The GPS benchmark data set was obtained from a combination of three data sources:

• A synoptic data base retrieval on August 5, 1999, excluding the states of Washington and Oregon
• A newly adjusted, but unofficial, set of Washington FBN/CBN coordinates
• A newly adjusted, but unofficial, set of Oregon FBN/CBN coordinates

The National Geodetic Survey (NGS) has recently completed a major project: establishment of a high accuracy Federal Base Network (FBN), and an associated Cooperative Base Network (CBN), through nationwide measurement of GPS baselines of 1 ppm accuracy or better. The FBN stations are located at a nominal 1x1 degree spacing, are surveyed to 1 ppm accuracy, and are maintained at the expense of NGS. A portion of the FBN is set at a nominal 3x3 degree spacing, and is surveyed to 0.1 ppm accuracy. NGS encourages individual states to establish additional 1 ppm stations at about 15' x 15' spacing. These additional stations are designated CBN. The FBN and CBN stations are often observed in a single cooperative GPS survey, frequently known as a High Accuracy Reference Network (HARN). These surveys are typically performed on a state-by-state basis (Milbert and Milbert 1994, Bodnar 1990). After completion of the individual statewide HARNs, the re-observation of the HARNs was begun. The old GPS data, combined with the new re-observations are being re-adjusted on a state-by-state basis and superceding the old HARN coordinates in the database. As of this documentation, only the state of Wisconsin had the re-obs HARN data loaded in the database. Although the re-obs Washington and Oregon data were used in this data set, they were not yet loaded into the NGS IDB database and should therefore be considered preliminary data.
 

One of the objectives of the FBN/CBN effort is to upgrade the accuracy of the geodetic control within a state. This is done by occupation of existing high order control points, connected by classical, terrestrial measurements, with subsequent readjustment. It is clear that those FBN/CBN points which are on NAVD 88 leveled benchmarks provide a powerful data set for accuracy assessment and improvement of geoid and global geopotential models. Figure 1 displays the locations of 6169 points that are leveled benchmarks with NAVD 88 Helmert orthometric heights, and which have GPS measured ellipsoidal heights in the NAD 83 reference system, and are considered reliably free of GPS or leveling blunders as of August 27, 1999. The irregular distribution illustrates the state-by-state approach to the surveying, and the differing levels of state participation.
 

The original FBN/CBN (HARN) survey effort began with Tennessee in 1990, and fieldwork on the project was completed in Illinois in 1997. Over this period major advances were made in GPS receivers, processing models, vector reduction software, orbit accuracy, and in the GPS constellation itself. In addition, the original surveys were designed to provide accurate horizontal control. Data reduction and analysis procedures focused on horizontal accuracies. Typical observing procedures were (and still are) static, and involved occupation of a point for about 6 hours on two different days (three days for 0.1 ppm). Orbit relaxation was used for the 0.1 ppm coordinates until 1994, when improved orbit accuracies removed the need for that particular process. Meteorological data were not always taken on site. Only toward the end of the original surveys was the influence of antenna phase center variation (Schluper et al. 1994) incorporated into processing software. For these reasons, the original FBN/CBN surveys can not be considered as a homogenous set. And, one must expect a level of error in the GPS ellipsoidal heights greater than that associated with continuously operating GPS receivers.

The re-observation of the 48 CONUS HARN surveys (also known as the FBN Vertical Component, or FBNVC for short) began with Wisconsin in 1997. A greater emphasis was placed on vertical accuracy for the re-observations, and more stringent guidelines for achieving 2 cm (2 sigma) ellipsoid heights (Frakes, 1999) were used. Unfortunately, only the state of Wisconsin had been completely observed, processed, and loaded into the NGS database by August 5, 1999 for use in GEOID99. However, processing of Washington and Oregon data was nearly complete in July 1999, and preliminary coordinates for those two states were used in GEOID99. Caution must be used, therefore, when working in those two states, as the final coordinates may be slightly different than the ones provided to the geoid team.

