GPS-Derived Heights Part 1 Development and Description of NGS Guidelines Detailing heights, height systems, their relationships, and development through.

GPS-Derived Heights Part 1 Development and Description of NGS Guidelines
Detailing heights, height systems, their relationships, and development through the use of the Global Positioning System (GPS). Discussion focuses on the use of NGS GPS-Derived Ellipsoid Heights Guidelines and the development of sample project. Instructor: Curtis L. Smith, Geodesist, National Geodetic Survey I. Heights, Height Systems and Their Relationships Types of Heights NAVD 88 Helmert Orthometric Heights Ellipsoid Heights Geoid Heights Accuracies GPS; Sources of Error II. GPS-Derived Ellipsoid Height Guidelines Guideline Basics Project Development and Station Hierarchy Network Configuration Sample Project Development

2) How are these heights defined and related?
To understand how to achieve GPS-derived orthometric heights at centimeter-level accuracy, three questions must be answered: 1) What types of heights are involved? • Orthometric heights • Ellipsoid heights • Geoid heights 2) How are these heights defined and related? 3) How accurately can these heights be determined? GOAL: Ultimately obtaining GPS derived orthometric heights. Need to understand the three different heights to fully understand GPS derived orthometric heights. Heights & Datums - traditionally orthometric heights meant above sea level. Now we must be aware of factors affecting our understanding and use of level interpretations. You need to be aware of the pitfalls of each height system and potential problems encountered which may not be fully understood when using GPS to determine heights.

Leveled Height Differences
B Topography A C Begin our understanding of orthometric heights. Heights & Datums - traditionally orthometric heights meant above sea level. Now we must be aware of factors affecting our understanding and use of height interpretations. Determining elevation differences through use of conventional leveling procedures. Conventional spirit-leveled height from points A to B and B to C. Differential leveling surveys, being a “piecewise” metric measurement technique, accumulate local height differences (dh).

Level Surfaces and Orthometric Heights
Earth’s Surface WP Level Surfaces P Plumb Line Mean “Geoid” Sea Level WO PO Level surfaces - imagine earth standing still - ocean standing still; no effects such as currents, tides, winds; except for slight undulations created by gravity effects = level surface. Geoid is this level surface relating to today’s mean sea level surface - this does not truly coincide with mean sea level because of the non-averaging effects of currents, tides, water temperatures, salinity, weather, solar/lunar cycle, etc. The geoid is a best fit mean sea level surface. Equipotential surfaces - add or subtract water and level surface changes parallel to previous surface = infinite number of possible level surfaces. Each equipotential surface has one distinct potential quantity along its surface. Point on earth’s surface is the level surface parallel to the geoid achieved by adding or subtracting potential. Lines don’t appear parallel; they are based on the gravity field and are affected by mass pluses and minuses. Geopotential number is the numerical difference between two different equipotential surfaces. W = potential along a level surface. CP = geopotential number at a point. Plumb line (over exaggerated in drawing) - is a curved distance due to effects of direction of gravity- known as deflection of the vertical. Orthometric height is exactly the distance along this curved plumb line between the geoid and point on the earth’s surface. We can make close approximations but to be exact we would need to measure gravity along this line requiring a bored hole which is impractical. Level Surface = Equipotential Surface (W) Ocean Geopotential Number (CP) = WP -WO H (Orthometric Height) = Distance along plumb line (PO to P)

Heights Based on Geopotential Number (C)
Normal Height (NGVD 29) H* = C /   = Average normal gravity along plumb line Dynamic Height (IGLD 55, 85) Hdyn = C / 45 45 = Normal gravity at 45° latitude Orthometric Height H = C / g g = Average gravity along the plumb line Helmert Height (NAVD 88) H = C / (g H0) g = Surface gravity measurement (mgals) Heights based on Geopotential Number - all heights relate to geopotential number but with different components. Normal Height - ( (gamma) = average normal gravity; value determined equal around equator then equal around lines of latitude. NGVD29 did not have very much gravity information known in the U.S. or world; made simple model by latitude. Need accurate gravity data to fill equation for proper determination. H* is not true orthometric height. Dynamic Height - (45 is value of normal gravity determined at 45E latitude. Designed for use by IGLD55, 85 International Great Lakes Datum. Orthometric Height - g average gravity along plumb line; definition is true but impractical to obtain - measurements obtained through bored hole with gravity meter due to layer changes. Helmert Height - g is surface gravity measurement; provides very close approximation of height above geoid and a model with 3 cm differences (better than previous 2 m model) - achievable - practical. Helmert - Geodesist 1860's - designed formula based upon a surface gravity measurement which provides an assumption of the density of underlying rock. The average interpretation of rock density is good across most of the U.S. and provides value in equation used in iterative determination of H NAVD88.

