CN103792558B - GNSS carrier phase smoothing pseudo-range processing method - Google Patents
GNSS carrier phase smoothing pseudo-range processing method Download PDFInfo
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- CN103792558B CN103792558B CN201410015871.0A CN201410015871A CN103792558B CN 103792558 B CN103792558 B CN 103792558B CN 201410015871 A CN201410015871 A CN 201410015871A CN 103792558 B CN103792558 B CN 103792558B
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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
- G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/13—Receivers
- G01S19/35—Constructional details or hardware or software details of the signal processing chain
- G01S19/37—Hardware or software details of the signal processing chain
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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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Abstract
The invention belongs to Global Satellite Navigation System (GNSS) technical fields, disclose a kind of GNSS carrier phase smoothing pseudo-range processing method.The present invention passes through the resolving to smoothing constant, extrapolation of the next epoch pseudorange obtained by the carrier phase of current epoch, the thick code pseudorange of next epoch and carrier phase, first carrier phase smoothing pseudo-range initial value, calculates the carrier phase smoothing pseudo-range value of next epoch.It repeats the above process, obtains GNSS carrier phase smoothing pseudo-range value in real time.Carrier phase smoothing pseudo-range precision is improved using the present invention, and then substantially increases GNSS positioning accuracy.
Description
Technical field
The present invention relates to Global Satellite Navigation System (GNSS) technical field more particularly to a kind of GNSS smoothing the phase of carrier wave
Pseudorange processing method.
Background technique
Global Satellite Navigation System GNSS positioning principle is: the distance of the satellite observed using receiver to receiver
Observed quantity calculates the position of receiver using geometry intersection according to known satellite position.GNSS is disclosed for civilian users
There is provided apart from observed quantity be thick code pseudorange.
The thick code pseudorange error of GNSS is larger, and the thick code pseudo range measurement error of GNSS receiver output is when including multipath
Up to 1m~3m or so.In contrast, GNSS carrier phase random error is only grade, even if including multipath effect,
Random meausrement error is again smaller than 1cm.When there is no cycle slip, theoretically poor (being converted to range difference) and thick code between carrier phase epoch
Pseudorange difference should be equal.Therefore, the carrier phase smoothing pseudo-range of more epoch can be used, the mesh for compressing thick code pseudorange error is reached
, referred to as carrier phase smoothing pseudo-range.Carrier phase smoothing pseudo-range is to reduce thick code pseudorange error, improves positioning accuracy, especially
It is the classical means for improving Differential positioning precision, is widely used in Differential positioning data processing.
Carrier phase smoothing pseudo-range principle is as follows:
The thick code pseudorange of GNSS and the observational equation of carrier phase may be expressed as:
Wherein, P indicates observation pseudorange；L indicates to be converted to the carrier phase of distance, also referred to as carrier phase pseudorange；K indicates to see
Survey epoch；R indicates true geometric distance；I indicates ionosphere delay；N indicates carrier phase complete cycle number；λ indicates carrier wavelength；εP
Indicate the thick code pseudo range measurement error including multipath；εφIndicate that the carrier phase pseudorange equipment including multipath is surveyed
Measure error；C indicates common error item, including ephemeris error, star clock error, tropospheric delay and receiver clock-offsets.
If then asking the difference to be between epoch respectively thick code pseudorange and carrier phase pseudorange without cycle slip between adjacent epoch
The time-varying characteristics of ionosphere delay are very slow, therefore ionosphere delay changes between negligible epoch, that is, thinks:
I(k)≈I(k-1) (3)
It can obtain:
Theoretically, difference should be poor equal between thick code pseudorange epoch between carrier phase epoch, it may be assumed that
P(k)-P(k-1)≈L(k)-L(k-1) (5)
Therefore, thick code pseudorange can be rebuild by difference between carrier phase epoch according to formula (4), i.e.,
Assuming that the carrier phase observed quantity since k=0 epoch continues no cycle slip, and enableThen according to public affairs
Formula (6) can continuously rebuild the thick code pseudorange of k=0 epoch using the observed quantity of subsequent n epoch, i.e.,
Adduction various in formula (7) is asked, the pseudorange smoothing value of k=0 epoch can be obtained:
In formula, subscript sm indicates smooth value.
