CN103713303A - Navigational satellite positioning method and system based on ionospheric delay improvement - Google Patents

Navigational satellite positioning method and system based on ionospheric delay improvement Download PDF

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CN103713303A
CN103713303A CN201410002208.7A CN201410002208A CN103713303A CN 103713303 A CN103713303 A CN 103713303A CN 201410002208 A CN201410002208 A CN 201410002208A CN 103713303 A CN103713303 A CN 103713303A
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ionosphere
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ionosphere delay
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许婧
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Dongguan Techtotop Microelectronics Coltd
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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

Abstract

A navigational satellite positioning method based on the ionospheric delay improvement includes the steps of obtaining GIM data, utilizing the GIM data to conduct model parameter estimation, introducing model parameters into a parameter fitting model to conduct ionospheric delay fitting, and calculating the navigation positioning coordinate according to the ionospheric delay. According to the method, the positioning accuracy of a system can be greatly improved, and therefore the performance of the whole navigation system or a device terminal is improved. Meanwhile, the invention further provides a navigational satellite positioning system based on the ionospheric delay improvement.

Description

A kind of based on the improved Navsat localization method of ionosphere delay and system
Technical field
The present invention relates to satellite navigation field, particularly a kind of based on the improved Navsat localization method of ionosphere delay and system.
Background technology
At present, an ionospheric delay model generally being adopted by single-frequency GPS/BDS user is Klobuchar (Crow cloth is had a rest) model, and the expression formula of Klobuchar model is:
Figure 391161DEST_PATH_IMAGE001
In formula,
Figure 538108DEST_PATH_IMAGE002
be to take the vertical delay that s is unit, t locates to obtain local time for take receiver to the satellite line and ionosphere, center intersection point (M) that s is unit,
Figure 379156DEST_PATH_IMAGE003
=
Figure 560739DEST_PATH_IMAGE004
for the vertical delay constant at night,
Figure 78308DEST_PATH_IMAGE005
for the amplitude of cosine curve on daytime, in GPS broadcast ephemeris, provided
Figure 791180DEST_PATH_IMAGE006
coefficient,
Figure 357291DEST_PATH_IMAGE005
with
Figure 393380DEST_PATH_IMAGE006
the relation of coefficient is as follows:
Figure 81850DEST_PATH_IMAGE007
In formula
Figure 13510DEST_PATH_IMAGE008
it is the magnetic latitude of ionosphere point of puncture.
Figure 383311DEST_PATH_IMAGE009
for initial phase, corresponding to the local time of cosine curve limit, generally get 50400s(local time 14:00). for the cycle of cosine curve, in broadcast ephemeris
Figure 398857DEST_PATH_IMAGE011
coefficient is tried to achieve, and relational expression is as follows:
Figure 820743DEST_PATH_IMAGE012
This was given orders the beginning of the eighties, was subject to the restriction of theory and technology at that time, also had many other weak points:
1. will
Figure 728656DEST_PATH_IMAGE003
be fixed as 5ns, Global Ionospheric zenith direction at night total electron content VTEC is seen as constant term, is equivalent to 9.0TECU.And mass data analysis shows, on different latitudes, the mean value of ionosphere VTEC at night can change, in fact, organize the observed result of IGS according to international GPS service, the mean value of Global Ionospheric VTEC at night is relevant with solar activity, in a solar cycle, variation range can be increased to about 20TECU from 6TECU, therefore, fixing
Figure 801654DEST_PATH_IMAGE003
can cause the deviation that whole model is very large, mean deviation is in 20% ~ 30% left and right;
2. used fixing initial phase, supposed that, on the zenith direction of any magnetic latitude overhead, vertical total electron content VTEC maximal value appears at 2 hours later local high noon.
For the Radio Satellite navigation positioning systems such as GPS/BDS, ionosphere delay error is one of main error source affecting navigation and positioning accuracy and accuracy, and the distance error that ionosphere causes generally can reach 15m by day, and can reach 3m night; In zenith direction maximum, can reach 50m, maximum can reach 150m in the horizontal direction, and above-mentioned two weak points of Klobuchar model will cause that deviation appears in range observation, thus the precision of impact location and navigation results.