In addition to the heterogenous character of the FBN/CBN, an additional category of GPS surveys is designated the User Densification Network (UDN). The UDN consists of GPS or conventional horizontal surveys of 10 ppm relative accuracy or better and/or second-order, class II geodetic leveling. These surveys were performed by (or for) national, state, or local governments or other entities, and are deemed as providing significant contribution to the public good. NGS acts as a depository and dissemination point for these data. Since UDN surveys are frequently performed for horizontal control requirements, one can see a wide variation in the ellipsoid height accuracies. Sometimes, UDN height accuracy is very good, due to the shorter line spacing of the survey points. The UDN GPS benchmarks were retrieved due to the information they may provide on fine scale geoid model error. One should note that the character of UDN surveys, plus the issues discussed above regarding the original FBN/CBN surveys, cause the GPS benchmark ellipsoid heights to have heterogenous accuracy.
 

The original high accuracy GPS surveys (1 ppm or better) were processed through either OMNI or PAGE4 reduction software. More recently, the GPS surveys were processed using the PAGES software. These programs do a computational removal of the solid Earth tide, including the permanent part of the solid Earth tide. While solid Earth tide corrections are not required for lower accuracy (10 ppm) GPS surveys, these data are constrained to fit the FBN/CBN. Thus, the GPS ellipsoidal heights are in a tide free system.
 
 

The coordinates of the GPS benchmarks stored in the NGS database are in the NAD 83 datum. While most of the points in that datum are from a horizontal, classical network, the NAD 83 was controlled by VLBI and Doppler data sets, and can be considered three-dimensional. Over the years, as GPS surveys were incorporated into the network, they were connected into the three-dimensional framework. The NAD 83 reference system differs from modern ITRF systems, primarily due to a non-geocentricity. A cooperative effort between NGS and the Canadian geodetic survey have computed (in the summer of 1998) the seven parameter Helmert transformation from NAD 83 to ITRF96(1997.0) with 12 points common to both reference systems. The RMS of fit was 5.8 millimeters (mm) in latitude, 18.3 mm in longitude, and 72.7 mm in height. Previously, the ITRF system for this transformation was identified as ITRF97(1997.0). However, due to a recent adoption of different standard for ITRF97(1997.0), the previously identified ITRF system has been redesignated ITRF96(1997.0). See the web page discussing these changes for further details of the reason for this change in designation.
 

Transformation from NAD 83 to ITRF96(1997.0):

Delta X     -0.9910  +/- 0.0108  m

Delta Y     +1.9072  +/- 0.0101  m

Delta Z     +0.5129  +/- 0.0094  m

Rotation X  -0.02579 +/- 0.00041 arc sec

Rotation Y  -0.00965 +/- 0.00033 arc sec

Rotation Z  -0.01166 +/- 0.00027 arc sec

Scale       -0.00662 +/- 0.00093 ppm        (0.0 scale difference applied)

The transformation above was applied to the set of GPS benchmarks in the NAD 83 reference system to obtain the file of GPS benchmarks in the ITRF96(1997.0) system. All points, whether flagged as outliers or not, were transformed. Note that the transformation has no influence whatsoever on the NAVD 88 orthometric heights.
 
 

The NAVD 88 datum is expressed in Helmert orthometric heights, and was computed in 1991. The network contains over 1 million kilometers (km) of leveling at precisions ranging from 0.7 to 3.0 mm/km, and incorporates corrections for rod scale, temperature, level collimation, astronomic, refraction, and magnetic effects (Zilkoski et al. 1992). For geoid analysis in a local region, leveling can be considered nearly error free. Accuracy assessment of leveling at a national scale is problematic. An interesting result is that shown in Figure 8 of Zilkoski et al. (1992). Two independent leveling data sets, that of Canada and that of the United States, match at the 11 cm level or better at 14 points along the Canadian-U.S. border. While repeatability is not a measure of accuracy, the agreement is remarkable.

The NAVD 88 datum was realized by a single datum point, Father Point/Rimouski, in Quebec, Canada. The strategy and the value of the constraint were based on a number of factors. But, the foremost requirement was to minimize recompilation of national mapping products. Thus, there is no guarantee that the NAVD 88 datum coincides with the normal potential, U₀, defined by the GRS80 system, nor with the level of global mean sea level. Smith and Milbert (1998) estimate that the NAVD 88 vertical datum is 31.1 cm below the current best estimate of the Earth's best-fit global geopotential. More recently, during the production of GEOID99, that estimate was changed to 52 cm. Tests show the vertical datum bias to be nearly constant throughout the conterminous United States.
 