Further, by Psm(0) value replaces various in formula (7)The smooth value of each epoch code pseudorange can be rebuild
It is as follows:
Formula (8) and formula (9) are exactly carrier phase smoothing pseudo-range basic model, also referred to as phase difference averaging model.It is aobvious
So, phase difference averaging model is not easy to data processing, it is practical in mostly use the recurrence model based on Hatch filtering, model is as follows:
Wherein, PexIndicate extrapolation pseudorange；The pseudorange weight of w (k) expression epoch k；M is smoothing constant.
Formula (10) is GNSS smoothing the phase of carrier wave recurrence formula, and the smoothing pseudo range of each epoch is that observation pseudorange and extrapolation are pseudo-
Away from weighted sum, weight w (k) is that epoch is reciprocal, while the minimum value of weight is limited by smoothing constant M.It sets restricted
Smoothing constant M the reason of, be that carrier phase smoothing pseudo-range can be introduced with the increased ionosphere epoch k diverging error.If
Weight is not limited, then diverging error in ionosphere is eventually more than compression effectiveness of the carrier wave to pseudorange error.
As it can be seen that smoothing constant M is the important parameter for influencing carrier phase smoothing pseudo-range precision.It, can shadow if M value is too small
It rings smoothly to the compression effectiveness of pseudorange error；If M value is too big, insufferable ionosphere diverging error can be introduced.Mesh
Before, the solution of smoothing constant M passes through two kinds of approach: first is that artificially specifying according to user experience, having very big randomness；Second is that strong
M is set as the equivalence value of 100s by system, i.e., M is set as to the ratio of 100s and data sampling period.Both setting M approach be all
Non- objective means, so there are biggish mistakes for the carrier phase smoothing pseudo-range that obtains of traditional smoothing the phase of carrier wave processing method
Difference.
Summary of the invention
The technical problem to be solved by the present invention is providing a kind of GNSS carrier phase smoothing pseudo-range processing method.This method
Make to realize more accurate positioning using carrier phase smoothing pseudo-range.
To solve above-mentioned technical problem: the invention proposes a kind of GNSS carrier phase smoothing pseudo-range processing methods, including
Following steps:
Step 1: GNSS receiver exports thick code pseudorange and carrier phase in real time；
Step 2: the thick code pseudorange of the current epoch by GNSS receiver output, it is initial to obtain carrier phase smoothing pseudo-range
Value, the current epoch are first thick code pseudorange of receiver output；
Step 3: being obtained according to the thick code pseudorange of current epoch of step 1 acquisition and next epoch carrier phase with step 2
The carrier phase smoothing pseudo-range initial value obtained, obtains the extrapolation pseudorange P of next epochex(k)；
Step 4: obtaining the carrier phase smoothing pseudo-range value P of next epochsm(k)
Psm(k)=w (k) × P (k)+[1-w (k)] × Pex(k)
Wherein, w (k) is the pseudorange weight of preceding epoch k, if smoothing constant M value is greater than epoch k, pseudorange weight takes w
(k)=1/k, if smoothing constant M value is not more than epoch k, pseudorange weight takes w (k)=1/M；
Wherein, M is smoothing constant,For the variance of the device measuring error of the thick code pseudorange of GNSS, TmFor data sampling week
Phase, IdFor the divergence variations rate of ionosphere delay；
P (k) is the thick code pseudorange for the current epoch that step 1 obtains, Pex(k) current epoch obtained for rapid three is extrapolated pseudo-
Away from；
Step 5: the thick code pseudorange of next epoch obtained according to step 1 next epoch carrier phase under, with step 4
The carrier phase smoothing pseudo-range value of acquisition, the extrapolation pseudorange of next epoch under acquisition；
Step 6: repeating step 4 and step 5, GNSS carrier phase smoothing pseudo-range value is obtained in real time.