Summary of the invention
Based on above-mentioned situation, the present invention proposes a kind of based on the improved Navsat localization method of ionosphere delay, the method is for ionospheric delay model---Klobuchar (Crow cloth is had a rest) model improves, by initial phase and night VTEC flat field all write as the function of latitude, set up improved Klobuchar model, improve the precision of ionosphere delay modeling, calculate more accurate ionosphere and correct, thereby obtain more high-precision location and navigation results.
The invention discloses a kind ofly based on the improved Navsat localization method of ionosphere delay, comprise step:
Obtain GIM data, utilize described GIM data to carry out model parameter estimation; Described model parameter is imported in parameter fitting model and carries out ionosphere delay matching; By described ionosphere delay, calculate navigator fix coordinate.
Described model parameter estimation is on the basis of described GIM data least square adjustment, to introduce inequality constrain adjustment.
Described ionosphere delay fits to according to different latitude sections and carries out different ionosphere delay parameter fittings.
Described parameter fitting model adopts following formula:
Figure 769610DEST_PATH_IMAGE013
In formula,
Figure 678791DEST_PATH_IMAGE014
on 50 ° of expression north and south latitudes
Figure 390395DEST_PATH_IMAGE015
mean value (i=2,3,4), when
Figure 583479DEST_PATH_IMAGE016
time, in formula
Figure 722337DEST_PATH_IMAGE017
number get , when time, in formula number get
Figure 725879DEST_PATH_IMAGE020
. be the vertical zenith delay in ionosphere, unit is TECU, and corresponding frequencies is
Figure 412128DEST_PATH_IMAGE022
, t be take the local time at the point of puncture place, ionosphere that h is unit,
Figure 314225DEST_PATH_IMAGE008
it is the geodetic latitude at point of puncture place, ionosphere.For calculating different frequency signals through ionospheric zenith ionosphere delay
Figure 607934DEST_PATH_IMAGE021
, need to take advantage of a mapping function k (f) relevant with frequency.
A. with B be the constant that postpones of Nighttime ionosphere and with the linear change item of latitude, wherein:
B.
Figure 779656DEST_PATH_IMAGE005
for the amplitude of ionosphere delay cosine curve on daytime, use
Figure 431217DEST_PATH_IMAGE006
coefficient calculations obtains:
Figure 24003DEST_PATH_IMAGE024
C.
Figure 481529DEST_PATH_IMAGE010
for the cycle of cosine curve, use
Figure 295902DEST_PATH_IMAGE011
coefficient is tried to achieve:
D.
Figure 198447DEST_PATH_IMAGE009
be the initial phase of cosine function, corresponding to the local time of curve limit, use coefficient is tried to achieve:
Figure 128543DEST_PATH_IMAGE027
。
The invention also discloses and a kind ofly based on the improved Navsat positioning system of ionosphere delay, it is characterized in that, comprising: GIM data acquisition module, parameter estimation module, ionosphere delay fitting module, navigation positioning module, modules successively signal connects; GIM data acquisition module, for the GIM data of obtaining; Parameter estimation module, for utilizing GIM data to carry out real-time foundation and the parameter estimation of parameter fitting model; Ionosphere delay fitting module is for receiving the estimated parameter of the estimation module output that gets parms, and local time t and the latitude of the point of puncture using according to estimated parameter, user
Figure 932026DEST_PATH_IMAGE008
, carry out the matching of ionosphere Global Ionospheric delay; Navigation positioning module, for according to the fitting result of ionosphere delay fitting module, navigation location algorithm, calculates navigator fix coordinate.
Described model parameter estimation is on the basis of described GIM data least square adjustment, to introduce inequality constrain adjustment.
Described ionosphere delay fits to according to different latitude sections and carries out different ionosphere delay parameter fittings.
With respect to prior art, provided by the invention proposed a kind of based on the improved Navsat localization method of ionosphere delay, can be applied to existing vehicle mounted guidance terminal or integrated navigation system or terminal, neither need user to increase extra hardware spending, do not need user to modify to existing software architecture yet, can directly embed in integrated navigation system, utilize existing resource can realize the judgement of drifting about of GNSS signal.Use this method can greatly improve the positioning precision of system, and then promote the performance of whole navigational system or device end.
Accompanying drawing explanation
Fig. 1 is a kind of schematic flow sheet based on the improved Navsat localization method of ionosphere delay embodiment of the present invention;
Fig. 2 is 2008 ~ 2012 years fitting result RMS comparison diagrams of employing different parameters model of fit of the present invention;
Fig. 3 is of the present invention a kind of based on the improved Navsat positioning system structure of ionosphere delay schematic diagram.
