Least-Square Collocation and Its Application in GPS Elevation

Fitting

Ruifang Yang

Henan Quality Polytechnic, Pingdingshan, Henan, 467000, China

Keywords: Least-square collocation, GPS, elevation fitting, application.

Abstract: Measurement technology is constantly applied in industrial field, and GPS technology has made great

contribution to the efficiency and accuracy of measurement. GPS elevation fitting is researched on the basis

of geodetic height elevation and normal height elevation. There are some abnormalities and errors between

the two elevations, so elevation fitting is adopted to eliminate the abnormalities and errors. The work mainly

discussed the application of least-square collocation in GPS elevation fitting, and then explored its future

development in this field. In a word, the application of elevation fitting based on the optimization of least-

square collocation can effectively solve elevation abnormalities and errors.

1 INTRODUCTION

GPS technology is widely used in measurement field

in which measurement accuracy is highly required.

Therefore, it is very necessary to adopt GPS

technology to achieve high efficient and accurate

measuring results. GPS technology is not only

applied in measurement field but also widely used in

navigation. However, GPS technology has a very

high standard on its accuracy in measurement field

and navigation field. The basic principle of GPS is

making use of positioning satellites to conduct

precision measurement for earth forms (Du Hongfei,

Xie Shaofeng, Sun Changyu, 2013). Thus, certain

elevation abnormalities or errors happen in the

application process due to the influence from

geodetic height elevation and normal height

elevation. Therefore, GPS elevation fitting is

adopted to conduct corresponding error analysis and

abnormality treatment. Meanwhile, least-square

collocation is adopted to perform corresponding

mathematical optimization and find out the best

processing function, thus achieving the application

of least-square collocation in GPS elevation fitting.

2 GPS TECHNOLOGY AND ITS

APPLICATION FIELDS

GPS is an abbreviation of Global Positioning

System. Positioning system is built on the basis of

fixed-point satellites in the outer space of earth.

Thus, positioning satellites actually contribute to

global positioning system. Based on such core

technology and technical means, GPS is mainly

applied in navigation positioning and measurement

fields (Li Chengren, Yue Dongjie, Ding Xu, Yuan

Bao, 2013).

2.1 Positioning Navigation of GPS

Usually, at least 3 satellites are needed to realize

global coverage and establish global positioning

system. Thus, navigation becomes the main

application field in the actual application of GPS.

The main function of GPS is to collect information

on earth, and then satellites can receive information

through feedback method. Following that, satellites

transfer the information to control center on earth

through digitization and imagination treatment.

Then, it represents the information in audio or image

ways to help people for positioning and navigation.

At present, vehicle navigation is the key field of

GPS application (Liu Hao, 2013). Thus, GPS

Yang R.

Least-Square Collocation and Its Application in GPS Elevation Fitting.

DOI: 10.5220/0006444100790082

In ISME 2016 - Information Science and Management Engineering IV (ISME 2016), pages 79-82

ISBN: 978-989-758-208-0

positioning navigation is most widely used in

vehicle navigation.

2.2 Application of GPS Technology in

Measurement Field

Based on the positioning technology and calculation

methods, GPS also has achieved wide application in

measurement field when combined with advanced

measuring technologies. In engineering

measurement field, some measuring errors always

happen in the process of wide-area construction due

to the differences between actual data and theoretical

data. For example, when conducting distance

measurement for some regions of complex

geography, induction method is usually adopted for

measuring and corresponding data calculation,

ensuring very detailed technical methods in

measuring. However, it still cannot achieve

precision in a true sense. Therefore, it is essential to

use global positioning system to achieve high

efficient and accurate region measurement and data

calculation. GPS makes use of the advantage of

collection information on earth to realize accurate

distance measurement, thus ensuring the

achievement of a high-precision measurement

method in measurement field. In short, according to

the core technology of GPS, its main application

fields are positioning navigation and precise

measurement.

3 RESEARCH OF GPS

ELEVATION FITTING

This work focused on the analysis of the application

of least-square collocation in GPS elevation fitting.

Therefore, it is very important to firstly understand

what GPS elevation fitting is and why elevation-

fitting operation is essential. Those questions need to

be analyzed from several aspects. More specifically,

GPS elevation fitting should be analyzed from its

technology and practical design.

