Determination of Orthometric Height of NJI2 CORS Station
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Determination of Orthometric Height of NJI2 CORS Station
Joshua Greenfeld1 and James D. Sens2
Abstract: Many surveyors use the network of global positioning system 共GPS兲 Continuously Operating Reference Stations 共CORS兲 as
accurate ‘‘free’’ control monuments in their projects. The National Geodetic Survey 共NGS兲 publishes and maintains coordinates for these
stations in terms of X, Y, Z, and latitude, longitude, and ellipsoidal heights. This information is very useful for horizontal positioning but
not for vertical positioning. Establishing the orthometric heights of a CORS station will enhance its usefulness to surveyors and geod-
esists. In this paper, a method for determining orthometric heights for CORS is described and evaluated. The implementation of the
proposed procedure at the NJI2 CORS station produced an orthometric height with a standard deviation of ⫾1 mm.
DOI: 10.1061/共ASCE兲0733-9453共2003兲129:3共110兲
CE Database subject headings: Surveys; Height; Methodology.
Introduction arises from the difficulty in accurately determining the geoid
height differences. Geoid height differences are used to convert
Two developments have made an enormous impact on surveying GPS derived ellipsoid height differences to orthometric heights
practice. The first development is the global positioning system 共Zilkoski 2001兲.
共GPS兲 and the other is a network of Continuously Operating Ref- GPS observations yield ellipsoid heights 共h兲, which are defined
erence Stations 共CORS兲 coordinated by the National Geodetic relative to a reference ellipsoid. The ellipsoidal height of a given
Survey 共NGS兲. GPS has proven to be an invaluable tool for sur- point is defined as the distance from the reference ellipsoid to the
veyors for the determination of relative three-dimensional posi- point, measured as an extension to the ellipsoid normal 共Henning
tioning and coordinates. According to Anderson and Mikhail et al. 1998; Zilkoski 2001兲. Surveyors, however, are primarily
共1998兲, relative positioning with GPS was repeatedly shown concerned with the orthometric height of an object 共H兲. The
共where applicable兲 to be the most economical and accurate pro- orthometric height of a point on the topographic surface of the
cedure available to surveyors. The efficiency and accuracy of earth is the distance from the vertical datum reference surface to
GPS has allowed it to replace classical survey methods for the the point, measured along the plumb line 共Zilkoski 2001兲. The
establishment of horizontal control in most situations. problem is to relate elevation differences measured by GPS 共dh兲
The CORS provides GPS carrier phase and code range mea- to elevation differences 共dH兲 measured by traditional leveling.
surements in support of 3D positioning activities throughout the The ellipsoid height is a straight-line distance from a point to the
United States and its territories. Surveyors, GIS/LIS profession- ellipsoid, whereas elevation measured with leveling is a curved
als, engineers, scientists, and others can apply CORS data to po- distance shaped by the gravity field from a point to the datum
sition points at which other GPS data have been collected. The surface 共geoid兲.
CORS network is, in essence, a network of control points that can The orthometric height differences 共dH兲 are obtained from the
be used as a replacement for the traditional control point monu- ellipsoid height differences 共dh兲 and the geoid height differences
ments that have to be physically occupied by the surveyor. CORS 共dN兲 from the following equation:
data enable positioning accuracies that approach a few centime-
ters relative to the National Spatial Reference System, both hori- dH⫽dh⫺dN (1)
zontally and vertically. In the relative mode, horizontal position- Many factors affect the accuracy of orthometric, ellipsoid, and
ing of new points located in the proximity of a CORS station can geoid heights; however, the impact of these factors on the heights
approach subcentimeter accuracies with as few as five minutes of is generally similar for points in close proximity. For this reason,
observations. the determination of height differences between points in a rela-
Regrettably, surveyors are unable to utilize CORS as vertical tively small area contains far less uncertainty than the absolute
control, mainly because almost all of them have only ellipsoidal heights of each point. This concept is critical to the determination
height and do not have accurate orthometric height. The primary of accurate orthometric heights from GPS observations 共Henning
cause for the limited accuracy of GPS derived vertical control et al. 1998; Zilkoski 2001兲.