Embodiment
Below in conjunction with better embodiment wherein, the present invention program is described in detail.
A kind of schematic flow sheet based on the improved Navsat localization method of ionosphere delay embodiment has been shown in Fig. 1.
S101: obtain GIM data, utilize described GIM data to carry out model parameter estimation.
The Global Ionospheric model GIM obtaining by European orbit determination center (CODE) (Global Ionosphere Model) data, and utilize GIM data to carry out real-time foundation and the parameter estimation of parameter fitting model.Here, what parameter estimation mainly adopted is that the GIM data of obtaining are carried out to least square adjustment, can obtain corresponding estimated parameter.On the basis of least square adjustment of the present invention, introduce inequality constrain adjustment.Because when above-mentioned parameter model of fit builds Global Ionospheric model, need to increase to the parameter value in model all multi-constraint conditions, to guarantee the accuracy of parameter calculation.The present invention sets up the linear inequality constraint to N parameter according to the Changing Pattern of each all Diurnal Variation parameter in ionosphere, latitude area, on the basis of least square adjustment, introduce inequality constrain adjustment, improve parameter calculation result, reduce the impact of model error, thereby improve the precision of parameter calculation, reach the object that improves positioning precision.Introducing with after the constraint adjustment of linear inequality, the absolute value of the residual error mean value that model parameter is resolved reduces, standard deviation also has corresponding improvement, the precision of parameter calculation result is improved, (vertical ionospheric electron density (vertical total electron content, VTEC) approaches the VTEC result of CODE analytic centre issue to the VTEC value that parameter fitting model calculates more.The impact of the error that the introducing of therefore, inequality constrain adjustment can improve parameter fitting model effectively on navigation precision.
S102: described model parameter is imported in parameter fitting model and carries out ionosphere delay matching.
According to the S101 parameter of undated parameter model of fit at times, user can be according to the local time t of point of puncture and latitude
Figure 686355DEST_PATH_IMAGE008
, utilize parameter fitting model just can carry out (comprising N the parameter of exporting in S102) matching of Global Ionospheric delay.The process of matching is the process that following parameter fitting model is asked parameter I z (t).Existing parameter fitting model, generally carries out use scenes idealizedly, can not carry out different parameter fittings according to current magnetic latitude, although calculated easyly, the error being actually used in product is larger.And different from existing parameter fitting process, the present invention must first obtain user's point of puncture latitude, then according to different latitude sections carry out different ionosphere delay parameter fittings (as
Figure 751263DEST_PATH_IMAGE028
or be one section), can solve the problem of the bigger error that existing idealized model brings.The concrete formula of parameter fitting model of the present invention is as follows:
Figure 251963DEST_PATH_IMAGE013
In formula,
Figure 555905DEST_PATH_IMAGE014
on 50 ° of expression north and south latitudes
Figure 96608DEST_PATH_IMAGE015
mean value (i=2,3,4), when
Figure 287549DEST_PATH_IMAGE016
time, in formula
Figure 888295DEST_PATH_IMAGE017
number get
Figure 351637DEST_PATH_IMAGE018
, when time, in formula
Figure 803795DEST_PATH_IMAGE017
number get . be the vertical zenith delay in ionosphere, unit is TECU, and corresponding frequencies is
Figure 470903DEST_PATH_IMAGE022
, t be take the local time at the point of puncture place, ionosphere that h is unit,
Figure 639366DEST_PATH_IMAGE008
it is the geodetic latitude at point of puncture place, ionosphere.For calculating different frequency signals through ionospheric zenith ionosphere delay
Figure 581914DEST_PATH_IMAGE021
, need to take advantage of a mapping function k (f) relevant with frequency.
Figure 82166DEST_PATH_IMAGE030
. with B be the constant that postpones of Nighttime ionosphere and with the linear change item of latitude, wherein:
Figure 788402DEST_PATH_IMAGE023
2.
Figure 901851DEST_PATH_IMAGE005
for the amplitude of ionosphere delay cosine curve on daytime, use
Figure 889399DEST_PATH_IMAGE006
coefficient calculations obtains:
3.
Figure 253832DEST_PATH_IMAGE010
for the cycle of cosine curve, use
Figure 272604DEST_PATH_IMAGE011
coefficient is tried to achieve:
Figure 747447DEST_PATH_IMAGE032
4.
