CN103823993A - Correlation coefficient-based method for weakening CME (common mode error) influence in coordinate time sequence - Google Patents

Abstract

The invention provides a correlation coefficient-based method for weakening the CME (common mode error) influence in a coordinate time sequence. The correlation degree of the GPS (global positioning system) measuring interstation coordinate time sequence is represented by adopting correlation coefficients between a reference station and common measuring stations, and the correlation coefficient is used as the weight for calculating the GPS measuring interstation common-mode error. Meanwhile, the GPS measuring interstation negative correlation is not omitted, a positive correlation and a negative correlation are substituted into the CME calculation system at the same time, positive and negative correlation are equally treated as the weight factor for measuring the GPS measuring interstation CME influence. According to the correlation coefficient-based method, the technical problems that the existing method for weakening the CME influence in the coordinate time sequence is limited in interstation distance, low in space accuracy and the like are solved, and the method can process the measuring interstation CME influence of a GPS network being more than 2000km and can ensure the space response accuracy.

Description

The method of CME impact in weakening coordinate time sequence based on related coefficient

Technical field

The invention belongs to the accurate process field of gps data, relate to a kind of method of cutting down CME impact in time series, especially relate to the method for CME impact in a kind of reduction coordinate time sequence based on related coefficient.

Background technology

Common-mode error (CME), refers within the scope of specific region, all survey stations are subject to the common error of space correlation.CME concept is proposed in 1997 by Wdowinski at first, has significant spatial distribution characteristic.But owing to being subject to the different factor impacts in space, there is heterogeneity (Nikolaidis, 2002) in the space distribution of CME.Therefore, conventionally pass through the related coefficient of survey station residual error coordinate time sequence as characteristic index (Marquez-Azua, Demets, 2003 of correlativity; SimonWilliams, 2004).

In space correlation error field, existing Traditional Space stack filter method, principal component analysis (PCA) (PCA), KLE(Karhunen-Loeve expansion) etc. method, these filtering methods are the hypothesis based on space uniform all.Stack filter method in space is supposed the impact of the common-mode error that all survey stations are subject to, and causes the size of target area net to be restricted.Principal component analysis (PCA) will have three Component Matrices Orthogonal Decompositions of residual error gps time sequence of certain correlativity, obtain one group of mutually orthogonal vector, the coordinate of the residual vector that these major component vectors have reflected the corresponding moment on the additional space axle with proper vector statement, has good roomage response.But in the time containing stronger local noise in time series and affect, PCA method extracts signal and corresponding spatial character will be affected.KLE method, by the covariance matrix standardization adopting in PCA method, obtains correlation matrix, utilizes correlation matrix to calculate orthogonal vector.KLE method can effectively suppress local effect impact, but spatial character accuracy is not high.Coordinate time serial correlation coefficient stack filtering (Tian Yunfeng etc. based between the GPS station, 2011), correlativity size between the employing station is as the weight of spatial filtering, consider the factors such as distance, overall relevance level, without the required space uniform of existing filtering method this hypothesis that distributes simultaneously.Related coefficient stack filtering can be isolated the common-mode error on Dan Zhanyi field and different spaces yardstick, improves the ability that detects weak tectonic information.On 200km yardstick, have stronger common-mode error, along with the increase of distance, the correlativity between survey station weakens gradually, until 2000km left and right is no longer relevant.The method is still limited by the relative distance between survey station.

Mainly there are two large deficiencies in the method that weakens at present CME impact in coordinate time sequence: 1) filter effect is limited by the size (being survey station spacing) of gps coordinate time series place net; 2) can effectively suppress local effect impact, but spatial character accuracy is not high.

Summary of the invention

The deficiency existing for prior art, the invention provides a kind of method that is applicable to the GPS net of any size and can improves CME impact in weakening coordinate time sequence spatial character accuracy, based on related coefficient.

For solving the problems of the technologies described above, the present invention adopts following technical scheme:

The method of CME impact in weakening coordinate time sequence based on related coefficient, comprises step:

Step 1, obtains GPS survey station coordinate time sequence observed reading, and obtains the residual error coordinate time sequence of GPS survey station;

Step 2, from selected reference station s in GPS net, calculates the public epoch between common survey station in base station s and GPS net, and definite public epoch number; Described common survey station is the survey station except base station s in GPS net;

Step 3, calculates the correlation coefficient r between base station s and common survey station p in public epoch _sp;

Step 4, obtains the interior all common survey station actings in conjunction of GPS net in the common-mode error of base station s according to the related coefficient between base station s and common survey station p

wherein, S-1 is the common survey station number that GPS net internal reference and common-mode error are calculated; r _spfor the related coefficient between base station s in public epoch and common survey station p; v _p,kwith

be respectively the residual sum standard deviation of common survey station p coordinate time sequence under k public epoch;

Step 5, from the original coordinates time series observed reading of base station s, the common survey station acting in conjunction of corresponding deduction is in the common-mode error of base station s.