Accurate ellipsoidal heights and accurate geoid height differ-
1
New Jersey Institute of Technology, Newark, NJ 07102. ences are needed to obtain accurate orthometric height. With the
2
New Jersey Institute of Technology, Newark, NJ 07102. completion of the national high-resolution geoid model, Geoid
Note. Discussion open until January 1, 2004. Separate discussions 99, the problem of obtaining accurate geoid height differences
must be submitted for individual papers. To extend the closing date by
was significantly alleviated. The problem of obtaining accurate
one month, a written request must be filed with the ASCE Managing
Editor. The manuscript for this paper was submitted for review and pos- ellipsoid heights has been addressed by Zilkoski et al. 共1997兲 in a
sible publication on November 29, 2001; approved on May 20, 2002. form of guidelines for obtaining accurate ellipsoidal height with
This paper is part of the Journal of Surveying Engineering, Vol. 129, GPS. These guidelines, if adhered to, can yield ellipsoid height
No. 3, August 1, 2003. ©ASCE, ISSN 0733-9453/2003/3- differences, over short baselines, that typically contain uncer-
110–114/$18.00. tainty smaller than ⫾2 cm 共Zilkoski 2001兲. The final obstacle is
110 / JOURNAL OF SURVEYING ENGINEERING © ASCE / AUGUST 2003NGS Guidelines
NGS has issued guidelines for the establishment of ellipsoid
heights, that, if adhered to, typically yield heights with uncer-
tainty that is better than ⫾2 cm. These guidelines are comprised
of two major categories, observation guidelines and vector pro-
cessing guidelines. In addition, the guidelines contain an assump-
tion that a statewide High Accuracy Reference Network 共HARN兲
has been completed, or that there are GPS Continuously Operat-
ing Reference Stations 共CORS兲 located within 75 km of the
project area. The existence of first-order monuments is necessary
because accurate horizontal coordinates must be obtained in order
to determine the geoid separation 共dN兲. Monuments used for ver-
tical control should have ‘‘A’’ order orthometric heights. If ‘‘A’’
order monuments are not available, ‘‘B’’ order monuments can be
used, but the likelihood of obtaining a network accuracy of ⫾2
cm is greatly reduced.
NGS requires that, for observations for baselines greater than
10 km dual frequency, full wavelength GPS receivers be used,
and it is strongly recommended they be used regardless of base-
line length. Guidelines also suggest that identical antennas be
used. The survey must be referenced to at least three existing
National Geodetic Reference System A or B order control stations
near the project area in three different quadrants. For establish-
ment of control stations and primary base stations, receivers shall
collect data continuously for at least three 5 h sessions on 3 dif-
ferent days. The observing scheme for all primary base stations
requires that the baseline to each station must be traceable back to
two control stations along independent paths. The data should be
collected when the vertical dilution of precision 共VDOP兲 is less
than six for at least 90% of each observation session. The data
should be collected at 15 s epoch intervals, and satellites should
be tracked down to at least the 10° elevation angle. NGS also
Fig. 1. NJI2 CORS station stipulates that meteorological data, including temperature, relative
humidity, and atmospheric pressure, be taken at control stations
and at primary and secondary base stations. If the sessions are
longer than two hours, the meteorological data must be collected
at the beginning, middle, and end of the session. In order to meet
ensuring that the control benchmarks that are being used in the
the 2 cm standard, fixed height tripods are required. Rubbings or
computations have valid 共NAVD 88 or another datum兲 orthomet-
plan sketches must be made at each station occupation.
