CN104598746A - Applicability discrimination method for coordinate transformation model - Google Patents

Abstract

The invention provides an applicability discrimination method for a coordinate transformation model. The applicability discrimination method comprises the following steps: comparing transformation coordinates generated by a common transformation model by using a side length difference and an azimuth angle difference model of a CGCS2000 geodetic coordinate system and a national reference-ellipsoid-centric coordinate system; carrying out check analysis on the characteristics of the transformation model by using a side length difference and an azimuth angle difference according to the variation quantity and the variation trend; verifying data by using two stages of GPS (Global Positioning System) control networks in one region to reflect the characteristics of the transformation model; verifying the characteristics of the transformation coordinates by utilizing data of the GPS control network and transforming between the CGCS2000 geodetic coordinate system and the national reference-ellipsoid-centric coordinate system. According to the applicability discrimination method provided by the invention, the problem of difficult model selection for different demands in the coordination transformation process is solved, the problems that the precision is evaluated by completely depending on transformation residual and the precision estimation of the transformation residual has certain limitation in the previous coordinate transformation are solved, vast transformation workload is avoided, a large amount of cost and time are reduced and saved, and popularization and application of the CGCS2000 geodetic coordinate system are facilitated.

Description

Coordinate Transformation Models applicability method of discrimination

Technical field

The present invention relates to geodetic surveying and engineering measuring technology field, particularly a kind of Coordinate Transformation Models applicability method of discrimination.

Background technology

China has vast territory, with a varied topography, and current most cities independent coordinate system sets up based on national referenced-centric system in eighties of last century five sixties, affects, be difficult to meet Present Economical demand by technical conditions restriction at that time and precision of control point.

Country's referenced-centric system (54 is be with 80) Controling network is limited by scientific and technological level at that time, and the relative accuracy of geodetic control point is 10 ^-6, and along with socioeconomic development, the progress of scientific and technological level, being enabled as of the CGCS2000 i.e. Urban Independent Coordinate System of 2000 national earth coordinates designs is set up high precision coordinate system and is provided opportunity and platform, and the relative accuracy of geodetic control point is 10 ^-7~ 10 ^-8.Both change by coordinate system mutually, because respective precision is different, have different requirements to the coordinate that conversion produces:

1) when CGCS2000 earth coordinates are to national referenced-centric system conversion, belong to high precision achievement and change to low precision.If converted coordinate reaches high precision, there is high accordance with the very difficult of national referenced-centric system achievement.

2) when national referenced-centric system coordinate is changed to CGCS2000, belong to low precision achievement and change to high precision, usually require that converted coordinate meets with CGCS2000 coordinate as far as possible.

When adopting coincide point and transformation model to carry out coordinate conversion, under coincide point precision and quantity one stable condition, converted coordinate characteristic can only be reflected by different model.And obtain Coordinate Transformation Models characteristic, just can be convenient to select best transition model, reach the high precision of converted coordinate or high accordance.But the coordinate conversion related in prior art, all do not consider the precision changing coincide point achievement, but rely on conversion residual error size to determine transformation model, conversion residual error is the back substitution error of coincide point under same coordinate system, majority of case reflection is coincidence loss, instead of converted coordinate precision.

Summary of the invention

For the above-mentioned defect and the problem that lack the accuracy coordinate conversion considering conversion coincide point achievement in prior art, the object of the embodiment of the present invention is to provide a kind of better Coordinate Transformation Models applicability method of discrimination, thus the transformation model that is applicable to can be selected according to demand, ensure the precision of converted coordinate, avoid huge conversion work amount.

In order to achieve the above object, the embodiment of the present invention provides following technical scheme:

A kind of Coordinate Transformation Models applicability method of discrimination, it is characterized in that, step is as follows:

Q1: the length of side difference and the angle of cut model that utilize CGCS2000 earth coordinates and national referenced-centric system coordinate, produce converted coordinate to conventional transformation model and compare; Utilize the conversion residual error that the back substitution error of the coincide point under same coordinate system calculates, the precision of evaluation converted coordinate;

Q2: according to its variable quantity size and variation tendency, utilizes length of side difference and angle of cut check analysis transformation model characteristic:

Using the high precision CGCS2000 earth coordinates Calculation Plane length of side and position angle as reference point, the length of side of national referenced-centric system and position angle are compared with it, by the characteristic of variable quantity size reflection model;

For relatively not on a large scale, when converted coordinate and CGCS2000 earth coordinates have same precision, its plane length of side is poor and the angle of cut is minimum, close to a constant; Specifically reflect converted coordinate characteristic with length of side difference and the maximum difference of the angle of cut and amplitude; Maximum difference refers to maximal side difference and the difference of minimum length of side difference, reflects that maximum fluctuation is poor; Amplitude refers to that the ultimate range length of side leaving mean value position is poor; Using every km length of side difference as unit of measurement, computing formula is as follows:

The maximum difference of length of side difference: Δ d _max=max (Δ d _i)-min (Δ d _i)

Length of side difference amplitude:

Wherein, length of side difference Δ d _i=(d _2k-d _solely) × 1000/d _2k

The maximum difference of the angle of cut: Δ T _max=max (Δ T _i)-min (Δ T _i)

Angle of cut amplitude:

Wherein, angle of cut Δ T _i=T _2k-T _solely;

Q3: verify by areal two phase GPS Controling network data, the characteristic of transformation model is reflected: utilize areal, different times twice GPS Controling network data by chart, changed by CGCS2000 earth coordinates and national referenced-centric system, checking converted coordinate characteristic;

The coincide point that twice conversion is chosen and coordinate variant, first time national referenced-centric system select low precision triangulation coordinates, second time select first time produce converted coordinate; When high precision achievement is changed to low precision, converted coordinate has high precision, second time is converted between two high-precision coordinates carries out, generation converted coordinate is high precision, be embodied in conversion residual error less, the length of side formed before and after conversion is poor and the angle of cut is very close, otherwise converted coordinate is low precision.

Preferred as technique scheme, in Q1 step, coordinate conversion mathematical model is selected as Bursa three-dimensional seven parameter models:

$\left[\begin{array}{c}{X}_N\\ Y_N\\ Z_N\end{array}\right]=\left[\begin{array}{c}\mathrm{\ΔX}\\ \mathrm{\ΔY}\\ \mathrm{\ΔZ}\end{array}\right]+\left[\begin{array}{ccc}0& -Z& Y\\ Z& 0& -X\\ -Y& X& 0\end{array}\right]\left[\begin{array}{c}{\mathrm{\ω}}_X\\ {\mathrm{\ω}}_Y\\ {\mathrm{\ω}}_Z\end{array}\right]+m\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]+\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]$

Wherein, 3 translation parameterss [Δ X Δ Y Δ Z] ^t, 3 rotation parameter [ω _xΔ _yΔ _z] ^twith 1 scale factor m.[X _ny _nz _n] be target-based coordinate system coordinate;

Or

Polynomial expression multiple stepwise regression model:

B _T＝B _S+ΔB

L _T＝L _S+ΔL

In formula: B _t, L _tbe respectively target-based coordinate system terrestrial coordinate; B _s, L _sbe respectively source coordinate system terrestrial coordinate;

Δ B, Δ L are respectively coordinate conversion reduction, calculate with following formula;

Δ B or Δ L=a ₁+ a ₂b+a ₃l+a ₄b ²+ a ₅bL+a ₆l ²+ ... + a ₂₀bL ⁴+ a ₂₁l ⁵

Wherein: a ₁, a ₂, a ₃, a ₄, a ₅, a ₆for coefficient, solved by least square.

Preferred as technique scheme, in Q1 step, conversion residual error is:

X and y coordinate conversion medial error: $\left.\begin{array}{c}{M}_X=\±\sqrt{{\left[v_i{v}_i\right]}_x/(n-1)}\\ M_Y=\±\sqrt{{\left[v_i{v}_i\right]}_y/(n-1)}\end{array}\right\}$

Converted coordinate medial error (conversion residual error):

Wherein, n is coincide point number, participates in the v of conversion coincide point _i=known coordinate _i-converted coordinate _i.

A kind of Coordinate Transformation Models applicability method of discrimination that the embodiment of the present invention provides, compared with traditional technology, structure is simple, in solution coordinate conversion, different demand is to problem of model selection, solving coordinate conversion is in the past that residual error evaluating precision is changed in dependence, conversion residual precision estimates at certain circumscribed problem completely, avoid huge conversion work amount, save a large amount of expense and time, contribute to applying of CGCS2000 geodetic coordinate system.

Accompanying drawing explanation

In order to be illustrated more clearly in the embodiment of the present invention or technical scheme of the prior art, be briefly described to the accompanying drawing used required in embodiment or description of the prior art below, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skill in the art, under the prerequisite not paying creative work, other accompanying drawing can also be obtained according to these accompanying drawings.

Fig. 1 is twice conversion coincide point distribution schematic diagram of a kind of Coordinate Transformation Models applicability method of discrimination of the embodiment of the present invention 1.

Fig. 2 is that the early stage CGCS2000 geodetic coordinate system of a kind of Coordinate Transformation Models applicability method of discrimination of the embodiment of the present invention 1 is to coordinate system conversion length of side difference distribution schematic diagram.

Fig. 3 is that the early stage CGCS2000 geodetic coordinate system of a kind of Coordinate Transformation Models applicability method of discrimination of the embodiment of the present invention 1 is to coordinate system conversion position angular difference schematic diagram.

