CN105549050B - A kind of Big Dipper deformation monitoring localization method based on fuzzy believable degree filtering - Google Patents

A kind of Big Dipper deformation monitoring localization method based on fuzzy believable degree filtering Download PDF

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CN105549050B
CN105549050B CN201510896845.8A CN201510896845A CN105549050B CN 105549050 B CN105549050 B CN 105549050B CN 201510896845 A CN201510896845 A CN 201510896845A CN 105549050 B CN105549050 B CN 105549050B
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CN105549050A (en
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夏娜
马培明
王桃
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Hefei University of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position

Abstract

The invention discloses a kind of Big Dipper deformation monitoring localization method based on fuzzy believable degree filtering, it is characterized in that carrying out as follows：Monitoring period of time is divided into multiple sub-periods first, calculates the positioning result of each sub-period respectively；Then according to the satellite distribution of each sub-period, error source, satellite epoch number, the fuzzy believable degree of each positioning result is determined using Fuzzy Set Theory；Finally go out the final positioning result of whole monitoring period of time using fuzzy believable degree weighted filtering.The present invention has refined positioning calculation process, having taken into full account influences every factor of positioning precision, final positioning result is set to reach higher positioning precision, positioning precision advantage is notable in the case of Changes in weather particularly in monitoring period of time, has broad application prospects.

Description

A kind of Big Dipper deformation monitoring localization method based on fuzzy believable degree filtering
Technical field
The invention belongs to satellite navigation positioning field, specifically a kind of Big Dipper deformation based on fuzzy believable degree filtering Monitoring and positioning method.
Background technology
Big Dipper deformation monitoring refers to that obtain monitoring point using Beidou navigation satellite " static relative positioning technology " sits in high precision Mark (grade), so as to analyze the displacement or sedimentation that judge dam, bridge, ground etc., there is important application value.
At present, when carrying out earth deformation monitoring using aeronautical satellite (GPS, GLONASS, the Big Dipper) technology, using " static Relative positioning method ".This method thinks monitoring station transfixion, should by gathering prolonged, substantial amounts of Satellite Observations With the baseline vector between least square adjustment principle solving base station and monitoring station.Because possess substantial amounts of moonscope number According to, it is possible to by iterating to calculate Stepwise Refinement, high-precision baseline vector is calculated, so as to obtain the positioning of " grade " As a result, and then long term monitoring can be carried out to the object (dam, bridge, ground etc.) slowly deformed.
As shown in figure 1, traditional static relative positioning method is using all Satellite Observations of a longer period of time, Positioning result L is calculated in a manner of post processing.Because satellite spatial distribution can change within this period, weather can also become Change, therefore it is change to receive satellite data quality, some sub-period satellite data quality are good, some sub-period satellite datas Quality is general or poor.Conventional method and the otherness for not differentiating between this quality of data, broadly utilize all satellite data meters Positioning result is calculated, so as to result in the increase of positioning result error, it is difficult to meet high-precision applications demand.
The content of the invention
The present invention is to overcome above-mentioned the deficiencies in the prior art part, it is proposed that a kind of north based on fuzzy believable degree filtering Struggle against deformation monitoring localization method, to improve the precision of positioning result, the situation of Changes in weather particularly in monitoring period of time Lower positioning precision advantage is notable.
