CN108732597A - A kind of the time reference method for building up and system of multi-satellite navigation system - Google Patents

A kind of the time reference method for building up and system of multi-satellite navigation system Download PDF

Info

Publication number
CN108732597A
CN108732597A CN201810564951.XA CN201810564951A CN108732597A CN 108732597 A CN108732597 A CN 108732597A CN 201810564951 A CN201810564951 A CN 201810564951A CN 108732597 A CN108732597 A CN 108732597A
Authority
CN
China
Prior art keywords
satellite
clock
navigation system
time
satellite navigation
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN201810564951.XA
Other languages
Chinese (zh)
Other versions
CN108732597B (en
Inventor
穆旭成
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beijing Future Navigation Technology Co Ltd
Original Assignee
Beijing Future Navigation Technology Co Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Beijing Future Navigation Technology Co Ltd filed Critical Beijing Future Navigation Technology Co Ltd
Priority to CN201810564951.XA priority Critical patent/CN108732597B/en
Publication of CN108732597A publication Critical patent/CN108732597A/en
Application granted granted Critical
Publication of CN108732597B publication Critical patent/CN108732597B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S19/00Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13Receivers
    • G01S19/23Testing, monitoring, correcting or calibrating of receiver elements
    • G01S19/235Calibration of receiver components
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S19/00Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13Receivers
    • G01S19/35Constructional details or hardware or software details of the signal processing chain
    • G01S19/37Hardware or software details of the signal processing chain

Landscapes

  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Signal Processing (AREA)
  • Position Fixing By Use Of Radio Waves (AREA)

Abstract

The invention discloses a kind of time reference method for building up of multi-satellite navigation system and system, the method includes:The earth station GNSS observation data and spaceborne GNSS for obtaining multi-satellite navigation system observe data, observe data according to earth station GNSS respectively and spaceborne GNSS observation data build corresponding earth station's observation model and spaceborne GNSS observation models;According to earth station's observation model and spaceborne GNSS observation models, in multi-satellite navigation system navigation satellite and low orbit satellite carry out joint precise orbit determination and time synchronization, obtain the clock correction of each satellite navigation system;The time scale of multi-satellite navigation system is built according to the clock correction of each satellite navigation system;Time scale is tied under the system time of a certain satellite navigation system, generates the uniform time reference of each satellite in multi-satellite navigation system.The present invention can be based on multi-satellite navigation system satellite atomic clock, realize continuous, stable time reference the foundation and maintenance of multi-satellite navigation system.

