rtk elevation accuracy test project report

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Project Report – RTK Elevation Accuracy Test

DWR Standard Agreement No. 4600007950, Task Order No. 4

November, 2011

Figure 1.

Introduction

In September of 2009 the California Department of Water Resources (DWR) contracted with

Frame Surveying & Mapping (FSM) to design a test range, develop an observation plan, and

analyze observation data for testing the elevation accuracies obtainable with dual-frequency GPS

Real Time Kinematic (RTK) equipment. The purpose of the project was to determine the

suitability and cost efficiency of RTK for elevation transfer over medium-range (1 to 10 km)

distances. The area chosen for the test range is in and near the City of Woodland, Yolo County,

California.

Jim Frame

Signed Copy On File

Project Report – RTK Elevation Accuracy Test – DWR Standard Agreement No. 4600007950, Task Order No. 4

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A test range approximately 35 km long (see Figure 1, above) was established in April of 2010

using a combination of existing geodetic control marks and new marks installed specifically for

the RTK test. The test range station list is shown in Appendix A. (Note that test range stations

are generally referenced by their 4-character identifiers throughout this document. Appendix A

features complete station names as well as 4-character identifiers.) The observation plan was

developed shortly after establishment of the test range, but observations were delayed until May

of 2011 in order to accommodate DWR field crew schedules.

Observations comprised geodetic leveling (Second Order Class II) followed by RTK

observations. The leveling was used to establish elevation values for the test range marks against

which the RTK results were compared.

Observation Plan

Observations for the project were divided into two categories: leveling and GPS. The leveling

plan called for Second Order Class II geodetic leveling to be run over all 32 marks in the project.

The BFFB method was chosen by DWR staff in order to reduce field time. Leveling was

performed between May 26 and July 11, 2011 using a Leica NA3003 digital level (S/N 92346)

and 2 each Leica invar barcode rods (S/Ns 25700 and 26483).

Task 9 of Task Order 4 calls for submitting the leveling data to NGS for publication in the

Integrated Data Base (“bluebooking”). However, after leveling operations were completed it

was learned that some of the field procedures did not comply with NGS bluebooking

requirements. The non-compliant procedures were: use of the BFFB observation method,

performing level collimation checks weekly rather than daily, and the use of temporary bench

marks at section ends. Because of this, Task 9 could not be completed. Nevertheless, the

accuracy of the leveling is more than adequate for the analysis of RTK results.

GPS observations were structured so that three base stations were operating simultaneously at

three marks (DUFO, LIBR and OATT) that are evenly distributed along the test range. Three

RTK observers each recorded 8 positions at each visit to a mark, with observation times of 5, 15,

30, 60, 120, 180 and 240 seconds. Upon completing the observation sequence, the RTK

observer moved to the next mark in his assigned section of the range and repeated the sequence.

Upon reaching the end of his assigned section, the observer went back to the beginning of his

section and continued observing.

The following GPS base station receiver/antenna combinations were used in the project:

Trimble R7 (S/N 4811K31795) Trimble Zephyr Geodetic 2 (S/N 30941416)

Trimble R7 GNSS (S/N 4811K31745) Trimble Zephyr Geodetic 2 (S/N 30959980)

Trimble R7 (S/N 4811K37143) Trimble Zephyr Geodetic 2 (S/N 30959966)

Base station antennas were supported by fixed-height poles.


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The RTK receivers, which were used with fixed-height rover poles, were integrated-antenna

models:

Trimble R8 Model 2 (S/N 4819152207)



Trimble R8 (S/N 4602105531)

Trimble 5800 (S/N 4347129359)

GPS observations were conducted on July 13 and 14, 2011. A total of 727 RTK positions were

recorded, with an approximately equal distribution among the 8 observation durations (5, 15, 30,

45, 60, 120, 180 and 240 seconds). Stations near the junctions between base station coverage

sections received more observation sequences (as many as 40) than those toward the ends of the

test range (as few as 14). RTK vector lengths ranged from 840 meters to 8618 meters.

GEOID09 was used in all RTK calculations.