In addition to the general requirement of having an NAVD 88 Helmert height in the conterminous United States, the leveled benchmarks were also selected according to a number of categories:
 

A - Adjusted.

B - Hand Keyed but not Verified.

C - Computed from nearby Bench Marks.

R - Reset.

M - Readjusted due to earth movement.

H - From Horizontal Branch.

P - POSTED - Force Fix to NAVD88.

N - Determined by Single Spur.

O - From Horizontal Branch but Other Agency.

For the categories that were not retrieved: "Posted" benchmarks were withheld from the NAVD 88 general readjustment due to excessive misclosures. After the readjustment, the troublesome survey lines were fit to the network, and the points were flagged. "Determined by single spur" benchmarks are established from only one network point, and are not considered sufficiently reliable for this data set. "From horizontal branch but other agency" benchmarks are short level ties performed by other agencies when conducting horizontal control surveys. Due to issues of data reduction, this category was not retrieved. In addition, control points obtained from standard trigonometric leveling were not considered to be of sufficient accuracy. And, benchmarks established from GPS surveys were not used. While such orthometric heights can be accurate, a data set independent of any underlying geoid model was desired.
 

Note that no retrieval criterion was placed on the accuracy of the leveling surveys for the benchmarks. Instead, the data set format contains codes for the relative accuracy of the orthometric heights. It was felt that, given the high relative accuracy of geodetic leveling, that even lower order leveling could provide valuable checks.
 

The NAVD 88 vertical datum (while subject to a constant offset) should be considered as a tide free system. The leveling reduction program does a complete computational removal of both the direct and indirect components of the Earth tide, including the permanent part, as part of the "astronomic" correction (Balazs and Young 1982).
 

In closing this section one must recall that a Helmert orthometric height is not a true orthometric height. This difference lies in the error in the estimate of the mean value of gravity along the plumb line between the surface and the geoid. The Helmert height is based on a model of an infinite Bouguer plate with a uniform density of 2.67 gm/cm³. Variations in density and topographic relief will cause departures of Helmert heights from true orthometric heights. As a gauge on the influence of rock density variation, Heiskanen and Moritz (1967, pp.169) show a 4 mm error in Helmert height for a point at 1000 m elevation and with a constant 0.1 gm/cm³ surficial density departure from 2.67 gm/cm³. Such error is proportional, so that if one assumes an average density of 2.87 gm/cm³ (e.g., diorite/gabbro combination or an alkaline basalt as found in the Rocky Mountains) distributed as a Bouguer plate with an elevation of 3000 m, then one would obtain a Helmert height error of 2.4 cm. Terrain variations also influence the mean value of gravity along the plumb line. Heiskanen and Moritz (1967, pp.169) quote a comparison of a Niethammer height and a Helmert height for a point at 2504 m elevation in the Alps. The error in estimating the mean gravity (23 mGal) causes a height error of 6 cm. Thus, one can expect a certain level of GPS benchmark/geoid model misclosure in the mountains solely due to the character of Helmert orthometric heights.
 
 

The objective in cleaning the August 5, 1999 GPS/BM data set was to flag those points whose error could not be ascribed to a high resolution geoid height model. The basic approach entails locating misclosures between a point's ellipsoid height, h, orthometric height, H, and geoid height, N, where these heights are expected to obey the theoretical relationship:
 

h = H + N .
 

Since the geoid is formed by integration of gravity data, one can expect geoid error to be correlated over distance. Thus, the appearance of a large (e.g., 20 cm) misclosure in close proximity to a number of small misclosures (e.g., 3 cm) leads one to suspect the GPS or the leveled heights as the probable source. Such outliers are flagged in the data set (see data set formats ), the data record is never deleted.
 

A geoid model was created by applying the NAD 83/ITRF96(1997.0) datum transformation in reverse to the G99SSS geoid height model. The result is a gravimetric geoid model in the NAD 83 system, which is denoted G99S83. This model is used to compute misclosures in the sense of:
 

e = G99S83 geoid height - (NAD 83 ellipsoid height - NAVD 88 orthometric height).
 