3.1 Reasons of GPS Elevation Fitting

In fact, the technology advantages of GPS are very

vital for corresponding measurement in both

positioning navigation and precise measurement.

The measurement of GPS for geography should be

conducted based on reference points. Generally,

GPS measurement standards are based on the

geodetic height of WGS-84 ellipsoid. Therefore,

those data are obtained on the basis of theoretical

standard. However, in actual engineering

application, the horizontal surface of earth is usually

considered as the measurement standards. Thus, this

causes the discrepancies of those elevation data to a

certain extent. So, it is necessary to fit those two

elevation data in practical engineering construction,

thus ensuring a better data use in actual GPS

application. GPS elevation fitting is just one of the

most common methods in elevation transformation

modes. However, GPS elevation fitting can realize

an accurate treatment of elevation discrepancies,

thus matching the elevation data in practical

application.

3.2 Principles of GPS Elevation

Measurement

Before analyzing the principles of GPS elevation

fitting, the work firstly explored the principles of

GPS elevation measurement. Following that, some

basic concepts of GPS elevation-fitting process was

further studied to fundamentally interpret the

practical process of GPS elevation fitting and its

application principles.

3.2.1 GPS Elevation Measurement

GPS elevation measurement is to measure the

coordinates on the ground and obtain geodetic-

height data based on its positioning principles. Thus,

geodetic coordinates play a very important role in

the measuring process. Besides, systematic

measuring technologies are required to carry out

corresponding fixed-point measurement for

geodetic-height data, thus guaranteeing accurate data

in the application process.

3.2.2 System of Elevation Fitting

GPS elevation fitting system is a generalized and

relative concept, and the measurement of different

coordinates will generate different elevation

systems. Elevation system is highly related to

elevation, thus resulting in different elevation

system. At present, elevation systems mostly used

include geodetic height system, orthometric system

and normal height system. These systems are named

based on their corresponding treatment according to

different elevation.

First of all, geodetic height system actually

conducts measurement based on WGS-84 standard.

This system uses theoretical ellipsoid as its

measuring standard, so the data obtained from

calculation belongs to theoretical data. Thus, certain

ISME 2016 - Information Science and Management Engineering IV

ISME 2016 - International Conference on Information System and Management Engineering

discrepancies happen in practical engineering

application, leading to the necessity of elevation

fitting.

Secondly, orthometric system is one of the most

precise measurement systems that uses practical

horizontal surface as the reference for measurement.

Although this system adopts practical measurement

standard, there are still some difficulties in the

application process. In fact, GPS elevation fitting is

to fit the data gained from orthometric system and

geodetic height system, thus obtaining the most

accurate elevation data.

Finally, normal height system is actually a

compromised system out of geodetic height system

and orthometric system. As discussed above,

geodetic height system gets some theoretical

elevation data, so those data shows a low application

value to some extent. Meanwhile, orthometric

system adopts gravity measuring method, which

causes some difficulty in practical operation.

Besides, orthometric system results in too much

work of measurement. Therefore, normal height

system adopts a compromised method based on the

problems of the other two systems. Normal height

system makes use of average value for

measurement, thus ensuring the reliability of data

and largely reducing some complex and redundant

measuring steps in actual measurement. In

conclusion, normal height system is most commonly

used in elevation measurement.

3.3 Research of GPS Elevation Fitting

Above analysis shows that GPS elevation fitting has

obvious advantages including high efficiency and

precision. Besides, GPS elevation fitting can achieve

no cumulative errors of elevation measurement.

Thus, GPS elevation fitting has a very important

significance in practical application. In the

following, the work discussed how GPS elevation

fitting works out in practical application and how

GPS elevation fitting technology is achieved.

First of all, isoline map is used in GPS elevation

fitting. Isoline is a very common method for

measuring and fitting. In fact, isoline is a method to

obtain average value. So, the measurement data from

GPS can be used to figure out several contour lines

of some normal heights, and then complete the

drawing of all contour lines based on the calculation.

Here, the concept of contour line is consistent with

the concept of isoline.

Secondly, curve fitting method is also used in

GPS fitting. In fact, curve fitting method is the most

mainstream calculation method out of all

mathematical methods for GPS elevation fitting.

This method carries out corresponding data

calculation through one curve, thus geting relative

average value. Curve fitting is a relatively

commonly used GPS elevation fitting method.