The residual error coordinate time sequence of above-mentioned GPS survey station adopts following formula to obtain:

$y\left(t\right)=a+\mathrm{bt}+c\sin \left(2\mathrm{\πt}\right)+d\cos \left(2\mathrm{\πt}\right)+e\sin \left(4\mathrm{\πt}\right)+f\cos \left(4\mathrm{\πt}\right)+\underset{j=1}{\overset{n_g}{\mathrm{\Σ}}}{g}_{j}H(t-T_{\mathrm{gj}})+v_i$

Wherein:

Y (t) is the GPS survey station coordinate survey value that moment t is corresponding;

T represents day coordinate solution epoch, unit: year;

A is GPS survey station position, and b is linear speed;

Coefficient c, d are used for describing motion annual period of GPS survey station, and coefficient e, f are used for describing periodic motion half a year of GPS survey station, and c, d, e, f, for treating estimated parameter, obtain through matching;

for saltus step correction member, g _jrepresent saltus step amplitude, T _gjrepresent to occur the epoch of saltus step, n _grepresent saltus step number, j is saltus step numbering, and H is sea dimension Seat step function (Heaviside step function), and before saltus step, H value is 0, and after saltus step, H value is 1;

V _ifor the observed reading residual error of moment t.

Correlation coefficient r in above-mentioned public epoch between base station s and common survey station p _spfor:

$r_{\mathrm{sp}}=\frac{\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\left[(m_k-\stackrel{\‾}{m})(n_k-\stackrel{\‾}{n})\right]}{\sqrt{\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{(m_k-\stackrel{\‾}{m})}^2\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{(n_k-\stackrel{\‾}{n})}^2}}$

Wherein:

N be between common survey station p and base station s public epoch number, k represents public epoch of numbering;

M _k, n _krepresent respectively base station s and common survey station _pthe residual error coordinate of k public epoch, can directly calculate and obtain by residual error coordinate time retrieval or according to formula (1);

with be respectively base station s and common survey station p residual error coordinate time serial mean under public epoch.

Compared with prior art, the present invention has feature:

Related coefficient between employing base station and common survey station characterizes the degree of correlation of coordinate time sequence between GPS survey station, and using this related coefficient as the weight of calculating common-mode error between GPS survey station.Meanwhile, do not ignore the negative correlation between GPS survey station, include positive correlation coefficient and negative correlation coefficient in CME counting system simultaneously, and align, negative correlation puts on an equal footing, as the weight factor of weighing CME impact between GPS survey station.

The method that the present invention can solve the impact of CME in existing weakening coordinate time sequence exists that survey station spacing is limited, not high-technology problem of space accuracy, and the CME that can process between the GPS net survey station that is greater than 2000km affects, and guarantees roomage response accuracy.

Accompanying drawing explanation

Fig. 1 is the idiographic flow schematic diagram of the inventive method;

Fig. 2 is 5 IGS base station distribution schematic diagrams to be analyzed in contrast test.

Embodiment

In order to make the object of the invention, technical scheme and beneficial effect clearer, below in conjunction with the drawings and the specific embodiments, further illustrate the present invention.Should be appreciated that embodiment described below, only in order to explain the present invention, is not intended to limit the present invention.

A method for CME impact in reduction coordinate time sequence based on related coefficient, concrete steps are as follows:

Step 1, the GPS survey station coordinate time sequence accumulating by data analysis data acquisition.

This step belongs to prior art, specifically can obtain data by the high accuracy data process software such as GAMIT/GLOBK, Bernese, GIPSY or IGS analytic centre ripe in prior art.

Step 2, according to the residual error coordinate time sequence of GPS survey station coordinate time retrieval GPS survey station.

Being subject to tectonic movement with respect to GPS survey station affects the secular trend that cause, the same shake impact of anniversary/half's anniversary effect of signals, earthquake that other factors cause, and utilizes formula (1) to calculate the residual error coordinate time sequence v of GPS survey station _i:

$y\left(t\right)=a+\mathrm{bt}+c\sin \left(2\mathrm{\πt}\right)+d\cos \left(2\mathrm{\πt}\right)+e\sin \left(4\mathrm{\πt}\right)+f\cos \left(4\mathrm{\πt}\right)+\underset{j=1}{\overset{n_g}{\mathrm{\Σ}}}{g}_{j}H(t-T_{\mathrm{gj}})+v_i---\left(1\right)$

In formula (1):

Y (t) is the GPS survey station coordinate survey value that moment t is corresponding;

T represents day coordinate solution epoch, take year as unit;

A is GPS survey station position, and b is the linear speed of GPS survey station;

Coefficient c, d are used for describing motion annual period of GPS survey station, and coefficient e, f are used for describing periodic motion half a year of GPS survey station, and c, d, e, f, for treating estimated parameter, adopt weighted least-squares method to estimate the above-mentioned estimated parameter for the treatment of in this embodiment;

for saltus step correction member, g _jrepresent saltus step amplitude, T _gjrepresent to occur the epoch of saltus step, n _grepresent saltus step number, j is saltus step numbering, and H is sea dimension Seat step function (Heaviside step function), and before saltus step, H value is 0, and after saltus step, H value is 1, the jumping moment T here _gjby analysis determine after as known;

V _ifor the observed reading residual error of moment t.