The present invention to achieve the above object of the invention, adopts the following technical scheme that：
A kind of Big Dipper deformation monitoring localization method based on fuzzy believable degree filtering of the present invention, is applied to by Beidou navigation In the monitoring of environmental of satellite, base station and rover station composition；The base station receives the benchmark that the Beidou navigation satellite is sent Satellite epoch Data Concurrent of standing gives rover station；The rover station receives the rover station satellite that the Beidou navigation satellite is sent and gone through Metadata and the base station satellite epoch data of base station transmission simultaneously carry out difference processing, obtain Differential positioning data, note For X；It is characterized in, the Big Dipper deformation monitoring localization method is carried out as follows：
Step 1, the Differential positioning data X to the rover station are split according to the period, obtain N number of sub- period Differential positioning data, it is designated as X={ X1,X2,…,Xn,…,XN}；XnRepresent n-th of period of the day from 11 p.m. to 1 a.m in the Differential positioning data X of rover station Between section Differential positioning data；1≤n≤N；
Step 2, the Differential positioning data X to N number of sub- period are respectively adopted static relative positioning algorithm and counted Calculate, obtain N number of positioning result, be designated as L={ L1,L2,…,Ln,…,LN}；LnRepresent that the difference of n-th of sub- period of rover station is determined Position data xnPositioning result；
Step 3, the offline parameter matrix S for establishing confidence levelm×3；
The credibility of the positioning result of rover station is mainly influenceed by three parameters, and they can be calculated as follows：
Step 3.1, the positioning result L using formula (1) n-th of sub- period of acquisitionnGeometric dilution of precision average value
In formula (1),Represent the positioning result L of n-th of sub- period of rover stationnHorizontal component dilution of precision Average value；Represent the positioning result L of n-th of sub- period of rover stationnVertical component dilution of precision average value；Represent the positioning result L of n-th of sub- period of rover stationnClock correction dilution of precision average value；
Step 3.2, the positioning result L using formula (2) n-th of sub- period of acquisitionnUpper atmosphere AME
In formula (2),Represent the positioning result L of n-th of sub- period of rover stationnIonospheric error average value；Represent the positioning result L of n-th of sub- period of rover stationnTropospheric error average value；
Step 3.3, the satellite epoch quantity N in statistics n-th of sub- period of rover stationn；
Step 3.4, the credibility that confidence level T ∈ { 1,2 ..., j ..., m } represent positioning result is defined, wherein m is just Integer；The parameter vector for defining confidence level is S={ S1,S2,…,Sj,…,Sm}；SjRepresent the parameter corresponding to confidence level T=j Vector；And haveGeometric dilution of precision parameter value is represented, is calculated by formula (3)；Represent high-altitude Atmosphere errors parameter value, it is calculated by formula (4)；Satellite epoch number parameter value is represented, is calculated by formula (5).
In formula (3),Represent the optimum value of geometric dilution of precision；Represent confidence level T=j geometry essence Spend the factor；In formula (4),Represent the optimum value of upper atmosphere error；Represent confidence level T=j upper atmosphere error； In formula (5), N*Represent the optimum value of satellite epoch quantity；NjRepresent confidence level T=j satellite epoch quantity；
Step 3.5, the parameter matrix for establishing confidence level
Step 4, the Evaluations matrix E for establishing positioning resultN×3；
Step 4.1, definition positioning result evaluation vector are E={ E1,E2,…,En,…,EN}；EnRepresent rover station n-th The evaluation vector of sub- period positioning result；And haveRepresent the geometry of n-th of sub- period of rover station Dilution of precision evaluation of estimate, it is calculated by formula (6)；Represent the upper atmosphere error assessment of n-th of sub- period of rover station Value, is calculated by formula (7)；The satellite epoch quantitative assessment value of n-th of sub- period of rover station is represented, is passed through formula (8) It is calculated；
Step 4.2, the Evaluations matrix for establishing positioning result
Step 5, using formula (9) establish membership function
In formula (9),
Step 6, opening relationships matrix
Step 7, utilize formula (10) acquisition threshold value λ；
Step 8, using formula (11) to the relational matrix R processing, obtain Boolean matrix
In formula (11),Represent that n-th of sub- time segment difference of rover station divides location data xnPositioning result Ln's Confidence level T=j；
Step 9, filtering process is weighted to N number of positioning result of rover station using formula (12), obtains final positioning knot Fruit L*；
In formula (12), T (k) represents the positioning result L of k-th of sub- period of rover stationkConfidence level.
Compared with prior art, beneficial effects of the present invention are embodied in：
1st, a longer monitoring period of time is divided into multiple sub-periods by the present invention, utilizes the moonscope number of each sub-period According to the positioning result for calculating respective sub-period respectively, positioning calculation process has been refined, has avoided " the cage of conventional mapping methods The calculating theory of system ", contribute to the otherness using each sub-period satellite data quality, to improve positioning precision.
2nd, present invention introduces the concept of confidence level, according to the satellite data mass parameter of each sub-period, (satellite distribution is several What dilution of precision, upper atmosphere error, satellite epoch quantity) change divide different confidence levels, taken into full account and defended Influence of the every factor such as star changes in spatial distribution, Changes in weather to positioning result, improve the reliability of positioning result；Together When, employ Fuzzy Set Theory and determine the confidence level of each sub-period positioning result, and solved in a manner of weighted filtering Final positioning result, so as to improve the precision of positioning result, have broad application prospects.
