CN109613579A - A kind of method and system calculating integer ambiguity based on least-squares algorithm - Google Patents
A kind of method and system calculating integer ambiguity based on least-squares algorithm Download PDFInfo
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- CN109613579A CN109613579A CN201811406825.8A CN201811406825A CN109613579A CN 109613579 A CN109613579 A CN 109613579A CN 201811406825 A CN201811406825 A CN 201811406825A CN 109613579 A CN109613579 A CN 109613579A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/42—Determining position
- G01S19/43—Determining position using carrier phase measurements, e.g. kinematic positioning; using long or short baseline interferometry
- G01S19/44—Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/03—Cooperating elements; Interaction or communication between different cooperating elements or between cooperating elements and receivers
- G01S19/04—Cooperating elements; Interaction or communication between different cooperating elements or between cooperating elements and receivers providing carrier phase data
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/03—Cooperating elements; Interaction or communication between different cooperating elements or between cooperating elements and receivers
- G01S19/08—Cooperating elements; Interaction or communication between different cooperating elements or between cooperating elements and receivers providing integrity information, e.g. health of satellites or quality of ephemeris data
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/40—Correcting position, velocity or attitude
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- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Computer Networks & Wireless Communication (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Computer Security & Cryptography (AREA)
- Position Fixing By Use Of Radio Waves (AREA)
Abstract
The present invention relates to it is a kind of based on least-squares algorithm calculate integer ambiguity method and system, method the following steps are included: obtain any satellite any one observation the moment amendment co-ordinates of satellite, amendment satellite clock correction, first stop star away from and carrier phase；Projective parameter based on amendment co-ordinates of satellite and first stop star away from determining satellite in three dimensions at observation moment；All projective parameters, all amendment satellite clock corrections and all carrier phases based on multi-satellite respectively at multiple observation moment construct matrix equation；Matrix equation is calculated using least-squares algorithm, obtains at least two integer ambiguities.The method and system provided by the invention that integer ambiguity is calculated based on least-squares algorithm, it can be on the basis of guaranteeing integer ambiguity precision, reduce the calculation amount of integer ambiguity, the computational efficiency of integer ambiguity is improved, and then improves location efficiency when using integer ambiguity absolute fix receiver location.
Description
Technical field
The present invention relates to satellite navigation positioning technical fields, more particularly to a kind of least-squares algorithm that is based on to calculate complete cycle mould
The method and system of paste degree.
Background technique
As user is higher and higher to navigation accuracy requirement, the positioning accuracy and real-time of Technique of Satellite Navigation and Positioning are also wanted
It is improved, satellite navigation and positioning mainly has the satellite positioning method based on pseudorange and the satellite positioning side based on carrier phase
Method.
In the satellite positioning method based on pseudorange, since ranging code has biggish noise, symbol width is long, therefore phase
It is big with the pseudorange error that the light velocity is obtained multiplied by signal propagation time than the actual distance between satellite and receiver, pseudorange
Positioning accuracy is low；Satellite positioning method based on carrier phase is believed using the received carrier wave with Doppler frequency shift of receiver
The phase difference between the reference carrier signal that its is generated receiver number is calculated, phase difference position receiver location, phase are passed through
The positioning accuracy of difference is higher than the positioning accuracy of pseudorange.
According to the rover station and base station in receiver, there are two types of modes for the satellite positioning method based on carrier phase, should
Two ways is respectively that the carrier phase relative positioning based on rover station and base station and the carrier phase based on rover station are exhausted
To positioning, satellite position and satellite clock correction are often calculated using the IGS Ultrarapid ephemeris provided or broadcast ephemeris, still
Ultrarapid ephemeris satellite position and satellite clock correction also can with the time extension or constantly increase error, broadcast ephemeris obtains
Error it is big, absolute fix needs to solve integer ambiguity, and the derivation algorithm of integer ambiguity mainly has fast ambiguity resolving
Method (FRAR) and least square fuzziness drop adjustment of correlated observations method (LAMBDA), although integer ambiguity precision with higher,
It is the computationally intensive of the derivation algorithm of both integer ambiguities, the hardware supported that receiver needs to have higher configured can increase
Add the cost of receiver.
Summary of the invention
The technical problem to be solved by the present invention is to cannot be considered in terms of complete cycle for carrier phase absolute fix in the prior art
The precision of fuzziness and the deficiency of calculation amount, provide it is a kind of based on least-squares algorithm calculate integer ambiguity method and be
System.
The technical scheme to solve the above technical problems is that
According to the present invention in a first aspect, provide it is a kind of based on least-squares algorithm calculate integer ambiguity method,
The following steps are included:
Step 1, obtain any satellite any one observation the moment amendment co-ordinates of satellite, amendment satellite clock correction, first
Stand star away from and carrier phase；
Step 2, based on the amendment co-ordinates of satellite and the first stop star away from the determination satellite at the observation moment
Three dimensions on projective parameter；
Step 3, based on the more satellites respectively it is multiple it is described observation the moment all projective parameters, Suo Yousuo
State amendment satellite clock correction and all carrier phase building matrix equations；
Step 4 calculates the matrix equation using least-squares algorithm, obtains at least two integer ambiguities.
Second aspect according to the present invention provides a kind of system for calculating integer ambiguity based on least-squares algorithm,
It include: to obtain module, determining module, building module and computing module；
The acquisition module is defended for obtaining any satellite in the amendment co-ordinates of satellite at any one observation moment, amendment
Star clock deviation, first stop star away from and carrier phase；
The determining module is used for based on the amendment co-ordinates of satellite and the first stop star away from the determination satellite in institute
State the projective parameter in three dimensions at observation moment；
The building module, for based on the more satellites respectively it is multiple it is described observation the moment all projections
Parameter, all amendment satellite clock corrections and all carrier phases construct matrix equation；
The computing module obtains at least two for calculating using least-squares algorithm the matrix equation
Integer ambiguity.