Generally, accurate method is needed in curve fitting

to ensure the accuracy after the fitting.

Thirdly, multiplication curve fitting is another

method applied in GPS fitting. Based on the

extension way and advantages of curve fitting, GPS

fitting makes use of multiplication curve fitting to

maximumly reduce fitting errors. In fact, any kind of

calculation contains the risks of errors, and the

differentials of the errors to some extent determine

the accuracy of the measurement. Multiplication

curve fitting method mainly focuses on making use

of the advantages of curve fitting. Individual curve

fitting still causes some errors, so multiplication

curve fitting method is applied to minimize errors.

Therefore, multiplication curve fitting method

becomes the most commonly used method in GPS

elevation fitting.

4 LEAST SQUARE ALGORITHM

AND LEAST-SQUARE

COLLOCATION

Least square algorithm is acutally the most

commonly used data fitting method in data

optimization. Its main role is to reduce calculation

errors and problems happened in data calculation

process. In practical application, least square

algorithm usually appears in the form of least-square

collocation, because it is widely used in practical

application especially in high-precision data

calculation. Error is inevitable in many calculations.

Using least square algorithm to avoid errors is

actually to figure out the most suitable ratio function

based on the square or differential of errors and then

conduct corresponding data calculation. In addition,

least square algorithm can be easily figured out for

unknown data calculation, greatly minimize errors in

application. This is why least square algorithm is so

commonly used and why least-square collocation

method achieves so obvious achievements on

minimizing errors.

Least-Square Collocation and Its Application in GPS Elevation Fitting

5 APPLICATION OF LEAST-

SQUARE COLLOCATION IN

GPS ELEVATION FITTING

GPS elevation fitting system, a generalized and

relative concept, generates different elevation

systems for the measurement of different

coordinates. Elevation system is closely related to

elevations, thus resulting in the emergence of many

different elevation systems. Based on above analysis

of the principles of GPS elevation fitting and least-

square collocation, the work further studied why it

was necessary to apply least-square collocation in

GPS elevation fitting. Least square algorithm in fact

is a very common data fitting method in data

optimization field. Its main function is to reduce

calculation errors and avoid problems during data

calculation. In practical measuring process, GPS

elevation fitting usually adopts normal-height fitting

system and multiplication curve fitting to conduct

calculation. In fact, least-square collocation method

is more suitable for GPS elevation fitting, and it

helps to minimize measuring errors. Besides, least-

square collocation method can easily figure out

some unknown data in the elevation measuring

process. Meanwhile, this method can carry out

proper configuration for calculation errors in

elevation fitting process. So it can figure out the best

data collocation, ensuring that the calculation result

is maximumly close to accurate data in using

measurement data. In GPS elevation fitting,

multiplication curve fitting method is used for

calculation, and least-square collocation is applied to

rematch the calculation errors, thus figuring out the

minimum error ratio and corresponding error data.

Therefore, a comparison list of best error ratio can

be generated, thus achieving the most accurate data

6 CONCLUSIONS

Through the analysis of GPS measurement

technology and GPS elevation fitting principles, the

work concluded that it was essential to minimize

error data and make perfect collocation of errors in

practical application. In practical GPS elevation

fitting, multiplication curve fitting is usually applied

to make use of normal-height system. GPS elevation

fitting, an important research field, can better

achieve the application of GPS through analyzing its

principle of data measurement. Besides, it can

effectively minimize or avoid errors. Least-square

collocation is to figure out the best treatment

function in order to obtain corresponding

mathematical optimization more precisely, thus

achieving the application of least-square collocation

in GPS elevation fitting.

REFERENCES

Du Hongfei, Xie Shaofeng, Sun Changyu. Application of

Least-Square Collocation in GPS Elevation

Abnormality Prediction. Henan Science, 2013(02): 208-

211

Li Chengren, Yue Dongjie, Ding Xu, Yuan Bao.

Comparison of the Application of Least-Square

Collocation and Multisurface Function in Elevation

Abnormality Prediction. Site Investigation Science and

Technology, 2013(03): 40-42

Liu Hao. Application of Least-Square Collocation and

Kriging Method in GPS Elevation. Management &

Technology of SME, 2013(34): 163-164

ISME 2016 - Information Science and Management Engineering IV

ISME 2016 - International Conference on Information System and Management Engineering