Brief description of the drawings
Fig. 1 is traditional static relative positioning method；
Fig. 2 is the Method And Principle of the present invention；
Fig. 3 is the internal association figure that the present invention is determined positioning result confidence level by the quality of data；
Fig. 4 is Big Dipper deformation monitoring localization method flow chart of the present invention based on fuzzy believable degree filtering；
Fig. 5 is the inventive method and the Comparison of experiment results of traditional static relative positioning method.
Embodiment
It is a kind of based on fuzzy believable degree filtering Big Dipper deformation monitoring localization method, be applied to by Beidou navigation satellite, In the monitoring of environmental of base station and rover station composition；Base station receives the base station satellite epoch data that Beidou navigation satellite is sent And it is sent to rover station；The base that rover station receives the rover station satellite epoch data of Beidou navigation satellite transmission and base station is sent Quasi- station satellite epoch data, the two carries out difference processing and obtains Differential positioning data, is designated as X；
As shown in figure 4, Big Dipper deformation monitoring localization method is carried out as follows：
Step 1, the Differential positioning data X to rover station are split according to the period, obtain the difference of N number of sub- period Location data, such as 24 hours observation periods are divided into 12 sub-periods, each sub-period 2 hours；It is designated as X={ X1, X2,…,Xn,…,XN}；XnRepresent the Differential positioning data of n-th of sub- period in the Differential positioning data X of rover station；1≤n ≤N；
Step 2, the Differential positioning data X to N number of sub- period are respectively adopted static relative positioning algorithm and calculated, and obtain N number of positioning result is obtained, is designated as L={ L1,L2,…,Ln,…,LN}；LnRepresent the Differential positioning number of n-th of sub- period of rover station According to XnPositioning result；The content of static relative positioning algorithm, which is shown in, refers to " method of the king into carrier phase differential dynamic positionings Study [D] Xi'an:Chang An University, 2010. "
Step 3, the offline parameter matrix S for establishing confidence levelm×3；
The credibility of the positioning result of rover station is mainly influenceed by three parameters, and they can be calculated as follows：
Step 3.1, the positioning result L using formula (1) n-th of sub- period of acquisitionnGeometric dilution of precision average valueIt reflects the space geometry relation between monitoring station and satellite.Value is sweared with monitoring station to satellite activity The polyhedron volume that amount end points is formed is inversely proportional, the bigger combinations of satellites of polyhedron volumeIt is worth smaller.Observing The timing of error one,It is worth smaller, positioning precision is higher.
In formula (1),Represent the positioning result L of n-th of sub- period of rover stationnHorizontal component dilution of precision Average value；Represent the positioning result L of n-th of sub- period of rover stationnVertical component dilution of precision average value；Represent the positioning result L of n-th of sub- period of rover stationnClock correction dilution of precision average value；They can pass through instruction Obtained from receiver.Within n-th of sub- period of rover station,As commenting for the sub-period positioning result credibility One of valency parameter.
Abundant experimental results show：WhenWhen, the result precision that location algorithm resolves is high；Otherwise, positioning is calculated The resultant error that method resolves is larger；Therefore, in the present embodiment, optimum value is made
Step 3.2, the positioning result L using formula (2) the n-th period of acquisitionnUpper atmosphere AMEIt Reflect influence of the monitoring station overhead Atmosphere changes to positioning result.
In formula (2),Represent the positioning result L of n-th of sub- period of rover stationnIonospheric error average value；Represent the positioning result L of the sub- period of rover stationnTropospheric error average value；They can be by instructing from reception Machine obtains.Within n-th of sub- period of rover station,As the sub-period positioning result credibility evaluating it Two.
Abundant experimental results show：WhenWhen, the result precision that location algorithm resolves is high；Otherwise, location algorithm The resultant error of resolving is larger.Therefore, in the present embodiment, optimum value is made
Step 3.3, the satellite epoch quantity N in statistics n-th of sub- period of rover stationn；
The whether sufficient precision for directly determining positioning result of satellite epoch quantity.For static relative positioning, satellite is gone through First quantity is bigger, and positioning result precision is higher；Conversely, positioning result precision is lower.Within n-th of sub- period of rover station, I Count satellite epoch quantity Nn, three as the evaluating of the sub-period positioning result credibility；As shown in Figure 3.