A kind of beneficial effect of method and system calculating integer ambiguity based on least-squares algorithm of the invention is: benefit
With amendment co-ordinates of satellite and projective parameter of the star away from determining satellite in three dimensions at observation moment of standing, amendment co-ordinates of satellite is mentioned
The high precision of projective parameter, projective parameter can simplify the representation of error in three dimensions；Distinguished based on multi-satellite
Matrix equation is constructed in all projective parameters, all amendment satellite clock corrections and all carrier phases at multiple observation moment, is used
Least-squares algorithm is obtained all satellites in the integer ambiguity at all observation moment, is thrown with matrix operation solution matrix equation
Shadow parameter and amendment satellite clock correction ensure that the precision of integer ambiguity, and least-squares algorithm and matrix equation quickly calculate multiple
Integer ambiguity improves the computational efficiency of integer ambiguity.
Detailed description of the invention
Fig. 1 is a kind of process of method that integer ambiguity is calculated based on least-squares algorithm provided in an embodiment of the present invention
Schematic diagram；
Fig. 2 is the carrier phase observation data and complete cycle mould that a satellite provided in an embodiment of the present invention observes the moment at three
The schematic diagram of relationship between paste degree；
Fig. 3 is the signal that four satellites provided in an embodiment of the present invention observe matrix equation corresponding to the moment at three
Figure.
Fig. 4 is a kind of structure of system that integer ambiguity is calculated based on least-squares algorithm provided in an embodiment of the present invention
Schematic diagram.
Specific embodiment
The principle and features of the present invention will be described below with reference to the accompanying drawings, and the given examples are served only to explain the present invention, and
It is non-to be used to limit the scope of the invention.
Embodiment one
As shown in Figure 1, a kind of stream of method for calculating integer ambiguity based on least-squares algorithm of the embodiment of the present invention
Journey schematic diagram, comprising the following steps:
Step 1, obtain any satellite any one observation the moment amendment co-ordinates of satellite, amendment satellite clock correction, first
Stand star away from and carrier phase；
Step 2, the throwing based on amendment co-ordinates of satellite and first stop star away from determining satellite in three dimensions at observation moment
Shadow parameter；
Step 3, based on multi-satellite respectively multiple observation all projective parameters at moment, all amendment satellite clock corrections and
All carrier phases construct matrix equation；
Step 4 calculates matrix equation using least-squares algorithm, obtains at least two integer ambiguities.
Projective parameter using amendment co-ordinates of satellite and first stop star away from determining satellite in three dimensions at observation moment,
Amendment co-ordinates of satellite improves the precision of projective parameter, and projective parameter can simplify the representation of error in three dimensions；Base
In multi-satellite respectively in all projective parameters at multiple observation moment, all amendment satellite clock corrections and the building of all carrier phases
Matrix equation uses least-squares algorithm with matrix operation solution matrix equation, obtains all satellites at all observation moment
Integer ambiguity, projective parameter and amendment satellite clock correction ensure that the precision of integer ambiguity, and then by integer ambiguity application
It positions in carrier phase, is positioned compared to traditional pseudorange, positioning accuracy, least square can be improved in carrier phase absolute fix
Algorithm and matrix equation quickly calculate multiple integer ambiguities, compared to the derivation algorithm of two kinds of traditional integer ambiguities, mention
The high computational efficiency of integer ambiguity, can reduce the cost of receiver.
Preferably, step 1 specifically includes:
Step 11 obtains satellite in the broadcast ephemeris at observation moment；
Step 12, based in broadcast ephemeris satellite orbit parameter set determine amendment the argument of latitude, amendment satellite radius vector,
Correct inclination of satellite orbit and satellite clock correction；
Step 13 determines satellite in agreement based on the amendment argument of latitude, amendment satellite radius vector and amendment inclination of satellite orbit
Three-dimensional coordinate vector in terrestrial coordinate system；
Step 14 corrects vector to satellite in conventional terrestrial coordinate system based on co-ordinates of satellite of the satellite in ground heart is admittedly
In three-dimensional coordinate vector be modified, obtain amendment co-ordinates of satellite；
Step 15, the satellite clock correction correction member based on satellite at the observation moment are modified satellite clock correction, obtain
Correct satellite clock correction；
Step 16 is based on amendment co-ordinates of satellite calculating first stop star away from based on amendment satellite clock correction calculating carrier phase.
Preferably, the argument of latitude, amendment satellite radius vector and amendment inclination of satellite orbit are corrected with the first constraint condition set
It indicates, the first constraint condition set is combined into:
Wherein, μ represents the amendment argument of latitude, and r represents the amendment satellite radius vector, and σ represents the amendment satellite rail
Road inclination, δμRepresent perturbation correction member corresponding with argument of latitude μ ', δrPerturbation correction member corresponding with satellite radius vector r' is represented,
δσPerturbation correction member corresponding with inclination of satellite orbit σ ' is represented, Δ σ is represented in satellite orbit parameter set and corrected satellite orbit
The change rate of inclination angle σ, t represent observation moment, toeIt represents and refers to the moment.
Three perturbation correction members indicate that the second constraint condition set is combined into the second constraint condition set:
Wherein, CμcAnd CμsRepresent perturbation correction member δ in satellite orbit parameter setμCorresponding perturbation parameter, CrcWith
CrsRepresent perturbation correction member δ in satellite orbit parameter setrCorresponding perturbation parameter, CicAnd CisRepresent satellite orbit
Perturb correction member δ in parameter setsσCorresponding perturbation parameter.