The invention has the following advantages:
The purpose of carrier phase smoothing pseudo-range is to reduce thick code pseudorange error, improves GNSS positioning accuracy.Carrier phase is flat
Smoothing constant is the important parameter for influencing carrier phase smoothing pseudo-range precision in sliding pseudorange processing method, it should according to certain criterion
Calculated value and guides smoothing processing.The present invention is by analysis carrier phase smoothing pseudo-range error main composition factor, by objective
Method obtain the mathematical relationship between smoothing constant and the variance of measuring device error, using Lagrangian extremum method, obtain
The processing method of smoothing constant, the processing method data are adaptable, avoid as force or experience value and caused by put down
The problem of sliding ineffective or even smooth failure, thick code pseudorange error is greatly reduced, it is suppressed that ionosphere dissipates error, improves
Carrier phase smoothing pseudo-range precision, and then GNSS positioning accuracy is substantially increased, have in satellite navigation and positioning field extensive
Application prospect.
Detailed description of the invention
Fig. 1 is the equivalent low-pass filter schematic diagram of carrier phase smoothing pseudo-range in the present invention.
Fig. 2 is using the calculated smoothing constant of the method for the present invention with the variation of the device measuring error of the thick code pseudorange of GNSS
Curve graph.
Fig. 3 is using the smoothing pseudo range of the smoothing constant of calculation method of the present invention calculating and the difference of raw pseudo range with smooth
Time changing curve figure.
Fig. 4 is using the smoothing pseudo range for the smoothing constant for being equivalent to 100s smoothingtime and the difference of raw pseudo range with smooth
Time changing curve figure.
Fig. 5 is using the difference between the smoothing pseudo range and raw pseudo range of smoothing constant 710 with smoothingtime change curve
Figure
Specific embodiment
Present invention is further described in detail with reference to the accompanying drawing, it is necessary to and it is indicated herein to be, implement in detail below
Mode is served only for that the present invention is further detailed, and should not be understood as limiting the scope of the invention, the field
Those of ordinary skill can make some nonessential modifications and adaptations to the present invention according to foregoing invention content.
GNSS carrier phase smoothing pseudo-range processing method of the invention, includes the following steps:
Step 1: GNSS receiver exports the thick code pseudorange and carrier phase of each epoch in real time.
Step 2: the thick code pseudorange of the current epoch by GNSS receiver output, it is initial to obtain carrier phase smoothing pseudo-range
Value Psm(0)；The current epoch is first thick code pseudorange of receiver output.
Psm(0)=P (0)
Step 3: being obtained according to the thick code pseudorange of current epoch of step 1 acquisition and next epoch carrier phase with step 2
The carrier phase smoothing pseudo-range initial value obtained, obtains the extrapolation pseudorange P of next epochex(k)。
Step 4: obtaining the carrier phase smoothing pseudo-range value P of next epochsm(k)。
Psm(k)=w (k) × P (k)+[1-w (k)] × Pex(k)
Wherein, w (k) is the pseudorange weight of preceding epoch k, if smoothing constant M value is greater than epoch k, pseudorange weight takes w
(k)=1/k, if smoothing constant M value is not more than epoch k, pseudorange weight takes w (k)=1/M；
Wherein,For the variance of the device measuring error of the thick code pseudorange of GNSS, unit m2；Be equipment thermal noise and
Multipath effect passes through the equivalent range error after thick code delay locking ring (DLL).The parameter can both be obtained by device parameter,
It can count to obtain by pseudorange random error.The thick code pseudo range data random error statistical method of GNSS is referring to " GJB 5830-2006
Guided missile, spacecraft testing GPS measuring system off-line data processing method " Appendix B.TmFor data sampling period, unit s.IdFor
The divergence variations rate of ionosphere delay, unit m/s usually take mid latitudes ionosphere divergence speed representative value upper bound 0.1m/
Min converts into 0.0017m/s.M is smoothing constant.