In the interest of time, the first step in cleansing the 6341 points in the August 5, 1999 GPS/BM data set was to transfer 188 rejection flags from the 23-July-98 GPS/BM data into the data set of August 5, 1999. While this has the danger of rejecting points that may have been repaired since July 23, 1998, it was not clear that any points had yet been fixed.

The second step was the removal of all Washington and Oregon data (206 total points with 3 bad flags transferred from the 23-July-98 GPS/BM data set) which had come in from the synoptic database retrieval on August 5, 1999, and replacing those data with the new preliminary values, (280 points) provided to the geoid team. This preliminary data set was designated gpsbm99.013 and contained 6415 total points, with 185 bad points flagged.

The third step was removal of obvious blunders. A quick set of residuals in the form of:

e = G99S83 geoid height - (NAD 83 ellipsoid height - NAVD 88 orthometric height).

were made, and residuals exceeding 1 meter (there were 5 such points) were immediately flagged as obvious blunders. This new data set was designated gpsbm99.016 and contained 6415 total points, with 190 bad points flagged.

Once data set gpsbm99.016 was in place, a comprehensive cleansing of the data, point by point, was made. A mean offset of 51.7 cm was computed and removed from the misclosures. This mean offset is considered the estimate in the offset in the NAVD 88 vertical datum (when both are referred to global mean sea level). A fit of a tilted plane to the misclosures indicates the possibility of a 0.14 ppm trend in the North-South direction (azimuth = 327 degrees). The lack of an East-West tilt indicates that there is no strong height dependence in the NAVD 88 datum bias, as heights in the conterminous U.S. have a strong East-West correlation.
 

The simple Gaussian covariance function of Smith and Milbert (1999) (where L = 400 km and C₀ = (0.095)² m²) was modified slightly for GEOID99 to L = 400 km and C₀ = (0.182)² m² and used to predict the expected misclosure by using least-squares collocation with noise (Moritz 1980, p.102-106). The collocation was not used to establish an optimal height conversion or geoid improvement. Rather, collocation was used to model the general trends of the misclosures and easily highlight local departures (outliers) from the trend.
 

The residuals from the collocation fits were examined over a progressively tighter set of tolerances, where a new collocation computation was performed after a given set of outliers were flagged for rejection. The first round of rejections were made with a +/- 12 cm tolerance. And, in a 2nd round, the tolerance was lowered to +/- 10 cm. In no circumstance was a point automatically rejected for exceeding a tolerance. Each large misclosure was graphically displayed to show its relationship to its neighbors in a 1x1 (or 2x2) degree block before a judgement was made. In addition, when outliers were found in mountainous regions, such as the Rocky Mountains or the Appalachians, those points were typically not flagged for rejection. This is due to certain theoretical and computational inaccuracies related to terrain corrections and gravity reductions in the G99SSS geoid model computation. While it is likely that a number of GPS benchmark outliers in the mountains are due to GPS or leveling error, the points are not rejected unless the error source is unequivocal. In addition, an outlier was not rejected if it did not have sufficient neighbors to verify that it was a localized error.
 

After all cleansing was done, 246 GPS benchmark points were flagged for rejection. The final data set was internally designated gpsbm99.022, and contains 6415 points. It is distributed with GPS ellipsoid heights in the NAD 83 reference frame (under the name "gpsbm99.nad83" ) and with GPS ellipsoid heights in the ITRF96(1997.0) reference frame (under the name "gpsbm99.itrf96" ). The misclosures range from a maximum of +/- 4 meters to +/- 12.5 cm. It was found that one could not reliably identify outliers below a 10 cm level, although this varied with the region of the country. The RMS of 6169 collocation residuals, after cleansing, was 4.6 cm. This RMS value was assigned as the random error component in the last round of the collocation with noise computation.
 

Some patterns of outlier rejection were seen, often of a regional character. For example, the GPS benchmark misclosures in South Carolina are remarkably small. This HARN survey was one of the most recent GPS surveys, and was performed with short station spacing. The GPS ellipsoid heights are extremely accurate in this state. In addition, recent, extensive leveling was performed. These data show very small misclosures (2.6 cm RMS), and demonstrate the high accuracy of the geoid model in low elevation areas. However, even mountainous regions don't necessarily have many outliers. As an example, Washington and Oregon had few outliers (2 in WA and 1 in OR). This was attributed to both the new DEM (NGSDEM99) used for the geoid model as well as to the new GPS surveys performed in those states.
 