The calculation formula of argument of latitude μ ' are as follows: μ '=ω+f, wherein ω is represented, and it is true on satellite orbit that f represents satellite
Anomaly.
The calculation formula of true anomaly f are as follows:
Wherein, e represents eccentricity of the satellite orbit parameter set Satellite on satellite orbit, and E represents eccentric anomaly.
The calculation formula of eccentric anomaly E is Kepler's equations, Kepler's equations are as follows: E=M+e × sinE, wherein M is flat
Anomaly.
The calculation formula of mean anomaly M are as follows: M=Mo+n(t-toe), wherein MoRepresent satellite orbit parameter set Satellite
In reference moment toeMean anomaly, n represent satellite observation the moment mean angular velocity.
The calculation formula of mean angular velocity n are as follows: n=no+ Δ n, wherein noSatellite is represented in reference moment toeAverage angle
Speed, Δ n represent the perturbation parameter in satellite orbit parameter set.
Mean angular velocity noCalculation formula are as follows:
Wherein, G is universal gravitational constant, the oval major radius of satellite orbit where A represents satellite.
Satellite radius vector indicates with the first calculation formula, the first calculation formula are as follows: r'=A × (1-e × cosE), wherein r'
The satellite radius vector is represented, the oval major radius of satellite orbit, e represent satellite orbit parameter set Satellite where representing satellite
Eccentricity of the orbit parameter set Satellite on satellite orbit, E represent eccentric anomaly.
Preferably, step 13 specifically includes:
Step 131 determines two dimension of the satellite in track areal coordinate system based on the amendment argument of latitude and amendment satellite radius vector
Coordinate vector；
Step 132 determines satellite in instantaneous terrestrial coordinate system based on two-dimensional coordinate vector sum amendment inclination of satellite orbit
Three-dimensional coordinate vector；
Step 133 determines that satellite is sat in the agreement earth based on three-dimensional coordinate vector of the satellite in instantaneous terrestrial coordinate system
Three-dimensional coordinate vector in mark system.
Preferably, in step 133, three-dimensional coordinate vector of the satellite in conventional terrestrial coordinate system is with the second calculation formula
It indicates, the second calculation formula are as follows:
Wherein, xb、ybAnd zbRepresent coordinate of the satellite in conventional terrestrial coordinate system, xpAnd ypRepresent two-dimensional coordinate to
Abscissa and ordinate in amount, σ represent amendment inclination of satellite orbit, and H represents the longitude of ascending node at the observation moment.
Abscissa and ordinate in two-dimensional coordinate vector indicate with the 4th constraint condition set, the 4th constraint condition set
Are as follows:
Wherein, xpAnd ypThe abscissa and ordinate in two-dimensional coordinate vector are represented, r represents amendment satellite radius vector, and μ is repaired
The positive argument of latitude.
The longitude of ascending node H at observation moment indicates that the 5th constraint condition set is combined into the 5th constraint condition set:
Wherein, Ω0It represents in reference moment toeWhen right ascension of ascending node,It represents in reference moment toeWhen ascending node it is red
The change rate of warp, ωeRotational-angular velocity of the earth is represented, t represents the observation moment,It represents in satellite orbit parameter set and is joining
Examine moment toeWhen right ascension of ascending node corresponding to time rate of change, GASTweekThe Greenwich for representing this week initial time is permanent
When star.
Preferably, step 14 specifically includes:
Step 141 determines in SSR information correct vector sum satellite velocities with co-ordinates of satellite corresponding to the reference moment respectively
Correct vector；
Step 142 is determined based on the observation moment, with reference to moment, co-ordinates of satellite correction vector sum satellite velocities correction vector
Co-ordinates of satellite of the satellite in satellite orbit coordinate system corrects vector；
Co-ordinates of satellite correction vector of the satellite in satellite orbit coordinate system is transformed into satellite in ground heart by step 143
Gu the co-ordinates of satellite in system corrects vector；
Step 144 corrects vector sum satellite in conventional terrestrial coordinate system to co-ordinates of satellite of the satellite in ground heart is admittedly
In three-dimensional coordinate vector sum, obtain amendment co-ordinates of satellite.
SSR information is to obtain the data of GNSS in real time by Internet, and each analysis center of data IGS-RTPP generates
Real-time satellite track and clock error correction data, using meet RTCM standard SSR information format issue.
SSR information has the effect of preferable amendment broadcast ephemeris error in real time, and the observation moment sits with reference to moment, satellite
Mark correction vector sum satellite velocities correction vector determines that co-ordinates of satellite of the satellite in satellite orbit coordinate system corrects vector jointly,
The precision of co-ordinates of satellite correction vector is improved, so that the satellite being converted to by co-ordinates of satellite correction vector is in ground heart
Gu the co-ordinates of satellite correction vector in system is more accurate, and then obtains amendment co-ordinates of satellite in a manner of vector summation, can either
Guarantee the precision of amendment co-ordinates of satellite, and the calculation of amendment co-ordinates of satellite can be simplified, reduces calculation amount.
Preferably, in step 144, co-ordinates of satellite correction vector of the satellite in ground heart is admittedly is with third constraint condition
Set expression, third constraint condition set are combined into:
Wherein,Co-ordinates of satellite of the satellite in ground heart is admittedly corrects vector, and r' represents satellite radius vector,Represent satellite
Satellite velocities in orbit parameter,Represent co-ordinates of satellite correction vector of the satellite in satellite orbit coordinate system.
