system through the following relation:

at the node points of a regular grid (i.e., a 2' x 2' grid

spacing). Biquadratic interpolation procedures can be

used within a grid cell boundary to approximate the geoid

height at a given geodetic latitude and longitude. The

where,

NGS GEOID96 model for the United States indicates

geoid heights range from a low of -51.6 meters in the

Atlantic to a high of -7.2 meters in the Rocky Mountains.

For more information on geoid modeling, see Milbert

and by convention *N *being a positive height above the

(1996).

ellipsoid.

EARTH SURFACE

A

B

H

h

GEOID

coordinate differences that establish the baseline between

N

two given stations. Baseline solutions produce relative

ELLIPSOID

positioning results at a greater accuracy than can now be

achieved from point positioning. The expected accuracy

H = ORTHOMETRIC HEIGHT

Differencing Technique:

of such ellipsoidal height difference measurements is

N = GEOID HEIGHT

HB = ∆h - ∆N + HA

h = ELLIPSOIDAL HEIGHT

based on several factors such as GPS receiver

h=H+N

manufacture type, observation session duration, and the

measured baseline distance, but it does not depend greatly

on prior knowledge of the absolute vertical position of

either occupied station. Dual frequency, carrier phase

measurement based GPS surveys are usually able to

produce 3-D relative positioning accuracies under 30 mm

at the 95% confidence level over baseline distances less

than 20 km, depending on the type of GPS surveying

which are mathematical surfaces representing the shape

method used. This situation exists mainly because GPS

of the Earth's gravity field. The geoid model is

range biases are physically well correlated over relatively

constructed from a truncated functional series

short distances and tend to cancel out as a result of

approximation using a spherical harmonics expansion

forming double differences for carrier phase data

and an extensive set of globally available gravity data.

processing. In contrast, GPS absolute code positioning

The model is determined from the unique coefficients of

accuracy will contain the full effects of any GPS range

the finite series representing the geoid surface. Its

measurement errors. The method explained below to

accuracy depends on the coverage and accuracy of the

obtain NAVD88 elevations from satellite surveys is

gravity measurements used as boundary conditions.

based on the relative vertical positioning capability of

Former geoid models produced for general use limit

GPS.

absolute accuracies for geoid heights to no less than 1

meter. More recent geoid models have shown a

significant increase in absolute accuracy for geoid heights

vertical position of the geoid with respect to the ellipsoid

to a few centimeters.

between two stations. These relative geoidal heights can

be more accurate than the modeled absolute separation

values within extended areas because the relative geoidal

estimated globally as a function of horizontal coordinates

height accuracy is based on the continuous surface

referenced to a common geocentric position. Specific

characteristics of the geoid model, where only small

geoid height values are extracted from the model surface