By contrast, the GPS benchmark misclosures in Florida show systematic patterns of approximately +10 cm and - 10 cm. The misclosures are so prevalent that it is essentially impossible to distinguish points as outliers. Many points share systematic offsets in the ellipsoid heights. These problems are also seen in network adjustments of GPS vectors (which do not involve the geoid or leveled benchmarks). The GPS network in Florida was only the second HARN ever performed. And, the adjusted ellipsoid heights were subject to all the systematic effects discussed at the beginning of this paper. While newer GPS surveys have been performed, they often tie into the old, erroneous control, and propagate these systematic errors.
 

One component of GPS height error of particularly obvious character were state-by-state biases. When comparing G99SSS to the GPS/BM data (after outlier rejection), it is clear that the 0.14 ppm N/S tilt is driven almost completely by a few states whose residuals (even after removal of a national average) average a few decimeters. These states with largest biases and the standard deviation of those biases are:

State            # of points  Average Residual (cm)  StDev about average (cm)

North Dakota         28              +39.3             +/-  6.1 

Oregon              115              +37.9             +/- 16.6

Wisconsin            55              +30.9             +/-  7.6

Washington          165              +30.8             +/- 14.3

Minnesota           606              +30.1             +/-  6.3



New York             59              -28.9             +/-  9.9

Maine                38              -33.1             
+/-  5.7

Rhode Island          1              -37.0             --------

Connecticut           1              -38.0             --------

Vermont             262              -41.3             +/-  6.9

New Hampshire        14              -42.1             +/-  6.0

Massachusetts        15              -48.0             +/-  7.8

It must be repeated that GPS benchmarks were only flagged if the misclosure was clearly due to a GPS or a level network source. Patterns of misclosures can be found, for example, in the Rocky Mountains. But, such misclosures may be due to the geoid model and are retained.
 
 

A brief sketch is now made of geoid and global geopotential tests that have been performed with the growing NGS GPS benchmark data set. This section illustrates the utility of GPS benchmarks in the evaluation and improvement of geoid and global geopotential models.
 

Milbert (1991a) reported one of the first evaluations of the GEOID90 model using data in the Commonwealth of Virginia. Even at this early time of GPS surveying, it was possible to isolate a 13 cm discrepancy at benchmark TOANO 2. This discrepancy was traced to the fact that TOANO 2 was on a local mean sea level datum, and not part of NGVD 29. A portion of that report can be found in Milbert (1992). Some results from one of the first studies of a statewide HARN (Oregon) can be found in Milbert (1991b).
 

Milbert (1995) first used a nationwide GPS benchmark data set for geoid improvement in computing the G9501C geoid model by collocation of 1889 geoid/GPS benchmark misclosures. The empirical covariance function was extremely smooth, having a correlation length of 500 km (and power of (18.5)² cm²). The residual statistics for G9501 had a variance of (6.5)² cm² which dropped to a covariance of (2.6)² cm² for points spaced only 5 km apart. This 6.5 cm figure was an independent measure of the random noise in the GPS ellipsoid heights.
 

Rapp (1997) discusses the problem of computing a geoid undulation from a set of geopotential coefficients, and uses GPS benchmarks to illustrate the need to apply an appropriate correction. This study lead to the computation of the correction coefficients available at the NIMA EGM96 WWW page.
 

The global geopotential model, EGM96 , was computed after the "beta" test of 5 models (Lemoine el al., 1997). Smith and Milbert (1997a) analyzed the beta models with 2497 GPS benchmarks in the conterminous United States. Through analysis of misclosure statistics gathered into elevation cohorts, the X02 and X05 models were found to be best. In addition, commission error was identified in the Northwest United States. When the EGM96 model was released, Smith and Milbert (1997b) found a quasi-periodic error around spherical harmonic degree 40 that was confirmed with GPS benchmarks in Oklahoma. One can also find tests of these models by Bursa, et al. (1997) and Bursa, et al. (1998) using a 1835 point GPS benchmark data set.
 