Co-ordinates of satellite of the satellite in satellite orbit coordinate system corrects vectorCalculation formula are as follows:
Wherein, δr、δaAnd δcRepresent the corrected value in co-ordinates of satellite correction vector, drRepresent co-ordinates of satellite correction vector
In it is corresponding with the reference moment through to reduction, daRepresent tangential correction corresponding with the reference moment in co-ordinates of satellite correction vector
Amount, dcNormal direction reduction corresponding with the reference moment in co-ordinates of satellite correction vector is represented,WithSuccessively represent through to
Reduction drChange rate, tangential reduction daChange rate and normal direction reduction dcChange rate.
Preferably, in step 15, amendment satellite clock correction is indicated with third calculation formula, third calculation formula are as follows: Δ ts
=Δ t- δc/ C, wherein Δ tsAmendment satellite clock correction is represented, Δ t represents satellite clock correction, δcRepresent satellite clock correction correction member, C generation
Mass color speed.
The calculation formula of satellite clock correction Δ t are as follows: Δ t=α0+α1+α2(t-t0)+Δtr, wherein α0Satellite is represented multiple
Observe the initial observation moment t in the moment0Satellite clock correction, α1Represent initial observation moment of the satellite in multiple observation moment
t0Clock rate, α2Satellite is represented in initial observation moment t0Frequency drift, Δ trRepresent the relativistic effect value of satellite clock.
Satellite clock correction correction member δcCalculation formula are as follows: δc=c0+c1+c2(t-t0)2, wherein c0、c1And c2Represent SSR
In reference moment t in informationoeCoefficient.
It is roughly calculated to obtain satellite clock correction by satellite clock correction, clock rate and the frequency drift in broadcast ephemeris, by SSR information
In reference moment toeCoefficient simple computation satellite clock correction correction member, accurately calculate to obtain amendment using satellite clock correction correction member and defend
Star clock deviation, so that the computational accuracy and real-time of amendment satellite clock correction get a promotion.
Preferably, in step 3, any one carrier phase is indicated with the 4th calculation formula, the 4th calculation formula are as follows:Wherein,Represent the carrier wave phase that i-th satellite observes the moment at j-th
Position, λ represent the carrier wavelength that i-th satellite observes the moment at j-th, which is constant, φi(tj) represent i-th and defend
Carrier phase observation data of the star j-th of observation moment,I-th satellite is represented at j-th of observation moment to receiver
Second station star away from DtroRepresent tropospheric delay, DionRepresent ionosphere delay, Δ tsI-th satellite is represented to observe at j-th
The amendment satellite clock correction at moment, C represent the light velocity.
Preferably, the matched curve D (t) of doppler measurement is accumulated in the range of the two neighboring observation moment
Point, obtain the phase difference of doppler measurement；If φi(tj+1)-φi(tj) in first threshold range and aforementioned phase differenceWithin the scope of second threshold, it is determined that there is no cycle slip, otherwise, it determines there is cycle slip.
Aforementioned phase differenceCalculation formula are as follows:
As shown in the figure 2 be that a satellite of the embodiment of the present invention observes the carrier phase observation data and complete cycle at moment at three
The schematic diagram of relationship between fuzziness.
I-th satellite observes the moment at j-th to the second station star of receiver away from indicating with the 5th calculation formula, and the 5th counts
Calculate formula are as follows:Wherein,I-th satellite is represented to exist
The integer ambiguity at j-th of observation moment, Δ tuRepresent receiver clock-offsets,I-th satellite is represented in j-th of the observation
The error at quarter.
I-th satellite observes the error at moment at j-thIn three projective parameters with the 4th constraint condition set table
Show, the 4th constraint condition set is combined into:
Wherein,WithThe projective parameter that i-th satellite observes the moment at j-th is represented,
WithRepresent a coordinate in amendment co-ordinates of satellite, xu、yuAnd zuA coordinate in receiver three-dimensional coordinate is represented,Represent i-th satellite j-th observe the moment to receiver first stop star away from.
I-th satellite observes the moment at j-th to the first stop star of receiver away from indicating with the 6th calculation formula, and the 6th counts
Calculate formula are as follows:
At any one is observed the moment for any satellite, the 6th calculation formula is respectively adopted and the 5th calculation formula is independent
Calculate first stop star away from second station star away from, as shown in the 6th calculation formula, first stop star away from be using amendment co-ordinates of satellite with
The three-dimensional coordinate of receiver is directly calculated, and second station star is away from being based on carrier phase observation data, tropospheric delay, ionosphere
Delay, amendment satellite clock correction and receiver clock-offsets are calculated.
The 4th calculation formula of simultaneous, the 5th calculation formula, the 4th constraint condition and the 6th calculation formula obtain the 7th calculating
Formula, and matrix equation, the 7th calculation formula are constructed by the 7th calculation formula are as follows:
Wherein, Δ x, Δ y and Δ z represent the error that i-th satellite observes the moment at j-thIn a coordinate difference
Value,
Receiver clock-offsets Δ tuCalculation formula are as follows: Δ tu=b0+b1(t-t0)+b2(t-t0)2, wherein b0Satellite is represented to exist
Initial observation moment t in multiple observation moment0Satellite clock correction, b1Represent initial observation of the satellite in multiple observation moment
Moment t0Clock rate, b2Satellite is represented in initial observation moment t0Frequency drift.
By xu、yu、zu、b0、b1、b2WithAs value to be solved, the shared i of the total number of the integer ambiguity solved ×
J-6, such as: in i=4 and j=3, the total number of integer ambiguity is 6, improves the computational stability of value to be solved
And computational efficiency；Circulation executes step 1-5, until xu、yuAnd zuRespectively less than given threshold, it is determined that receiver location improves
The accuracy of the receiver location is illustrated in figure 3 four satellites of the embodiment of the present invention corresponding to three observation moment
The schematic diagram of matrix equation.