Data Analysis – Leveling

The test range includes six marks that were positioned as part of a 2008 height modernization

campaign (NGS Project No. GPS2516): 0308, 1031, 1075, DUFO, LIBR and X200. The

published NAVD88 heights for these marks were used as seed values in adjusting the leveling

data. Based upon extrapolated subsidence rates for these marks, their published NAVD88

heights were assigned standard errors (in meters) as follows:

Mark Published Elevation Standard Error

0308 23.690 0.040

1031 10.260 0.020

1075 14.890 0.020

DUFO 20.220 0.040

LIBR 19.900 0.030

X200 29.880 0.020

A standard error of 1 mm per km was assigned to the leveling data, and Star*Net Pro v6.0 was

used to accomplish the adjustment. The adjusted elevations and residuals (in meters) at the six

height modernization stations are shown below:

Mark Adjusted Elevation Residual Standard Residual

0308 23.637 -0.053 1.3

1031 10.247 -0.013 0.7

1075 14.912 0.022 1.1

DUFO 20.201 -0.019 0.5

LIBR 19.845 -0.055 1.8

X200 29.913 0.033 1.7

The residuals at LIBR and X200 are higher than expected, but the source of the seed values (GPS

with geoid modeling) and the subsiding nature of the area are assumed to be responsible for this.


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The leveled height differences were allowed to control the mark-to-mark elevation differences

due to the more precise equipment and procedures employed.

As expected due to the geologic makeup of the area, the gravity field was found to be

substantially uniform across the entire test range. Gravity values obtained using the NGS

NAVGRAD online tool run between 980.0204 and 980.0326 gals throughout the test range. As

a result of this consistency, orthometric height corrections were determined to be below the noise

level of the measurements, and were ignored in the adjustment.

Note also that there are no leveled NAVD88 bench marks in the test range. As a result, the

NAVD88 accuracies of the test range marks are not known. This had no effect upon the RTK

testing, since all elevation values in the test are referenced to the test range marks.

Data Analysis – RTK

RTK data files were imported into Trimble Business Center v2.60 for initial processing. Point

merging was disabled during import in order to preserve each recorded RTK position as a unique

observation for analysis.

RTK base stations were located at DUFO, LIBR and OATT. The base station observation data

files (approximately 7 hours of data at each station on each of 2 days) were processed using IGS

precise orbits and NGS relative antenna models. Vectors to OATT from both DUFO and LIBR

were produced, using the published California Coordinate System (CCS83 Zone 2) positions for

LIBR and DUFO as seed coordinates. Those same positions were then constrained in an

adjustment to produce a refined horizontal position for OATT. The adjustment produced a

standard error of unit weight of 3.69. Elevations for the base station marks from the leveling

adjustment were then applied to the base station positions, and all RTK positions were

recomputed to place all GPS observations in the project on the same coordinate basis.

The manufacturer elevation accuracy specification for the RTK equipment used in this test is 20

mm + 1 ppm of vector length root mean square (RMS). The manufacturer does not make any

distinction in elevation accuracy based upon observation time.

Horizontal error was not a focus of this investigation. However, it should be noted that the test

measurements conform to the manufacturer accuracy specification of 10 mm + 1 ppm RMS.

The 727 RTK-derived elevations were compared to the leveled elevations. The primary

variables under investigation are observation time and vector length. Atmospheric effects,

satellite visibility and receiver model are secondary variables.

Satellite visibility was investigated only cursorily. Almost all RTK observations had 7 to 10

satellites in view. Station U849 is located between a road and a railroad that run generally north-

south, with tall eucalyptus trees lining the right-of-way. Some observations at U849 had

compromised constellations.

Differences between receiver model results were not evaluated.


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Cost Efficiency

There is little question that RTK elevation transfer is markedly less expensive than conventional

or trigonometric leveling over the distances under study in this project, as long as accuracy

requirements can be met and equipment acquisition cost is not a factor. Field crew size is

comparable for all three methods, as is time-on-mark. However, RTK confers an enormous

advantage over leveling because the base receiver remains stationary while the rover receiver is

transported directly to the target mark. Leveling processes, both conventional and trigonometric,

require multiple short-distance (generally between 120 m and 300 m) instrument position

spacings, with corresponding intermediate measurement marks, in order to effect elevation

transfer over the desired distance, thus requiring much longer time-to-completion.

Atmospheric Effects

Atmospheric refraction affects the apparent speed of radio signal transmission and constitutes an

error source in GPS positioning. Ionospheric refraction is the largest source of GPS signal delay,

although tropospheric effects can also be a consideration. Dual-frequency GPS provides enough

information to allow the ionospheric delay to be calculated, and the relative consistency of

weather across the Sacramento Valley generally renders tropospheric effects negligible. Still,

this test included observations on two days in order to look for effects of atmospheric conditions

upon elevation accuracy. A comparison between elevation errors seen on the two observation

dates is shown in Figure 2:

July 13, 2011 July 14, 2011

Figure 2. Elevation error (in meters) by observation date/time.


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Although elevation errors on Day 2 (July 14) exhibit a slightly wider range than those of Day 1

(July 13), the difference is not significant.