Description

A kind of the time reference method for building up and system of multi-satellite navigation system
Technical field
The present invention relates to technical field of satellite navigation more particularly to a kind of based on multi-satellite navigation system satellite atomic clock The time reference method for building up and system of multi-satellite navigation system.
Background technology
Three big basic factors (time, track, signal) one of of the time as composition satellite navigation system, to satellite navigation System plays a supportive role, and is the important leverage of maintenance system normal operation order and workflow, largely determines Satellite navigation system provides positioning, time service, the function and performance to test the speed.
The time reference of navigation system is referred to as the unified time of satellite navigation system, is the comparison according to backup clock group A kind of time scale that data generate, navigation system need, by the time unification to time reference of each satellite atomic clock, to send out It penetrates and is used to user.Each navigation system establishes special time reference (system time).Currently, when satellite navigation system Between benchmark include the following two kinds definition mode:
1) master clock:It is defined by the master clock of master station, such as the system time GLONASST of GLONASS, by ground monitoring part Several high-precision atomic clocks of configuration are traced to the source by data comparison to GLONASST to Russian national standard time UTC (SU), the GLONASS satellite time is kept by satellite atomic clock, and Complex Control Center compares it with GLONASST twice daily, Star clock correction value is reached into satellite;The system time BDT of the Big Dipper is also a kind of mode that master clock defines, by with being located at Beidou II The time frequency system at face fortune control system master station is established and is maintained, and is traced to the source to country of Chinese Academy of Sciences time service center UTC (NTSC), using defending Star two-way time transfer technology is transmitted to each monitoring station clock, and each satellite clock is passed to the two-way Time transfer receiver technology of radio, The time synchronization of guarantee system.
2) paper clock:It is a kind of for synthesis master slave mode, the clock group being made of all ground clocks and satellite clock defines, when system Between scale obtain synthesizing clock by the weighted average of each clock.If the system time of GPS is GPST, by Kalman filter algorithm, Common weight is carried out to the combination clock of the high-precision atomic clock of monitoring station and the satellite atomic clock of satellite by ground master station, is established With safeguard GPST, trace to the source to USNO-US Naval Observatory UTC (USNO).The time system GST of Galileo is equally fixed using combination clock Justice receives the observation data from survey station by ground control centre, obtains UTC by regarding method altogether, filtering generates clock error correction number And average frequency, average frequency act on Galileo system master clocks, are used for the foundation of system benchmark GST.And world GNSS takes It is also a kind of mode of synthesis clock that the time scale of business tissue (IGS), which is established, logical using the survey station and GPS satellite clock of several stabilizations It crosses weighted average and obtains the time reference of an inside, and be tied on GPST so that finally comprehensive clock correction product has phase Same time reference.
Since there is differences in design concept, time, track, frequency etc. for different satellite navigation systems, cause There are following problems for the method for existing settling time benchmark:
1) the system time existence time deviation that each system determines, cause the satellite clock correction finally solved there is also when Between deviation;
2) each system more than does not utilize the spaceborne atom of low orbit satellite when establishing and safeguarding respective system time reference Clock only uses navigation satellite satellite atomic clock in satellite end, can not be suitable for including each satellite navigation system and low orbit satellite Multi-satellite navigation system.
Invention content
In view of the above problems, the present invention proposes a kind of the time reference method for building up and system of multi-satellite navigation system, It can be based on multi-satellite navigation system satellite atomic clock, realize the foundation and maintenance of time reference that is continuous, stablizing.
One aspect of the present invention provides a kind of time reference method for building up of multi-satellite navigation system, including:
The earth station GNSS observation data and spaceborne GNSS for obtaining multi-satellite navigation system observe data, respectively according to Earth station GNSS observes data and the spaceborne GNSS observations data build corresponding earth station's observation model and spaceborne GNSS is seen Survey model;
According to earth station's observation model and spaceborne GNSS observation models, to the navigation in the multi-satellite navigation system Satellite and low orbit satellite carry out joint precise orbit determination and time synchronization, obtain the clock correction of each satellite navigation system;
The time scale of multi-satellite navigation system is built according to the clock correction of each satellite navigation system;
The time scale is tied under the system time of a certain satellite navigation system, generates the multi-satellite navigation system The uniform time reference of each satellite in system, for each satellite navigation system by the uniform time reference be attached to respectively it is right In the original clock correction answered, to obtain the satellite clock correction under each leisure uniform time reference.
Optionally, described according to earth station's observation model and spaceborne GNSS observation models, to the multi-satellite navigation Navigation satellite and low orbit satellite in system carry out joint precise orbit determination and time synchronization, obtain each satellite navigation system Clock correction, including:
According to preset initial parameter value respectively to earth station's observation model and spaceborne GNSS observation models into line Propertyization processing;
Earth station's observation model after linearization process and spaceborne GNSS observation models are calculated using least square method, Obtain the clock correction parameter of each satellite navigation system;
By the clock correction restriction on the parameters of each satellite navigation system to corresponding navigation ephemeris.
Optionally, the time ruler that multi-satellite navigation system is built according to the clock correction of each satellite navigation system Degree, including:
Phase transition is carried out to the clock correction of each satellite navigation system, the frequency for obtaining each satellite navigation system is seen Measured value;
The clock status equation of each satellite clock is built, clock observational equation is built based on the clock status equation;
Each navigation satellite and the corresponding satellite clock of low orbit satellite are combined into clock group, according to the clock of each satellite clock State equation builds the state equation of the clock group;
The clock is built according to the frequency observation value of the state equation of the clock group and each satellite navigation system The observational equation of group;
According to the observational equation of the clock group, calculate each satellite clock is relative to the satellite navigation system to be tied to The frequency sequence of system time;
Time series of each satellite clock relative to the system time is calculated according to the frequency sequence, and according to described Time series builds the time scale.
Optionally, described that time series of each satellite clock relative to the system time is calculated according to the frequency sequence Including:
To the frequency sequence carry out integral operation obtain corresponding satellite clock time relative to the system time when Between sequence.
Optionally, described to be tied to the time scale under the system time of a certain satellite navigation system, described in formation The uniform time reference of each satellite in multi-satellite navigation system, including:
Build the state equation and observational equation of bounding algorithm;
According to the state equation and observational equation of the bounding algorithm, a certain defend is tied to using Kalman filtering method calculating Time series under the system time of star navigation system, using the time series as each satellite in the multi-satellite navigation system Uniform time reference.
Another aspect of the present invention provides a kind of time reference of multi-satellite navigation system and establishes system, including:
Model construction unit, the earth station GNSS for obtaining multi-satellite navigation system observe data and spaceborne GNSS observations Data observe data according to the earth station GNSS respectively and the spaceborne GNSS observations data build corresponding earth station and observe Model and spaceborne GNSS observation models;
Clock correction acquiring unit, for according to earth station's observation model and spaceborne GNSS observation models, more being defended to described Navigation satellite and low orbit satellite in star navigation system carry out joint precise orbit determination and time synchronization, obtain each satellite navigation The clock correction of system;