This embodiment, has only considered linear speed and anniversary/half's anniversary isoperimetric phase property effect of signals of survey station while calculating the residual error coordinate time sequence of GPS survey station.

Step 3, selected reference station s.

Suppose total S GPS survey station in GPS net, a selected GPS survey station s is base station s arbitrarily, and the survey station in GPS net except base station s is common survey station.

Step 4, calculates the public epoch between base station s and common survey station, determines public epoch of number N.

To any common survey station p(p=1 in GPS net, 2 ..., S-1), obtain respectively the public epoch between common survey station p and base station s.

Step 5, calculates the related coefficient between base station s and common survey station p in public epoch.

Correlation coefficient r between base station s and common survey station p _sppublic epoch of the residual error coordinate time sequence of calculating based on two survey station coordinate components carry out:

$r_{\mathrm{sp}}=\frac{\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\left[(m_k-\stackrel{\‾}{m})(n_k-\stackrel{\‾}{n})\right]}{\sqrt{\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{(m_k-\stackrel{\‾}{m})}^2\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{(n_k-\stackrel{\‾}{n})}^2}}---\left(2\right)$

In formula (2):

N be between common survey station p and base station s public epoch number, k represents public epoch of numbering;

M _k, n _krepresent respectively base station s and common survey station _pthe residual error coordinate of k public epoch, can directly calculate and obtain by residual error coordinate time retrieval or according to formula (1);

with

the residual error coordinate time serial mean under public epoch for base station s and common survey station p.

The present invention adopts the related coefficient between base station s and common survey station p to characterize the degree of correlation of coordinate time sequence between GPS survey station, and nets the weight of common-mode error between interior survey station using this related coefficient as calculating GPS.

Step 6, obtains the interior all common survey station j acting in conjunction of GPS net in the common-mode error of base station s according to the related coefficient between base station s and common survey station p.

Common survey station p acting in conjunction is ε in the common-mode error of base station s _s:

${\mathrm{\ϵ}}_s=\frac{{\mathrm{\Σ}}_{p=1}^{S-1}\frac{v_{p,k}}{{\mathrm{\σ}}_{p,k}^2}\×r_{\mathrm{sp}}}{{\mathrm{\Σ}}_{p=1}^{S-1}\frac{1}{{\mathrm{\σ}}_{p,k}^2}\×\left|r_{\mathrm{sp}}\right|}---\left(3\right)$

In formula (3):

ε _sfor all common survey station p acting in conjunction is in the common-mode error of base station s;

S-1 participates in the common survey station number that CME calculates in GPS net;

R _spfor the related coefficient between base station s in public epoch and common survey station p;

V _p,kwith

be respectively common survey station p k public epoch the residual sum standard deviation of the coordinate time sequence of (in this concrete enforcement, epoch take the odd-numbered day is unit).Coordinate time sequence standard deviation

can directly from residual error coordinate time sequence, obtain.

The method of calculating CME different from the past, the present invention does not ignore the negative correlation between GPS survey station, include positive correlation coefficient and negative correlation coefficient in CME counting system simultaneously, and align, negative correlation puts on an equal footing, as the weight factor of weighing CME impact between survey station.

Step 7, from the original coordinates time series of base station s, correspondence is deducted common survey station j acting in conjunction in the common-mode error of base station s, thereby weakens the impact of CME.

Concrete enforcement described herein is only to the explanation for example of the present invention's spirit.Those skilled in the art can make various modifications or supplement or adopt similar mode to substitute described concrete enforcement, but can't depart from spirit of the present invention or surmount the defined scope of appended claims.

Further illustrate beneficial effect of the present invention below in conjunction with contrast test.

The common method of cutting down at present CME impact comprises space stack filter method, and the method is proposed in 1997 by people such as Wdowinski, calculates common-mode error corrected value according to odd-numbered day coordinate residual epsilon, as follows:

$\mathrm{\ϵ}\left(d\right)=\frac{\underset{s=1}{\overset{S}{\mathrm{\Σ}}}{\mathrm{\ϵ}}_s\left(d\right)}{S}---\left(4\right)$

Wherein, d represents the time; S is survey station number; ε _s(d) represent that s survey station is in the odd-numbered day of time d coordinate residual error; ε (d) is the CME corrected value that time d is corresponding.