Note that the errors distributions on both days are centered between 0.01 and 0.02 m, rather than

at zero as would be expected for a random distribution. This offset is assumed to be the effect of

geoid model error, and it can be seen in all of the scatter diagrams in Appendix B, Elevation

Errors as a Function of Vector Length. This error source may be a factor whenever elevation

transfer via RTK is accomplished without benefit of site calibration techniques. (A site

calibration effectively creates a custom geoid model for a project by calculating geoid model

offsets at a group of bench marks surrounding the project and distributing those offsets across the

project area.) Geoid model error can be ignored if a single base station mark is used, relative

elevations within the project area are sufficient for the application, and the effect of geoid slope

is below the measurement noise level within the project area.

Vector Length

Elevation error as a function of vector length for all of the RTK measurements is shown in

Figure 3:

Figure 3.

Figure 3 indicates that vector length alone is not a reliable predictor of elevation error. Some

evidence of the vector-length 1-ppm error appears to be present, though it does not appear in the

8600-meter group.

Somewhat more useful is Figure 4, which shows elevation errors as a function of observation

time for all of the RTK measurements.


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Figure 4.

Elevation errors at observation times of less than 60 seconds exhibit a larger spread than those at

longer times. The error range from observations times of 60 seconds to 240 seconds is

essentially the same at approximately +/- 0.04 m.

More useful yet are histograms showing the distribution of errors at various observation

durations. In these, the x-axis represents error level in meters, and the y-axis represents the

number of errors at each level. The associated mean and standard deviation are shown below

each histogram.

Mean: 0.011 m Standard deviation: 0.022 m


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Observation Time: 180s to 196s

Frequency


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These histograms illustrate that as observation time increases from 5 seconds to 240 seconds, the

standard deviation of the elevation errors decreases from 0.022 m to 0.016 m. However, even at

240 seconds, there are still outliers as large as 0.06 m.

Repeatability

Repeated RTK measurements taken within a short time span often produce elevation values that

are very closely grouped. This is not surprising due to the similarity of the conditions under

which the measurements are taken. Figure 5 shows the frequency of error spreads (the maximum

difference between errors) for repeat measurements taken within the approximate ten-minute

time window of the test measurement sequence.

Figure 5.

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Observation Time: 240s to 294s

Frequency


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In order to test the value of tightly-grouped repeat measurements taken in quick succession,

Figure 6 was compiled to show the frequency of differences between sequence error spread and

the absolute value of the mean error of the spread.

Figure 6. Error spread minus mean error for full 12-minute measurement sequences.

Positive values in Figure 6 represent instances in which the mean error of all measurements in a

sequence is less than the maximum difference between errors (the error spread) of the sequence.

Of the 91 measurement sequences represented in Figure 6, a total of 68 (or 75%) are greater than

zero, indicating that the error spread is greater than the mean of the errors.

While actual errors cannot be known at the time measurements are taken, the spread of the

elevations recorded by the data collector corresponds directly with the spread of the errors. Thus

there is a 75% chance that the elevation spread of a 12-minute measurement sequence as used in

this project will indicate the maximum error to be expected from the sequence.

To better illustrate this concept, consider the following observation sequence taken at REOR

with the base at DUFO:

Duration Elevation Error

(seconds) (meters) (meters)

6 15.572 0.004

16 15.569 0.007

30 15.571 0.005

46 15.574 0.002

60 15.572 0.004

120 15.572 0.004

180 15.573 0.003

240 15.575 0.001

The error spread for this sequence – the largest error minus the smallest error – is 0.006 m. The

elevation spread is also 0.006 m, because these two quantities are always equal. Over the entire

project data set, 75% of the time the mean error of a complete 12-minute measurement sequence


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is equal to or smaller than the elevation spread, and this holds true for the example at hand: the

average of all the errors is 0.004 m. Thus the 0.006 m elevation spread indicates that the error of

the sequence is likely to be less than or equal to 0.006 m.

To further test this concept, a comparison was made using abbreviated sequences that include

only the 5-second, 15-second and 30-second observations. With this data set, the correlation is

not as strong: the elevation spread is greater than the mean error in only 54% of the sample

sequences.

Using only the 30-second, 45-second and 60 second observations, the correlation erodes a bit

further: only 48% of the sample sequences show elevation spreads greater than the mean error.

Using the 120, 180 and 240 second observations, this figure drops to 47%.

A 75% correlation, which requires a 12-minute observation sequence, may be useful in some

applications.

Conclusions

RTK GPS is a valuable tool for elevation transfer over distances in the 1 km to 9 km range, but

its limitations are clear. The conclusions drawn from the analysis of measurements taken in this

project are:

RTK is much more cost-efficient than leveling, as long as accuracy requirements are

attainable and equipment acquisition costs are not a factor. RTK is not a substitute for

high-order geodetic leveling due to its reliance upon geoid modeling, but it is suitable for

many intermediate-range elevation transfer applications.