Leveled Height vs. Orthometric Height
 h = local leveled differences H = relative orthometric heights Equipotential Surfaces B Topography  hAB =  hBC A C HA HC HAC  hAB + hBC Reference Surface (Geoid) Combining what we’ve discussed. For illustration, let’s assume the same equipotential (level) surface runs through points A and C. As discussed, there are an infinite number of level surfaces; another illustrated through point B. Conventional spirit-leveled height from points A to B and B to C. Differential leveling surveys, being a “piecewise” metric measurement technique, accumulate local height differences (dh). Leveled height difference from point A to B equals the leveled height difference from point B to C; (dhAB) = (dhBC). The sum of these leveled differences is not, however, equal to the difference in orthometric height (dH) between two bench marks A and C. This is due to the non-parallelism of level surfaces (dHAC)  (dhAB) + (dhBC). The difference between leveled height (dhAC) and relative orthometric height (dHAC) is orthometric correction. The difference is usually greater in mountainous regions where level surfaces exhibit much greater local warping due to more pronounced changes in local gravity. The orthometric height is determined by the distance along the plumb line from the reference surface (Geoid) to the point. Observed difference in orthometric height, H, depends on the leveling route.

Global Positioning System
27 Satellites 6 Planes, 55° Rotation 4/5 Satellites /Plane 20,183 km Orbit 1 Revolution /12 Hrs This illustration depicts the relationship of the earth with the space based GPS. Let’s explore using GPS to derive heights at the 2 to 5 cm level of accuracy from interpreting information from satellite signals originating 20,183 km (12,500 miles) in space.

Zero Meridian Mean Equatorial Plane
-X -Y Y X GPS Coordinate System - works with X, Y, Z coordinate frame based on center of mass Earth-Centered-Earth-Fixed (ECEF) coordinate system; changed into ellipsoidal latitude, longitude, and height through transformation. Cartesian Coordinate System. Mean Equatorial Plane -Z

Earth-Centered-Earth-Fixed Coordinates
Conventional Z Axis Terrestrial Pole P (X,Y,Z) Earth’s Surface Zero Meridian Z Origin (0,0,0) Y Axis Center of Mass X Point on the Earth’s surface positionally defined with an X, Y, Z coordinate. The distance along the Z axis is not a height. Height information is not apparent in this system. Y X Axis Mean Equatorial Plane

The Ellipsoid a = Semi major axis N b = Semi minor axis
f = a-b = Flattening a b a Ellipsoid - a smooth mathematical surface which resembles a squashed sphere that is used to represent the earth’s surface. NAD83 or WGS84 - need to know defined datum in software. The point remains the same; identify and work with reference ellipsoid. Defining parameters for the size and shape of these two ellipsoids are equal at the equator and mm difference at the poles. The definition of the origin is the noticeable difference. The origin for NAD83 is defined at a point known to be 1 to 2 meters from the center of mass. The origin for WGS84 moves with updated information; currently about 5 cm relative to ITRF94. This latest change taking place in late 1996 or early 1997. There are no WGS84 coordinates because of the changes in its reference origin. Surveys must always be traceable and consistent. Geodetic Reference System 1980 S a = 6,378, meters (semi-major axis) b = 6,356, m (semi-minor axis) 1/f = (flattening)

GPS - Derived Ellipsoid Heights
Z Axis P (X,Y,Z) = P (,,h) h Earth’s Surface Zero Meridian Reference Ellipsoid Y Axis  Curvilinear Coordinate System Same point on Earth’s surface positionally defined by latitude, longitude and ellipsoid height. Ellipsoid height is the height of the point relative to the reference ellipsoid surface. Same point can be positionally defined as and X, Y, Z or latitude, longitude, ellipsoid height.  X Axis Mean Equatorial Plane