ric heights 共Henning et al. 1998兲. This must be determined on a
Vector processing must be performed using the NGS program
project-by-project basis. For many surveying projects, heights dif-
OMNI, or software that will produce similar results. NGS stipu-
ferences of ⫾2 cm 共0.06 ft兲 are of insufficient accuracy. Other
lates that the processing shall be done using the precise ephem-
projects may require using benchmarks with an accuracy of 3 mm
eris. The integers must be fixed, and a model of the tropospheric
共0.01 ft兲. Therefore, it is beneficial to develop a methodology for
effects must be used. The measured meteorological data may be
determining an orthometric height of CORS for the more strin-
used if it has been determined that all instruments were properly
gent accuracy requirements.
calibrated and are accurate; however, a standard model can be
The purpose of this study was to determine an accurate ortho-
used.
metric height of the CORS station located on the roof of Colton
Hall at the New Jersey Institute of Technology in Newark, New
Jersey. This station is a member of NGS’s national CORS net- Equipment Used and Field Procedures
work, known as NJI2. As seen in Fig. 1, the station is not ‘‘level-
able;’’ therefore, one cannot determine its orthometric height by Equipment utilized for performing this study included both con-
means of traditional leveling procedures. Thus, the objective was ventional surveying equipment and GPS equipment. A Sokkisha
to determine the orthometric height of the antenna center of NJI2. B2C Automatic Level and a Philadelphia rod were used for con-
The methodology used was based on NGS standards and guide- ventional leveling. The level was peg tested, and the rod was
lines 共Zilkoski et al. 1997兲. Some deviations that were made from calibrated prior to use. GPS observations were made using five
the NGS guidelines are discussed and evaluated. Leica System 200 and 300 dual frequency, full wavelength re-
This paper begins with a summary of the NGS guidelines. This ceivers, four receivers using Leica CR 233 controllers, and the
is followed by a description of the equipment and field procedure fifth using a Leica CR 333 controller. The NJI2 receiver is a Leica
that were used to carry out our study. The results of the different RS500 with an AT303 Choke Ring antenna. Vector processing
observations scenarios are then presented and evaluated. Finally, was done utilizing SKI-Pro software and SKI 2.3 software.
conclusions are made with some remarks on how to obtain accu- The initial step in the study was to find the nearest control
rate orthometric heights of CORS. stations to NJI2. Because NJI2 is a CORS with known coordi-
JOURNAL OF SURVEYING ENGINEERING © ASCE / AUGUST 2003 / 111Table 2. Benchmarks Established for Study
Orthometric height Standard deviation
Monument 共m兲 共mm兲
9656 5.908 ⫾1
TP17 10.758 ⫾2
TP32 23.043 ⫾2
TP38 31.884 ⫾2
TP41 31.730 ⫾2
TP48 15.546 ⫾2
network geometry. The level run was adjusted using the least
squares observation equation method. The standard deviation of
the adjusted values for the computed network points was ⫾0.003
m. In addition, no systematic errors were detected between the
benchmarks, which, as mentioned earlier, came from two differ-
ent NGS leveling projects. The orthometric heights of the NGS
benchmarks and the newly established benchmarks are presented
in Tables 1 and 2, respectively.
Once the orthometric height of each benchmark was estab-
lished, GPS observations could begin. GPS mission planning
identified the optimum time periods to avoid high VDOP values.
The original plan was to occupy one of the originally recovered
NGS monuments and all five benchmarks established during the
level run. In this way, the orthometric height of NJI2 could be
established from four benchmarks, and the other two monuments
could then be used to check the computed height. As NGS only
requires that three benchmarks be used, the extra benchmark
would add redundancy to the observations. However, on the first
day of observations, one of the receivers malfunctioned, and no
data from that station were available. Although data from five
benchmarks were available for the height computation, only a
Fig. 2. Leveling network used to determine elevation of NJI2 minimum of three NGS benchmarks were used as control, while
the remaining two points were used as checks.