Under normal circumstances, operation of receiver frequency is 1Hz, can receive 7200 satellite epoch, Ke Yibao within every 2 hours Demonstrate,prove the high accuracy of positioning result.But be blocked, in the case of receiver power supply instability or even power failure in satellite-signal, receive The satellite epoch quantity N that machine receivesn<When 3600, the resultant error of static relative positioning is larger.Make optimum value N*=7200.
Step 3.4, the credibility that confidence level T ∈ { 1,2 ..., j ..., m } represent positioning result is defined, wherein m is just Integer；T values are bigger to represent that credibility is higher；The parameter vector for defining confidence level is S={ S1,S2,…,Sj,…,Sm}；Sj Represent the parameter vector corresponding to confidence level T=j；And haveGeometric dilution of precision parameter value is represented, is led to Formula (3) is crossed to be calculated；Upper atmosphere error parameter value is represented, is calculated by formula (4)；Represent satellite epoch number Parameter value is measured, is calculated by formula (5)：
In formula (3),Represent the optimum value of geometric dilution of precision；Represent confidence level T=j geometry essence Spend the factor；In formula (4),Represent the optimum value of upper atmosphere error；Represent confidence level T=j upper atmosphere error； In formula (5), N*Represent the optimum value of satellite epoch quantity；NjRepresent confidence level T=j satellite epoch quantity；
Step 3.5, the parameter matrix for establishing confidence level
The parameter matrix of confidence level lists 3 parameter values of different confidence levels respectively.Embody the difference of different confidence levels It is different.
In actual applications, 3 parameter values that each confidence level can be set are as shown in table 1.It is carried out using optimum value The parameter vector S of the order of magnitude after reunificationjAs shown in table 2.
The parameter value of the confidence level of table 1.
The parameter vector S of the confidence level of table 2.j
So, a kind of parameter matrix of effective confidence level is：
Step 4, the Evaluations matrix E for establishing positioning resultN×3；
Step 4.1, definition positioning result evaluation vector are E={ E1,E2,…,En,…,EN}；EnRepresent rover station n-th The evaluation vector of sub- period positioning result；And haveRepresent the geometry of n-th of sub- period of rover station Dilution of precision evaluation of estimate, it is calculated by formula (6)；Represent the upper atmosphere error assessment of n-th of sub- period of rover station Value, is calculated by formula (7)；The satellite epoch quantitative assessment value of n-th of sub- period of rover station is represented, is passed through formula (8) It is calculated；
Step 4.2, the Evaluations matrix for establishing positioning result
The Evaluations matrix of positioning result lists 3 evaluations of estimate of N number of positioning result of N number of sub-period respectively；Reflect The similarities and differences of each positioning result in 3 evaluations of estimate.
Step 5, using formula (9) establish membership function
In formula (9),Positioning result evaluation vector EiTo confidence level parameter vector Sj's The situation of being subordinate to is integrated.
Step 6, opening relationships matrix
Matrix R calculates gained according to formula (9), and its row represents N number of positioning result evaluation vector, and row represent m confidence level ginseng Number vector, so allow for positioning result and set up relation with confidence level, so as to be provided for the determination of positioning result confidence level Calculation basis.
Step 7, utilize formula (10) acquisition threshold value λ：
Threshold value λ size directly affects the determination of the confidence level of positioning result.λ value is bigger, and positioning result can be confirmed as Fewer confidence level is higher so as to be absorbed in rate；Conversely, positioning result can be confirmed as more confidence levels.It is fixed in view of one Position result will at least have a confidence level, then
Step 8, using formula (11) to the relational matrix R processing, obtain Boolean matrix
In formula (11),Represent that n-th of sub- time segment difference of rover station divides location data xnPositioning result Ln's Confidence level T=j；Here fuzzy relation matrix is converted into Boolean matrix according to λ-Level Matrix theory in fuzzy clustering.
Because this patent method is the confidence level of each sub-period positioning result determined based on Fuzzy Set Theory, therefore should Confidence level is referred to as " fuzzy believable degree ".