Matrix equation can indicate are as follows: L=GX, it can be first based on least square method and pseudorange rough estimate position and reception
Machine clock deviation then solves X=(G using least square methodTG)-1GTL can obtain receiver location, b simultaneously0、b1、b2With it is more
A integer ambiguity improves multiple complete cycle moulds to accurately calculate multiple integer ambiguities, receiver location and receiver clock-offsets
The computational efficiency of paste degree.
Embodiment two
In the present embodiment, as shown in figure 4, a kind of system for calculating integer ambiguity based on least-squares algorithm, comprising: obtain
Modulus block, determining module, building module and computing module.
The acquisition module is defended for obtaining any satellite in the amendment co-ordinates of satellite at any one observation moment, amendment
Star clock deviation, first stop star away from and carrier phase；
The determining module, for based on amendment co-ordinates of satellite and first stop star away from determining satellite in observation three of the moment
Projective parameter in dimension；
The building module, for based on multi-satellite respectively it is multiple observation the moment all projective parameters, Suo Youxiu
Positive satellite clock correction and all carrier phases construct matrix equation；
The computing module obtains at least two complete cycles for calculating using least-squares algorithm matrix equation
Fuzziness.
Preferably, it obtains module to be specifically used for: obtaining satellite in the broadcast ephemeris at observation moment；Based in broadcast ephemeris
Satellite orbit parameter set determines the amendment argument of latitude, amendment satellite radius vector, amendment inclination of satellite orbit and satellite clock correction；It is based on
The amendment argument of latitude, amendment satellite radius vector and amendment inclination of satellite orbit determine three-dimensional seat of the satellite in conventional terrestrial coordinate system
Mark vector；Three-dimensional of the co-ordinates of satellite correction vector to satellite in conventional terrestrial coordinate system based on satellite in ground heart is admittedly
Coordinate vector is modified, and obtains amendment co-ordinates of satellite；Based on satellite the observation moment satellite clock correction correction member to defending
Star clock deviation is modified, and obtains amendment satellite clock correction；First stop star is calculated away from based on amendment satellite clock based on amendment co-ordinates of satellite
Difference calculates carrier phase.
Preferably, the argument of latitude, amendment satellite radius vector and amendment inclination of satellite orbit are corrected with the first constraint condition set
It indicates, the first constraint condition set is combined into:
Wherein, μ represents the amendment argument of latitude, and r represents the amendment satellite radius vector, and σ represents the amendment satellite rail
Road inclination, δμRepresent perturbation correction member corresponding with argument of latitude μ ', δrPerturbation correction member corresponding with satellite radius vector r' is represented,
δσPerturbation correction member corresponding with inclination of satellite orbit σ ' is represented, Δ σ is represented in satellite orbit parameter set and corrected satellite orbit
The change rate of inclination angle σ, t represent observation moment, toeIt represents and refers to the moment.
Three perturbation correction members indicate that the second constraint condition set is combined into the second constraint condition set:
Wherein, CμcAnd CμsRepresent perturbation correction member δ in satellite orbit parameter setμCorresponding perturbation parameter, CrcWith
CrsRepresent perturbation correction member δ in satellite orbit parameter setrCorresponding perturbation parameter, CicAnd CisRepresent satellite orbit
Perturb correction member δ in parameter setsσCorresponding perturbation parameter.
The calculation formula of argument of latitude μ ' are as follows: μ '=ω+f, wherein ω is represented, and it is true on satellite orbit that f represents satellite
Anomaly.
The calculation formula of true anomaly f are as follows:
Wherein, e represents eccentricity of the satellite orbit parameter set Satellite on satellite orbit, and E represents eccentric anomaly.
The calculation formula of eccentric anomaly E is Kepler's equations, Kepler's equations are as follows: E=M+e × sinE, wherein M is flat
Anomaly.
The calculation formula of mean anomaly M are as follows: M=Mo+n(t-toe), wherein MoRepresent satellite orbit parameter set Satellite
In reference moment toeMean anomaly, n represent satellite observation the moment mean angular velocity.
The calculation formula of mean angular velocity n are as follows: n=no+ Δ n, wherein noSatellite is represented in reference moment toeAverage angle
Speed, Δ n represent the perturbation parameter in satellite orbit parameter set.
Mean angular velocity noCalculation formula are as follows:
Wherein, G is universal gravitational constant, the oval major radius of satellite orbit where A represents satellite.
Satellite radius vector indicates with the first calculation formula, the first calculation formula are as follows: r'=A × (1-e × cosE), wherein r'
The satellite radius vector is represented, the oval major radius of satellite orbit, e represent satellite orbit parameter set centre halfback where A represents satellite
Eccentricity of the star orbital road parameter sets Satellite on satellite orbit, E represent eccentric anomaly.
Preferably, it obtains module to be specifically used for: determining satellite in track based on the amendment argument of latitude and amendment satellite radius vector
Two-dimensional coordinate vector in areal coordinate system；Determine satellite in the instantaneous earth based on two-dimensional coordinate vector sum amendment inclination of satellite orbit
Three-dimensional coordinate vector in coordinate system；Determine satellite in agreement based on three-dimensional coordinate vector of the satellite in instantaneous terrestrial coordinate system
Three-dimensional coordinate vector in terrestrial coordinate system.
Preferably, three-dimensional coordinate vector of the satellite in conventional terrestrial coordinate system is indicated with the second calculation formula, the second meter
Calculate formula are as follows:
Wherein, xb、ybAnd zbRepresent coordinate of the satellite in conventional terrestrial coordinate system, xpAnd ypRepresent two-dimensional coordinate to
Abscissa and ordinate in amount, σ represent amendment inclination of satellite orbit, and H represents the longitude of ascending node at the observation moment.