Figure 775446DEST_PATH_IMAGE009
be the initial phase of cosine function, corresponding to the local time of curve limit, use coefficient is tried to achieve:
Figure 225330DEST_PATH_IMAGE033
This parameter fitting model
Figure 921891DEST_PATH_IMAGE003
, B,
Figure 298121DEST_PATH_IMAGE034
,
Figure 599789DEST_PATH_IMAGE035
,
Figure 288260DEST_PATH_IMAGE036
14 parameters such as (n=0,1,2,3).
Fig. 2 shows parameter fitting model that the present invention uses and Klobuchar model the VTEC result of 2008-2012 years.As shown in the figure, K8 is used for identifying Klobuchar model, and K14 is for identification parameter model of fit, and in figure, top curve is the result curve of Klobuchar model, and lower curve is the result curve of parameter fitting model.2008, the parameter fitting models fitting ionosphere VTEC result that the present invention in 2009 and 2010 uses is better, RMS is less than 5TECU substantially, residual error statistics standard deviation is also all less than 5TECU, the parameter fitting models fitting VTEC result that the present invention in 2011 and 2012 uses is poor, RMS is between 4 ~ 11TECU, and the standard deviation of residual error is in 7TECU left and right.The reason that occurs this phenomenon is mainly, solar activity peak period is probably between 2013～2014 years, though within 2011 and 2012, be not the highest year of kurtosis, but it is strong that solar activity is tending towards, there is disturbance in ionosphere, therefore the precision of models fitting ionosphere VTEC reduces, but still the grid points residual distribution that can guarantee 95% left and right is between-14TECU ~ 14TECU, correct effect and can reach 70%, even 80%.
S103: calculate navigator fix coordinate by described ionosphere delay.
In the result substitution location algorithm of the ionosphere delay that S102 matching is obtained (as single-point location algorithm, relative localization algorithm and Static Precise Point Positioning algorithm), can carry out ionosphere delay correction, obtain navigator fix coordinate, and then realize navigator fix.
As shown in Figure 3, a kind of based on the improved Navsat positioning system structure of ionosphere delay schematic diagram.
Based on the improved Navsat positioning system of ionosphere delay, comprise, GIM data acquisition module, parameter estimation module, ionosphere delay fitting module, navigation positioning module, modules successively signal connects.
GIM data acquisition module, for GIM (the Global Ionosphere Model) data of obtaining; Parameter estimation module, for utilizing GIM data to carry out real-time foundation and the parameter estimation of parameter fitting model; Ionosphere delay fitting module is for receiving the estimated parameter of the estimation module output that gets parms, and local time t and the latitude of the point of puncture using according to estimated parameter, user
Figure 409799DEST_PATH_IMAGE008
, carry out the matching of ionosphere Global Ionospheric delay; Navigation positioning module, for according to the fitting result of ionosphere delay fitting module, navigation location algorithm, calculates navigator fix coordinate.
Wherein, what parameter estimation mainly adopted is that the GIM data of obtaining are carried out to least square adjustment, can obtain corresponding estimated parameter, and this part and the inventive method are similar, are no longer repeated in this description herein.
Local time t and the latitude of the above said point of puncture using according to estimated parameter, user
Figure 779601DEST_PATH_IMAGE008
, the fit procedure of carrying out ionosphere Global Ionospheric delay, existing parameter fitting model, generally use scenes is carried out idealized, can not carry out different parameter fittings according to current magnetic latitude, although calculated easyly, the error being actually used in product is larger.And different from existing parameter fitting process, the present invention must first obtain user's point of puncture latitude, then carries out different ionosphere delay parameter fittings according to different latitudes, can solve the problem of the bigger error that existing idealized model brings.The concrete formula of parameter fitting model adopting is as follows:
In formula, on 50 ° of expression north and south latitudes mean value (i=2,3,4), when
Figure 937995DEST_PATH_IMAGE016
time, in formula number get
Figure 978949DEST_PATH_IMAGE018
, when
Figure 75081DEST_PATH_IMAGE019
time, in formula number get
Figure 464922DEST_PATH_IMAGE020
. be the vertical zenith delay in ionosphere, unit is TECU, and corresponding frequencies is
Figure 249525DEST_PATH_IMAGE022
, t be take the local time at the point of puncture place, ionosphere that h is unit,
Figure 569080DEST_PATH_IMAGE008
it is the geodetic latitude at point of puncture place, ionosphere.For calculating different frequency signals through ionospheric zenith ionosphere delay
Figure 288774DEST_PATH_IMAGE021
, need to take advantage of a mapping function k (f) relevant with frequency.