P (k) is the thick code pseudorange for the current epoch that step 1 obtains, Pex(k) current epoch obtained for rapid three is extrapolated pseudo-
Away from
Step 5: the thick code pseudorange of next epoch obtained according to step 1 next epoch carrier phase under, with step 4
The carrier phase smoothing pseudo-range value of acquisition, the extrapolation pseudorange of next epoch under acquisition；
Step 6: repeating step 4 and step 5, GNSS carrier phase smoothing pseudo-range value is obtained in real time.
Smoothing constant M specific derivation process of the invention is as follows:
One, on continuous time analytical smoothing error main composition
According to aforementioned background art introduction, smooth basic principle is contracted thick code pseudorange with the epoch differential pressure of carrier phase
The error of epoch difference, smoothing process equivalent can be considered as the low-pass filtering for thick code pseudorange and carrier phase pseudorange difference, such as attached
Shown in Fig. 1.
Filter time constant is τ, and the difference single order of thick code pseudorange and carrier phase pseudorange determines gain continuous model can table
It is shown as
Wherein: P indicates thick code pseudorange, PsmIndicate smoothing pseudo range；L indicates carrier phase pseudorange, and s is laplace transform
Complex variable.
Further, thick code pseudorange and carrier phase pseudorange are decomposed, is expressed as
Wherein, R indicates the sum of geometric distance, ephemeris error, star clock error and tropospheric delay；I indicates ionosphere delay；
ε indicates thick code pseudorange device measuring error.Formula (13) has ignored carrier phase pseudorange device measuring error, this be it is reasonable,
Because carrier phase pseudorange device measuring error is far smaller than ε.
(13) are updated to (12), can be obtained
Analytical formula (14), it is known that there are following characteristics for smoothed out pseudorange:
(1) the 1st R of formula (14) right formula, show geometric distance, ephemeris error, star clock error and tropospheric delay not by
Smoothing effect；
(2) formula (14) right formula the 2ndShow that thick code pseudorange device measuring error ε is low pass filtering, i.e. carrier wave
Carrier phase smoothed pseudorange can reduce receiver device thermal noise and multipath delay error, this fractional error is DLL tracking error；
(3) formula (14) right formula the 3rdShow that carrier phase smoothing pseudo-range will lead to the generation of ionosphere delay item
Variation.It enables Δ I indicate instantaneous ionosphere delay and the smooth rear difference postponed, and increases time independent variable t, it may be assumed that
The reason of Δ I (t) occur is that ionosphere delay dissipates at any time: first is that phase retardation and group delay are contrary, two
It is that delay has time-varying characteristics.Δ I (t) is the new error term introduced by smoothing process, referred to as the ionosphere diverging of smoothing pseudorange
Error.
Two, the DLL tracking error variance for deriving carrier phase smoothing pseudo-range estimates formula.
Analytical formula (12), the discrete equation with formula (12) equivalence are as follows:
Wherein: α indicates index weight；TmIndicate data sampling period, k is epoch of observation.
Continuous pseudo range observed quantity approximation is considered as independent sequence, then has ignored ionosphere delay diverging error completely.By
It is public
Formula (16) can obtain the stable state variance of carrier phase smoothing pseudo-range are as follows:
Wherein:For the DLL tracking error variance of smoothing pseudo range；For the DLL tracking error variance of thick code pseudorange.
Enable n=τ/Tm, solutionIt can obtain:
Series expansion is carried out, and ignores higher order term, is obtainedIt substitutes into formula (18), obtains:
Formula (19) is the DLL tracking error variance estimation formula of carrier phase smoothing pseudo-range.