Ellipsoid, Geoid, and Orthometric Heights “h = H + N”
Earth’s Surface P Ellipsoid Plumb Line h Q Mean N Sea “Geoid” Level PO Ocean Relationship of the mathematical ellipsoid surface with the previously developed diagram of level surfaces and orthometric heights. There is no relationship between the ellipsoid and the gravity field. It has nothing to do with level surfaces and its surface cuts through all level surfaces; not parallel. GPS heights are not related with the geoid - no relation to gravity field; required model to obtain differences between the geoid and ellipsoid to determine orthometric height. Ellipsoid is above the geoid in the U.S. - why its drawn this way; geoid always negative. Geoid height (separation, undulation) - difference between the geoid and ellipsoid at any given point on the earth’s surface. H = orthometric height, h = ellipsoid height, and N = geoid height. h=H+N - accurate to mm as long as all the components are known. h (Ellipsoid Height) = Distance along ellipsoid normal (Q to P) N (Geoid Height) = Distance along ellipsoid normal (Q to PO) H (Orthometric Height) = Distance along plumb line (PO to P)

Ellipsoid Heights (NAD 83 vs. ITRF 97)
NAD 83: Origin and ellipsoid (GRS-80) a = 6,378, meters (semi-major axis) 1/f = (flattening) ITRF 97: Origin (best estimate of earth’s C.O.M.) NAD 83 is non-geocentric relative to ITRF97 origin by meters ITRF 97 ellipsoid heights: Use a NAD 83 shaped ellipsoid centered at the ITRF97 origin Ellipsoid height differences between NAD 83 and ITRF97 reflect the non-geocentricity of NAD 83 Ellipsoid heights NAD83 vs. ITRF97 - Defined origins are best estimate of the center of mass; NAD83 is not geocentric. Move origin; move ellipsoid surface by scale on map in meters. ITRF (International Terrestrial Reference Frame) just has an origin; take NAD83 shaped ellipsoid centered at the ITRF origin to derive ITRF97 ellipsoid heights. Ellipsoid height differences reflect the non-geocentricity of NAD83.

Simplified Concept of ITRF 97 vs. NAD 83
h83 h97 Earth’s Surface ITRF 97 ITRF (International Terrestrial Reference Frame) just has an origin; take NAD83 shaped ellipsoid centered at the ITRF origin to derive ITRF97 ellipsoid heights. Ellipsoid heights NAD83 vs. ITRF97 - Defined origins are best estimate of the center of mass; NAD83 is not geocentric. Move origin; move ellipsoid surface as illustrated. Ellipsoid height differences reflect the non-geocentricity of NAD83. Origin 2.2 meters NAD 83 Identically shaped ellipsoids (GRS-80) a = 6,378, meters (semi-major axis) 1/f = (flattening) Origin

NAD83(86) to ITRF97(97) Ellipsoid Heights (meters)
Looking down on offset between ITRF97 and NAD83 ellipsoid heights. Note smooth curved contours as ellipsoidal surfaces move apart. ITRF (International Terrestrial Reference Frame) just has an origin; take NAD83 shaped ellipsoid centered at the ITRF origin to derive ITRF97 ellipsoid heights. Ellipsoid heights NAD83 vs. ITRF97 - Defined origins are best estimate of the center of mass; NAD83 is not geocentric. Move origin; move ellipsoid surface as indicated by scale shown on map. Ellipsoid height differences reflect the non-geocentricity of NAD83.

High Resolution Geoid Models
G96SSS 1.8 million gravity measurements (marine, land, altimetry) 30 second DTED updated with Canadian Rockies data Earth Gravity Model of 1996 (EGM96) 2 min x 2 min spacing International Terrestrial Reference Frame ITRF94 (1996.0) GEOID96 Begin with G96SSS model 2951 GPS/Level Bench Marks (NAD83/NAVD88) Converts NAD83 (86) into NAVD 88 Relative to non-geocentric GRS-80 ellipsoid GEOID90 to GEOID93 to GEOID96 - grid to interpolate in model becomes smaller and smaller to 2 arc minutes. OSU91A was previous Ohio State University model of 1991 before EGM96. Creating the geoid translation surface - use of gravity measurements, equations and translation techniques to define a best fit model for North America. Geoid96 - built to supply components in required in equation N96 = h83 - H88. Model – we know it’s not perfect but can work with it; NAD83 has the wrong origin, NAVD88 biased - Father Point, Rimouski has the wrong 0 height. Slide to illustrate differences/improvements between Geoid96 and Geoid99.