Figure 660850DEST_PATH_IMAGE030
. with B be the constant that postpones of Nighttime ionosphere and with the linear change item of latitude, wherein:
Figure 598030DEST_PATH_IMAGE023
2.
Figure 437810DEST_PATH_IMAGE005
for the amplitude of ionosphere delay cosine curve on daytime, use coefficient calculations obtains:
Figure 538807DEST_PATH_IMAGE031
3.
Figure 943375DEST_PATH_IMAGE010
for the cycle of cosine curve, use
Figure 637661DEST_PATH_IMAGE011
coefficient is tried to achieve:
Figure 617118DEST_PATH_IMAGE037
4. be the initial phase of cosine function, corresponding to the local time of curve limit, use
Figure 605114DEST_PATH_IMAGE026
coefficient is tried to achieve:
Figure 419486DEST_PATH_IMAGE038
This parameter fitting model
Figure 304266DEST_PATH_IMAGE003
, B,
Figure 571299DEST_PATH_IMAGE034
,
Figure 580319DEST_PATH_IMAGE035
,
Figure 249198DEST_PATH_IMAGE036
14 parameters such as (n=0,1,2,3).
The above embodiment has only expressed several embodiment of the present invention, and it describes comparatively concrete and detailed, but can not therefore be interpreted as the restriction to the scope of the claims of the present invention.It should be pointed out that for the person of ordinary skill of the art, without departing from the inventive concept of the premise, can also make some distortion and improvement, these all belong to protection scope of the present invention.Therefore, the protection domain of patent of the present invention should be as the criterion with claims.

Claims (8)

1. based on the improved Navsat localization method of ionosphere delay, it is characterized in that, comprise step:
Obtain GIM data, utilize described GIM data to carry out model parameter estimation; Described model parameter is imported in parameter fitting model and carries out ionosphere delay matching; By described ionosphere delay, calculate navigator fix coordinate.
2. Navsat localization method according to claim 1, is characterized in that, described model parameter estimation is on the basis of described GIM data least square adjustment, to introduce inequality constrain adjustment.
3. Navsat localization method according to claim 1, is characterized in that, described ionosphere delay fits to according to different latitude sections and carries out different ionosphere delay parameter fittings.
4. according to the Navsat localization method described in claim 1-3, it is characterized in that, described parameter fitting model adopts following formula:
In formula,
Figure 639520DEST_PATH_IMAGE002
on 50 ° of expression north and south latitudes
Figure 94772DEST_PATH_IMAGE003
mean value (i=2,3,4), when
Figure 56912DEST_PATH_IMAGE004
time, in formula
Figure 623023DEST_PATH_IMAGE005
number get
Figure 472161DEST_PATH_IMAGE006
, when
Figure 98314DEST_PATH_IMAGE007
time, in formula
Figure 282171DEST_PATH_IMAGE005
number get
Figure 651973DEST_PATH_IMAGE008
;
Figure 621197DEST_PATH_IMAGE009
be the vertical zenith delay in ionosphere, unit is TECU, and corresponding frequencies is
Figure 418251DEST_PATH_IMAGE010
, t be take the local time at the point of puncture place, ionosphere that h is unit,
Figure 89404DEST_PATH_IMAGE011
it is the geodetic latitude at point of puncture place, ionosphere; For calculating different frequency signals through ionospheric zenith ionosphere delay
Figure 997317DEST_PATH_IMAGE009
, need to take advantage of a mapping function k (f) relevant with frequency;
A.
Figure 818118DEST_PATH_IMAGE012
with B be the constant that postpones of Nighttime ionosphere and with the linear change item of latitude, wherein:
B.
Figure 944523DEST_PATH_IMAGE014
for the amplitude of ionosphere delay cosine curve on daytime, use
Figure 656127DEST_PATH_IMAGE015
coefficient calculations obtains:
Figure 599944DEST_PATH_IMAGE016
C.