The manufacturer specification of 20 mm + 1 ppm RMS is upheld by this test, as is the

implied but unstated fact that errors well outside the 20-mm figure can be expected.

The technique is vulnerable to geoid model errors except where site calibration

techniques are feasible.

Observation times shorter than 60 seconds exhibit larger errors than those of 60 seconds

and longer. No clear benefit to observing at 120, 180 or 240 seconds was demonstrated.

In 75% of test samples, the elevation spread of repeat measurements taken over a 12-

minute time span was greater than the error of the mean measured elevation. If a 12-

minute observation sequence is feasible for a project, this metric can assist the observer

in making an on-site decision regarding the acceptability of the elevation solution.

Appendix A -- Station List

STATION 4 Ch-ID LATITUDE LONGITUDE PID LEVELED NOTES

ELEVATION

(METERS)

C 625 C625 38 52 07.6 121 57 21.2 JS2135 16.044 EXISTING

DUFOUR DUFO 38 45 48.1 121 50 39.1 JS2238 20.201 EXISTING SAC VALLEY STATION

DUNN DUNN 38 53 12.3 121 58 16.6 22.171 NEW, DISK IN HEADWALL

FIELD FILD 38 49 37.2 121 54 42.0 13.337 NEW, DISK IN HEADWALL

FRED FRED 38 48 16.0 121 53 17.4 14.706 NEW, DISK IN HEADWALL

G 201 G201 38 42 08.2 121 46 47.3 JS2229 17.551 EXISTING

G 967 X G967 38 44 49.2 121 49 38.3 JS2235 19.783 EXISTING

GRAIN GRAI 38 46 20.3 121 51 14.3 16.678 NEW, FENO MONUMENT

HEADWALL HEAD 38 47 09.5 121 52 06.0 16.795 NEW, DISK IN HEADWALL

HPGN CA 03 08 0308 38 43 02.0 121 48 07.5 JS4668 23.637 EXISTING SAC VALLEY STATION

J 967 X J967 38 45 26.6 121 50 17.7 JS2236 18.998 EXISTING

JACK JACK 38 40 34.6 121 43 39.5 12.393 NEW

JEHOVA JEHO 38 44 07.4 121 48 56.2 21.454 NEW

K 967 X K967 38 46 50.2 121 51 45.0 JS2242 16.114 EXISTING

KATHY KATH 38 52 34.4 121 57 49.2 17.802 NEW, DISK IN HEADWALL

LIBRARY LIBR 38 40 44.2 121 46 28.1 AI5066 19.845 EXISTING SAC VALLEY STATION

M 1075 M107 38 50 00.8 121 55 07.4 JS2125 12.961 EXISTING

M 644 RESET M644 38 41 30.7 121 46 09.2 JS2228 16.258 EXISTING

MORA MORA 38 47 40.4 121 52 39.0 16.090 NEW, DISK IN HEADWALL

N 644 N644 38 42 47 121 47 29 JS2230 21.142 EXISTING

OAT OATT 38 50 30.4 121 55 38.2 16.444 NEW, REPLACES N 1075

P 1031 1031 38 40 38.1 121 42 34.1 JS2344 10.247 EXISTING SAC VALLEY STATION

P 1075 1075 38 50 51.3 121 56 00.3 JS2130 14.912 EXISTING SAC VALLEY STATION

Q 1075 Q107 38 51 52.0 121 57 04.5 JS2134 16.707 EXISTING

REORA REOR 38 48 46.3 121 53 48.2 15.576 NEW, REPLACES ORA RM 2

TRACK TRAK 38 49 10.7 121 54 14.7 13.312 NEW, FENO MONUMENT

U 849 U849 38 53 41.0 121 58 33.7 JS2142 24.009 EXISTING

WL18 WL18 38 40 37.9 121 45 55.9 18.500 CITY OF WOODLAND FENO MARK

WP18 WP18 38 40 37.3 121 44 49.0 14.786 CITY OF WOODLAND FENO MARK

WASH RM 2 WASH 38 51 22.4 121 56 33.0 JS2133 18.779 EXISTING

X 200 RESET X200 38 54 20.7 121 58 59.8 JS2144 29.913 EXISTING SAC VALLEY STATION

YOLO YOLO 38 43 38.0 121 48 22.8 JS2232 26.574 EXISTING

Appendix B

Elevation Errors as a Function of Vector Length

Figure 4. Elevation error by observation time (800-900 meter vectors).


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