Step 9, filtering process is weighted to N number of positioning result of rover station using formula (12), obtains final positioning knot Fruit L*As shown in Figure 2；
In formula (12), T (k) represents the positioning result L of k-th of sub- period of rover stationkFuzzy believable degree.
Experimental verification：
On on October 8th, 2015 to November 8, it is quiet to apply tradition simultaneously in the high roadbed deformation monitoring project of Hefei somewhere State relative positioning method and this patent method, the deformation monitoring of 30 days is carried out, their settlement monitoring result such as Fig. 5 institutes Show.It can be seen that the monitoring result big rise and fall of traditional static relative positioning method, error is obvious, and it mainly receives Changes in weather With the influence of the factor such as satellite epoch quantity；The monitoring result of this patent method is more accurate, more stable, more realistically reflects height The Continuous Settlement process of embankment.

Claims (1)

1. a kind of Big Dipper deformation monitoring localization method based on fuzzy believable degree filtering, it is applied to by Beidou navigation satellite, base In the monitoring of environmental of quasi- station and rover station composition；The base station receives the base station satellite that the Beidou navigation satellite is sent and gone through Metadata is simultaneously sent to rover station；The rover station receive the rover station satellite epoch data that the Beidou navigation satellite sends and The base station satellite epoch data of the base station transmission simultaneously carry out difference processing, obtain Differential positioning data, are designated as X；It is special Sign is that the Big Dipper deformation monitoring localization method is carried out as follows：
Step 1, the Differential positioning data X to the rover station are split according to the period, obtain the difference of N number of sub- period Location data, it is designated as X={ X1,X2,…,Xn,…,XN}；XnRepresent n-th of sub- period in the Differential positioning data X of rover station Differential positioning data；1≤n≤N；
Step 2, the Differential positioning data X to N number of sub- period are respectively adopted static relative positioning algorithm and calculated, and obtain N number of positioning result is obtained, is designated as L={ L1,L2,…,Ln,…,LN}；LnRepresent the Differential positioning number of n-th of sub- period of rover station According to XnPositioning result；
Step 3, the offline parameter matrix S for establishing confidence levelm×3；
The credibility of the positioning result of rover station is mainly influenceed by three parameters, and they can be calculated as follows：
Step 3.1, the positioning result L using formula (1) n-th of sub- period of acquisitionnGeometric dilution of precision average value
<mrow> <mover> <mrow> <msub> <mi>GDOP</mi> <mi>n</mi> </msub> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <mover> <mrow> <msub> <mi>HDOP</mi> <mi>n</mi> </msub> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mover> <mrow> <msub> <mi>VDOP</mi> <mi>n</mi> </msub> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mover> <mrow> <msub> <mi>TDOP</mi> <mi>n</mi> </msub> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
In formula (1),Represent the positioning result L of n-th of sub- period of rover stationnHorizontal component dilution of precision be averaged Value；Represent the positioning result L of n-th of sub- period of rover stationnVertical component dilution of precision average value；Table Show the positioning result L of n-th of sub- period of rover stationnClock correction dilution of precision average value；
Step 3.2, the positioning result L using formula (2) n-th of sub- period of acquisitionnUpper atmosphere AME
<mrow> <mover> <mrow> <msub> <mi>&amp;Delta;&amp;tau;</mi> <mi>n</mi> </msub> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <mover> <mrow> <msub> <mi>&amp;Delta;</mi> <mi>I</mi> </msub> <msub> <mi>&amp;tau;</mi> <mi>n</mi> </msub> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mover> <mrow> <msub> <mi>&amp;Delta;</mi> <mi>T</mi> </msub> <msub> <mi>&amp;tau;</mi> <mi>n</mi> </msub> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
In formula (2),Represent the positioning result L of n-th of sub- period of rover stationnIonospheric error average value；Represent The positioning result L of n-th of sub- period of rover stationnTropospheric error average value；
Step 3.3, the satellite epoch quantity N in statistics n-th of sub- period of rover stationn；
Step 3.4, the credibility that confidence level T ∈ { 1,2 ..., j ..., m } represent positioning result is defined, m is positive integer；Definition The parameter vector of confidence level is S={ S1,S2,…,Sj,…,Sm}；SjRepresent the parameter vector corresponding to confidence level T=j；And have Geometric dilution of precision parameter value is represented, is calculated by formula (3)；Represent upper atmosphere error parameter Value, is calculated by formula (4)；Satellite epoch number parameter value is represented, is calculated by formula (5)：
<mrow> <msubsup> <mi>s</mi> <mi>j</mi> <mn>1</mn> </msubsup> <mo>=</mo> <msup> <mover> <mrow> <mi>G</mi> <mi>D</mi> <mi>O</mi> <mi>P</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>*</mo> </msup> <mo>/</mo> <msup> <mover> <mrow> <mi>G</mi> <mi>D</mi> <mi>O</mi> <mi>P</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> <mi>j</mi> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msubsup> <mi>s</mi> <mi>j</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msup> <mover> <mrow> <mi>&amp;Delta;</mi> <mi>&amp;tau;</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>*</mo> </msup> <mo>/</mo> <msup> <mover> <mrow> <mi>&amp;Delta;</mi> <mi>&amp;tau;</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> <mi>j</mi> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msubsup> <mi>s</mi> <mi>j</mi> <mn>3</mn> </msubsup> <mo>=</mo> <msup> <mi>N</mi> <mi>j</mi> </msup> <mo>/</mo> <msup> <mi>N</mi> <mo>*</mo> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
In formula (3),Represent the optimum value of geometric dilution of precision；Represent confidence level T=j geometric accuracy because Son；In formula (4),Represent the optimum value of upper atmosphere error；Represent confidence level T=j upper atmosphere error；Formula (5) In, N*Represent the optimum value of satellite epoch quantity；NjRepresent confidence level T=j satellite epoch quantity；
Step 3.5, the parameter matrix for establishing confidence level
Step 4, the Evaluations matrix E for establishing positioning resultN×3；
Step 4.1, definition positioning result evaluation vector are E={ E1,E2,…,En,…,EN}；EnRepresent n-th of period of the day from 11 p.m. to 1 a.m of rover station Between section positioning result evaluation vector；And have Represent n-th of sub- period of rover station geometric accuracy because Sub- evaluation of estimate, it is calculated by formula (6)；The upper atmosphere error assessment value of n-th of sub- period of rover station is represented, is passed through Formula (7) is calculated；The satellite epoch quantitative assessment value of n-th of sub- period of rover station is represented, is calculated by formula (8) Arrive；
<mrow> <msubsup> <mi>e</mi> <mi>n</mi> <mn>1</mn> </msubsup> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <mo>|</mo> <mover> <mrow> <msub> <mi>GDOP</mi> <mi>n</mi> </msub> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>-</mo> <msup> <mover> <mrow> <mi>G</mi> <mi>D</mi> <mi>O</mi> <mi>P</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>*</mo> </msup> <mo>|</mo> </mrow> <msup> <mover> <mrow> <mi>G</mi> <mi>D</mi> <mi>O</mi> <mi>P</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>*</mo> </msup> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msubsup> <mi>e</mi> <mi>n</mi> <mn>2</mn> </msubsup> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <mo>|</mo> <mover> <mrow> <msub> <mi>&amp;Delta;&amp;tau;</mi> <mi>n</mi> </msub> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>-</mo> <msup> <mover> <mrow> <mi>&amp;Delta;</mi> <mi>&amp;tau;</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>*</mo> </msup> <mo>|</mo> </mrow> <msup> <mover> <mrow> <mi>&amp;Delta;</mi> <mi>&amp;tau;</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>*</mo> </msup> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msubsup> <mi>e</mi> <mi>n</mi> <mn>3</mn> </msubsup> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <mo>|</mo> <msub> <mi>N</mi> <mi>n</mi> </msub> <mo>-</mo> <msup> <mi>N</mi> <mo>*</mo> </msup> <mo>|</mo> </mrow> <msup> <mi>N</mi> <mo>*</mo> </msup> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
Step 4.2, the Evaluations matrix for establishing positioning result
Step 5, using formula (9) establish membership function
<mrow> <msub> <mi>&amp;mu;</mi> <msub> <mi>S</mi> <mi>j</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>v</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>3</mn> </munderover> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>e</mi> <mi>n</mi> <mi>v</mi> </msubsup> <mo>-</mo> <msubsup> <mi>s</mi> <mi>j</mi> <mi>v</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
In formula (9),
Step 6, opening relationships matrix
Step 7, utilize formula (10) acquisition threshold value λ；
<mrow> <mi>&amp;lambda;</mi> <mo>&amp;le;</mo> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mi>j</mi> </munder> <mo>{</mo> <munder> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> <mi>n</mi> </munder> <mo>{</mo> <msub> <mi>&amp;mu;</mi> <msub> <mi>S</mi> <mi>j</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>}</mo> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
Step 8, using formula (11) to the relational matrix R processing, obtain Boolean matrix
<mrow> <msup> <mi>R</mi> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msup> <msub> <mi>&amp;mu;</mi> <msub> <mi>S</mi> <mn>1</mn> </msub> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msup> <msub> <mi>&amp;mu;</mi> <msub> <mi>S</mi> <mn>2</mn> </msub> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mrow> <msup> <msub> <mi>&amp;mu;</mi> <msub> <mi>S</mi> <mi>j</mi> </msub> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mrow> <msup> <msub> <mi>&amp;mu;</mi> <msub> <mi>S</mi> <mi>m</mi> </msub> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <msub> <mi>&amp;mu;</mi> <msub> <mi>S</mi> <mn>1</mn> </msub> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msup> <msub> <mi>&amp;mu;</mi> <msub> <mi>S</mi> <mn>2</mn> </msub> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mrow> <msup> <msub> <mi>&amp;mu;</mi> <msub> <mi>S</mi> <mi>j</mi> </msub> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mrow> <msup> <msub> <mi>&amp;mu;</mi> <msub> <mi>S</mi> <mi>m</mi> </msub> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <msub> <mi>&amp;mu;</mi> <msub> <mi>S</mi> <mn>1</mn> </msub> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msup> <msub> <mi>&amp;mu;</mi> <msub> <mi>S</mi> <mn>2</mn> </msub> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mrow> <msup> <msub> <mi>&amp;mu;</mi> <msub> <mi>S</mi> <mi>j</mi> </msub> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mrow> <msup> <msub> <mi>&amp;mu;</mi> <msub> <mi>S</mi> <mi>m</mi> </msub> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <msub> <mi>&amp;mu;</mi> <msub> <mi>S</mi> <mn>1</mn> </msub> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msup> <msub> <mi>&amp;mu;</mi> <msub> <mi>S</mi> <mn>2</mn> </msub> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mrow> <msup> <msub> <mi>&amp;mu;</mi> <msub> <mi>S</mi> <mi>j</mi> </msub> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mrow> <msup> <msub> <mi>&amp;mu;</mi> <msub> <mi>S</mi> <mi>m</mi> </msub> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
<mrow> <msup> <msub> <mi>&amp;mu;</mi> <msub> <mi>S</mi> <mi>j</mi> </msub> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mn>1</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;mu;</mi> <msub> <mi>S</mi> <mi>j</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;GreaterEqual;</mo> <mi>&amp;lambda;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>0</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;mu;</mi> <msub> <mi>S</mi> <mi>j</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>&lt;</mo> <mi>&amp;lambda;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
In formula (11),Represent that n-th of sub- time segment difference of rover station divides location data XnPositioning result LnConfidence Spend T=j；
Step 9, using formula (12) filtering process is weighted to N number of positioning result of rover station, obtains final positioning result L*；
<mrow> <msup> <mi>L</mi> <mo>*</mo> </msup> <mo>=</mo> <mfrac> <mrow> <mi>T</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>T</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <msub> <mi>L</mi> <mn>1</mn> </msub> <mo>+</mo> <mfrac> <mrow> <mi>T</mi> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>T</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <msub> <mi>L</mi> <mn>2</mn> </msub> <mo>+</mo> <mn>...</mn> <mo>+</mo> <mfrac> <mrow> <mi>T</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>T</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <msub> <mi>L</mi> <mi>n</mi> </msub> <mo>+</mo> <mn>...</mn> <mo>+</mo> <mfrac> <mrow> <mi>T</mi> <mrow> <mo>(</mo> <mi>N</mi> <mo>)</mo> </mrow> </mrow> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>T</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <msub> <mi>L</mi> <mi>N</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
In formula (12), T (k) represents the positioning result L of k-th of sub- period of rover stationkConfidence level.
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