Time scale establishes unit, for building multi-satellite navigation system according to the clock correction of each satellite navigation system Time scale;
Time reference generation unit, the system time for the time scale to be tied to a certain satellite navigation system Under, the uniform time reference of each satellite in the multi-satellite navigation system is generated, so that each satellite navigation system will be described Uniform time reference is attached in corresponding original clock correction, to obtain the satellite clock under each leisure uniform time reference Difference.
Optionally, the clock correction acquiring unit, including:
Linear processing module, for according to preset initial parameter value respectively to earth station's observation model and spaceborne GNSS observation models carry out linearization process;
First computing module, for using least square method calculate linearization process after earth station's observation model and Spaceborne GNSS observation models obtain the clock correction parameter of each satellite navigation system;
Processing module is constrained, is used for the clock correction restriction on the parameters of each satellite navigation system to corresponding navigation Ephemeris.
Optionally, the time scale establishes unit, including:
Phase conversion carries out phase transition for the clock correction to each satellite navigation system, obtains each defend The frequency observation value of star navigation system;
First model construction module, the clock status equation for building each satellite clock are based on the clock status side Journey builds clock observational equation;
Second model construction module, for each navigation satellite and the corresponding satellite clock of low orbit satellite to be combined into clock Group builds the state equation of the clock group according to the clock status equation of each satellite clock;
Third model construction module, for according to the state equation of the clock group and each satellite navigation system Frequency observation value builds the observational equation of the clock group;
Second computing module, for according to the observational equation of the clock group, calculating each satellite clock relative to being intended to be tied to Satellite navigation system system time frequency sequence;
Time scale builds module, for calculating each satellite clock relative to the system time according to the frequency sequence Time series, and the time scale is built according to the time series.
Optionally, the time scale builds module, and phase is obtained specifically for carrying out integral operation to the frequency sequence Time series of the satellite clock time answered relative to the system time.
Optionally, the time reference generation unit, including:
4th model construction module, state equation and observational equation for building bounding algorithm;
Third computing module, for the state equation and observational equation according to the bounding algorithm, using Kalman filtering Method calculates the time series being tied under the system time of a certain satellite navigation system, using the time series as more satellites The uniform time reference of each satellite in navigation system.
The time reference method for building up and system of multi-satellite navigation system provided in an embodiment of the present invention, it is all using covering When the earth station net GNSS and spaceborne GNSS observation data setup time benchmark of system, the stability of result and reliable ensure that Property;During the foundation of time reference, atomic clock group is formed using all satellite atomic clocks, and maintain by weighting, protected Demonstrate,prove the higher stability of time reference short-period term and precision;By the way that time reference to be finally tied to some satellite navigation system It unites under the time, the clock correction for each satellite that ensure that the stabilization of time reference long period term, and finally obtain has unification Time reference facilitates fusion treatment and the application of multi-satellite navigation system data.
Above description is only the general introduction of technical solution of the present invention, in order to better understand the technical means of the present invention, And can be implemented in accordance with the contents of the specification, and in order to allow above and other objects of the present invention, feature and advantage can It is clearer and more comprehensible, below the special specific implementation mode for lifting the present invention.
Description of the drawings
By reading the detailed description of hereafter preferred embodiment, various other advantages and benefit are common for this field Technical staff will become clear.Attached drawing only for the purpose of illustrating preferred embodiments, and is not considered as to the present invention Limitation.And throughout the drawings, the same reference numbers will be used to refer to the same parts.In the accompanying drawings:
Fig. 1 is the flow chart of the time reference method for building up of the multi-satellite navigation system of the embodiment of the present invention;
Fig. 2 be the embodiment of the present invention multi-satellite navigation system time reference method for building up in step S12 subdivision stream Cheng Tu;
Fig. 3 be the embodiment of the present invention multi-satellite navigation system time reference method for building up in step S13 subdivision stream Cheng Tu;
Fig. 4 is that the time reference of the multi-satellite navigation system of the embodiment of the present invention establishes the structural schematic diagram of system.
Specific implementation mode
The exemplary embodiment of the disclosure is more fully described below with reference to accompanying drawings.Although showing the disclosure in attached drawing Exemplary embodiment, it being understood, however, that may be realized in various forms the disclosure without should be by embodiments set forth here It is limited.On the contrary, these embodiments are provided to facilitate a more thoroughly understanding of the present invention, and can be by the scope of the present disclosure Completely it is communicated to those skilled in the art.
Those skilled in the art of the present technique are appreciated that unless expressly stated, singulative " one " used herein, " one It is a ", " described " and "the" may also comprise plural form.It is to be further understood that is used in the specification of the present invention arranges It refers to there are the feature, integer, step, operation, element and/or component, but it is not excluded that presence or addition to take leave " comprising " Other one or more features, integer, step, operation, element, component and/or their group.
Those skilled in the art of the present technique are appreciated that unless otherwise defined, all terms used herein (including technology art Language and scientific terminology), there is meaning identical with the general understanding of the those of ordinary skill in fields of the present invention.Should also Understand, those terms such as defined in the general dictionary, it should be understood that have in the context of the prior art The consistent meaning of meaning, and unless by specific definitions, otherwise will not be explained with the meaning of idealization or too formal.
Fig. 1 diagrammatically illustrates the stream of the time reference method for building up of the multi-satellite navigation system of one embodiment of the invention Cheng Tu.Referring to Fig.1, the time reference method for building up of the multi-satellite navigation system of the embodiment of the present invention specifically includes following steps:
S11, the earth station GNSS observation data for obtaining multi-satellite navigation system and spaceborne GNSS observe data, respectively basis Earth station GNSS observation data and the spaceborne GNSS observations data build corresponding earth station's observation model and spaceborne GNSS observation models.
The GNSS observational equations of earth station are:
Spaceborne GNSS observational equations are:
In formula, f is frequency,It (is indicated with distance) for carrier phase observation data, s indicates that navigation satellite, k indicate survey station Or low orbit satellite,For Pseudo-range Observations,For fuzziness,For earth station or low orbit satellite and navigation satellite geometry away from From dtkFor survey station or low orbit satellite clock correction, dtsFor navigation satellite clock correction,It is ionosphere to phase With the influence of pseudorange,For tropospheric delay, For other various correction (including multipath, antennas Phase center, earth tide, oceanic load tide, relativistic effect etc.) influence to phase and pseudorange.
S12, according to earth station's observation model and spaceborne GNSS observation models, in the multi-satellite navigation system Navigation satellite and low orbit satellite carry out joint precise orbit determination and time synchronization, obtain the clock correction of each satellite navigation system.
S13, the time scale that multi-satellite navigation system is built according to the clock correction of each satellite navigation system.
S14, the time scale is tied under the system time of a certain satellite navigation system, generates more satellites and leads The uniform time reference of each satellite in boat system, so that the uniform time reference is attached to respectively by each satellite navigation system In self-corresponding original clock correction, to obtain the satellite clock correction under each leisure uniform time reference, multi-satellite navigation system is realized The satellite clock correction of the uniform time reference of system.