All five benchmarks were occupied for 5 h on three separate
days in order to satisfy NGS requirements. Prior to the com-
nates, it would serve as the horizontal control monument. There- mencement of the project, all level bubbles were checked and
fore, the search focused on first order vertical monuments and adjusted if necessary. In addition, observation logs were kept for
was limited to a 5 km radius of NJI2. Many first order vertical all setups for all three sessions. The dilution of precision values
monuments are located within this radius. However, they are all for these sessions are summarized in Table 3. The duration of
located in the northeast and southeast quadrants. The four closest high GDOP 共13.65兲 was only for 20 min out of a total of 900 min
first order monuments were recovered, monuments 7 L 1 共PID of observations. The PDOP during those 20 min was 1.73. There-
AI7801兲, 9656 共PID AI7802兲, B 101 共PID KV3408兲, and A 101 fore, the dilution of precision requirement as stated in the NGS
共PID KV3407兲. The selected benchmarks were within a radius of guidelines was met.
1 km of NJI2. Fig. 2 shows the relationship between NJI2 and the Fixed height tripods were not utilized as required by the NGS
selected benchmarks. guidelines. In order to stay within the spirit of the guidelines, a
Elevations of the selected benchmarks were established from procedure was established to determine the antenna heights. Each
two different NGS leveling projects: 1979 and 1991. In order to antenna utilized a tape measure that attached to the tribrach. The
satisfy the NGS monument requirement and to check the accuracy height of the antenna was measured by three different people at
of the published orthometric heights, a three wire level run was the beginning and end of each session, and the average height was
run between them. In addition, five project benchmarks were set utilized in the computation. While this is not in strict adherence to
to the northwest and southwest of NJI2 in order to strengthen the the standards, it can be considered appropriate when fixed an-
tenna rods are not available.
Table 1. Control Benchmarks
Table 3. DOP Summary
Published orthometric
Monument height 共m兲 Level PDOP GDOP
B101/KV3408 10.797 High 2.50 13.65
9656/AI7802 5.908 Low 1.16 2.16
7 L 1/AI7801 5.543 Average 1.41 3.31
A101/KV3407 11.420 Standard deviation 0.02 0.22
112 / JOURNAL OF SURVEYING ENGINEERING © ASCE / AUGUST 2003Table 4. Elevation Comparison, Leveling versus GPS from Com- Table 5. Elevation Comparison of Points TP38 and TP48, Leveling
plete Observation Data Sets versus GPS
Leveled height GPS height Difference Leveled height GPS height Difference
Monument 共m兲 共m兲 共m兲 Monument 共m兲 共m兲 共m兲
9656 5.908 5.906 0.002 TP38 31.884 31.883 0.001
TP32 23.043 23.041 0.002 TP48 15.546 15.548 0.002
TP38 31.884 31.885 0.001
TP41 31.730 31.733 0.003
TP48 15.546 15.548 0.002 elevations can be computed with sufficient accuracy by using
NJI2 as the only vertical control. The results of this process are
shown in Table 4.
Table 4 shows that the computed height of the benchmarks
Precise ephemeris was not utilized in our study. Instead, only varied very little following the two-stage computation process.
broadcast ephemeris was used. This is because, according to This result does not prove anything about the accuracy of the
Ayers and Bourdon 共1993兲, vector solutions between broadcast orthometric height of NJI2 except that the proposition that one
and precise ephemeris processing do not show any difference for can use the elevation of NJI2 to compute the elevations of the
short 共⬍20 km兲 and medium 共50 km兲 baselines. Since our net- other nearby benchmarks is valid. It also computes the residuals
work was comprised of extremely short 共⬍1 km兲 GPS vectors, of the computation process.
using the precise ephemeris would not contribute to improving The second processing scenario was to compute the orthomet-
the accuracy of the results. ric height of NJI2 using the data from complete 5 h observation
Meteorological data were not collected during the sessions. sessions from all three days but using only three benchmarks,
Due to the extreme shortness of the baselines 共less than 1 km兲 and monuments 9565, TP32, and TP41. This was done in order to
the little change in elevation over the project area, it is extremely evaluate the computed elevation if only the minimum number of
unlikely there would be any significant difference between the benchmarks 共per NGS guidelines兲 is used. In this scenario the
atmospheric conditions at each station. Therefore, it was decided orthometric height of NJI2 was found to be 50.2391 m. This is a
that the standard atmospheric model could suffice under these mere 0.0003 m difference as compared with using all five bench-
circumstances. marks. Therefore, using only three benchmarks to compute the
Rubbings for each session were made only on the occupied orthometric height of NJI2 is deemed to be sufficient.
NGS monument. The newly established monuments were brass The third scenario was to compute the orthometric height of
disks with simple IDs. Since all of these points were local 共around NJI2 from only three benchmarks 共monuments 9656, TP32, and
the campus兲 and since the same people who did the observations TP 41兲. Once the height of NJI2 was determined, it was used to
also did the data processing, it was felt that primary reason for determine the orthometric heights of the two remaining bench-
rubbing 共correct identification of the points兲 was not an issue. marks 共TP38 and TP48兲. The heights were then compared to
those determined by the leveling adjustment in order to assess the
accuracy of the orthometric height of NJI2. For this analysis, only
Vector Processing and Analysis of Results one hour of time from each session was used. The sessions used
were:
The initial step of the processing was to establish the horizontal • Day one: 8:00 am–9:00 am
coordinates of all the established benchmarks. These values were • Day two: 9:00 am–10:00 am
necessary in order to determine the geoid separation at these • Day three: 10 am–11:00 am
points. Because NJI2 is an NGS monitored CORS with known The same data sets were used for computing the orthometric
three-dimensional Cartesian coordinate values, the geodetic hori- height for NJI2 and for computing the orthometric heights for
zontal coordinates—and therefore the geoid separation—could be TP38 and TP48.
determined from it. The purpose here was not to determine the Based on these constraints, the orthometric heights of NJI2,
precise horizontal coordinates of the benchmarks, because ap- TP38, and TP48 were found to be 50.2397, 31.883, and 15.480 m,
proximate values are sufficient for the determination of the geoid respectively. Table 5 presents the accuracy assessment of the
height. height determination by comparing the leveling and GPS derived
The data were processed considering several different cases or orthometric heights of points TP38 and TP48. It can be seen that
scenarios. In each scenario, a different number of benchmarks the heights that were derived independently are well within the 3
was used for control, and the heights were computed from vary- mm 共0.01 ft兲 range that would satisfy most surveying require-
ing lengths of observation sessions. The analysis of the results ments.
from each scenario was done in two stages. The first stage was to The final processing scenario was similar to the previous one,
determine the orthometric height of NJI2; the second stage was to except only 20 min of data were used from each session. The 20
determine the accuracy of that height by some comparison analy- min sets were taken at different times from each session so that
sis.
The first processing scenario was to compute the orthometric
height of NJI2 by using all five benchmarks and the complete 5 h Table 6. Elevation Comparison, Leveling versus GPS with 20 min
data set from each observation session, thus maximizing the re- Observation Data
dundancy of the computation. The orthometric height of NJI2 was Leveled height GPS height Difference
found to be 50.2388 m. Once the orthometric height of NJI2 was Monument 共m兲 共m兲 共m兲
determined, it was then used as the only control point for com-
TP38 31.884 31.884 0.000
puting the elevations of the benchmarks. In essence this was done
TP48 15.546 15.547 0.001
to verify that the two-stage process works and that the benchmark
JOURNAL OF SURVEYING ENGINEERING © ASCE / AUGUST 2003 / 113Table 7. Average Height of NJI2 Based on All Processing Scenarios lowed; it is just an observation based on our experiment with very
Orthometric height short baselines. The very short baselines of this project allowed
Scenario 共m兲 greater leeway in the observation and processing methods. If the
project area were larger, or if the distance between project control
1 50.2388 monuments were greater, then longer observation periods would
2 50.2391 probably be necessary.