Abscissa and ordinate in two-dimensional coordinate vector indicate with the 4th constraint condition set, the 4th constraint condition set
Are as follows:
Wherein, xpAnd ypThe abscissa and ordinate in two-dimensional coordinate vector are represented, r represents amendment satellite radius vector, and μ is repaired
The positive argument of latitude.
The longitude of ascending node H at observation moment indicates that the 5th constraint condition set is combined into the 5th constraint condition set:
Wherein, Ω0It represents in reference moment toeWhen right ascension of ascending node,It represents and refers to moment t describedoeWhen liter hand over
The change rate of point right ascension, ωeRotational-angular velocity of the earth is represented, t represents the observation moment,It represents in satellite orbit parameter set
In reference moment toeWhen right ascension of ascending node corresponding to time rate of change, GASTweekRepresent the Green Buddhist nun of this week initial time
Control the sidereal time.
Preferably, it obtains module to be specifically used for: determining change in SSR information with co-ordinates of satellite corresponding to the reference moment respectively
Positive vector and satellite velocities correct vector；Based on the observation moment, with reference to moment, co-ordinates of satellite correction vector sum satellite velocities correction
Vector determines co-ordinates of satellite correction vector of the satellite in satellite orbit coordinate system；By satellite defending in satellite orbit coordinate system
Star coordinate correction vector is transformed into co-ordinates of satellite correction vector of the satellite in ground heart is admittedly；To satellite in ground heart is admittedly
Three-dimensional coordinate vector of the co-ordinates of satellite correction vector sum satellite in conventional terrestrial coordinate system sum, obtain amendment satellite
Coordinate；Based on amendment co-ordinates of satellite computer installation star away from based on amendment satellite clock correction calculating carrier phase.
Preferably, co-ordinates of satellite correction vector of the satellite in ground heart is admittedly is indicated with third constraint condition set, the
Three constraint condition sets are combined into:
Wherein,Co-ordinates of satellite of the satellite in ground heart is admittedly corrects vector, and r' represents satellite radius vector,Represent satellite
Satellite velocities in orbit parameter,Represent co-ordinates of satellite correction vector of the satellite in satellite orbit coordinate system.
Preferably, amendment satellite clock correction is indicated with third calculation formula, third calculation formula are as follows: Δ ts=Δ t- δc/ C,
In, Δ tsAmendment satellite clock correction is represented, Δ t represents satellite clock correction, δcSatellite clock correction correction member is represented, C represents the light velocity.
The calculation formula of satellite clock correction Δ t are as follows: Δ t=α0+α1+α2(t-t0)+Δtr, wherein α0Satellite is represented multiple
Observe the initial observation moment t in the moment0Satellite clock correction, α1Represent initial observation moment of the satellite in multiple observation moment
t0Clock rate, α2Satellite is represented in initial observation moment t0Frequency drift, Δ trRepresent the relativistic effect value of satellite clock.
Satellite clock correction correction member δcCalculation formula are as follows: δc=c0+c1+c2(t-t0)2, wherein c0、c1And c2Represent SSR
In reference moment t in informationoeCoefficient.
Preferably, any one carrier phase is enabled to indicate with the 4th calculation formula, the 4th calculation formula are as follows:Wherein,Represent the carrier wave phase that i-th satellite observes the moment at j-th
Position, λ represent the carrier wavelength that i-th satellite observes the moment at j-th, which is constant, φi(tj) represent i-th and defend
Carrier phase observation data of the star j-th of observation moment,I-th satellite is represented j-th of observation moment
To receiver second station star away from DtroRepresent tropospheric delay, DionRepresent ionosphere delay, Δ tsI-th satellite is represented to exist
The amendment satellite clock correction at j-th of observation moment, C represent the light velocity.
For example, tropospheric delay DtroIt can be using Sa Sitamoning model to being obtained after the amendment of former tropospheric delay,
Ionosphere delay DionIt can be using double frequency correction model to what is obtained after primary ionization layer Deferred Correction, be single-frequency in receiver
When receiver, ionosphere delay DionIt can be using Klobuchar model to obtaining after primary ionization layer Deferred Correction.
Preferably, the matched curve D (t) of doppler measurement is accumulated in the range of the two neighboring observation moment
Point, obtain the phase difference of doppler measurement；If φi(tj+1)-φi(tj) in first threshold range and aforementioned phase differenceWithin the scope of second threshold, it is determined that there is no cycle slip, otherwise, it determines there is cycle slip.
Aforementioned phase differenceCalculation formula are as follows:
I-th satellite observes the moment at j-th to the second station star of receiver away from indicating with the 5th calculation formula, and the 5th counts
Calculate formula are as follows:Wherein,I-th satellite is represented to exist
The integer ambiguity at j-th of observation moment, Δ tuRepresent receiver clock-offsets,I-th satellite is represented in j-th of the observation
The error at quarter.
I-th satellite observes the error at moment at j-thIn three projective parameters with the 4th constraint condition set table
Show, the 4th constraint condition set is combined into:
Wherein,WithThe projective parameter that i-th satellite observes the moment at j-th is represented,
WithRepresent a coordinate in amendment co-ordinates of satellite, xu、yuAnd zuA coordinate in receiver three-dimensional coordinate is represented,Represent i-th satellite j-th observe the moment to receiver first stop star away from.