Figure 738801DEST_PATH_IMAGE017
for the cycle of cosine curve, use
Figure 118967DEST_PATH_IMAGE018
coefficient is tried to achieve:
D. be the initial phase of cosine function, corresponding to the local time of curve limit, use
Figure 742343DEST_PATH_IMAGE021
coefficient is tried to achieve:
Figure 609805DEST_PATH_IMAGE022
。
5. based on the improved Navsat positioning system of ionosphere delay, it is characterized in that, comprising: GIM data acquisition module, parameter estimation module, ionosphere delay fitting module, navigation positioning module, modules successively signal connects; GIM data acquisition module, for the GIM data of obtaining; Parameter estimation module, for utilizing GIM data to carry out real-time foundation and the parameter estimation of parameter fitting model; Ionosphere delay fitting module is for receiving the estimated parameter of the estimation module output that gets parms, and local time t and the latitude of the point of puncture using according to estimated parameter, user , carry out the matching of ionosphere Global Ionospheric delay; Navigation positioning module, for according to the fitting result of ionosphere delay fitting module, navigation location algorithm, calculates navigator fix coordinate.
6. Navsat positioning system according to claim 5, is characterized in that, described model parameter estimation is on the basis of described GIM data least square adjustment, to introduce inequality constrain adjustment.
7. Navsat positioning system according to claim 5, is characterized in that, ionosphere delay fits to according to different latitude sections and carries out different ionosphere delay parameter fittings.
8. according to the Navsat positioning system described in claim 5-7, it is characterized in that, described parameter fitting model adopts following formula:
Figure 316041DEST_PATH_IMAGE001
In formula,
Figure 859018DEST_PATH_IMAGE002
on 50 ° of expression north and south latitudes
Figure 417038DEST_PATH_IMAGE003
mean value (i=2,3,4), when
Figure 824535DEST_PATH_IMAGE004
time, in formula
Figure 846718DEST_PATH_IMAGE005
number get , when
Figure 91066DEST_PATH_IMAGE007
time, in formula
Figure 548592DEST_PATH_IMAGE005
number get
Figure 362964DEST_PATH_IMAGE008
; be the vertical zenith delay in ionosphere, unit is TECU, and corresponding frequencies is , t be take the local time at the point of puncture place, ionosphere that h is unit,
Figure 526726DEST_PATH_IMAGE011
it is the geodetic latitude at point of puncture place, ionosphere; For calculating different frequency signals through ionospheric zenith ionosphere delay , need to take advantage of a mapping function k (f) relevant with frequency;
A.
Figure 2018DEST_PATH_IMAGE012
with B be the constant that postpones of Nighttime ionosphere and with the linear change item of latitude, wherein:
Figure 756347DEST_PATH_IMAGE013
B.
Figure 821255DEST_PATH_IMAGE014
for the amplitude of ionosphere delay cosine curve on daytime, use
Figure 154760DEST_PATH_IMAGE015
coefficient calculations obtains:
Figure 319025DEST_PATH_IMAGE016
C.
Figure 622968DEST_PATH_IMAGE017
for the cycle of cosine curve, use coefficient is tried to achieve:
Figure 354612DEST_PATH_IMAGE019
D.
Figure 17674DEST_PATH_IMAGE020
be the initial phase of cosine function, corresponding to the local time of curve limit, use coefficient is tried to achieve:
Figure 638459DEST_PATH_IMAGE023
。
CN201410002208.7A 2014-01-03 2014-01-03 Navigational satellite positioning method and system based on ionospheric delay improvement Pending CN103713303A (en)

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CN106405582B (en) * 2016-08-31 2019-01-15 和芯星通科技(北京)有限公司 A kind of processing method and processing device of ionospheric error
CN107966717A (en) * 2017-11-23 2018-04-27 千寻位置网络有限公司 The Multi-GNSS Deformation Monitoring Data processing methods of low cost terminals
CN108169776A (en) * 2017-11-23 2018-06-15 中国科学院光电研究院 Ionosphere delay error modification method based on background model and measured data
CN107966717B (en) * 2017-11-23 2021-05-28 千寻位置网络有限公司 Multi-GNSS deformation monitoring data processing method of low-cost terminal
CN108169776B (en) * 2017-11-23 2022-01-21 中国科学院光电研究院 Ionospheric delay error correction method based on background model and measured data
CN114488227A (en) * 2022-01-26 2022-05-13 西南交通大学 Multipath error correction method based on spatial correlation
CN114488227B (en) * 2022-01-26 2023-10-20 西南交通大学 Multipath error correction method based on spatial correlation

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