmental arc sum；For k-th of continuous tracking segmental arc f2The list of frequency is poor
Phase ambiguity；ε is observation error；
Ionosphere delay is eliminated using iono-free combinationThe poor observational equation (2) of electric eliminating absciss layer list is obtained,
Wherein " IF " represents iono-free combination；For the moment t poor pseudo-code iono-free combination data of list；For
The moment t poor phase iono-free combination data of list；The corresponding poor phase electric eliminating absciss layer of list of segmental arc is continuously tracked for k-th
Fuzziness；Single poor geometric distanceCalculated by formula (3),
Wherein | | represent to calculate the length of trivector；rA(t)、rB(t) it is the absolute orbit of Satellite Formation Flying A, B in moment t
Put；Be GNSS satellite j in moment t position, obtained using the IGS interpolation of the precise ephemeris afterwards meters provided；
WillIn outline pointPlace's linearisation expansion, obtains formula (4),
Represent the direction of visual lines unit vector in moment t from satellite B to GNSS satellite j；ForOutline
Point, Satellite Formation Flying A, B that its initial value is obtained using second step absolute orbit position, which are calculated, to be obtained；ΔrB(t) exist for satellite B
The orbital position improvement of t,
ΔrB(t)=rAC(yB0+ΔyB,t)-rAC(yB0,t) (5)
Wherein rACRepresent orbital mechanics integral function, rAC(yB0, t) represent to orbital mechanics model parameter yB0Carry out Adams-
Orbital positions of the satellite B that Cowell Multi-step Integrations are obtained in moment t；yB0、ΔyBSatellite B orbital mechanics model is represented respectively
The initial value and improvement of parameter vector, including initial time orbital position and speed, solar light pressure coefficient, atmospheric drag coefficient
With experience acceleration factor；yB0The orbital mechanics model parameter exported using second step；ΔyBA most young waiter in a wineshop or an inn is used according to formula (6)
Multiply estimation to obtain；
The poor observational equation (2) of the electric eliminating absciss layer list at multiple moment is organized into matrix form, single poor observation corrected value vector is obtained
zSD,
zSD=HSD·xSD+eSD (6)
Wherein " SD " represents single poor；Single poor observation corrected value vector[]T
Representing matrix transposition；Design matrix Represent partial derivative；Error vector
Parameter vector to be estimatedNow parameter to be estimated includes：Receiver is with respect to clock correction δ tAB
(t), single poor phase electric eliminating absciss layer fuzzinessVectorial Δ y is improved with orbital mechanics model parameterB；
3.2 obtain x using the estimation of weighted least-squares methodSD,
Wherein single poor observation weight matrixσLRepresent phase observations precision, σPRepresent pseudo-
Code accuracy of observation；
3.3 calculate single poor geometric distance：Satellite orbital position rB(t) Adams-Cowell Multi-step Integrations r is passed throughAC(yB0+ΔyB,
T) obtain, then by rB(t) substitute into formula (3) and update the single poor geometric distance of calculating
3.4 eliminate single poor geometric distance in difference observation dataWith clock correction δ tAB(t)：The poor geometry of list that 3.3 are obtained
DistanceWith 3.2 obtained clock correction δ tAB(t) deducted from the observation data in formula (1), obtain multiple moment deductions
The poor observational equation of list (8) after geometric distance and clock correction,
4th step, the single poor phase ambiguity float-solution of estimation and single poor ionosphere delay parameter：
4.1 set pseudo-code weight wPWith phase weight wLThe ratio between, take wP:wL=σL:σP, σLRepresent phase observations precision, σPRepresent pseudo-
Code accuracy of observation；
4.2 using the single poor phase ambiguity float-solution of weighted least-squares method estimation and single poor ionosphere delay parameter；In kth
In individual continuous tracking segmental arc, the poor observational equation of list (8) that multiple moment are deducted into geometric distance and clock correction is organized into matrix form,
zk=Hk·xk+ek (9)
Wherein single poor observation correction vectorError vectorIf
Count matrixParameter vector to be estimatedNow parameter to be estimated includes：
Single poor ionosphere delay, the poor phase ambiguity parameter of 2 listsWithObtain xkWeighted least square value
For,
Wherein observe weight matrixDiag () represents diagonal matrix；Output estimation is obtained
To the poor phase ambiguity parameter of list of k-th of continuous tracking segmental arcWith single poor ionosphere delay parameter
5th step, the wide lane ambiguity float-solution of double difference and covariance matrix are obtained using double difference conversion：
The poor phase ambiguity parameter of list of 5.1 k-th of continuous tracking segmental arc for obtaining the 4th stepSubtract each other, obtain
To the poor wide lane ambiguity of corresponding listThen nbThe corresponding Dan Chakuan lanes phase of individual continuous tracking segmental arc
Fuzziness is respectivelyDefine floating-point solution vectorAnd its covariance matrixStructure
Make single poor wide lane ambiguity floating-point solution vectorVariance isNow
5.2 according to the relation between double difference and single poor observational equation, construction double difference linear transformation operator TDD, obtain the wide lane mould of double difference
Paste degree float-solution is,
Wherein
Calculated by formula (12) and obtain the wide lane ambiguity covariance matrix of double difference