3 50.2397 The NGS standards provide a cookbook method for determin-
4 50.2380 ing high accuracy ellipsoid heights. When these standards are
Average 50.2389 used in conjunction with the National High-Resolution Geoid
Standard deviation 0.0007 Model 共Geoid 99兲, high accuracy orthometric heights can be de-
termined. However, this study reveals that, depending on the pur-
pose of the project, and under the proper conditions with the
the satellite constellation in each data set would be different. The proper research, certain parts of the guidelines can be relaxed and
result of this computation was that the orthometric height of NJI2 high quality results can still be obtained. If accurate orthometric
was found to be 50.2380 m. As before, that elevation was used to heights are to be determined for CORS, the procedure outlined in
compute the elevations of TP38 and TP48. The result of this this paper could be followed. The main thrust of the procedure is
computation is presented in Table 6. Table 6 shows that identical establishing a temporary high quality benchmark network in the
results were obtained with this reduced data set. vicinity of the CORS and using it as a control for computing the
Table 7 summarizes all the computed orthometric heights of station’s orthometric height.
NJI2. The difference between the two extreme values 共50.2397
and 50.2380兲 is less than 0.002 m and the standard deviation is
less than 1 mm. Therefore, it is safe to conclude that the ortho- Acknowledgments
metric height of NJI2 is 50.239 m.
The writers want to extend their sincerest thank you to Borbas
Surveying and Mapping, LLC, of Boonton, N.J., for their gra-
cious donation of personnel, facilities, and equipment. Without
Summary and Conclusions
their support and expertise, this project could not have been com-
pleted. In addition, they would like to thank Henri Ayers and
The results found in this project clearly show that GPS is a viable
Michel Bourdon of Leica Geosystems for their advice and help in
means for determining orthometric heights. In some ways this is a
vector processing.
typical project a surveyor may encounter; in other ways it is not.
The primary difference between this project and a typical project
is the need to utilize monuments with first order horizontal and References
vertical coordinates. Because NJI2 is a CORS, we needed to find
only first order vertical control monuments. Anderson, J. M., and Mikhail, E. M. 共1998兲. Surveying theory and prac-
The various processing scenarios produced remarkably similar tice, WCB/McGraw-Hill, New York.
orthometric heights for NJI2. The standard deviation of the height Ayers, H. B., and Bourdon, M. 共1993兲. Evaluation of System-200 over
from the different processing methods was less than 1 mm. In long baselines measured on the Ottawa GPS basenet, Leica Canada,
addition, when comparing the benchmark heights measured by Ontario, Canada.
leveling and the heights measured by GPS, the maximum differ- Henning, W. E., Carlson, E. E., and Zilkoski, D. B. 共1998兲. ‘‘Baltimore
ence was 2 mm. The small differences and consistency of the County, Maryland, NAVD 88 GPS-derived orthometric height
project.’’ Surv. Land Inf. Serv., 58共2兲, 97–113.
results indicate that the sought accuracy of 3 mm was met.
Zilkoski, D. B., D’Onofrio, J. D., and Frakes, S. J. 共1997兲. ‘‘Guidelines
The data demonstrate that over very short baselines quality for establishing GPS-derived ellipsoid heights 共standards: 2 cm and 3
results can be achieved with substantially less than 5 h sessions. cm兲, version 4.3.’’ NOAA Technical Memorandum NOS NGS-58, Na-
In fact, the result using 5 h sessions for three days is only a tional Geodetic Survey Information Center, Silver Spring, Md.
millimeter different than when using 20 min sessions for three Zilkoski, D. B. 共2001兲. ‘‘NAVD 88 GPS-derived orthometric heights.
days. This is not to say that NGS guidelines should not be fol- Part 1.’’ 具http://www.pobonline.com典 共July 1, 2001兲.
114 / JOURNAL OF SURVEYING ENGINEERING © ASCE / AUGUST 2003You can also read