High Resolution Geoid Models G99SSS (Scientific Model)
2.6 million terrestrial, ship, and altimetric gravity measurements 30 arc second Digital Elevation Data 3 arc second DEM for the Northwest USA Decimated from 1 arc second NGSDEM99 Earth Gravity Model of 1996 (EGM96) Computed on 1 x 1 arc minute grid spacing GRS-80 ellipsoid centered at ITRF97 origin G99SSS (scientific model) - determined from 2.6 million gravity measurements taken over the last century and stored in NGS database. Major improvements over previous models; more data. 30 arc second, 1 km x 1 km, grid of digital elevation data; with updated Canadian Rockies data from G96SSS. 3 arc second digital elevation model from satellite imagery for the northwestern portion of U.S. which has history of poor geoid interpretation. EGM96 (Earth Gravity Model of 1996) developed by National Imaging and Mapping Agency (NIMA) - global model of gravity and geoid undulations; good in large areas but not as good for smaller areas. 1-D dimensional spherical Stokes’ FFT (Fast Forward Transformation) - “remove-compute-restore” (fix and put back into model - iterative process). Final outcome is the 1 x 1 arc minute spacing interpolation of the geoid model; 2' x 2' in Alaska. 1 arc minute equals about 1.8 km on ground. ITRF97 (1997.0) COM (Center Of Mass) based origin for model.

Satellite derived digital elevation model for the Northwest U.S.
Improvements such as this will enhance future iterations of the geoid model. NGSDEM99 is a 1 x 1 arc-second Digital Elevation Model (DEM) of the Northwest United States, covering the region N latitude, and E longitude.

High Resolution Geoid Models GEOID99
Begin with G99SSS model 6169 NAD83 GPS heights on NAVD88 leveled benchmarks Determine national bias and trend relative to GPS/BMs Create grid to model local (state-wide) remaining differences ITRF97/NAD83 transformation Compute and remove conversion surface from G99SSS Relative to non-geocentric GRS-80 ellipsoid 4.6 cm RMS nationally when compared to BM data RMS 16% improvement over GEOID96 GEOID99 - best model for North America; not as true interpretation of the geoid but includes errors to establish best orthometric heights. G99SSS + GPS/levels augmentation = GEOID99 6169 GPS/levels bench marks (NAD83/NAVD88); more to be included to further improve future models. GPS/BM constrained to help model reflect NAVD88 orthometric heights then unconstrained for final model. NAD83 non-COM - model warped to reflect NAD83 (86) non-COM origin. 4.6 cm RMS ( 9.2 cm absolute geoid height) when comparing to bench mark data.

Plot of 6169 GPS/levels bench marks used in Geoid99 model; overrides gravity information by computing model relative to GPS/NAVD88 bench marks. NAVD88 to Geoid99 - comparisons between level surfaces; 31 cm NAVD88 bias is consistent around U.S. reflecting the difference determined at Father Point, Rimouski. This shows that the error at any given point is fairly relative to the error at another point.

GEOID99 GEOID99 is a refined model of the geoid in the United states, which supersedes the previous models GEOID90, GEOID93, and GEOID96. For the conterminous United States (CONUS), GEOID99 heights range from a low of –50.97 meters (magenta) in the Atlantic Ocean to a high of 2.23 meters (red) in the Labrador Strait. However, these geoid heights are only reliable within CONUS due to the limited extents of the data used to compute it. GEOID99 models are also available for Alaska, Hawaii, and Puerto Rico and the U.S. Virgin Islands. For the conterminous United States (CONUS), GEOID99 heights range from a low of meters (magenta) in the Atlantic Ocean to a high of 3.23 meters (red) in the Labrador Strait.

Tidal Datums Heights Measured Above Local Mean Sea Level
National Tidal Datum epoch; 19 year series Encompasses all significant tidal periods including 18.6 year period for regression of Moon’s nodes Averages out nearly all meteorological, hydrological, and oceanographic variability Leveling is used to determine relationship between bench marks and tidal gauges Sea level heights - we want heights relative to mean sea level to equal that of the geoid but we cannot achieve this goal; always differences between levels and local mean sea level.. National Tidal Datum epoch - 19 year period of averaging phases such as lower low water almost eliminates effects within ocean caused by lunar phases, meteorological, hydrological, and oceanographic variability.