The time reference method for building up of multi-satellite navigation system provided in an embodiment of the present invention, it is systematic using covering When GNSS and spaceborne GNSS observation data setup time benchmark are netted by earth station, the stability and reliability of result ensure that;When Between benchmark foundation during, form atomic clock group using all satellite atomic clocks, and maintained by weighting, ensure time base The higher stability of quasi- short-period term and precision;By the way that time reference to be finally tied to some satellite navigation system time Under, the clock correction for each satellite that ensure that the stabilization of time reference long period term, and finally obtain has unified time base Standard facilitates fusion treatment and the application of multi-satellite navigation system data.
In the embodiment of the present invention, as shown in Fig. 2, in step S12 according to earth station's observation model and spaceborne GNSS Observation model, in the multi-satellite navigation system navigation satellite and low orbit satellite carries out joint precise orbit determination and the time is same Step, obtains the clock correction of each satellite navigation system, specifically includes following steps:
S121, according to preset initial parameter value respectively to earth station's observation model and spaceborne GNSS observation models into Row linearization process.It specifically includes:According to pretreated middle high rail GNSS satellite Deep space tracking data and low orbit satellite High rail GNSS satellite is to low orbit satellite and the observed range O of earth station during GNSS satellite observation data generate respectively;According to default Initial parameter value calculate in high rail GNSS satellite to low orbit satellite and the geometric distance of earth station;To the geometry that calculates away from From being corrected, middle high rail GNSS satellite is obtained to low orbit satellite and the calculating distance C of earth station;Middle high rail GNSS satellite is arrived The observed range O of earth station carries out difference operation with distance C is calculated, and generates the priori residual error of earth station's observation model, and will in The observed range O and the calculating distance C of high rail GNSS satellite to low orbit satellite carry out difference operation, generate spaceborne GNSS The priori residual error of observation model;According to the approximation of parameter vector in each observation model, using observation model to joining accordingly Number vector calculates partial derivative, obtains the second information of the first information matrix and spaceborne GNSS observation models of earth station's observation model Matrix;It is corresponding that the first observation model is built according to first information matrix described in the priori residual sum of earth station's observation model Observational equation after linearisation, and the second information matrix structure described in priori residual sum according to the spaceborne GNSS observation models Build the observational equation after the corresponding linearisation of the second observation model.
S122, using least square method calculate linearization process after earth station's observation model and spaceborne GNSS observe Model obtains the clock correction parameter of each satellite navigation system.
S123, by the clock correction restriction on the parameters of each satellite navigation system to corresponding navigation ephemeris.
Reduced-dynamic OD is used in more GNSS navigation satellites and low orbit satellite fusion precise orbit determination and time synchronization, Estimation obtains the state vectors such as each satellite orbit parameter and power model parameter and earth station, the spaceborne clock correction parameter of low rail, navigation Satellite clock correction parameter etc., while by the clock correction restriction on the parameters of each navigation satellite to respective navigation ephemeris, i.e.,
In formula,The satellite clock correction parameter of the jth satellite of some satellite navigation system is represented, n indicates defending for the system Star number.
In the embodiment of the present invention, as shown in figure 3, being built according to the clock correction of each satellite navigation system in step S13 The time scale of multi-satellite navigation system, specifically includes following steps:
S131, phase transition is carried out to the clock correction of each satellite navigation system, obtains each satellite navigation system Frequency observation value.
In a particular application, phase change component frequency observation is carried out by the clock correction to different navigation satellite, be located at The clock correction of satellite j is under some time system (by taking ORIT as an example)According to
Observation of the component frequency at ORIT
The clock status equation of S132, each satellite clock of structure, based on clock status equation structure clock observation side Journey.
The state equation of single satellite clock can be written as form:
Wherein
In formula,Frequency deviation and frequency drift are indicated respectively,Indicate the random walk of the white noise and frequency of frequency Noise.
If the Allan variances of clock areThe random walk that white noise and frequency can be obtained by the Allan variance methods of inversion is made an uproar The variance of soundI.e.:
Then drive noiseCovariance q be:
The observational equation of single satellite clock can be written as form:
In formula, n indicates that measurement noise, generally white noise, variance r are:
In formula,Indicate the middle error of satellite j clock correction.
S133, each navigation satellite and the corresponding satellite clock of low orbit satellite are combined into clock group, according to each satellite clock Clock status equation build the state equation of the clock group.
Clock group is constituted with N number of satellite clock of all systems (including each navigation system and low orbit satellite), then the shape of clock group State equation is:
For state equation, the state variable of clock groupTransfer matrix Φ, driving noiseCovariance Q be respectively:
WhereinIndicate the state vector of the i-th table clock, q(1)Indicate the covariance of the driving noise of the i-th table clock.
According to every table clock τ Allan variancesWeighting obtains the time scale after weighted average
The calculation formula of weight is:
S134, institute is built according to the state equation of the clock group and the frequency observation value of each satellite navigation system State the observational equation of clock group.
If Then the observational equation of clock group is:
For observational equation, the observed quantity of clock groupThe covariance matrix R of observing matrix H, clock correction observation noise is respectively:
S135, according to the observational equation of the clock group, calculate each satellite clock relative to the satellite navigation system to be tied to The frequency sequence of the system time of system.
S136, time series of each satellite clock relative to the system time, and root are calculated according to the frequency sequence The time scale is built according to the time series.Further, described that each satellite clock phase is calculated according to the frequency sequence Time series for the system time includes:Integral operation is carried out to the frequency sequence and obtains corresponding satellite clock time Time series relative to the system timeWherein, when GPST is the satellite clock of a certain navigational satellite system Between, NEWT is the system time.
In a specific embodiment, clock rate and the clock drift of the clock under new scale can be calculated by Kalman filter, And a new dimensions in frequency sequence relative to system time ORIT, it is denoted asI.e.:
Then above formula frequency sequence is integrated to obtain corresponding time series, is denoted as
In the embodiment of the present invention, the system that the time scale is tied to a certain satellite navigation system in step S14 Under time, the uniform time reference of each satellite in the multi-satellite navigation system is formed, following steps are specifically included:
Build the state equation and observational equation of bounding algorithm;
According to the state equation and observational equation of the bounding algorithm, a certain defend is tied to using Kalman filtering method calculating Time series under the system time of star navigation system, using the time series as each satellite in the multi-satellite navigation system Uniform time reference.
It is tied to the secular term that a certain system time can utilize the system time reference to stablize, makes the short week of new benchmark Phase item is more stablized, and equally for being tied to ORIT, the state equation and observational equation of bounding algorithm can be expressed as:
In formulaThe matrix-vector tieed up for one 2 × 1, two parts are respectively the difference that clock is inclined at GPST and NEWT, clock rate Difference,Indicate that the random noise of the process noise and observational equation of state equation, u are for constraining frequency observation respectively with ξ Value variation Model by Stochastic Model Error and meet the loss function minimum.
The time series for being tied to the original first time is calculated using Kalman filterObtain new time reference NEWT, the time reference as multi-satellite navigation systematic unity.