Three, it derives the ionosphere diverging error variance that carrier phase smoothing pseudo-range introduces and estimates formula
Ionosphere delay is slowly varying at any time, and it is inclined to can be analyzed to the slope that a constant deviations are changed over time with one
Difference, it may be assumed that
I (t)=I0+Idt (20)
Wherein: IdIndicate ionosphere delay change rate.I0For the delay of initial ionization layer, formula (20) are substituted into formula (15),
Ionosphere diverging error delta I (t), which can be obtained, is
When filtering enters stable state, using Laplace transform final-value theorem, it is as follows that ionosphere diverging steady-state error can be obtained:
Formula (22) shows: since ionosphere delay changes over time (Id≠ 0), therefore carrier phase smoothing pseudo-range can draw
Enter ionosphere diverging error, magnitude and smoothing time constant τ and ionosphere delay change rate IdProduct it is directly proportional.Statistics is ground
Study carefully and shows (Patricia H etc., The Spatial and Temporal Variations in Ionospheric Range
Delay, ION GPS 97), in the sun is in when low active degree, mid latitudes ionosphere divergence variations rate is usually obeyed
Normal distribution, and magnitude is typically not greater than 0.1m/min.
Obviously, meet between the smoothing time constant τ under continuous state, with the smooth epoch k under discrete case:
τ=kTm (23)
Formula (23) are substituted into formula (22) and both sides are squared, the ionosphere diverging that can obtain carrier phase smoothing pseudo-range misses
Poor variance estimates formula:
Four, it derives carrier phase smoothing pseudo-range overall error variance and estimates formula
According to error propagation Computing Principle, formula (19) and formula (24) are summed, smoothing the phase of carrier wave puppet can be provided
Variance away from overall errorEstimation formula:
Take carrier phase smoothing pseudo-range the recursive calculative formula (10) into account, completely estimate formula are as follows:
Five, smoothing constant M is obtainedbestCalculation formula
According to the third formula of formula (26)If known σDLL、TmAnd Id,
Then find M optimal value MbestStandard be exactly the overall error σ for enabling carrier phase smoothing pseudo-rangesm(k) minimum.It is asked using Lagrange
Extreme value algorithm: by formula (26) third formula to M derivation, and the expression formula after derivation is enabled to be equal to 0, it may be assumed that
Formula (26) third formula is substituted into, it may be assumed that
M optimal value M can be obtained after solution formula (28)bestCalculating formula:
That is:
For example:
Example 1: when receiver output frequency is 1Hz, 10Hz and 20Hz, using the calculated smoothing constant of the method for the present invention
MbestWith the device measuring error σ of the thick code pseudorange of GNSSDLLChange curve as shown in Fig. 2, in figure ionosphere delay diverging become
Rate Id, take mid latitudes ionosphere divergence variations rate representative value upper bound 0.1m/min.Fig. 2 shows as the thick code of GNSS is pseudo-
Away from device measuring error σDLLDifferent with receiver output frequency, smoothing constant is also more big changes, and is arbitrarily designated smooth normal
Smoothing constant is forced to be set as the equivalence value of 100s and improper by number.
Example 2: the smoothing the phase of carrier wave of 14000 epoch observation data of a GPS receiver handles comparison.
(1) data known parameters are as follows: satellite number is 11, sampling period Tm=0.25s, the DLL of thick code pseudorange, which is tracked, to be missed
Difference isIdTake mid latitudes ionosphere divergence speed representative value upper bound 0.1m/min.
(2) it selects comparison other: selecting three smoothing constants as comparison other:
(a) smoothing constant for using calculation method of the present invention to obtain for
(b) the equivalent smoothing constant of 100s is
M100s=100/0.25=400
(c) smoothing constant artificially specified, specifying the smoothing constant value is 10 times of smoothing constant, i.e.,
M710=710
(3) omparison purpose: to compare using three smoothing constants, after carrying out smoothing the phase of carrier wave according to formula (10), smoothly
Error changes with time situation.