Chart illustrating relationship of tidal information, vertical datums, and bench marks.

Importance of Shoreline
AL, AK, CA, CT, FL, GA, LA, MD, MS, NJ, NY, NC, OR, RI, SC, WA Territorial Seas Privately Owned Uplands State Owned Tidelands Contiguous Zone Exclusive Economic Zone State Submerged Lands Federal Submerged Lands 3 n. mi. High Seas 12 n. mi. MHHW 200 n. mi. MHW State define boundaries by statute which varies around the United States. Changes in sea level will affect these boundaries. MLLW Chart Datum Privately Owned State Owned Privately Owned State Owned TX DE, MA, ME, NH, PA, VA

NAVD 88 minus LMSL (1960-1978) (units = cm)
Note differences along coasts and that there is a slope to LMSL (local mean sea level).

National Geodetic Vertical Datum 1929 (NGVD 29)
Defined by heights of 26 tidal stations in U.S. and Canada Tide gages were connected to the network by leveling from tide gage staffs to bench marks Water-level transfers used to connect leveling across Great Lakes Normal Orthometric Heights: H* = C /  C = model (“normal”) geopotential number  = from normal gravity formula H* = 0 level is NOT a level surface Vertical Datums - heights relative to defined datum. NGVD height (mean sea level) - not true level surface due to inherent problems; normal heights (averaged gravity). NGVD29 “warped” to fit 26 tide gages; disparity between Pacific and Atlantic Oceans, mean sea level … geoid. Individual tide gages are not the same; affected by sea surface topography due to currents, salinity, temperature, weather patterns, etc.; USC&GS forced heights to tide gages creating biases; knew bad but presented a fair approximation. Normal heights + bias … level surface.

First-Order Leveling Network NGVD 29
Levels and tide station connections included in NGVD29.

North American Vertical Datum 1988 (NAVD 88)
Defined by one height (Father Point/Rimouski) Water-level transfers connect leveling across Great Lakes Adjustment performed in Geopotential Numbers Helmert Orthometric Heights: H = C / (g H0) C = geopotential number g = surface gravity measurement (mgals) H0 = approximate orthometric height (km) H = 0 level is nearly a level surface H = 0 level is biased relative to global mean sea level NAVD height - took the opportunity to produce a close approximation to a level surface within ± 3 cm; only one bias introduced; defining the 0 height at Father Point, Rimouski, Quebec, Canada. Problems - height based on Father Point, Rimouski - minimizes changes to USGS maps but adds about 30 cm error relative to global mean sea level at Father Point, Rimouski. Utilizes good gravimetric coverage of the U.S.

Vertical Control Network NAVD 88
Levels and only the one connection to tide gage included in NAVD88.

NGVD 29 Versus NAVD 88 (normal gravity) (observed gravity)
Datum Considerations: NGVD NAVD 88 Defining Height(s) Local MSL Local MSL Tidal Epoch Various (18.6 years) Treatment of Leveling Data: Gravity Correction Ortho Correction Geopotential Nos. (normal gravity) (observed gravity) Other Corrections Level, Rod, Temp Level, Rod, Astro, Temp, Magnetic, and Refraction Differences between NGVD29 and NAVD88 - summation of defining characteristics. Basis for defining heights; biases and tidal epochs used, treatment of data, adjustment considerations, adjustment statistics, and published information.

NGVD 29 Versus NAVD 88 (continued)
Adjustments Considerations: NGVD NAVD 88 Method Least-squares Least-squares Technique Condition Eq. Observation Eq. Units of Measure Meters Geopotential Units Observation Type Links Between Height Differences Junction Points Between Adjacent BMs Differences between NGVD29 and NAVD88 - summation of defining characteristics.

NGVD 29 Versus NAVD 88 (continued)
Adjustments Statistics : NGVD NAVD 88 No. of Bench Marks ,000 (est) ,000 (US only) Km of Leveling Data ,159 (US) ,001,500 31,565 (Canada) Published Information: Orthometric Height Type Normal Helmert Orthometric Height Units Meters Meters Gravity Value Normal “Actual” Differences between NGVD29 and NAVD88 - summation of defining characteristics.