After obtaining the uniform time reference of multi-satellite navigation system, each satellite navigation system is by unified time reference It is attached in original clock correction, obtains the satellite clock correction with same time benchmark, realize defending for the unified space-time datum of multisystem Star clock correction;
By original clock correction reduction to NEWT, i.e.,
It can be obtained the satellite clock correction with uniform time reference.
The multi-satellite navigation system time reference that the embodiment of the present invention is established, also by calculating update in real time, when guarantee Between benchmark long and short cycle item stability and reliability.
For embodiment of the method, for simple description, therefore it is all expressed as a series of combination of actions, but this field Technical staff should know that the embodiment of the present invention is not limited by the described action sequence, because implementing according to the present invention Example, certain steps can be performed in other orders or simultaneously.Next, those skilled in the art should also know that, specification Described in embodiment belong to preferred embodiment, necessary to the involved action not necessarily embodiment of the present invention.
The time reference that Fig. 4 diagrammatically illustrates the multi-satellite navigation system of one embodiment of the invention establishes the knot of system Structure schematic diagram.With reference to Fig. 4, the time reference of the multi-satellite navigation system of the embodiment of the present invention establishes system and specifically includes model structure It builds unit 401, clock correction acquiring unit 402, time scale and establishes unit 403 and time reference generation unit 404, wherein:
Model construction unit 401, the earth station GNSS for obtaining multi-satellite navigation system observe data and spaceborne GNSS Data are observed, data are observed according to the earth station GNSS respectively and the spaceborne GNSS observations data build corresponding earth station Observation model and spaceborne GNSS observation models;
Clock correction acquiring unit 402 is used for according to earth station's observation model and spaceborne GNSS observation models, to described more Navigation satellite and low orbit satellite in satellite navigation system carry out joint precise orbit determination and time synchronization, obtain each satellite and lead The clock correction of boat system;
Time scale establishes unit 403, for building multi-satellite navigation according to the clock correction of each satellite navigation system The time scale of system;
Time reference generation unit 404, when system for the time scale to be tied to a certain satellite navigation system Between under, the uniform time reference of each satellite in the multi-satellite navigation system is generated, so that each satellite navigation system is by institute It states uniform time reference to be attached in corresponding original clock correction, to obtain the satellite under each leisure uniform time reference Clock correction.
In an alternate embodiment of the present invention where, the clock correction acquiring unit 402, including linear processing module, One computing module and constraint processing module, wherein:
Linear processing module, for according to preset initial parameter value respectively to earth station's observation model and spaceborne GNSS observation models carry out linearization process;
First computing module, for using least square method calculate linearization process after earth station's observation model and Spaceborne GNSS observation models obtain the clock correction parameter of each satellite navigation system;
Processing module is constrained, is used for the clock correction restriction on the parameters of each satellite navigation system to corresponding navigation Ephemeris.
In an alternate embodiment of the present invention where, the time scale establishes unit 403, including phase conversion, First model construction module, the second model construction module, third model construction module, the second computing module and time scale structure Block is modeled, wherein:
Phase conversion carries out phase transition for the clock correction to each satellite navigation system, obtains each defend The frequency observation value of star navigation system;
First model construction module, the clock status equation for building each satellite clock are based on the clock status side Journey builds clock observational equation;
Second model construction module, for each navigation satellite and the corresponding satellite clock of low orbit satellite to be combined into clock Group builds the state equation of the clock group according to the clock status equation of each satellite clock;
Third model construction module, for according to the state equation of the clock group and each satellite navigation system Frequency observation value builds the observational equation of the clock group;
Second computing module, for according to the observational equation of the clock group, calculating each satellite clock relative to being intended to be tied to Satellite navigation system system time frequency sequence;
Time scale builds module, for calculating each satellite clock relative to the system time according to the frequency sequence Time series, and the time scale is built according to the time series.
Further, the time scale builds module, is obtained specifically for carrying out integral operation to the frequency sequence Corresponding time series of the satellite clock time relative to the system time.
In an alternate embodiment of the present invention where, the time reference generation unit 404, including the 4th model construction mould Block and third computing module, wherein:
4th model construction module, state equation and observational equation for building bounding algorithm;
Third computing module, for the state equation and observational equation according to the bounding algorithm, using Kalman filtering Method calculates the time series being tied under the system time of a certain satellite navigation system, using the time series as more satellites The uniform time reference of each satellite in navigation system.
For system embodiments, since it is basically similar to the method embodiment, so fairly simple, the correlation of description Place illustrates referring to the part of embodiment of the method.
The time reference method for building up and system of multi-satellite navigation system provided in an embodiment of the present invention, it is all using covering When the earth station net GNSS and spaceborne GNSS observation data setup time benchmark of system, the stability of result and reliable ensure that Property;During the foundation of time reference, atomic clock group is formed using all satellite atomic clocks, and maintain by weighting, protected Demonstrate,prove the higher stability of time reference short-period term and precision;By the way that time reference to be finally tied to some satellite navigation system It unites under the time, the clock correction for each satellite that ensure that the stabilization of time reference long period term, and finally obtain has unification Time reference facilitates fusion treatment and the application of multi-satellite navigation system data.
The apparatus embodiments described above are merely exemplary, wherein the unit illustrated as separating component can It is physically separated with being or may not be, the component shown as unit may or may not be physics list Member, you can be located at a place, or may be distributed over multiple network units.It can be selected according to the actual needs In some or all of module achieve the purpose of the solution of this embodiment.Those of ordinary skill in the art are not paying creativeness Labour in the case of, you can to understand and implement.
Through the above description of the embodiments, those skilled in the art can be understood that each embodiment can It is realized by the mode of software plus required general hardware platform, naturally it is also possible to pass through hardware.Based on this understanding, on Stating technical solution, substantially the part that contributes to existing technology can be expressed in the form of software products in other words, should Computer software product can store in a computer-readable storage medium, such as ROM/RAM, magnetic disc, CD, including several fingers It enables and using so that a computer equipment (can be personal computer, server or the network equipment etc.) executes each implementation Method described in certain parts of example or embodiment.
In addition, it will be appreciated by those of skill in the art that although some embodiments in this include institute in other embodiments Including certain features rather than other feature, but the combination of the feature of different embodiment means to be in the scope of the present invention Within and form different embodiments.For example, in the following claims, embodiment claimed it is arbitrary it One mode can use in any combination.
Finally it should be noted that:The above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations;Although Present invention has been described in detail with reference to the aforementioned embodiments, it will be understood by those of ordinary skill in the art that:It still may be used With technical scheme described in the above embodiments is modified or equivalent replacement of some of the technical features; And these modifications or replacements, various embodiments of the present invention technical solution that it does not separate the essence of the corresponding technical solution spirit and Range.