Fig. 4 is that the later stage CGCS2000 geodetic coordinate system of a kind of Coordinate Transformation Models applicability method of discrimination of the embodiment of the present invention 1 is to coordinate system conversion length of side difference distribution schematic diagram.

Fig. 5 is that the later stage CGCS2000 geodetic coordinate system of a kind of Coordinate Transformation Models applicability method of discrimination of the embodiment of the present invention 1 is to coordinate system conversion position angular difference schematic diagram.

Embodiment

Below in conjunction with accompanying drawing of the present invention, be clearly and completely described technical scheme of the present invention, obviously, described embodiment is only the present invention's part embodiment, instead of whole embodiments.Based on the embodiment in the present invention, those of ordinary skill in the art, not making the every other embodiment obtained under creative work prerequisite, belong to the scope of protection of the invention.

Embodiment 1

Certain Urban Independent Coordinate System that the embodiment of the present invention provides is set up based on Krasovsky ellipsoid, be projected on reference ellipsoid, early stage city Basic Control Networks lays with triangulation method, successively distributing GPS Controling network is transformed former Controling network, and the horizontal direction precision of twice adjustment CGCS2000 geodetic coordinate system achievement is respectively 1cm and 0.3cm.Two phase coordinate conversion adopt different coincide points, are 7 points in early days; Later stage 10 points, and independent coordinate is the coordinate that conversion in 01 year produces, as shown in Figure 1, A is early stage coincide point, and B is later stage coincide point.

1. coordinate conversion

Carry out coordinate conversion to two issues certificates respectively with same model, conversion residual error is shown in that CGCS2000 is to coordinate system conversion plane coordinate residual error table below:

2. early stage CGCS2000 compares to independent coordinate conversion

Before and after coincide point conversion, the coordinate system length of side and position angle are compared with CGCS2000, each model result is shown in that CGCS2000 is to independent coordinate conversion length of side difference and angle of cut table below, length of side difference and the angle of cut are fluctuated minimum Bursa, draw the length of side difference as Fig. 2 and the angle of cut as shown in Figure 3, wherein Bursa the length of side difference and angle of cut numerical value close, in straight line, illustrate that achievement keeps high precision; And the multinomial model conversion front and back length of side is poor and angle of cut numerical value is more close, figure tendency is similar, illustrates and keeps conversion triangulation achievement characteristic, have higher accordance.

3. later stage CGCS2000 geodetic coordinate system compares to independent coordinate conversion

If following table later stage CGCS2000 geodetic coordinate system is to shown in coordinate system conversion length of side difference and the angle of cut, and shown in Fig. 4 and Fig. 5, before and after Bursa model conversion the length of side difference and the angle of cut very close, an order of magnitude less of earlier results, be reflected on figure, article two, line unites two into one substantially in flat shape, change residual error in addition less, illustrate that the later stage changes the conversion belonged between two high-precision coordinates, converted coordinate has high accordance, illustrate that early stage high precision achievement is to low precision result transformation in addition, the converted coordinate of formation has high precision.

If only from the form conversion residual analysis of 1. coordinate conversion, multinomial model conversion accuracy is higher than Bursa, but compare from this table, Fig. 4 and Fig. 5, length of side difference and angle of cut figure tendency are basically identical before and after early stage conversion, illustrate that the accordance of conversion achievement is better.Although successively twice conversion residual error diminishes, the length of side is poor, the no change of the angle of cut order of magnitude, illustrates that what only improve is accordance.

4. early stage independent coordinate compares to the conversion of CGCS2000 geodetic coordinate system

Independent coordinate is changed to CGCS2000 geodetic coordinate system, for the low precision achievement of triangulation is to GPS high precision result transformation, each model length of side difference and angle of cut comparative result see the following form, wherein multinomial model fluctuation is minimum, its conversion achievement is the most close with CGCS2000 geodetic coordinate system achievement numerical value, illustrates that accordance is relatively best.

5 conclusions

By CGCS2000 geodetic coordinate system and Urban Independent Coordinate System transform instances, summarize common model adaptability:

1) when high precision achievement is to low precision result transformation, Bursa model produces converted coordinate and has high precision; And multinomial model generation converted coordinate has relatively better accordance.

2) when low precision achievement is to high precision result transformation, the converted coordinate that multinomial model produces has relatively better accordance.

3) when two different coordinates high precision achievements are changed mutually, Bursa model produces converted coordinate and namely keeps high precision, has again higher accordance.

The above; be only the specific embodiment of the present invention, but protection scope of the present invention is not limited thereto, is anyly familiar with those skilled in the art in the technical scope that the present invention discloses; change can be expected easily or replace, all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should described be as the criterion with the protection domain of claim.