The experiment in combining GPS benchmarks with a gravimetric geoid by Milbert (1995) led to the development of an operational product, GEOID96, which is described in Milbert and Smith (1996), Milbert and Smith (1997), and Smith and Milbert (1998). This latter study illustrates cases where the GPS benchmarks remove long-wavelength commission error in the underlying gravimetric geoid model, G96SSS , while retaining the high relative accuracy over shorter length scales. Smith and Milbert (ibid) also point out that systematic errors in the GPS or the leveling networks, that extend over long distances (e.g., 400 km), will be absorbed into the geoid in this approach.
 

Numerous studies have been performed of the GEOID96 model, typically using new GPS survey data on benchmarks. One test, by Milbert (1997) explored the GEOID96 model in Ohio. Milbert attempted to develop a local covariance function for geoid improvement, but was hampered by the current distribution and accuracy of the GPS benchmarks in the state. An abridged version of this study is available (Milbert 1998).
 

Although not within the conterminous United States, Smith and Small (1999) used an NGS GPS benchmark data set of 31 points to evaluate the CARIB97 geoid model. They found local leveling errors and inter-island discrepancies caused by use of local mean sea level datums for the islands. They recommend future studies that would incorporate models of permanent ocean dynamic topography.
 
 

The NGS GPS benchmark data set will evolve as the GPS network of the United States continues to grow and improve. The NGS is currently engaged in a new nationwide GPS survey effort for height modernization. The objective of this project is to obtain a set of GPS ellipsoid heights accurate to +/- 2 cm (two-sigma, relative to the CORS network). Associated with this new effort will be the analysis of existing GPS control, and the eventual readjustment of the network in 2002. This project will represent an approximate fivefold increase over the current ellipsoidal height accuracy of the nationwide GPS network. The first rewards of this re-observational effort are seen in the small number of outliers detected in the states of Washington and Oregon during the creation of GEOID99.
 

As the new surveys for height modernization proceed, it will be necessary to make format changes to this file to better characterize vertical accuracy in ellipsoidal and orthometric height. Note that in this document, vertical accuracies relative to the coordinate system origin are not stated. They are only inferred, in a qualitative sense, from various codes in the format. It is anticipated that realistic height accuracies in a network or datum sense will be assigned in the course of analysis of the national spatial reference system. The result will be future data sets that are not only more accurate, but will also have better defined accuracies, and will support more sophisticated statistical analysis.
 
 

This study incorporates the contributions of numerous NGS employees involved in the creation and evaluation of the gravity, NAVD 88, and GPS data sets. Mr. Craig Larrimore wrote the data base retrieval applications for the GPS benchmarks. The National Imagery and Mapping Agency (NIMA, formerly DMA) provided a major portion of the NGS land gravity data, and was instrumental in the creation of various 3" and 30" digital elevation data grids in use today. Special thanks go to Dale Pursell, Kathy Milbert and Gloria Evans, all of NGS, for their speedy processing of the Washington and Oregon GPS data.
 
 

Balazs, E. I, and G. M. Young, 1982: Corrections applied by the National Geodetic Survey to precise leveling observations. NOAA Technical Memorandum NOS NGS 34, June 1982, Information Services Branch, National Geodetic Survey, NOAA, Silver Spring, MD., 12 pp.
 

Bodnar, A.N., 1990: National geodetic reference system statewide upgrade policy. Technical Papers of ACSM-ASPRS Fall Convention, Nov. 5-10, 1990, pp. A71-82.
 

Bursa, M., K. Radej, Z. Sima, S.A. True, and V. Vatrt, 1997: Tests for accuracy of recent geopotential models. IGeS Bulletin N.6, "The Earth Gravity Model EGM96: Testing Procedures at IGeS", International Geoid Service, Milan, 1997, 167-188.
 

Bursa, M., J. Kouba, K. Radej, S.A. True, V. Vatrt, and M. Vojtiskova, 1998: Final report on testing accuracy of geopotential models EGMX01-X05, EGM 96. IGeS Bulletin N.7, International Geoid Service, Milan, 1998, 14-23.
 

Frakes, S., 1999: Surveying the Federal Base Network. ACSM Bulletin, in review.
 