Claims (10)

1. a kind of time reference method for building up of multi-satellite navigation system, which is characterized in that including:
The earth station GNSS observation data and spaceborne GNSS for obtaining multi-satellite navigation system observe data, respectively according to the ground The GNSS that stands observes data and the spaceborne GNSS observations data build corresponding earth station's observation model and spaceborne GNSS observes mould Type;
According to earth station's observation model and spaceborne GNSS observation models, to the navigation satellite in the multi-satellite navigation system And low orbit satellite carries out joint precise orbit determination and time synchronization, obtains the clock correction of each satellite navigation system;
The time scale of multi-satellite navigation system is built according to the clock correction of each satellite navigation system;
The time scale is tied under the system time of a certain satellite navigation system, is generated in the multi-satellite navigation system The uniform time reference of each satellite, for each satellite navigation system the uniform time reference is attached to it is corresponding In original clock correction, to obtain the satellite clock correction under each leisure uniform time reference.
2. according to the method described in claim 1, it is characterized in that, described according to earth station's observation model and spaceborne GNSS Observation model, in the multi-satellite navigation system navigation satellite and low orbit satellite carries out joint precise orbit determination and the time is same Step, obtains the clock correction of each satellite navigation system, including:
Earth station's observation model and spaceborne GNSS observation models are linearized respectively according to preset initial parameter value Processing;
Earth station's observation model after linearization process and spaceborne GNSS observation models are calculated using least square method, are obtained The clock correction parameter of each satellite navigation system;
By the clock correction restriction on the parameters of each satellite navigation system to corresponding navigation ephemeris.
3. method according to claim 1 or 2, which is characterized in that the clock according to each satellite navigation system The time scale of difference structure multi-satellite navigation system, including:
Phase transition is carried out to the clock correction of each satellite navigation system, obtains the frequency observation of each satellite navigation system Value;
The clock status equation of each satellite clock is built, clock observational equation is built based on the clock status equation;
Each navigation satellite and the corresponding satellite clock of low orbit satellite are combined into clock group, according to the clock status of each satellite clock Equation builds the state equation of the clock group;
The clock group is built according to the frequency observation value of the state equation of the clock group and each satellite navigation system Observational equation;
According to the observational equation of the clock group, when calculating system of each satellite clock relative to the satellite navigation system to be tied to Between frequency sequence;
Time series of each satellite clock relative to the system time is calculated according to the frequency sequence, and according to the time Time scale described in sequence construct.
4. according to the method described in claim 3, it is characterized in that, described calculate each satellite clock phase according to the frequency sequence Time series for the system time includes:
Integral operation is carried out to the frequency sequence and obtains time sequence of the corresponding satellite clock time relative to the system time Row.
5. according to the method described in claim 1, it is characterized in that, described be tied to a certain satellite navigation by the time scale Under the system time of system, the uniform time reference of each satellite in the multi-satellite navigation system is formed, including:
Build the state equation and observational equation of bounding algorithm;
According to the state equation and observational equation of the bounding algorithm, a certain satellite is tied to using Kalman filtering method calculating and is led Time series under the system time of boat system, using the time series as the system of each satellite in the multi-satellite navigation system One time reference.
6. a kind of time reference of multi-satellite navigation system establishes system, which is characterized in that including:
Model construction unit, the earth station GNSS for obtaining multi-satellite navigation system observes data and spaceborne GNSS observes number According to respectively according to earth station GNSS observation data and the corresponding earth station's observation mould of the spaceborne GNSS observations data structure Type and spaceborne GNSS observation models;
Clock correction acquiring unit, for according to earth station's observation model and spaceborne GNSS observation models, being led to more satellites Navigation satellite and low orbit satellite in boat system carry out joint precise orbit determination and time synchronization, obtain each satellite navigation system Clock correction;
Time scale establishes unit, for according to the clock correction of each satellite navigation system build multi-satellite navigation system when Between scale;
Time reference generation unit, it is raw for the time scale to be tied under the system time of a certain satellite navigation system At the uniform time reference of each satellite in the multi-satellite navigation system, when described will unify for each satellite navigation system Between benchmark be attached in corresponding original clock correction, to obtain the satellite clock correction under each leisure uniform time reference.
7. system according to claim 6, which is characterized in that the clock correction acquiring unit, including:
Linear processing module is used for according to preset initial parameter value respectively to earth station's observation model and spaceborne GNSS Observation model carries out linearization process;
First computing module, for calculating earth station's observation model and spaceborne after linearization process using least square method GNSS observation models obtain the clock correction parameter of each satellite navigation system;
Processing module is constrained, is used for the clock correction restriction on the parameters of each satellite navigation system to corresponding nautical star It goes through.
8. the system described according to claim 6 or 7, which is characterized in that the time scale establishes unit, including:
Phase conversion carries out phase transition for the clock correction to each satellite navigation system, obtains each satellite and lead The frequency observation value of boat system;
First model construction module, the clock status equation for building each satellite clock are based on the clock status equation structure Build clock observational equation;
Second model construction module, for each navigation satellite and the corresponding satellite clock of low orbit satellite to be combined into clock group, root The state equation of the clock group is built according to the clock status equation of each satellite clock;
Third model construction module, for according to the state equation of the clock group and the frequency of each satellite navigation system Observation builds the observational equation of the clock group;
Second computing module calculates each satellite clock and is defended relative to what is be tied to for the observational equation according to the clock group The frequency sequence of the system time of star navigation system;
Time scale build module, for according to the frequency sequence calculate each satellite clock relative to the system time when Between sequence, and the time scale is built according to the time series.
9. system according to claim 8, which is characterized in that the time scale builds module, is specifically used for described Frequency sequence carries out integral operation and obtains time series of the corresponding satellite clock time relative to the system time.
10. system according to claim 6, which is characterized in that the time reference generation unit, including:
4th model construction module, state equation and observational equation for building bounding algorithm;
Third computing module, for the state equation and observational equation according to the bounding algorithm, using Kalman filtering method meter Time series under operator restraint to the system time of a certain satellite navigation system, using the time series as the multi-satellite navigation The uniform time reference of each satellite in system.
CN201810564951.XA 2018-06-04 2018-06-04 Method and system for establishing time reference of multi-satellite navigation system Active CN108732597B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201810564951.XA CN108732597B (en) 2018-06-04 2018-06-04 Method and system for establishing time reference of multi-satellite navigation system