Height Differences Between NAVD 88 and NGVD 29
Area contour map - note areas of extreme and moderate changes between datums. If you check in to NGVD29 and not NAVD88 - need to apply orthometric correction to level heights in that area. LEVEL_DH program provides a means to remove orthometric corrections to level differences between adjacent bench marks. These corrections don’t allow direct comparisons between optically derived differences and those published.

National color map - differences between NGVD29 and NAVD88 datums
Portrays general east - west tilt; rugged areas indicate major changes whereas smooth are minor changes. 2 & 3 cm level differences over steep gradients.

Expected Accuracies GPS-Derived Ellipsoid Heights
2 centimeters Geoid Heights (GEOID99) 2.5 cm correlated error (randomizing at 40 km) Relative differences typically less than 1 cm in 10 km 4.6 cm RMS about the mean Leveling-Derived Heights Less than 1 cm in 10 km for third-order leveling Following developed guidelines, NOS NGS-58, produce ellipsoid heights to 2 cm. Latest geoid model produces relative differences typically less than 1 cm in 10 km. Inherent error sources in running levels produces 1 cm uncertainty in 10 km for Third Order leveling.

GPS-Derived Ellipsoid Height Guidelines
GPS related error sources Pilot projects were used to develop guidelines NOAA Technical Memorandum NOS NGS-58 Developing Guidelines - GPS positions and derived heights studied and analyzed at NGS since 1983; Guidelines developed from these studies that when followed will derive desired results. Following what is written down, can we guarantee the results? NAVD88 helped improve height models. General improvements in GPS; equipment, satellite availability, data processors, etc. only natural to look into improving GPS derived heights. Develop procedures to reduce or eliminate systematic errors & blunders. Analysis of errors compiled by Dennis Milbert; dug into data that provided problems for repeatability.

Execution of Surveys; Sources of Error
Errors may be characterized as random, systematic, or blunders Random error represents the effect of unpredictable variations in the instruments, the environment, and the observing procedures employed Systematic error represents the effect of consistent inaccuracies in the instruments or in the observing procedures Blunders or mistakes are typically caused by carelessness and are detected by systematic checking of all work through observational procedures and methodology designed to allow their detection and elimination As with any form of surveying you need to identify potential error sources then develop guidelines and procedures to detect, reduce, or eliminate error sources.

GPS Error Sources Precise or broadcast orbit error Multipath
Satellite relationship center-of-mass to L1 antenna phase center Satellite clock error (nominal) SA dither (minimized) Satellite inter-channel bias L1-L2 antenna phase center offset Transmission multipath Ionospheric effects Tropospheric effects Dry (hydrostatic) troposphere delay Wet troposphere delay Multipath Antenna phase center variation Circular polarization L1-L2 phase center offset Receiver clock offset Receiver inter-channel bias Height of phase center above mark Marker stability Earth tides - direct effect Ocean tide loading Atmospheric loading Crustal motion Develop procedures to reduce or eliminate systematic errors & blunders. Analysis of GPS error sources compiled by Dennis Milbert; dug into data that provided problems for repeatability. Precise orbits - maybe not much different compared to broadcast orbits but could be great - based on known Stations - compute satellites position from them instead of vice versa IGS orbits - combination of orbits from various sources - NGS is one supplier typically with a 7 day turn-around; possible “rapid orbits” maybe good, available 1 day for special purposes. Positioning is time dependent - since early times ships needed accurate clocks to navigate. GPS is all time - timing is the key issue. Improve chances for success by developing guidelines to reduce variables. This is from the list compiled by Dennis Milbert; atmospheric effects, multipath and HI discussed in detail later.

Removal of selective availability on May 2, 2000.

Plots illustrating the removal of selective availability in the horizontal component, epoch by epoch. The images compare the accuracy of GPS with and without selective availability (SA). Each plot shows the positional scatter of 24 hours of data (0000 to 2359 UTC) taken at one of the Continuously Operating Reference Stations (CORS) operated by the NCAD Corp. at Erlanger, Kentucky. On May 2, 2000, SA was set to zero. The plots show that SA causes 95% of the points to fall within a radius of 45.0 meters. Without SA, 95% of the points fall within a radius of meters. As illustration, consider a football stadium. With SA activated, you really only know if you are on the field or in the stands at that football stadium; with SA switched off, you know which yard marker you are standing on.

