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
79
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
Copyright
c
2016 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
79
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
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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.
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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
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