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201810564951.XA CN108732597B (en) 2018-06-04 2018-06-04 Method and system for establishing time reference of multi-satellite navigation system

Publications (2)

Publication Number Publication Date
CN108732597A true CN108732597A (en) 2018-11-02
CN108732597B CN108732597B (en) 2020-10-02

Family

ID=63931903

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201810564951.XA Active CN108732597B (en) 2018-06-04 2018-06-04 Method and system for establishing time reference of multi-satellite navigation system

Country Status (1)

Country Link
CN (1) CN108732597B (en)

Cited By (14)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109764879A (en) * 2018-12-28 2019-05-17 上海海积信息科技股份有限公司 A kind of Satellite Orbit Determination method, apparatus and electronic equipment
CN109870898A (en) * 2019-02-27 2019-06-11 武汉大学 GNSS Timing Receiver clock combinatorial regulation method and system based on PPP
CN110045395A (en) * 2019-05-17 2019-07-23 北京和协航电信息科技有限公司 A kind of inspection Target process, system and equipment based on navigation satellite signal
CN111948686A (en) * 2020-08-05 2020-11-17 航天恒星科技有限公司 Time synchronization method and device
CN112325879A (en) * 2020-11-03 2021-02-05 中国电子科技集团公司信息科学研究院 Bionic composite navigation time service microsystem based on multi-source sensor integration
CN112445120A (en) * 2020-11-27 2021-03-05 西安空间无线电技术研究所 Distributed center-free space-based time reference establishing and maintaining system
CN113253311A (en) * 2021-04-06 2021-08-13 探索数据科技(深圳)有限公司 Joint satellite navigation method, system, electronic device and storage medium
CN113253314A (en) * 2021-05-11 2021-08-13 中国科学院国家授时中心 Time synchronization method and system between low-earth-orbit satellites
CN113341685A (en) * 2021-06-30 2021-09-03 北京微纳星空科技有限公司 Satellite time management method, electronic device and medium
CN113608427A (en) * 2021-07-09 2021-11-05 中国科学院国家授时中心 Centralized space-based time reference establishing method
CN115639743A (en) * 2022-10-19 2023-01-24 中国科学院国家授时中心 Space-based time reference establishing method and system based on whole network time comparison
WO2023020056A1 (en) * 2021-08-19 2023-02-23 中国电力科学研究院有限公司 Positioning time service method and apparatus, terminal device, and computer readable storage medium
CN116299617A (en) * 2023-02-16 2023-06-23 北京航空航天大学 Method for establishing GNSS satellite-ground atomic clock real-time dynamic model
CN117377057A (en) * 2023-12-08 2024-01-09 中国科学院国家授时中心 Satellite-ground time synchronization method and system for low-orbit satellite and ground station

Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5963167A (en) * 1996-03-13 1999-10-05 California Institute Of Technology Analyzing system for global positioning system and general satellite tracking
US20070120733A1 (en) * 2005-10-03 2007-05-31 Trimble Navigation Limited Multiple-GNSS and FDMA high precision carrier-phase based positioning
CN102937710A (en) * 2012-11-13 2013-02-20 北京空间飞行器总体设计部 Method for determining user range errors caused by non-ideal characteristics of atomic clocks
CN103235321A (en) * 2013-03-29 2013-08-07 东南大学 GPS (global positioning system) pseudo-range positioning precision timing method
US20150212211A1 (en) * 2014-01-24 2015-07-30 Qualcomm Incorporated Methods and systems for multi-gnss operation
CN105158780A (en) * 2015-07-24 2015-12-16 北京跟踪与通信技术研究所 Navigation positioning method based on interchangeability of multiple navigation satellites
CN105867108A (en) * 2016-06-20 2016-08-17 中国科学院国家授时中心 National standard time remote recurrence method
CN106443739A (en) * 2016-09-09 2017-02-22 清华大学 Assisted enhancement navigation method and device
CN107153209A (en) * 2017-07-06 2017-09-12 武汉大学 A kind of low rail aeronautical satellite real-time accurate orbit determination method of short arc segments

Patent Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5963167A (en) * 1996-03-13 1999-10-05 California Institute Of Technology Analyzing system for global positioning system and general satellite tracking
US20070120733A1 (en) * 2005-10-03 2007-05-31 Trimble Navigation Limited Multiple-GNSS and FDMA high precision carrier-phase based positioning
CN102937710A (en) * 2012-11-13 2013-02-20 北京空间飞行器总体设计部 Method for determining user range errors caused by non-ideal characteristics of atomic clocks
CN103235321A (en) * 2013-03-29 2013-08-07 东南大学 GPS (global positioning system) pseudo-range positioning precision timing method
US20150212211A1 (en) * 2014-01-24 2015-07-30 Qualcomm Incorporated Methods and systems for multi-gnss operation
CN105158780A (en) * 2015-07-24 2015-12-16 北京跟踪与通信技术研究所 Navigation positioning method based on interchangeability of multiple navigation satellites
CN105867108A (en) * 2016-06-20 2016-08-17 中国科学院国家授时中心 National standard time remote recurrence method
CN106443739A (en) * 2016-09-09 2017-02-22 清华大学 Assisted enhancement navigation method and device
CN107153209A (en) * 2017-07-06 2017-09-12 武汉大学 A kind of low rail aeronautical satellite real-time accurate orbit determination method of short arc segments

Non-Patent Citations (5)

* Cited by examiner, † Cited by third party
Title
MARCELLO FARINA等: "A control theory approach to clock steering techniques", 《IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL》 *
PETER B WHIBBERLEY等: "Local representations of UTC in national laboratories", 《METROLOGIA》 *
伍贻威等: "原子钟两级驾驭算法及在建立GNSS基准中的应用", 《电子学报》 *
卫国: "原子钟时间尺度与Kalman滤波器", 《陕西天文台台刊》 *
郑子扬等: "伽利略系统GSTB-V1的时间尺度算法与实现", 《舰船电子工程》 *