6th step, the wide lane integer ambiguity of fixed double difference：
6.1 fix the wide lane integer ambiguity of double difference using integer least square method：The wide lane ambiguity of double difference that 5th step is obtained
Float-solutionAnd its covariance matrixAs input, the wide lane complete cycle of double difference is fixed using integer least square method
Fuzziness, that is, search for integer space and obtain the wide lane integer ambiguity fixed solution of double difference
So that formula (13) reaches minimum,
Wherein cov-1Represent the inverse of covariance matrix；Min { } represents to minimize；ZnRepresent integer space；Using least square
De-correlation LAMBDA scans for obtaining the integer solution of the wide lane phase ambiguity of double difference；
6.2 examine the wide lane integer ambiguity of double difference to fix correctness：Calculate the suboptimum integer ambiguity pair of LAMBDA methods output
The fuzziness residual error amount R answeredSFuzziness residual error amount R corresponding with optimal integer ambiguityBThe ratio between, if RS/RB≤kS/B, then double difference
Wide lane integer ambiguity fixed solution zW,DDIt is used, turns the 7th step；If RS/RB>kS/B, then the wide lane integer ambiguity fixed solution of double difference
zW,DDFixation is incorrect, and the wide lane ambiguity of double difference still uses its float-solutionEvenkS/BFor what is given
Threshold value, turns the 7th step；
7th step, the narrow lane integer ambiguity of fixed double difference：
The 7.1 wide lane integer ambiguity fixed solution z of the double difference for obtaining the 6th stepW,DDAs known quantity from double difference phase observation equation
Middle to deduct, double difference observation includes double difference pseudo-code and double difference phase, is again to different GNSS on the basis of single poor observational equation
The poor observation data of the list of satellite make poor, and cancellation receiver is with respect to clock correction, i.e.,
WhereinRepresent double difference；Subscript j, k represent jth, k GNSS satellite；Represent the double difference between GNSS satellite j, k
Pseudo-code electric eliminating absciss layer observation, Represent the double difference phase between GNSS satellite j, k
Electric eliminating absciss layer observation, The wide lane ambiguity of double difference is represented respectively
With the narrow lane ambiguity of double difference；The double difference geometric distance between GNSS satellite j, k is represented,
The double difference phase observation equation (14) at multiple moment is organized into matrix form, multiple moment double difference observational equations are obtained
(15)
zDD=HDD·xDD+eDD (15)
Wherein " DD " represents double difference；zDDVector is corrected for double difference observation,
Design matrixError vectorParameter vector to be estimated
7.2 according to multiple moment double difference observational equations (15), and using the least square estimation method, estimation obtains narrow lane phase ambiguity
Spend floating-point solution vectorAnd its covariance matrix
7.3 fix the narrow lane integer ambiguity of double difference using integer least square method；By narrow lane phase ambiguity float-solution
And its covariance matrixAs input, the narrow lane integer ambiguity of double difference is fixed using integer least square method, searched
Rope integer space obtains the narrow lane integer ambiguity fixed solution of double differenceSo that formula (16) reaches
Minimum,
7.4 examine the narrow lane integer ambiguity of double difference to fix correctness：Calculate the corresponding fuzziness residual error amount R of suboptimum integer ambiguityS
Fuzziness residual error amount R corresponding with optimal integer ambiguityBThe ratio between, if RS/RB≤kS/B, then the narrow lane integer ambiguity of double difference fix
Solve zN,DDIt is used, turns the 8th step；If RS/RB>kS/B, then the narrow lane integer ambiguity fixed solution z of double differenceN,DDFixation is incorrect, double
The narrow lane ambiguity of difference still uses its float-solutionEvenTurn the 8th step；
8th step, the relative positioning result that output fuzziness is fixed：
The 8.1 narrow lane integer ambiguity fixed solutions of the double difference for obtaining the 7th stepAs known quantity again from double difference phase
Deducted in observational equation (14), obtain deducting the double difference observational equation (17) after fuzziness：
Double difference observational equation (17) after the deduction fuzziness at multiple moment is organized into matrix form, multiple moment deductions are obtained
Double difference observational equation (18) after fuzziness
Wherein double difference observation correction is vectorial,
Design matrixParameter vector Δ y to be estimatedBVector is improved for orbital mechanics model parameter；
8.2 deduct the double difference observational equation (18) after fuzziness according to multiple moment, using the least square estimation method, estimate
Vectorial Δ y is improved to orbital mechanics model parameterB, satellite orbital position rB(t) r is integrated by orbital mechanicsAC(yB0+ΔyB,t)
Obtain, export the formation relative orbit r after final fuzziness is fixedB(t)-rA(t)。
2. the Long baselines satellites formation GNSS relative positioning methods that a kind of fuzziness as claimed in claim 1 is fixed, its feature
It is that second step determines that the method for Satellite Formation Flying A, B absolute orbit position is non-poor reduced-dynamic method.