Heiskanen, W.A. and H. Moritz, 1967: Physical Geodesy. W.H. Freeman, San Francisco.
 

Lemoine, F.G., D. E. Smith, L. Kunz, R. Smith, E. C. Pavlis, N. K. Pavlis, S. M. Klosko, D. S. Chinn, M. H. Torrence, R. G. Williamson, C. M. Cox, K. E. Rachlin, Y. M. Wang, S. C. Kenyon, R. Salman, R. Trimmer, R. H. Rapp, and R. S. Nerem, 1997: The development of the NASA GSFC and NIMA joint geopotential model. . In: Gravity, Geoid, and Marine Geodesy, International Association of Geodesy Symposium Vol. 117, Tokyo, Japan, Sept. 30 to October 5, 1996, Edited: J. Segawa, H. Fujimoto, and S. Okubo, Springer-Verlag, Berlin, 461-469.
 

Milbert, D. G., 1991a: An accuracy assessment of the GEOID90 geoid height model for the Commonwealth of Virginia. National Geodetic Survey Report (unnumbered series), June 1991, 52 pp.
 

Milbert, D. G., 1991b: GEOID90: A high-resolution geoid for the United States. Eos, 72(49), pp. 545-554.
 

Milbert, D. G., 1992: GPS and GEOID90 -- The new level rod. GPS World, 3(2), pp. 38-43.
 

Milbert, K.O. and D.G. Milbert, 1994: State readjustments at the National Geodetic Survey. Surv. and Land Info. Sys., 54(4), 219-230.
 

Milbert, D.G., 1995: Improvement of a high resolution geoid height model in the U.S. by GPS height on NAVD88 benchmarks. IGeS Bulletin N.4, "New Geoids in the World", International Geoid Service, Milan, 1995, 13-36.
 

Milbert, D. G. and D. A. Smith, 1996: Converting GPS height into NAVD88 elevation with the GEOID96 geoid height model . Proceedings of the GIS/LIS'96 Annual Conference, Denver, Colorado, November 19-21, pp. 681-692.
 

Milbert, D. G. and D. A. Smith, 1997: Converting GPS height into local elevation: the GEOID96 height model for the United States. Geomatics Info Magazine, 11(9), pp. 60-63.
 

Milbert, D.G., 1997: An accuracy assessment of the GEOID96 geoid height model for the State of Ohio . Unnumbered Report, February 1997, Information Services Branch, National Geodetic Survey, NOAA, Silver Spring, MD., 51pp.
 

Milbert, D.G., 1998: "Documentation for the GPS Benchmark Data Set of 23-July-98", IGeS Bulletin N.8, International Geoid Service, Milan, 1998, 29-42.
 

Rapp, R.H., 1997: Use of potential coefficient models for geoid undulation determinations using a spherical harmonic representation of the height anomaly/geoid undulation difference. Journal of Geodesy, 71(5), 282-289.
 

Schupler, B.R., R.L. Allshouse, and T.A. Clark, 1994: Signal characteristics of GPS user antennas. Navigation, 41(3), 277-295.
 

Smith, D.A. and D.G. Milbert, 1997a: Evaluation of preliminary models of the geopotential in the United States . IGeS Bulletin N.6, "The Earth Gravity Model EGM96: Testing Procedures at IGeS", International Geoid Service, Milan, 1997, 7-32.
 

Smith, D.A., and D.G. Milbert, 1997b: Evaluation of the EGM96 model of the Geopotential in the United States . IGeS Bulletin N.6, "The Earth Gravity Model EGM96: Testing Procedures at IGeS", International Geoid Service, Milan, 1997, 33-46.
 

Smith, D.A. and D.G. Milbert, 1999: The GEOID96 high resolution geoid height model for the United States. Journal of Geodesy, V. 73, No. 5, pp. 219-236.
 
 

Smith, D.A. and H.J. Small, 1999: The CARIB97 high resolution geoid height model for the Caribbean Sea. Journal of Geodesy, V. 73, No. 1, pp. 1-9.
 

Zilkoski, D.B., J.H. Richards, and G.M. Young, 1992: Results of the general adjustment of the North American Vertical Datum of 1988. Surv. and Land Info. Sys., 52(3), 133-149.