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APN-026 Rev 1 October 16, 2001

Geodetic Principles

The purpose of this document is to provide some insight into how certain geodetic

principles relate to your GPS receiver. Here you can find background information

relating to the geoid and ellipsoid, and how they are used to provide you with height

information.

What is the Geoid?

The geoid is a level, or equipotential surface, where the gravity potential is a constant

value. The gravity force vector acts perpendicular to this surface. A good example of a

level surface would be a large body of water where the force of gravity acts on the water

such that a constant surface is formed.

This is where the Mean Sea Level (MSL) height stems from. The surface of the ocean,

after some generalization, can be considered as a good approximation to the geoid.

Geoids are generally formed by way of gravity measurements and intensive computations

to formulate models. These models provide a reference from which heights can be

measured.

What is the Ellipsoid?

The ellipsoid is an approximation to the geoid. It can be derived mathematically and is

generally referred to as a terrestrial reference frame. The World Geodetic System 1984

(WGS-84) is an ellipsoid that all GPS measurements reference.

Position information can be displayed in two standard ways:

1. Curvilinear Coordinates

f - Latitude

l - Longitude

h – Ellipsoidal height

2. Cartesian or Earth Centered Earth Fixed (ECEF) Coordinates

x – Passing trough the Greenwich Meridian

y – Orthogonal to the x axis (left handed)

z – Perpendicular to the (x,y) origin; passing through the pole.

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How do the Ellipsoid and Geoid relate to the GPS receiver?

If you look at the height in the POSA log (OEM3) or a comparable OEM4 log such as

BESTPOSA, you are looking at Mean Sea Level (MSL) heights.

MSL heights are equivalent to the geoid. As mentioned earlier, the geoid is a constant

equipotential surface that has been defined by making gravity measurements all over the

earth.

The height that you are above this surface is known as an Orthometric Height and for our

purposes here we will define it as H. This H value is what we here at NovAtel provide

you with in the POS or BESTPOS logs.

How is the Orthometric Height Computed?

The receiver uses a scaled down version of the OSU89B model. This is mainly to save

space, thus resulting in an undulation value for every 1 x 3 degrees square on the earth.

The formula to use in deriving the ellipsoidal height is:

h = H + N

where

h - is your ellipsoidal height.

H - is your Mean Sea Level height.

N - is your undulation value.

The receiver uses an internal table to solve for H given the ellipsoidal height from the

GPS measurements and the undulation value from the table.

Rearranging the equation and solving for the orthometric height yields:

H = h – N

Please also see the NovAtel application note, The Geoid Issue, APN-006 for further

descriptions of the ellipsoid and geoid, and an illustration.

The undulation N is the separation between the ellipsoid and the geoid.

Examples:

The following data is from an OEM4 using the NovAtel roof top antenna network.

#BESTPOSA,COM2,0,76.5,FINESTEERING,1130,509422.000,00000000,5941,463;

SOL_COMPUTED,SINGLE,

51.11635716377,-114.03824520099, 1064.4853,-16.2713,

WGS84,3.1121,1.6792,4.6832,"",0.000,0.000,9,7,0,0,0,0,0,0*69af7c1c

The field in bold (#7) in the above log is known as the undulation value. The 6

field is

the MSL height computed using the onboard undulation table, therefore to convert this to

an ellipsoidal height:

h = 1064.4853 + (-16.2713)

= 1048.2140 m

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The ellipsoidal height at this location will be 1048.214 meters with respect to WGS84.

The same result can be achieved by using the undulation command. By providing the

receiver with the following command:

undulation user 0.0

This command will set the undulation value to a user defined value of 0.0 m.

#BESTPOSA,COM2,0,76.5,FINESTEERING,1130,511523.000,00000000,5941,463;

SOL_COMPUTED,SINGLE,

51.11635443024,-114.03825201489,1048.1984,0.0000,

WGS84,2.5753,1.5548,4.1891,"",0.000,0.000,11,9,0,0,0,0,0,0*bd2bfd97

h = 1048.1984 + 0.0000

= 1048.1984 m

You can see from the two ellipsoidal height computations that using the undulation

command and setting the value to 0.0 is similar to applying the value to achieve

ellipsoidal heights.

What if I’ve specified a different Datum?

If you have set the datum please note that this command specifically uses WGS84 as a

reference. Therefore you will be unable to apply the

“undulation user 0.0” command

directly. By implying a different datum than WGS84, there is an additional shift applied

to the coordinates that must be accounted for.

Examples:

#BESTPOSA,COM2,0,69.5,FINESTEERING,1131,143809.000,00000000,5941,463;

SOL_COMPUTED,SINGLE,

51.11639536799,-114.03825918769,1059.3276,-16.2713,

WGS84,2.4368,1.4047,6.5109,"",0.000,0.000,12,10,0,0,0,0,0,0*4fe97ef7

Above, in bold, you can see the undulation value and the current datum from the

BESTPOSA log. The ellipsoidal height computation is similar to the previous example.

h = 1059.3276 + (-16.2713)

= 1043.0563 m

The next log is the position determined relative to the TOKYO datum.