3. the Long baselines satellites formation GNSS relative positioning methods that a kind of fuzziness as claimed in claim 1 is fixed, its feature
It is that the 3rd step Adams-Cowell Multistep Integrator step-lengths take 10 seconds.
4. the Long baselines satellites formation GNSS relative positioning methods that a kind of fuzziness as claimed in claim 1 is fixed, its feature
It is the kS/B=2.5.
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| US10222483B2 (en) * | 2016-03-18 | 2019-03-05 | Deere & Company | Satellite navigation receiver with improved ambiguity resolution |
| CN105842721B (en) * | 2016-03-23 | 2018-01-23 | 中国电子科技集团公司第十研究所 | The method for improving medium-long baselines GPS Carrier Phase Ambiguity Resolution success rates |
| CN105607648B (en) * | 2016-03-29 | 2018-04-03 | 中国人民解放军国防科学技术大学 | Towards the radial direction underactuated spacecraft formation reconfiguration control method of input saturation |
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| CN107478904B (en) * | 2017-07-27 | 2020-04-28 | 中国科学院国家天文台 | Atmospheric phase disturbance correction method based on satellite positioning system difference |
| CN107193290B (en) * | 2017-08-03 | 2019-12-03 | 上海航天控制技术研究所 | Satellites formation payload relative position control method based on linear momentum exchange |
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| CN109116394B (en) * | 2018-09-10 | 2020-08-07 | 中国科学院国家授时中心 | Real-time dynamic positioning method suitable for baselines of different lengths |
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| CN109932736B (en) * | 2019-04-08 | 2022-05-10 | 上海致灵信息科技有限公司 | Outdoor full-scene all-weather centimeter-level positioning system and method |
| CN110031879B (en) * | 2019-04-17 | 2023-11-17 | 武汉大学 | High-precision post-processing positioning method and system for ambiguity domain information integration |
| CN110068850A (en) * | 2019-05-10 | 2019-07-30 | 东华理工大学 | A kind of obscure portions degree calculation method |
| CN110398762A (en) * | 2019-07-15 | 2019-11-01 | 广州中海达卫星导航技术股份有限公司 | Fuzziness fixing means, device, equipment and medium in real-time clock bias estimation |
| CN110764127B (en) * | 2019-10-08 | 2021-07-06 | 武汉大学 | Relative orbit determination method for formation satellite easy for satellite-borne on-orbit real-time processing |
| CN111638535B (en) * | 2020-05-15 | 2022-02-25 | 山东科技大学 | Hybrid ambiguity fixing method for GNSS real-time precise point positioning |
| CN111751853B (en) * | 2020-06-20 | 2023-10-03 | 北京华龙通科技有限公司 | GNSS dual-frequency carrier phase integer ambiguity resolution method |
| CN114779285A (en) * | 2022-04-18 | 2022-07-22 | 浙江大学 | Precise orbit determination method based on microminiature low-power-consumption satellite-borne dual-mode four-frequency GNSS receiver |
| CN115856982A (en) * | 2023-02-22 | 2023-03-28 | 广州导远电子科技有限公司 | Relative position acquisition method and device, storage medium and electronic equipment |
| CN117289311B (en) * | 2023-11-24 | 2024-02-23 | 航天宏图信息技术股份有限公司 | Satellite formation baseline processing method and device based on synchronous ring closure difference constraint |
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| CN102353969B (en) * | 2011-09-02 | 2013-07-31 | 东南大学 | Method for estimating phase deviation in precise single-point positioning technology |
| CN103837879B (en) * | 2012-11-27 | 2016-03-30 | 中国科学院光电研究院 | The method of hi-Fix is realized based on the civilian combination carrier phase observation of dipper system |
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