Cited By (23)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109764879A (en) * 2018-12-28 2019-05-17 上海海积信息科技股份有限公司 A kind of Satellite Orbit Determination method, apparatus and electronic equipment
CN109870898A (en) * 2019-02-27 2019-06-11 武汉大学 GNSS Timing Receiver clock combinatorial regulation method and system based on PPP
CN109870898B (en) * 2019-02-27 2020-11-17 武汉大学 GNSS time service receiver clock combination regulation and control method and system based on PPP
CN110045395A (en) * 2019-05-17 2019-07-23 北京和协航电信息科技有限公司 A kind of inspection Target process, system and equipment based on navigation satellite signal
CN111948686A (en) * 2020-08-05 2020-11-17 航天恒星科技有限公司 Time synchronization method and device
CN111948686B (en) * 2020-08-05 2024-04-26 航天恒星科技有限公司 Time synchronization method and device
CN112325879A (en) * 2020-11-03 2021-02-05 中国电子科技集团公司信息科学研究院 Bionic composite navigation time service microsystem based on multi-source sensor integration
CN112445120A (en) * 2020-11-27 2021-03-05 西安空间无线电技术研究所 Distributed center-free space-based time reference establishing and maintaining system
CN112445120B (en) * 2020-11-27 2022-04-22 西安空间无线电技术研究所 Distributed center-free space-based time reference establishing and maintaining system
WO2022111230A1 (en) * 2020-11-27 2022-06-02 西安空间无线电技术研究所 Distributed centerless space-based time reference establishing and maintaining system
CN113253311A (en) * 2021-04-06 2021-08-13 探索数据科技(深圳)有限公司 Joint satellite navigation method, system, electronic device and storage medium
CN113253311B (en) * 2021-04-06 2024-02-06 探索数据科技(深圳)有限公司 Combined satellite navigation method, system, electronic equipment and storage medium
CN113253314A (en) * 2021-05-11 2021-08-13 中国科学院国家授时中心 Time synchronization method and system between low-earth-orbit satellites
CN113253314B (en) * 2021-05-11 2023-06-23 中国科学院国家授时中心 Time synchronization method and system between low-orbit satellites
CN113341685A (en) * 2021-06-30 2021-09-03 北京微纳星空科技有限公司 Satellite time management method, electronic device and medium
CN113608427A (en) * 2021-07-09 2021-11-05 中国科学院国家授时中心 Centralized space-based time reference establishing method
CN113608427B (en) * 2021-07-09 2022-07-05 中国科学院国家授时中心 Centralized space-based time reference establishing method
WO2023020056A1 (en) * 2021-08-19 2023-02-23 中国电力科学研究院有限公司 Positioning time service method and apparatus, terminal device, and computer readable storage medium
CN115639743A (en) * 2022-10-19 2023-01-24 中国科学院国家授时中心 Space-based time reference establishing method and system based on whole network time comparison
CN116299617A (en) * 2023-02-16 2023-06-23 北京航空航天大学 Method for establishing GNSS satellite-ground atomic clock real-time dynamic model
CN116299617B (en) * 2023-02-16 2023-10-31 北京航空航天大学 Method for establishing GNSS satellite-ground atomic clock real-time dynamic model
CN117377057A (en) * 2023-12-08 2024-01-09 中国科学院国家授时中心 Satellite-ground time synchronization method and system for low-orbit satellite and ground station
CN117377057B (en) * 2023-12-08 2024-02-13 中国科学院国家授时中心 Satellite-ground time synchronization method and system for low-orbit satellite and ground station

Also Published As

Publication number Publication date
CN108732597B (en) 2020-10-02

Similar Documents

Publication Publication Date Title
CN108732597A (en) A kind of the time reference method for building up and system of multi-satellite navigation system
Shen et al. A review of global navigation satellite system (GNSS)-based dynamic monitoring technologies for structural health monitoring
Pepe et al. A review of interferometric synthetic aperture RADAR (InSAR) multi-track approaches for the retrieval of Earth’s surface displacements
Gonzalez et al. High-precision timing of five millisecond pulsars: Space velocities, binary evolution, and equivalence principles
Eustice et al. Synchronous‐clock, one‐way‐travel‐time acoustic navigation for underwater vehicles
Tawk et al. Implementation and performance of a GPS/INS tightly coupled assisted PLL architecture using MEMS inertial sensors
DE112006002381T5 (en) Ionosphere modeling apparatus and method
Abd Rabbou et al. Integration of GPS precise point positioning and MEMS-based INS using unscented particle filter
CN111736185B (en) Terminal positioning method and device, computer readable storage medium and terminal equipment
Rizos et al. Background and recent advances in the locata terrestrial positioning and timing technology
CN103033814B (en) Multi-source data mixed platform and method for sonar detection positioning
Fukuda et al. Performance evaluation of IMU and DVL integration in marine navigation
CN104199061A (en) Method for establishing carrier phase frequency standard of GPS (global position system) and BDS (BeiDou Navigation Satellite system)
CN109375248A (en) A kind of Kalman's multimodality fusion location algorithm model and its method serially updated
Felski et al. Analysis of satellite compass error’s spectrum
Su et al. Chang’E-5T orbit determination using onboard GPS observations
Geng et al. BDS precise point positioning for seismic displacements monitoring: benefit from the high-rate satellite clock corrections
Bhattacharyya et al. Kalman filter-based RAIM for reliable aircraft positioning with GPS and NavIC constellations
Li et al. Continuous decimeter-level positioning in urban environments using multi-frequency GPS/BDS/Galileo PPP/INS tightly coupled integration
Darugna et al. Sub-decimeter onboard orbit determination of leo satellites using ssr corrections: A galileo-based case study for the sentinel-6a satellite
Langel et al. Tightly coupled GPS/INS integration for differential carrier phase navigation systems using decentralized estimation
Lee et al. Carrier phase residual modeling and fault monitoring using short-baseline double difference and machine learning
Hobiger et al. Combining GPS and VLBI for inter-continental frequency transfer
Niu et al. An algorithm to assist the robust filter for tightly coupled RTK/INS navigation system
Jaskólski Methodology for Verifying the Indication Correctness of a Vessel Compass Based on the Spectral Analysis of Heading Errors and Reliability Theory

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant