CN105549050A - Beidou deformation monitoring and positioning method based on fuzzy confidence filtering - Google Patents

Abstract

The invention discloses a Beidou deformation monitoring and positioning method based on fuzzy confidence filtering. The method comprises the following steps of: firstly, dividing a monitoring period into a plurality of sub-periods, and calculating a positioning result of each sub-period; then according to satellite distribution, error sources and a satellite epoch number of each sub-period, adopting a fuzzy set theory to determine the fuzzy confidence of each positioning result; and finally, utilizing the fuzzy confidence to carry out weighted filtering so as to obtain a final positioning result of the whole monitoring period. According to the invention, the positioning calculation process is detailed, each factor influencing the positioning precision is fully considered, and the final positioning result is enabled to achieve a higher positioning precision; and especially when the weather changes in the monitoring period, the method has obvious advantages in positioning precision, so that the method has a wide application prospect.

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 monitoring localization method based on fuzzy believable degree filtering.

Background technology

Big Dipper deformation monitoring refers to and utilizes Beidou navigation satellite " static relative positioning technology " to obtain monitoring point high-precision coordinate (grade), thus analyzes the displacement or the sedimentation that judge dam, bridge, ground etc., has important using value.

At present, when adopting Navsat (GPS, GLONASS, the Big Dipper) technology to carry out earth deformation monitoring, all " static relative positioning method " is adopted.The method thinks monitoring station transfixion, by gathering long, a large amount of Satellite Observations, and the baseline vector between application least square adjustment principle solving base station and monitoring station.Because have a large amount of Satellite Observations, so can iterative computation Stepwise Refinement be passed through, calculate high-precision baseline vector, thus obtain the positioning result of " grade ", and then long term monitoring can be carried out to the object (dam, bridge, ground etc.) of slowly distortion.

As shown in Figure 1, traditional static relative positioning method is all Satellite Observations utilizing a longer period of time, calculates positioning result L in the mode of aftertreatment.Because within this period, satellite spatial distribution can change, weather also can change, and therefore receiving satellite data quality is change, and some sub-period satellite data quality is good, and some sub-period satellite data quality is general or poor.Classic method does not distinguish the otherness of this quality of data, broadly utilizes all satellite data compute location results, thus result in the increase of positioning result error, is difficult to meet high-precision applications demand.

Summary of the invention

The present invention is for overcoming above-mentioned the deficiencies in the prior art part, propose a kind of Big Dipper deformation monitoring localization method based on fuzzy believable degree filtering, to improving the precision of positioning result, particularly in monitoring period of time, when Changes in weather, positioning precision advantage is remarkable.

The present invention to achieve the above object of the invention, adopts following technical scheme:

A kind of Big Dipper deformation monitoring localization method based on fuzzy believable degree filtering of the present invention is applied in the monitoring of environmental that is made up of Beidou navigation satellite, base station and rover station; Base station satellite Data Concurrent epoch that described base station receives the transmission of described Beidou navigation satellite gives rover station; Described rover station receives rover station satellite data epoch that described Beidou navigation satellite sends and base station satellite data epoch that described base station sends and carries out difference processing, obtains Differential positioning data, is designated as X; Be characterized in, described Big Dipper deformation monitoring localization method carries out as follows:

Step 1, the Differential positioning data X of described rover station to be split according to the time period, obtain the Differential positioning data of N number of sub-time period, be designated as X={X ₁, X ₂..., X _n..., X _n; X _nrepresent the Differential positioning data of the n-th sub-time period in the Differential positioning data X of rover station; 1≤n≤N;

Step 2, adopt static relative positioning algorithm to calculate respectively to the Differential positioning data X of described N number of sub-time period, obtain N number of positioning result, be designated as L={L ₁, L ₂..., L _n..., L _n; L _nrepresent the Differential positioning data x of rover station n-th sub-time period _npositioning result;

Step 3, off-line set up the parameter matrix S of degree of confidence _{m × 3};

The credibility of the positioning result of rover station is mainly by the impact of three parameters, and they can be calculated as follows:

Step 3.1, formula (1) is utilized to obtain the positioning result L of the n-th sub-time period _ngeometric dilution of precision mean value

$\stackrel{\‾}{{\mathrm{GDOP}}_n}=\sqrt{{\left(\stackrel{\‾}{{\mathrm{HDOP}}_n}\right)}^2+{\left(\stackrel{\‾}{{\mathrm{VDOP}}_n}\right)}^2+{\left(\stackrel{\‾}{{\mathrm{TDOP}}_n}\right)}^2}---\left(1\right)$

In formula (1), represent the positioning result L of rover station n-th sub-time period _nhorizontal component dilution of precision mean value; represent the positioning result L of rover station n-th sub-time period _nvertical component dilution of precision mean value; represent the positioning result L of rover station n-th sub-time period _nclock correction dilution of precision mean value;

Step 3.2, formula (2) is utilized to obtain the positioning result L of the n-th sub-time period _nupper atmosphere AME

$\stackrel{\‾}{{\mathrm{\Δ\τ}}_n}=\sqrt{{\left(\stackrel{\‾}{{\mathrm{\Δ}}_I{\mathrm{\τ}}_n}\right)}^2+{\left(\stackrel{\‾}{{\mathrm{\Δ}}_T{\mathrm{\τ}}_n}\right)}^2}---\left(2\right)$

In formula (2), represent the positioning result L of rover station n-th sub-time period _nionospheric error mean value; represent the positioning result L of rover station n-th sub-time period _ntropospheric error mean value;

Step 3.3, satellite quantity N epoch added up in the rover station n-th sub-time period _n;

Step 3.4, definition degree of confidence T ∈ 1,2 ..., j ..., m} represents the credibility of positioning result, and wherein m is positive integer; The parameter vector of definition degree of confidence is S={S ₁, S ₂..., S _j..., S _m; S _jrepresent the parameter vector corresponding to degree of confidence T=j; And have represent geometric dilution of precision parameter value, through type (3) calculates; represent upper atmosphere error parameter value, through type (4) calculates; represent satellite number parameter epoch value, through type (5) calculates.

$s_j^1={\stackrel{\‾}{GDOP}}^{*}/{\stackrel{\‾}{GDOP}}^j---\left(3\right)$

$s_j^2={\stackrel{\‾}{\mathrm{\Δ}\mathrm{\τ}}}^{*}/{\stackrel{\‾}{\mathrm{\Δ}\mathrm{\τ}}}^j---\left(4\right)$

$s_j^3=N^j/N^{*}---\left(5\right)$

In formula (3), represent the optimum value of geometric dilution of precision; represent the geometric dilution of precision of degree of confidence T=j; In formula (4), represent the optimum value of upper atmosphere error; represent the upper atmosphere error of degree of confidence T=j; In formula (5), N ^*represent the optimum value of satellite quantity epoch; N ^jrepresent satellite quantity epoch of degree of confidence T=j;

Step 3.5, set up the parameter matrix of degree of confidence $S_{m\×3}=\left[\begin{array}{ccc}{s}_1^1& s_1^2& s_1^3\\ s_2^1& s_2^2& s_2^3\\ .& .& .\\ .& .& .\\ .& .& .\\ s_j^1& s_j^2& s_j^3\\ .& .& .\\ .& .& .\\ .& .& .\\ s_m^1& s_m^2& s_m^3\end{array}\right];$

Step 4, set up the Evaluations matrix E of positioning result _{n × 3};

Step 4.1, definition positioning result evaluation vector are E={E ₁, E ₂..., E _n..., E _n; E _nrepresent the evaluation vector of the sub-time period positioning result of rover station n-th; And have represent the geometric dilution of precision evaluation of estimate of rover station n-th sub-time period, through type (6) calculates; represent the upper atmosphere error assessment value of rover station n-th sub-time period, through type (7) calculates; represent the satellite quantitative assessment epoch value of rover station n-th sub-time period, through type (8) calculates;

$e_n^1=1-\frac{|\stackrel{\‾}{{\mathrm{GDOP}}_n}-{\stackrel{\‾}{GDOP}}^{*}|}{{\stackrel{\‾}{GDOP}}^{*}}---\left(6\right)$

$e_n^2=1-\frac{|\stackrel{\‾}{{\mathrm{\Δ\τ}}_n}-{\stackrel{\‾}{\mathrm{\Δ}\mathrm{\τ}}}^{*}|}{{\stackrel{\‾}{\mathrm{\Δ}\mathrm{\τ}}}^{*}}---\left(7\right)$

$e_n^3=1-\frac{|N_n-N^{*}|}{N^{*}}---\left(8\right)$

Step 4.2, set up the Evaluations matrix of positioning result $E_{N\×3}=\left[\begin{array}{ccc}{e}_1^1& e_1^2& e_1^3\\ e_2^1& e_2^2& e_2^3\\ .& .& .\\ .& .& .\\ .& .& .\\ e_n^1& e_n^2& e_n^3\\ .& .& .\\ .& .& .\\ .& .& .\\ e_N^1& e_N^2& e_N^3\end{array}\right];$

Step 5, formula (9) is utilized to set up membership function

${\mathrm{\μ}}_{S_j}\left(E_n\right)=\frac{1}{3}\underset{v=1}{\overset{3}{\Σ}}{e}^{-{(e_n^v-s_j^v)}^2}---\left(9\right)$

In formula (9), ${\mathrm{\μ}}_{S_j}\left(E_n\right)\∈\[0,1\];$

Step 6, opening relationships matrix $R=\left[\begin{array}{cccccc}{\mathrm{\μ}}_{S_1}\left(E_1\right)& {\mathrm{\μ}}_{S_2}\left(E_1\right)& \mathrm{...}& {\mathrm{\μ}}_{S_j}\left(E_1\right)& \mathrm{...}& {\mathrm{\μ}}_{S_m}\left(E_1\right)\\ {\mathrm{\μ}}_{S_1}\left(E_2\right)& {\mathrm{\μ}}_{S_2}\left(E_2\right)& \mathrm{...}& {\mathrm{\μ}}_{S_j}\left(E_2\right)& \mathrm{...}& {\mathrm{\μ}}_{S_m}\left(E_2\right)\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ {\mathrm{\μ}}_{S_1}\left(E_n\right)& {\mathrm{\μ}}_{S_2}\left(E_n\right)& \mathrm{...}& {\mathrm{\μ}}_{S_j}\left(E_n\right)& \mathrm{...}& {\mathrm{\μ}}_{S_m}\left(E_n\right)\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ {\mathrm{\μ}}_{S_1}\left(E_N\right)& {\mathrm{\μ}}_{S_2}\left(E_N\right)& \mathrm{...}& {\mathrm{\μ}}_{s_j}\left(E_N\right)& \mathrm{...}& {\mathrm{\μ}}_{S_m}\left(E_N\right)\end{array}\right];$

Step 7, utilize formula (10) obtain threshold value λ;

$\mathrm{\λ}\≤\underset{j}{min}\left\{\underset{n}{max}\right\{{\mathrm{\μ}}_{S_j}\left(E_n\right)\left\}\right\}---\left(10\right)$

Step 8, utilize formula (11) to described relational matrix R process, obtain Boolean matrix

$R^{\′}=\left[\begin{array}{cccccc}{{\mathrm{\μ}}_{S_1}}^{\′}\left(E_1\right)& {{\mathrm{\μ}}_{S_2}}^{\′}\left(E_1\right)& \mathrm{...}& {{\mathrm{\μ}}_{S_j}}^{\′}\left(E_1\right)& \mathrm{...}& {{\mathrm{\μ}}_{S_m}}^{\′}\left(E_1\right)\\ {{\mathrm{\μ}}_{S_1}}^{\′}\left(E_2\right)& {{\mathrm{\μ}}_{S_2}}^{\′}\left(E_2\right)& \mathrm{...}& {{\mathrm{\μ}}_{S_j}}^{\′}\left(E_2\right)& \mathrm{...}& {{\mathrm{\μ}}_{S_m}}^{\′}\left(E_2\right)\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ {{\mathrm{\μ}}_{S_1}}^{\′}\left(E_n\right)& {{\mathrm{\μ}}_{S_2}}^{\′}\left(E_n\right)& \mathrm{...}& {{\mathrm{\μ}}_{S_j}}^{\′}\left(E_n\right)& \mathrm{...}& {{\mathrm{\μ}}_{S_m}}^{\′}\left(E_n\right)\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ {{\mathrm{\μ}}_{S_1}}^{\′}\left(E_N\right)& {{\mathrm{\μ}}_{S_2}}^{\′}\left(E_N\right)& \mathrm{...}& {{\mathrm{\μ}}_{s_j}}^{\′}\left(E_N\right)& \mathrm{...}& {{\mathrm{\μ}}_{S_m}}^{\′}\left(E_N\right)\end{array}\right];$

${{\mathrm{\&mu;}}_{S_j}}^{\&prime;}\left(E_n\right)=\left\{\begin{array}{cc}1,& {\mathrm{\&mu;}}_{S_j}\left(E_n\right)\&GreaterEqual;\mathrm{\&lambda;}\\ 0,& {\mathrm{\&mu;}}_{S_j}\left(E_n\right)<\mathrm{\&lambda;}\end{array}\right.---\left(11\right)$

In formula (11), represent rover station n-th sub-time period Differential positioning data x _npositioning result L _ndegree of confidence T=j;

Step 9, utilize the N number of positioning result of formula (12) to rover station to be weighted filtering process, obtain final positioning result L ^*;

$L^{*}=\frac{T\left(1\right)}{\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}T\left(k\right)}{L}_1+\frac{T\left(2\right)}{\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}T\left(k\right)}{L}_2+\mathrm{...}+\frac{T\left(n\right)}{\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}T\left(k\right)}{L}_n+\mathrm{...}+\frac{T\left(N\right)}{\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}T\left(k\right)}{L}_N---\left(12\right)$

In formula (12), T (k) represents the positioning result L of a rover station kth sub-time period _kdegree of confidence.

Compared with prior art, beneficial effect of the present invention is embodied in:

1, a longer monitoring period of time is divided into multiple sub-period by the present invention, the Satellite Observations of each sub-period is utilized to calculate the positioning result of respective sub-period respectively, refinement positioning calculation process, avoid the calculating theory of " generally " of conventional mapping methods, contribute to the otherness utilizing each sub-period satellite data quality, to improve positioning precision.

2, the present invention introduces the concept of degree of confidence, change according to the satellite data mass parameter (satellite distribution geometric dilution of precision, upper atmosphere error, satellite quantity epoch) of each sub-period divides different confidence level, take into full account satellite spatial changes in distribution, every factor such as Changes in weather, on the impact of positioning result, improves the reliability of positioning result; Meanwhile, have employed the degree of confidence that Fuzzy Set Theory determines each sub-period positioning result, and solve final positioning result in the mode of weighted filtering, thus improve the precision of positioning result, have broad application prospects.

Accompanying drawing explanation

Fig. 1 is traditional static relative positioning method;

Fig. 2 is Method And Principle of the present invention;

Fig. 3 is the internal association figure of the present invention by quality of data determination positioning result degree of confidence;

Fig. 4 is the Big Dipper deformation monitoring localization method process flow diagram that the present invention is based on fuzzy believable degree filtering;

Fig. 5 is the Comparison of experiment results of the inventive method and traditional static relative positioning method.

Embodiment

Based on a Big Dipper deformation monitoring localization method for fuzzy believable degree filtering, be applied in the monitoring of environmental that is made up of Beidou navigation satellite, base station and rover station; Base station satellite Data Concurrent epoch that base station receives the transmission of Beidou navigation satellite gives rover station; Rover station receives rover station satellite data epoch of Beidou navigation satellite transmission and base station satellite data epoch of base station transmission, and 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 carries out as follows:

Step 1, the Differential positioning data X of rover station to be split according to the time period, obtain the Differential positioning data of N number of sub-time period, such as, 24 hours observation Time segments division are become 12 sub-periods, each sub-period 2 hours; Be designated as X={X ₁, X ₂..., X _n..., X _n; X _nrepresent the Differential positioning data of the n-th sub-time period in the Differential positioning data X of rover station; 1≤n≤N;

Step 2, adopt static relative positioning algorithm to calculate respectively to the Differential positioning data X of N number of sub-time period, obtain N number of positioning result, be designated as L={L ₁, L ₂..., L _n..., L _n; L _nrepresent the Differential positioning data X of rover station n-th sub-time period _npositioning result; The content of static relative positioning algorithm see can with reference to " king becomes. the technique study [D] of carrier phase differential dynamic positioning. Xi'an: Chang An University, 2010. "

Step 3, off-line set up the parameter matrix S of degree of confidence _{m × 3};

The credibility of the positioning result of rover station is mainly by the impact of three parameters, and they can be calculated as follows:

Step 3.1, formula (1) is utilized to obtain the positioning result L of the n-th sub-time period _ngeometric dilution of precision mean value it reflects the space geometry relation between monitoring station and satellite. the polyhedron volume that value and monitoring station are formed to satellite activity's vector end-points is inversely proportional to, the combinations of satellites that polyhedron volume is larger be worth less.In observational error one timing, be worth less, positioning precision is higher.

$\stackrel{\&OverBar;}{{\mathrm{GDOP}}_n}=\sqrt{{\left(\stackrel{\&OverBar;}{{\mathrm{HDOP}}_n}\right)}^2+{\left(\stackrel{\&OverBar;}{{\mathrm{VDOP}}_n}\right)}^2+{\left(\stackrel{\&OverBar;}{{\mathrm{TDOP}}_n}\right)}^2}---\left(1\right)$

In formula (1), represent the positioning result L of rover station n-th sub-time period _nhorizontal component dilution of precision mean value; represent the positioning result L of rover station n-th sub-time period _nvertical component dilution of precision mean value; represent the positioning result L of rover station n-th sub-time period _nclock correction dilution of precision mean value; They obtain from receiver by instruction.Within the rover station n-th sub-time period, as one of the evaluating of this sub-period positioning result credibility.

Abundant experimental results shows: when time, the result precision that location algorithm resolves is high; Otherwise the resultant error that location algorithm resolves is larger; Therefore, in the present embodiment, make optimum value

Step 3.2, formula (2) is utilized to obtain the positioning result L of the n-th time period _nupper atmosphere AME it reflects overhead, monitoring station Atmosphere changes to the impact of positioning result.

$\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&tau;}}_n}=\sqrt{{\left(\stackrel{\&OverBar;}{{\mathrm{\&Delta;}}_I{\mathrm{\&tau;}}_n}\right)}^2+{\left(\stackrel{\&OverBar;}{{\mathrm{\&Delta;}}_T{\mathrm{\&tau;}}_n}\right)}^2}---\left(2\right)$

In formula (2), represent the positioning result L of rover station n-th sub-time period _nionospheric error mean value; represent the positioning result L of the sub-time period of rover station _ntropospheric error mean value; They obtain from receiver by instruction.Within the rover station n-th sub-time period, as the evaluating two of this sub-period positioning result credibility.

Abundant experimental results shows: when time, the result precision that location algorithm resolves is high; Otherwise the resultant error that location algorithm resolves is larger.Therefore, in the present embodiment, make optimum value

Step 3.3, satellite quantity N epoch added up in the rover station n-th sub-time period _n;

The whether sufficient precision directly determining positioning result of satellite quantity epoch.For static relative positioning, satellite quantity epoch is larger, and positioning result precision is higher; Otherwise positioning result precision is lower.Within the rover station n-th sub-time period, we add up satellite quantity N epoch _n, as the evaluating three of this sub-period positioning result credibility; As shown in Figure 3.

Under normal circumstances, operation of receiver frequency is 1Hz, within every 2 hours, can receive 7200 satellite epoch, can ensure the high precision of positioning result.But be blocked at satellite-signal, receiver power supply instability is when even having a power failure, satellite quantity N epoch that receiver receives _nduring <3600, the resultant error of static relative positioning is larger.Make optimum value N ^*=7200.

Step 3.4, definition degree of confidence T ∈ 1,2 ..., j ..., m} represents the credibility of positioning result, and wherein m is positive integer; T value larger expression credibility is higher; The parameter vector of definition degree of confidence is S={S ₁, S ₂..., S _j..., S _m; S _jrepresent the parameter vector corresponding to degree of confidence T=j; And have represent geometric dilution of precision parameter value, through type (3) calculates; represent upper atmosphere error parameter value, through type (4) calculates; represent satellite number parameter epoch value, through type (5) calculates:

$s_j^1={\stackrel{\&OverBar;}{GDOP}}^{*}/{\stackrel{\&OverBar;}{GDOP}}^j---\left(3\right)$

$s_j^2={\stackrel{\&OverBar;}{\mathrm{\&Delta;}\mathrm{\&tau;}}}^{*}/{\stackrel{\&OverBar;}{\mathrm{\&Delta;}\mathrm{\&tau;}}}^j---\left(4\right)$

$s_j^3=N^j/N^{*}---\left(5\right)$

In formula (3), represent the optimum value of geometric dilution of precision; represent the geometric dilution of precision of degree of confidence T=j; In formula (4), represent the optimum value of upper atmosphere error; represent the upper atmosphere error of degree of confidence T=j; In formula (5), N ^*represent the optimum value of satellite quantity epoch; N ^jrepresent satellite quantity epoch of degree of confidence T=j;

Step 3.5, set up the parameter matrix of degree of confidence $S_{m\&times;3}=\left[\begin{array}{ccc}{s}_1^1& s_1^2& s_1^3\\ s_2^1& s_2^2& s_2^3\\ .& .& .\\ .& .& .\\ .& .& .\\ s_j^1& s_j^2& s_j^3\\ .& .& .\\ .& .& .\\ .& .& .\\ s_m^1& s_m^2& s_m^3\end{array}\right];$

The parameter matrix of degree of confidence lists different degree of confidence and divides other 3 parameter values.Embody the difference of different degree of confidence.

In actual applications, 3 parameter values that can arrange each degree of confidence are as shown in table 1.Optimum value is adopted to carry out order of magnitude parameter vector S after reunification to it _jas shown in table 2.

The parameter value of table 1. degree of confidence

The parameter vector S of table 2. degree of confidence _j

So, a kind of parameter matrix of effective degree of confidence is:

$S_{5\&times;3}=\left[\begin{array}{ccc}0.43& 0.3& 0.12\\ 0.6& 0.5& 0.42\\ 0.6& 1.0& 0.69\\ 1.0& 0.5& 0.69\\ 1.0& 1.0& 1.0\end{array}\right]$

Step 4, set up the Evaluations matrix E of positioning result _{n × 3};

Step 4.1, definition positioning result evaluation vector are E={E ₁, E ₂..., E _n..., E _n; E _nrepresent the evaluation vector of the sub-time period positioning result of rover station n-th; And have represent the geometric dilution of precision evaluation of estimate of rover station n-th sub-time period, through type (6) calculates; represent the upper atmosphere error assessment value of rover station n-th sub-time period, through type (7) calculates; represent the satellite quantitative assessment epoch value of rover station n-th sub-time period, through type (8) calculates;

$e_n^1=1-\frac{|\stackrel{\&OverBar;}{{\mathrm{GDOP}}_n}-{\stackrel{\&OverBar;}{GDOP}}^{*}|}{{\stackrel{\&OverBar;}{GDOP}}^{*}}---\left(6\right)$

$e_n^2=1-\frac{|\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&tau;}}_n}-{\stackrel{\&OverBar;}{\mathrm{\&Delta;}\mathrm{\&tau;}}}^{*}|}{{\stackrel{\&OverBar;}{\mathrm{\&Delta;}\mathrm{\&tau;}}}^{*}}---\left(7\right)$

$e_n^3=1-\frac{|N_n-N^{*}|}{N^{*}}---\left(8\right)$

Step 4.2, set up the Evaluations matrix of positioning result $E_{N\&times;3}=\left[\begin{array}{ccc}{e}_1^1& e_1^2& e_1^3\\ e_2^1& e_2^2& e_2^3\\ .& .& .\\ .& .& .\\ .& .& .\\ e_n^1& e_n^2& e_n^3\\ .& .& .\\ .& .& .\\ .& .& .\\ e_N^1& e_N^2& e_N^3\end{array}\right];$

N number of positioning result that the Evaluations matrix of positioning result lists N number of sub-period divides other 3 evaluations of estimate; Reflect the similarities and differences of each positioning result in 3 evaluations of estimate.

Step 5, formula (9) is utilized to set up membership function

${\mathrm{\&mu;}}_{S_j}\left(E_n\right)=\frac{1}{3}\underset{v=1}{\overset{3}{\&Sigma;}}{e}^{-{(e_n^v-s_j^v)}^2}---\left(9\right)$

In formula (9), positioning result evaluation vector E _ito degree of confidence parameter vector S _jthe situation that is subordinate to carry out comprehensive.

Step 6, opening relationships matrix $R=\left[\begin{array}{cccccc}{\mathrm{\&mu;}}_{S_1}\left(E_1\right)& {\mathrm{\&mu;}}_{S_2}\left(E_1\right)& \mathrm{...}& {\mathrm{\&mu;}}_{S_j}\left(E_1\right)& \mathrm{...}& {\mathrm{\&mu;}}_{S_m}\left(E_1\right)\\ {\mathrm{\&mu;}}_{S_1}\left(E_2\right)& {\mathrm{\&mu;}}_{S_2}\left(E_2\right)& \mathrm{...}& {\mathrm{\&mu;}}_{S_j}\left(E_2\right)& \mathrm{...}& {\mathrm{\&mu;}}_{S_m}\left(E_2\right)\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ {\mathrm{\&mu;}}_{S_1}\left(E_n\right)& {\mathrm{\&mu;}}_{S_2}\left(E_n\right)& \mathrm{...}& {\mathrm{\&mu;}}_{S_j}\left(E_n\right)& \mathrm{...}& {\mathrm{\&mu;}}_{S_m}\left(E_n\right)\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ {\mathrm{\&mu;}}_{S_1}\left(E_N\right)& {\mathrm{\&mu;}}_{S_2}\left(E_N\right)& \mathrm{...}& {\mathrm{\&mu;}}_{s_j}\left(E_N\right)& \mathrm{...}& {\mathrm{\&mu;}}_{S_m}\left(E_N\right)\end{array}\right];$

Matrix R calculates gained according to formula (9), its row represents N number of positioning result evaluation vector, row represent m degree of confidence parameter vector, so just make positioning result and degree of confidence set up relation, thus are that the determination of positioning result degree of confidence provides basis.

Step 7, utilize formula (10) obtain threshold value λ:

$\mathrm{\&lambda;}\&le;\underset{j}{min}\left\{\underset{n}{max}\right\{{\mathrm{\&mu;}}_{S_j}\left(E_n\right)\left\}\right\}---\left(10\right)$

The size of threshold value λ directly affects the determination of the degree of confidence of positioning result.λ value is larger, and positioning result can be confirmed as fewer degree of confidence, thus it is higher to be absorbed in rate; Otherwise positioning result can be confirmed as more degree of confidence.Consider that a positioning result at least will have a degree of confidence, then

Step 8, utilize formula (11) to described relational matrix R process, obtain Boolean matrix

$R^{\&prime;}=\left[\begin{array}{cccccc}{{\mathrm{\&mu;}}_{S_1}}^{\&prime;}\left(E_1\right)& {{\mathrm{\&mu;}}_{S_2}}^{\&prime;}\left(E_1\right)& \mathrm{...}& {{\mathrm{\&mu;}}_{S_j}}^{\&prime;}\left(E_1\right)& \mathrm{...}& {{\mathrm{\&mu;}}_{S_m}}^{\&prime;}\left(E_1\right)\\ {{\mathrm{\&mu;}}_{S_1}}^{\&prime;}\left(E_2\right)& {{\mathrm{\&mu;}}_{S_2}}^{\&prime;}\left(E_2\right)& \mathrm{...}& {{\mathrm{\&mu;}}_{S_j}}^{\&prime;}\left(E_2\right)& \mathrm{...}& {{\mathrm{\&mu;}}_{S_m}}^{\&prime;}\left(E_2\right)\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ {{\mathrm{\&mu;}}_{S_1}}^{\&prime;}\left(E_n\right)& {{\mathrm{\&mu;}}_{S_2}}^{\&prime;}\left(E_n\right)& \mathrm{...}& {{\mathrm{\&mu;}}_{S_j}}^{\&prime;}\left(E_n\right)& \mathrm{...}& {{\mathrm{\&mu;}}_{S_m}}^{\&prime;}\left(E_n\right)\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ {{\mathrm{\&mu;}}_{S_1}}^{\&prime;}\left(E_N\right)& {{\mathrm{\&mu;}}_{S_2}}^{\&prime;}\left(E_N\right)& \mathrm{...}& {{\mathrm{\&mu;}}_{s_j}}^{\&prime;}\left(E_N\right)& \mathrm{...}& {{\mathrm{\&mu;}}_{S_m}}^{\&prime;}\left(E_N\right)\end{array}\right];$

${{\mathrm{\&mu;}}_{S_j}}^{\&prime;}\left(E_n\right)=\left\{\begin{array}{cc}1,& {\mathrm{\&mu;}}_{S_j}\left(E_n\right)\&GreaterEqual;\mathrm{\&lambda;}\\ 0,& {\mathrm{\&mu;}}_{S_j}\left(E_n\right)<\mathrm{\&lambda;}\end{array}\right.---\left(11\right)$

In formula (11), represent rover station n-th sub-time period Differential positioning data x _npositioning result L _ndegree of confidence T=j; Here according to the λ in fuzzy clustering-Level Matrix theory, fuzzy relation matrix is converted into Boolean matrix.

Due to the degree of confidence that this patent method is each sub-period positioning result determined based on Fuzzy Set Theory, therefore this degree of confidence is called " fuzzy believable degree ".

Step 9, utilize the N number of positioning result of formula (12) to rover station to be weighted filtering process, obtain final positioning result L ^*as shown in Figure 2;

$L^{*}=\frac{T\left(1\right)}{\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}T\left(k\right)}{L}_1+\frac{T\left(2\right)}{\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}T\left(k\right)}{L}_2+\mathrm{...}+\frac{T\left(n\right)}{\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}T\left(k\right)}{L}_n+\mathrm{...}+\frac{T\left(N\right)}{\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}T\left(k\right)}{L}_N---\left(12\right)$

In formula (12), T (k) represents the positioning result L of a rover station kth sub-time period _kfuzzy believable degree.

Experimental verification:

On October 8th, 2015, in the high roadbed deformation monitoring project of somewhere, Hefei, apply traditional static relative positioning method and this patent method simultaneously, all carried out the deformation monitoring of 30 days, their settlement monitoring result as shown in Figure 5 to November 8.Visible, the monitoring result big rise and fall of traditional static relative positioning method, error is obvious, and it mainly receives the impact of the factor such as Changes in weather and satellite quantity epoch; The monitoring result of this patent method is more accurate, more stable, reflects the Continuous Settlement process of high roadbed more realistically.

Claims (1)

1., based on a Big Dipper deformation monitoring localization method for fuzzy believable degree filtering, be applied in the monitoring of environmental that is made up of Beidou navigation satellite, base station and rover station; Base station satellite Data Concurrent epoch that described base station receives the transmission of described Beidou navigation satellite gives rover station; Described rover station receives rover station satellite data epoch that described Beidou navigation satellite sends and base station satellite data epoch that described base station sends and carries out difference processing, obtains Differential positioning data, is designated as X; It is characterized in that, described Big Dipper deformation monitoring localization method carries out as follows:

Step 1, the Differential positioning data X of described rover station to be split according to the time period, obtain the Differential positioning data of N number of sub-time period, be designated as X={X ₁, X ₂..., X _n..., X _n; X _nrepresent the Differential positioning data of the n-th sub-time period in the Differential positioning data X of rover station; 1≤n≤N;

Step 2, adopt static relative positioning algorithm to calculate respectively to the Differential positioning data X of described N number of sub-time period, obtain N number of positioning result, be designated as L={L ₁, L ₂..., L _n..., L _n; L _nrepresent the Differential positioning data x of rover station n-th sub-time period _npositioning result;

Step 3, off-line set up the parameter matrix S of degree of confidence _{m × 3};

The credibility of the positioning result of rover station is mainly by the impact of three parameters, and they can be calculated as follows:

Step 3.1, formula (1) is utilized to obtain the positioning result L of the n-th sub-time period _ngeometric dilution of precision mean value

$\stackrel{\&OverBar;}{{\mathrm{GDOP}}_n}=\sqrt{{\left(\stackrel{\&OverBar;}{{\mathrm{HDOP}}_n}\right)}^2+{\left(\stackrel{\&OverBar;}{{\mathrm{VDOP}}_n}\right)}^2+{\left(\stackrel{\&OverBar;}{{\mathrm{TDOP}}_n}\right)}^2}---\left(1\right)$

In formula (1), represent the positioning result L of rover station n-th sub-time period _nhorizontal component dilution of precision mean value; represent the positioning result L of rover station n-th sub-time period _nvertical component dilution of precision mean value; represent the positioning result L of rover station n-th sub-time period _nclock correction dilution of precision mean value;

Step 3.2, formula (2) is utilized to obtain the positioning result L of the n-th sub-time period _nupper atmosphere AME

$\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&tau;}}_n}=\sqrt{{\left(\stackrel{\&OverBar;}{{\mathrm{\&Delta;}}_I{\mathrm{\&tau;}}_n}\right)}^2+{\left(\stackrel{\&OverBar;}{{\mathrm{\&Delta;}}_T{\mathrm{\&tau;}}_n}\right)}^2}---\left(2\right)$

In formula (2), represent the positioning result L of rover station n-th sub-time period _nionospheric error mean value; represent the positioning result L of rover station n-th sub-time period _ntropospheric error mean value;

Step 3.3, satellite quantity N epoch added up in the rover station n-th sub-time period _n;

Step 3.4, definition degree of confidence T ∈ 1,2 ..., j ..., m} represents the credibility of positioning result, and m is positive integer; The parameter vector of definition degree of confidence is S={S ₁, S ₂..., S _j..., S _m; S _jrepresent the parameter vector corresponding to degree of confidence T=j; And have represent geometric dilution of precision parameter value, through type (3) calculates; represent upper atmosphere error parameter value, through type (4) calculates; represent satellite number parameter epoch value, through type (5) calculates:

$s_j^1={\stackrel{\&OverBar;}{GDOP}}^{*}/{\stackrel{\&OverBar;}{GDOP}}^j---\left(3\right)$

$s_j^2={\stackrel{\&OverBar;}{\mathrm{\&Delta;}\mathrm{\&tau;}}}^{*}/{\stackrel{\&OverBar;}{\mathrm{\&Delta;}\mathrm{\&tau;}}}^j---\left(4\right)$

$s_j^3=N^j/N^{*}---\left(5\right)$

In formula (3), represent the optimum value of geometric dilution of precision; represent the geometric dilution of precision of degree of confidence T=j; In formula (4), represent the optimum value of upper atmosphere error; represent the upper atmosphere error of degree of confidence T=j; In formula (5), N ^*represent the optimum value of satellite quantity epoch; N ^jrepresent satellite quantity epoch of degree of confidence T=j;

Step 3.5, set up the parameter matrix of degree of confidence $S_{m\&times;3}=\left[\begin{array}{ccc}{s}_1^1& s_1^2& s_1^3\\ s_2^1& s_2^2& s_2^3\\ \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}\\ s_j^1& s_j^2& s_j^3\\ \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}\\ s_m^1& s_m^2& s_m^3\end{array}\right];$

Step 4, set up the Evaluations matrix E of positioning result _{n × 3};

Step 4.1, definition positioning result evaluation vector are E={E ₁, E ₂..., E _n..., E _n; E _nrepresent the evaluation vector of the sub-time period positioning result of rover station n-th; And have represent the geometric dilution of precision evaluation of estimate of rover station n-th sub-time period, through type (6) calculates; represent the upper atmosphere error assessment value of rover station n-th sub-time period, through type (7) calculates; represent the satellite quantitative assessment epoch value of rover station n-th sub-time period, through type (8) calculates;

$e_n^1=1-\frac{|\stackrel{\&OverBar;}{{\mathrm{GDOP}}_n}-{\stackrel{\&OverBar;}{GDOP}}^{*}|}{{\stackrel{\&OverBar;}{GDOP}}^{*}}---\left(6\right)$

$e_n^2=1-\frac{|\stackrel{\&OverBar;}{{\mathrm{\&Delta;\&tau;}}_n}-{\stackrel{\&OverBar;}{\mathrm{\&Delta;}\mathrm{\&tau;}}}^{*}|}{{\stackrel{\&OverBar;}{\mathrm{\&Delta;}\mathrm{\&tau;}}}^{*}}---\left(7\right)$

$e_n^3=1-\frac{|N_n-N^{*}|}{N^{*}}---\left(8\right)$

Step 4.2, set up the Evaluations matrix of positioning result $E_{N\&times;3}=\left[\begin{array}{ccc}{e}_1^1& e_1^2& e_1^3\\ e_2^1& e_2^2& e_2^3\\ \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}\\ e_n^1& e_n^2& e_n^3\\ \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}\\ e_N^1& e_N^2& e_N^3\end{array}\right];$

Step 5, formula (9) is utilized to set up membership function

${\mathrm{\&mu;}}_{S_j}\left(E_n\right)=\frac{1}{3}\underset{v=1}{\overset{3}{\&Sigma;}}{e}^{-{(e_n^v-s_j^v)}^2}---\left(9\right)$

In formula (9), ${\mathrm{\&mu;}}_{S_j}\left(E_n\right)\&Element;\&lsqb;0,1\&rsqb;;$

Step 6, opening relationships matrix $R=\left[\begin{array}{cccccc}{\mathrm{\&mu;}}_{S_1}\left(E_1\right)& {\mathrm{\&mu;}}_{S_2}\left(E_1\right)& ...& {\mathrm{\&mu;}}_{S_j}\left(E_1\right)& ...& {\mathrm{\&mu;}}_{S_m}\left(E_1\right)\\ {\mathrm{\&mu;}}_{S_1}\left(E_2\right)& {\mathrm{\&mu;}}_{S_2}\left(E_2\right)& ...& {\mathrm{\&mu;}}_{S_j}\left(E_2\right)& ...& {\mathrm{\&mu;}}_{S_m}\left(E_2\right)\\ \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}\\ \\ \end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}\\ \\ \end{array}& \begin{array}{c}.\\ .\\ .\end{array}\\ {\mathrm{\&mu;}}_{S_1}\left(E_n\right)& {\mathrm{\&mu;}}_{S_2}\left(E_n\right)& ...& {\mathrm{\&mu;}}_{S_j}\left(E_n\right)& ...& {\mathrm{\&mu;}}_{S_m}\left(E_n\right)\\ \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}\\ \\ \end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}\\ \\ \end{array}& \begin{array}{c}.\\ .\\ .\end{array}\\ {\mathrm{\&mu;}}_{S_1}\left(E_N\right)& {\mathrm{\&mu;}}_{S_2}\left(E_N\right)& ...& {\mathrm{\&mu;}}_{S_j}\left(E_N\right)& ...& {\mathrm{\&mu;}}_{S_m}\left(E_N\right)\end{array}\right];$

Step 7, utilize formula (10) obtain threshold value λ;

$\mathrm{\&lambda;}\&le;\underset{j}{\min }\left\{\underset{n}{\max }\left\{{\mathrm{\&mu;}}_{S_j}\left(E_n\right)\right\}\right\}---\left(10\right)$

Step 8, utilize formula (11) to described relational matrix R process, obtain Boolean matrix

$R^{\&prime;}=\left[\begin{array}{cccccc}{{\mathrm{\&mu;}}_{S_1}}^{\&prime;}\left(E_1\right)& {{\mathrm{\&mu;}}_{S_2}}^{\&prime;}\left(E_1\right)& ...& {{\mathrm{\&mu;}}_{S_j}}^{\&prime;}\left(E_1\right)& ...& {{\mathrm{\&mu;}}_{S_m}}^{\&prime;}\left(E_1\right)\\ {{\mathrm{\&mu;}}_{S_1}}^{\&prime;}\left(E_2\right)& {{\mathrm{\&mu;}}_{S_2}}^{\&prime;}\left(E_2\right)& ...& {{\mathrm{\&mu;}}_{S_j}}^{\&prime;}\left(E_2\right)& ...& {{\mathrm{\&mu;}}_{S_m}}^{\&prime;}\left(E_2\right)\\ \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}\\ \\ \end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}\\ \\ \end{array}& \begin{array}{c}.\\ .\\ .\end{array}\\ {{\mathrm{\&mu;}}_{S_1}}^{\&prime;}\left(E_n\right)& {{\mathrm{\&mu;}}_{S_2}}^{\&prime;}\left(E_n\right)& ...& {{\mathrm{\&mu;}}_{S_j}}^{\&prime;}\left(E_n\right)& ...& {{\mathrm{\&mu;}}_{S_m}}^{\&prime;}\left(E_n\right)\\ \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}\\ \\ \end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}\\ \\ \end{array}& \begin{array}{c}.\\ .\\ .\end{array}\\ {{\mathrm{\&mu;}}_{S_1}}^{\&prime;}\left(E_N\right)& {{\mathrm{\&mu;}}_{S_2}}^{\&prime;}\left(E_N\right)& ...& {{\mathrm{\&mu;}}_{S_j}}^{\&prime;}\left(E_N\right)& ...& {{\mathrm{\&mu;}}_{S_m}}^{\&prime;}\left(E_N\right)\end{array}\right];$

${{\mathrm{\&mu;}}_{S_j}}^{\&prime;}\left(E_n\right)=\left\{\begin{array}{cc}1,& {\mathrm{\&mu;}}_{S_j}\left(E_n\right)\&GreaterEqual;\mathrm{\&lambda;}\\ 0,& {\mathrm{\&mu;}}_{S_j}\left(E_n\right)<\mathrm{\&lambda;}\end{array}\right.---\left(11\right)$

In formula (11), represent rover station n-th sub-time period Differential positioning data x _npositioning result L _ndegree of confidence T=j;

Step 9, utilize the N number of positioning result of formula (12) to rover station to be weighted filtering process, obtain final positioning result L ^*;

$L^{*}=\frac{T\left(1\right)}{\underset{k=1}{\overset{N}{\&Sigma;}}T\left(k\right)}{L}_1+\frac{T\left(2\right)}{\underset{k=1}{\overset{N}{\&Sigma;}}T\left(k\right)}{L}_2+...+\frac{T\left(n\right)}{\underset{k=1}{\overset{N}{\&Sigma;}}T\left(k\right)}{L}_n+...+\frac{T\left(N\right)}{\underset{k=1}{\overset{N}{\&Sigma;}}T\left(k\right)}{L}_N---\left(12\right)$

In formula (12), T (k) represents the positioning result L of a rover station kth sub-time period _kdegree of confidence.