(4) comparative approach: difference is asked to ask poor with smoothing the phase of carrier wave value original thick code pseudorange: if smooth effect is good,
Then ask difference sequence that should show as the random error characteristics of 0 mean value；If smooth effect is poor, introduces excessive ionosphere diverging and miss
Difference can then show as mutual difference sequence and be gradually deviated from 0 mean value.As shown in figure 3, smoothly being imitated when using the smoothing constant of the invention calculated
Fruit is normal.As shown in figure 4, curve gradually deviates 0 axis when smoothing constant equivalent using 100s, show to introduce electricity in smooth
Absciss layer dissipates error, maximum up to 2m magnitude.Since the DLL tracking that the ionosphere diverging error of introducing has been more than thick code pseudorange misses
Difference, smoothing the phase of carrier wave have dissipated, so losing the meaning for realizing positioning using carrier phase smoothing pseudo-range.Such as Fig. 5 institute
Show, when using a smoothing constant artificially specified, curve gradually deviates 0 axis, shows to introduce ionosphere diverging in smooth
Error, it is maximum up to 3m magnitude.Since the ionosphere diverging error of introducing has been more than the DLL tracking error of thick code pseudorange, carrier wave
Smoothing pseudorange has dissipated, so losing the meaning for realizing positioning using carrier phase smoothing pseudo-range.
Claims (1)
1. a kind of GNSS carrier phase smoothing pseudo-range processing method, characterized by the following steps:
Step 1: GNSS receiver exports thick code pseudorange and carrier phase in real time；
Step 2: the thick code pseudorange of the current epoch by GNSS receiver output, obtains carrier phase smoothing pseudo-range initial value, institute
State first thick code pseudorange that current epoch is receiver output；
Step 3: being obtained according to the thick code pseudorange of current epoch of step 1 acquisition and next epoch carrier phase with step 2
Carrier phase smoothing pseudo-range initial value obtains the extrapolation pseudorange P of next epochex(k)；
Step 4: obtaining the carrier phase smoothing pseudo-range value P of next epochsm(k)
Psm(k)=w (k) × P (k)+[1-w (k)] × Pex(k)
Wherein, w (k) be preceding epoch k pseudorange weight, if smoothing constant M value be greater than epoch k, pseudorange weight take w (k)=
1/k, if smoothing constant M value is not more than epoch k, pseudorange weight takes w (k)=1/M；
Wherein, M is smoothing constant,For the variance of the device measuring error of the thick code pseudorange of GNSS, TmFor data sampling period, Id
For the divergence variations rate of ionosphere delay；
P (k) is the thick code pseudorange for the current epoch that step 1 obtains, Pex(k) the current epoch extrapolation pseudorange obtained for step 3；
Step 5: the thick code pseudorange of next epoch obtained according to step 1 next epoch carrier phase under, obtains with step 4
Carrier phase smoothing pseudo-range value, the extrapolation pseudorange of next epoch under acquisition；
Step 6: repeating step 4 and step 5, GNSS carrier phase smoothing pseudo-range value is obtained in real time.
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| CN104516006B (en) * | 2014-11-07 | 2017-04-12 | 中国电子科技集团公司第二十研究所 | Carrier phase smoothing pseudorange algorithm based on improved Kalman filtering |
| CN107748377B (en) * | 2017-12-06 | 2021-09-17 | 湖南国科微电子股份有限公司 | Differential positioning method based on GNSS and positioning system thereof |
| CN108549097A (en) * | 2018-03-26 | 2018-09-18 | 中国电子科技集团公司第二十八研究所 | Ground strengthening system Differential positioning method based on EKF filter |
| CN112380310B (en) * | 2020-11-26 | 2023-12-01 | 成都新橙北斗智联有限公司 | GNSS high-precision anti-aliasing resolving result smoothing method |
| CN115712134B (en) * | 2022-11-07 | 2023-09-01 | 北京航空航天大学合肥创新研究院(北京航空航天大学合肥研究生院) | Non-dispersive carrier phase smoothing pseudo-range smoothing method and storage medium |
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| US5796773A (en) * | 1994-03-22 | 1998-08-18 | Trimble Navigation Limited | Compensating for multipath errors, ionospheric time delay and noise errors in differential satellite positioning systems |
| CN101089650A (en) * | 2007-07-12 | 2007-12-19 | 北京航空航天大学 | Error separation method based on foundation strength system and foundation strength system |
| CN102565813A (en) * | 2010-12-31 | 2012-07-11 | 和芯星通科技(北京)有限公司 | Method and device for performing pseudorange observation estimation by carrier smoothing |
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