I-th satellite observes the moment at j-th to the first stop star of receiver away from indicating with the 6th calculation formula, and the 6th counts
Calculate formula are as follows:
The 4th calculation formula of simultaneous, the 5th calculation formula, the 4th constraint condition and the 6th calculation formula obtain the 7th calculating
Formula, and matrix equation, the 7th calculation formula are constructed by the 7th calculation formula are as follows:
Wherein, Δ x, Δ y and Δ z represent the error that i-th satellite observes the moment at j-thIn a coordinate difference
Value,
I-th satellite observes the receiver clock-offsets Δ t at moment at j-thuCalculation formula are as follows: Δ tu=b0+b1(t-t0)+
b2(t-t0)2, wherein b0Represent initial observation moment t of the satellite in multiple observation moment0Satellite clock correction, b1Represent satellite
Initial observation moment t in multiple observation moment0Clock rate, b2Satellite is represented in initial observation moment t0Frequency drift.
The foregoing is merely presently preferred embodiments of the present invention, is not intended to limit the invention, it is all in spirit of the invention and
Within principle, any modification, equivalent replacement, improvement and so on be should all be included in the protection scope of the present invention.
Claims (10)
1. a kind of method for calculating integer ambiguity based on least-squares algorithm, which comprises the following steps:
Step 1, obtain any satellite any one observation the moment amendment co-ordinates of satellite, amendment satellite clock correction, first stop star
Away from and carrier phase；
Step 2 observes the three of the moment described away from the determination satellite based on the amendment co-ordinates of satellite and the first stop star
Projective parameter in a dimension；
Step 3, based on the more satellites respectively in all projective parameters at multiple observation moment, all described repair
Positive satellite clock correction and all carrier phases construct matrix equation；
Step 4 calculates the matrix equation using least-squares algorithm, obtains at least two integer ambiguities.
2. a kind of method for calculating integer ambiguity based on least-squares algorithm according to claim 1, which is characterized in that
The step 1 specifically includes:
Step 11 obtains the satellite in the broadcast ephemeris at the observation moment；
Step 12, based in the broadcast ephemeris satellite orbit parameter set determine amendment the argument of latitude, amendment satellite radius vector,
Correct inclination of satellite orbit and satellite clock correction；
Step 13 determines institute based on the amendment argument of latitude, the amendment satellite radius vector and the amendment inclination of satellite orbit
State three-dimensional coordinate vector of the satellite in conventional terrestrial coordinate system；
Step 14 sits the satellite in the agreement earth based on co-ordinates of satellite correction vector of the satellite in ground heart is admittedly
Three-dimensional coordinate vector in mark system is modified, and obtains the amendment co-ordinates of satellite；
Step 15, the satellite clock correction correction member based on the satellite at the observation moment are modified the satellite clock correction,
Obtain the amendment satellite clock correction；
Step 16 calculates the first stop star based on the amendment co-ordinates of satellite away from based on amendment satellite clock correction calculating institute
State carrier phase.
3. a kind of method for calculating integer ambiguity based on least-squares algorithm according to claim 2, which is characterized in that
The amendment argument of latitude, the amendment satellite radius vector and the amendment inclination of satellite orbit are with the first constraint condition set table
Show, first constraint condition set is combined into:
Wherein, μ represents the amendment argument of latitude, and r represents the amendment satellite radius vector, and σ represents the amendment satellite orbit and inclines
Angle, δμRepresent perturbation correction member corresponding with argument of latitude μ ', δrRepresent perturbation correction member corresponding with satellite radius vector r', δσGeneration
Table perturbation correction member corresponding with inclination of satellite orbit σ ', Δ σ are represented and are corrected satellite described in the satellite orbit parameter set
The change rate of orbit inclination angle σ, t represent the observation moment, toeIt represents and refers to the moment；
Three perturbation correction members indicate that second constraint condition set is combined into the second constraint condition set:
Wherein, CμcAnd CμsRepresent perturbation correction member δ described in the satellite orbit parameter setμCorresponding perturbation parameter,
CrcAnd CrsRepresent perturbation correction member δ described in the satellite orbit parameter setrCorresponding perturbation parameter, CicAnd Cis?
Represent perturbation correction member δ described in the satellite orbit parameter setσCorresponding perturbation parameter；
The satellite radius vector indicates with the first calculation formula, first calculation formula are as follows:
R'=A × (1-e × cosE)
Wherein, r' represents the satellite radius vector, the oval major radius of satellite orbit where A represents the satellite, defends described in e representative
Eccentricity of the star orbital road parameter sets Satellite on satellite orbit, E represent eccentric anomaly.
4. a kind of method for calculating integer ambiguity based on least-squares algorithm according to claim 2, which is characterized in that
The step 13 specifically includes:
Step 131 determines the satellite in track areal coordinate system based on the amendment argument of latitude and the amendment satellite radius vector
In two-dimensional coordinate vector；
Step 132 determines the satellite in the instantaneous earth based on amendment inclination of satellite orbit described in the two-dimensional coordinate vector sum
Three-dimensional coordinate vector in coordinate system；
Step 133 determines the satellite in agreement based on three-dimensional coordinate vector of the satellite in instantaneous terrestrial coordinate system
Three-dimensional coordinate vector in spherical coordinate system.