Claims (3)

1. a Coordinate Transformation Models applicability method of discrimination, is characterized in that, step is as follows:

Q1: the length of side difference and the angle of cut model that utilize CGCS2000 earth coordinates and national referenced-centric system coordinate, produce converted coordinate to conventional transformation model and compare; Utilize the conversion residual error that the back substitution error of the coincide point under same coordinate system calculates, the precision of evaluation converted coordinate;

Q2: according to its variable quantity size and variation tendency, utilizes length of side difference and angle of cut check analysis transformation model characteristic:

Using the high precision CGCS2000 earth coordinates Calculation Plane length of side and position angle as reference point, the length of side of national referenced-centric system and position angle are compared with it, by the characteristic of variable quantity size reflection model;

For relatively not on a large scale, when converted coordinate and CGCS2000 earth coordinates have same precision, its plane length of side is poor and the angle of cut is minimum, close to a constant; Specifically reflect converted coordinate characteristic with length of side difference and the maximum difference of the angle of cut and amplitude; Maximum difference refers to maximal side difference and the difference of minimum length of side difference, reflects that maximum fluctuation is poor; Amplitude refers to that the ultimate range length of side leaving mean value position is poor; Using every km length of side difference as unit of measurement, computing formula is as follows:

The maximum difference of length of side difference: Δ d _max=max (Δ d _i)-min (Δ d _i)

Length of side difference amplitude:

Wherein, length of side difference Δ d _i=(d _2k-d _solely) × 1000/d _2k

The maximum difference of the angle of cut: Δ T _max=max (Δ T _i)-min (Δ T _i)

Angle of cut amplitude:

Wherein, angle of cut Δ T _i=T _2k-T _solely;

Q3: verify by areal two phase GPS Controling network data, the characteristic of transformation model is reflected: utilize areal, different times twice GPS Controling network data by chart, changed by CGCS2000 earth coordinates and national referenced-centric system, checking converted coordinate characteristic;

The coincide point that twice conversion is chosen and coordinate variant, first time national referenced-centric system select low precision triangulation coordinates, second time select first time produce converted coordinate; When high precision achievement is changed to low precision, converted coordinate has high precision, second time is converted between two high-precision coordinates carries out, generation converted coordinate is high precision, be embodied in conversion residual error less, the length of side formed before and after conversion is poor and the angle of cut is very close, otherwise converted coordinate is low precision.

2. a kind of Coordinate Transformation Models applicability method of discrimination according to claim 1, is characterized in that, in Q1 step, coordinate conversion mathematical model select into:

Three-dimensional seven parameter models of Bursa:

$\left[\begin{array}{c}{X}_N\\ Y_N\\ Z_N\end{array}\right]=\left[\begin{array}{c}\mathrm{\ΔX}\\ \mathrm{\ΔY}\\ \mathrm{\ΔZ}\end{array}\right]+\left[\begin{array}{ccc}0& -Z& Y\\ Z& 0& -X\\ -Y& X& 0\end{array}\right]\left[\begin{array}{c}{\mathrm{\ω}}_X\\ {\mathrm{\ω}}_Y\\ {\mathrm{\ω}}_Z\end{array}\right]+m\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]+\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]$

Wherein, 3 translation parameterss [Δ X Δ Y Δ Z] ^t, 3 rotation parameter [ω _xω _yω _z] ^twith 1 scale factor m.[X _ny _nz _n] be target-based coordinate system coordinate;

Or

Polynomial expression multiple stepwise regression model:

B _T＝B _S+ΔB

L _T＝L _S+ΔL

In formula: B _t, L _tbe respectively target-based coordinate system terrestrial coordinate; B _s, L _sbe respectively source coordinate system terrestrial coordinate;

Δ B, Δ L are respectively coordinate conversion reduction, calculate with following formula;

Δ B or Δ L=a ₁+ a ₂b+a ₃l+a ₄b ²+ a ₅bL+a ₆l ²+ ... + a ₂₀bL ⁴+ a ₂₁l ⁵

Wherein: a ₁, a ₂, a ₃, a ₄, a ₅, a ₆for coefficient, solved by least square.

3. a kind of Coordinate Transformation Models applicability method of discrimination according to claim 1, is characterized in that, in Q1 step, conversion residual error is:

X and y coordinate conversion medial error: $\left.\begin{array}{c}{M}_X=\±\sqrt{{\left[v_i{v}_i\right]}_x/(n-1)}\\ M_Y=\±\sqrt{{\left[v_i{v}_i\right]}_y/(n-1)}\end{array}\right\}$

Converted coordinate medial error (conversion residual error):

Wherein, n is coincide point number, participates in the v of conversion coincide point _i=known coordinate _i-converted coordinate _i.