From original GPS observed reading, deduct CME corrected value and obtain filtered coordinate time sequence.The method is the weighted mean value of each each epoch base station residual error to be used as to the common-mode error of this epoch in essence, but the space that can not reflect each station common-mode error due to the method is corresponding, therefore the prerequisite of its establishment is that regional network is less, and common-mode error distribution has consistance.

Process the situation of large spatial scale GPS net common-mode error in order to contrast Traditional Space stack filtering and the inventive method, 5 IGS base stations that exceed 2000km are apart analyzed, IGS base station to be analyzed is respectively DUBO station, MOBS station, POLV station, SUTH station and WUHN station, and its website distributes and sees Fig. 1.

To 5 IGS base stations in Fig. 1, adopt respectively Traditional Space stack filtering method and the inventive method to process common-mode error situation, wherein with DUBO base station N direction residual error coordinate time sequential filtering before and after related coefficient in table 1.

Related coefficient contrast before and after table 1N direction residual error coordinate time sequential filtering

After Traditional Space stack filtering is processed, the related coefficient between survey station has obtained significantly increasing on the contrary, shows that Traditional Space stack filtering method is not suitable for large spatial scale GPS net and carries out spatial filtering.And after the inventive method stack filtering, except MOBS station, the correlativity between all the other survey stations and DUBO station N direction residual error coordinate time sequence all reduces to some extent.

Claims (3)

1. the method for CME impact in the weakening coordinate time sequence based on related coefficient, is characterized in that, comprises step:

Step 1, obtains GPS survey station coordinate time sequence observed reading, and obtains the residual error coordinate time sequence of GPS survey station;

Step 2, from selected reference station s in GPS net, calculates the public epoch between common survey station in base station s and GPS net, and definite public epoch number; Described common survey station is the survey station except base station s in GPS net;

Step 3, calculates the correlation coefficient r between base station s and common survey station p in public epoch _sp;

Step 4, obtains the interior all common survey station actings in conjunction of GPS net in the common-mode error of base station s according to the related coefficient between base station s and common survey station p

wherein, S-1 is the common survey station number that GPS net internal reference and common-mode error are calculated; r _spfor the related coefficient between base station s in public epoch and common survey station p; v _p,kwith be respectively the residual sum standard deviation of common survey station p coordinate time sequence under k public epoch;

Step 5, from the original coordinates time series observed reading of base station s, the common survey station acting in conjunction of corresponding deduction is in the common-mode error of base station s.

2. the method for CME impact in the weakening coordinate time sequence based on related coefficient as claimed in claim 1, is characterized in that:

The residual error coordinate time sequence of described GPS survey station adopts following formula to obtain:

$y\left(t\right)=a+\mathrm{bt}+c\sin \left(2\mathrm{\πt}\right)+d\cos \left(2\mathrm{\πt}\right)+e\sin \left(4\mathrm{\πt}\right)+f\cos \left(4\mathrm{\πt}\right)+\underset{j=1}{\overset{n_g}{\mathrm{\Σ}}}{g}_{j}H(t-T_{\mathrm{gj}})+v_i$

Wherein:

Y (t) is the GPS survey station coordinate survey value that moment t is corresponding;

T represents day coordinate solution epoch, unit: year;

A is GPS survey station position, and b is linear speed;

Coefficient c, d are used for describing motion annual period of GPS survey station, and coefficient e, f are used for describing periodic motion half a year of GPS survey station, and c, d, e, f, for treating estimated parameter, obtain through matching;

for saltus step correction member, g _jrepresent saltus step amplitude, T _gjrepresent to occur the epoch of saltus step, n _grepresent saltus step number, j is saltus step numbering, and H is sea dimension Seat step function (Heaviside step function), and before saltus step, H value is 0, and after saltus step, H value is 1;

V _ifor the observed reading residual error of moment t.

3. the method for CME impact in the weakening coordinate time sequence based on related coefficient as claimed in claim 1, is characterized in that:

Correlation coefficient r in described public epoch between base station s and common survey station p _spfor:

$r_{\mathrm{sp}}=\frac{\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\left[(m_k-\stackrel{\‾}{m})(n_k-\stackrel{\‾}{n})\right]}{\sqrt{\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{(m_k-\stackrel{\‾}{m})}^2\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{(n_k-\stackrel{\‾}{n})}^2}}$

Wherein:

N be between common survey station p and base station s public epoch number, k represents public epoch of numbering;

M _k, n _kthe residual error coordinate that represents respectively base station s and common survey station p k public epoch, can pass through residual error coordinate time retrieval;

with

be respectively base station s and common survey station p residual error coordinate time serial mean under public epoch.

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