5. a kind of method for calculating integer ambiguity based on least-squares algorithm according to claim 4, which is characterized in that
In the step 133, three-dimensional coordinate vector of the satellite in conventional terrestrial coordinate system is indicated with the second calculation formula, institute
State the second calculation formula are as follows:
Wherein, xb、ybAnd zbRepresent coordinate of the satellite in conventional terrestrial coordinate system, xpAnd ypThe two dimension is represented to sit
The abscissa and ordinate in vector are marked, σ represents the amendment inclination of satellite orbit, and the liter that H represents at the observation moment is handed over
Point longitude；
Abscissa and ordinate in the two-dimensional coordinate vector indicate with the 4th constraint condition set, the 4th constraint condition
Set are as follows:
Wherein, xpAnd ypThe abscissa and ordinate in the two-dimensional coordinate vector are represented, r represents the amendment satellite radius vector,
The argument of latitude is corrected described in μ；
The longitude of ascending node at the observation moment indicates that the 5th constraint condition set is combined into the 5th constraint condition set:
Wherein, H represents the longitude of ascending node at the observation moment, Ω0It represents in reference moment toeWhen right ascension of ascending node,Generation
Table refers to moment t describedoeWhen the right ascension of ascending node change rate, ωeRotational-angular velocity of the earth is represented, described in t is represented
The moment is observed,It represents in the satellite orbit parameter set in reference moment toeWhen right ascension of ascending node corresponding to the time
Change rate, GASTweekRepresent the Greenwich sidereal time of this week initial time.
6. a kind of method for calculating integer ambiguity based on least-squares algorithm according to claim 2, which is characterized in that
The step 14 specifically includes:
Step 141 is determined in SSR information respectively and is corrected with the correction vector sum satellite velocities of co-ordinates of satellite corresponding to the reference moment
Vector；
Step 142 corrects satellite velocities described in vector sum based on the observation moment, the reference moment, the co-ordinates of satellite
Correction vector determines co-ordinates of satellite correction vector of the satellite in satellite orbit coordinate system；
Co-ordinates of satellite correction vector of the satellite in satellite orbit coordinate system is transformed into the satellite on ground by step 143
Heart be admittedly in co-ordinates of satellite correction vector；
Step 144 corrects satellite described in vector sum in agreement earth seat to co-ordinates of satellite of the satellite in ground heart is admittedly
Three-dimensional coordinate vector in mark system is summed, and the amendment co-ordinates of satellite is obtained.
7. a kind of method for calculating integer ambiguity based on least-squares algorithm according to claim 6, which is characterized in that
In the step 144, co-ordinates of satellite correction vector of the satellite in ground heart is admittedly is with third constraint condition set table
Show, the third constraint condition set is combined into:
Wherein,Co-ordinates of satellite correction vector of the satellite in ground heart is admittedly is represented, r' represents the satellite radius vector,
The satellite velocities in the satellite orbit parameter are represented,Co-ordinates of satellite of the satellite in satellite orbit coordinate system is represented to change
Positive vector.
8. a kind of method for calculating integer ambiguity based on least-squares algorithm according to claim 2, which is characterized in that
In the step 15, the amendment satellite clock correction is indicated with third calculation formula, the third calculation formula are as follows:
Δts=Δ t- δc/C
Wherein, Δ tsThe amendment satellite clock correction is represented, Δ t represents the satellite clock correction, δcRepresent the satellite clock correction correction
, C represents the light velocity.
9. a kind of method that integer ambiguity is calculated based on least-squares algorithm according to claim 1-8,
It is characterized in that, in the step 3, any one of carrier phase is indicated with the 4th calculation formula, and the described 4th calculates public affairs
Formula are as follows:
Wherein,I-th satellite is represented in the carrier phase at j-th of observation moment, λ is represented described in i-th
Carrier wavelength of the satellite j-th of observation moment, φi(tj) i-th satellite is represented j-th of observation moment
Carrier phase observation data,Represent i-th satellite j-th it is described observation the moment to receiver second station star away from,
DtroRepresent tropospheric delay, DionRepresent ionosphere delay, Δ tsI-th satellite is represented j-th of observation moment
The amendment satellite clock correction, C represents the light velocity；
I-th satellite is public away from calculating with the 5th in the second station star at j-th of observation moment to the receiver
Formula expression, the 5th calculation formula are as follows:
Wherein,I-th satellite is represented in an integer ambiguity at j-th of observation moment, Δ tuIt represents and receives
Machine clock deviation, θ represent i-th satellite in the error at j-th of observation moment；
Three projective parameters of i-th satellite in the error theta at j-th of observation moment are with the 4th constraint condition set
It indicates, the 4th constraint condition set is combined into:
Wherein,WithRepresent i-th satellite j-th it is described observation the moment a projective parameter,WithRepresent a coordinate in the amendment co-ordinates of satellite, xu、yuAnd zuIt represents in receiver three-dimensional coordinate
A coordinate,Represent i-th satellite j-th observe the moment to the receiver the first stop star away from；
I-th satellite observes the moment at j-th to the first stop star of the receiver away from the 6th calculation formula table
Show, the 6th calculation formula are as follows:
4th calculation formula, the 5th calculation formula described in simultaneous, the 4th constraint condition and the 6th calculation formula,
Obtain the 7th calculation formula, the 7th calculation formula are as follows:
Wherein, Δ x, Δ y and Δ z represent a seat of i-th satellite in the error theta at j-th of observation moment
Difference is marked,
The matrix equation is constructed by the 7th calculation formula.
10. a kind of system for calculating integer ambiguity based on least-squares algorithm characterized by comprising obtain module, determination
Module, building module and computing module；
The acquisition module, for obtaining amendment co-ordinates of satellite, amendment satellite clock of any satellite at any one observation moment
Difference, first stop star away from and carrier phase；
The determining module is used for based on the amendment co-ordinates of satellite and the first stop star away from the determination satellite in the sight
Survey the projective parameter in three dimensions at moment；
The building module is joined for all projections based on the more satellites respectively at multiple observation moment
Several, all amendment satellite clock corrections and all carrier phases construct matrix equation；
The computing module obtains at least two complete cycles for calculating using least-squares algorithm the matrix equation
Fuzziness.
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