#BESTPOSA,COM2,0,70.5,FINESTEERING,1131,143843.000,00000000,5941,463;

SOL_COMPUTED,SINGLE,

51.10935601226,-114.03379188039,1059.2592,409.5439,

TOKYO,2.4387,1.4072,6.5142,"",0.000,0.000,12,10,0,0,0,0,0,0*d381c672

From this it is evident that the MSL height is relatively similar to it’s WGS84 counterpart

when factoring in that the data is from single point measurements. The ellipsoidal height

is as follows:

h = 1059.2592 + (409.5439)

= 1468.8031 m

Due to the fact that the position was computed using the TOKYO datum that is based

upon the Bessel 1841 ellipsoid you can see a much different ellipsoidal height value.

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#BESTPOSA,COM2,0,71.0,FINESTEERING,1131,143866.000,00000000,5941,463;

SOL_COMPUTED,SINGLE,

51.10935710490,-114.03379219486,1042.8560,425.8152,

TOKYO,2.4399,1.4089,6.5155,"",0.000,0.000,12,10,0,0,0,0,0,0*a74582fd

The BESTPOS log shows the result of applying the “undulation user 0.0” command.

When the undulation value is set to 0.0 and a datum other than WGS84 is used, you

cannot achieve ellipsoidal heights as shown in the above example.

In this case N = -16.2713 m at the current location. Setting the undulation to 0.0 removes

the value from the MSL computation thus leaving 1042.8560 m. This does not provide

the correct ellipsoidal height because we are dealing with the TOKYO datum rather than

withWGS84.

How can I get the undulation values for pre- or post-mission

analysis?

If for any reason you require the undulation values that the receiver is applying to the

position logs, you can do the following:

Connect your PC to the card and issue a FIX POSITION command. Enter the latitude,

longitude and height for the general location of the survey.

Log either a POSA (OEM3) or BESTPOSA (OEM4) and retrieve an undulation value.

This does not require that the antenna be set up unless you do not know your general

location. The value is read directly from the table based on the location input to the

receiver.

If you require more precise undulation values then you should refer to an undulation data

table with respect to WGS84. This data will provide an undulation value for the survey

area, which can be applied to the receiver using the UNDULATION command.

Where can I find more precise geoid data?

You can find high precision geoid data from the following sources:

http://www.ngs.noaa.gov/

http://edc.usgs.gov

What does the FIX POSITION command require in terms of

height?

Fixing the position using MSL heights, allows you to enter the latitude, longitude and

height based solely on how well it is known. Therefore the significance of fixing the

position using MSL is that the base station coordinates are generally known from some

method of survey. Whether through conventional survey techniques, or using GPS, the

coordinates of the base station need to be known. In most instances the height is known

with respect to a specific datum.

If you have known coordinates in one of the supported datums all you need to do is set

the appropriate datum and fix the position. Once a datum is specified, the receiver

performs the correct position to WGS84, and vice versa, conversions internally. This

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provides a convenient method of not directly needing to know the undulation value or

converting non-WGS84 coordinates when fixing the position.

What about post-processing?

SoftSurv does not provide orthometric heights and there will be no further development

to implement this in the future, as version 1.52 will be the last revision of the software. If

this is of interest to you please contact Sokkia Corporation or Waypoint Consulting.

Here are a few of the features that their software has that SoftSurv does not:

1. Processed solutions in the forward and reverse directions (potentially giving a

much more accurate solution)

2. Superior ambiguity resolution techniques in both static and kinematic solutions

3. Orthometric heights from geoid tables (these come with the software!)

4. Multi-baseline adjustments in a network (SoftSurv processes each baseline

separately)

If you are looking for a complete Survey/GIS package (i.e. layout, attributes, etc.) we

recommend you contact Sokkia. If however, you are looking for a straight post-

processing package (i.e. log data, process it and plot the course) we recommend

Waypoint.

Sokkia and Waypoint fully support NovAtel data. One click of your mouse will easily

import all of your NovAtel GPS data.

Waypoint Consulting Inc. Sokkia Corporation

Suite 210, Riverbend Atrium One Point Inc.

200 Rivercrest Drive S.E. 8220 Melrose Drive

Calgary, Alberta, Canada Lenexa

T2C 2X5 Kansas 66214 U.S.A.

www.waypnt.com

www.sokkia.com

Final Points

If you require any further information regarding the topics covered within this

application, please contact:

NovAtel GPS Customer Support

1120 68 Avenue N.E.

Calgary, Alberta, Canada

T2E 8S5

email : support@Novatel.ca

Phone: 1.800.NOVATEL ext: 4595 (North America)

403.295.4900 ext: 4595 (International)

Fax: 403.295.4901

http://www.novatel.com/

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