Plots illustrating the removal of selective availability in the vertical component, epoch by epoch.
Dramatic improvement in the vertical component but still produces heights typically two to three times as uncertain as horizontal positions.

Atmospheric Error Sources
Ionosphere Greatest at 1400 (local time) Typical 5 to 15 m at zenith Extreme 0.15 to 50 m at zenith Higher frequencies have less effect Error correction by dual frequency “Wet” Troposphere 10% of total effect Model accuracy only 10 to 50% Need humidity along path About 20 cm at zenith Hydrostatic (“Dry”) Troposphere 90% of total effect Model accuracy only 2 to 5% Need surface atmospheric pressure and temperatures Accurate pressure is critical About 2.2 m at zenith Ionospheric effects - can produce major height problems; eliminate, reduce, identify errors LI/L2 differences - Iono free solution, combined L3 - removes effects caused by ionosphere. Most other errors created by ionospheric conditions are taken out in processing software. Most Ionospheric models work about the same above 15E; below 15 E is where the models differ. Wet troposphere - difficult to model out; how wet is wet? Nice weather; good results - bad weather; not so good results; 2-5 cm uncertainty; also affects multipath. Dry troposphere - can be modeled fairly well; required for long lines, different conditions, large height changes over short baselines. Can change heights by 3 to 7 cm through modeling. Be accurate in recording and applying weather data.

Signal Multipath Satellite signal arriving at receiver via multiple paths due to reflection (Leick 1995) Quasi-periodic signal; 5 to 50 minutes Maximum multipath is a fraction of wavelength (L1 = 19 cm; L2 = 24 cm) typically 2 cm to 5 cm Geometric relationship between satellite, antenna, and surroundings Same pattern in same satellite geometry on consecutive days produces similar results; similar effects Multipath - unpredictable; reflection of signals, time sent, time received (dithering). Detect and remove - software, choke ring antennas, etc. Runs up pole; does not average out; not able to eliminate through models as conditions change for every setup. Quasi-period affecting signal effects heights; different HI different quasi-period, won’t cancel. Maximum multipath is a fraction of the satellite signal’s wavelength. Similar patterns; due to geometry, etc., is not seen; you get great repeatability. Reduce unknowns; different times and days. Phase center - electronic point at which position is determined; moves per elevation of signal. Use similar antenna types fixed height poles; multipath due to setup and equipment tends to cancel. Models used to eliminate effects of multipath but cannot remove all variables. Algorithms in processing software recognize and remove some effects of multipath but at present not all; short baselines help identify effects because the ionosphere is not a factor. Effects of Multipath are site dependent. Wet weather typically increases the effects of multipath.

h ø ø Figure 1 Multipath Description
Multipath Delay : (meters) T = 2hSinø c Multipath Freq. : (Cycles/hr) d(T )ƒ~ hCosø dt  h d ø ~ 2 rad. dt hr. Signal received from satellite by the most direct route, shortest path is the signal we want. “Ghosting” is created by delayed signal bouncing from objects. ø ø Figure 1 Multipath Description August Ionospheric refraction and Multipath Effects in GPS Carrier Phase Observations Yola Georgiadou and Alfred Kleusberg IUGG XIX General Assembly Meeting, Vancouver, Canada

Equipment Requirements
Dual-frequency, full-wavelength GPS receivers Required for all observations greater than 10 km Preferred type for ALL observations regardless of length Geodetic quality antennas with ground planes Choke ring antennas; highly recommended Successfully modeled L1/L2 offsets and phase patterns Use identical antenna types if possible Corrections must be utilized by processing software when mixing antenna types Different receiver types and models - Trimble, Ashtech, Leica, Novatel, Allen Osborne, Topcon, Javad, etc.; full and half phase L1/L2 signal coding. Dual frequency correction - two different frequencies; remove iono effects - iono free solution, L1/L2 solution, L3 combined L1/L2 solution. Antenna phase center variation - there were error sources in conventional leveling - now there are problems in GPS. Using same antenna types tends to cancel some of the influences by antenna on satellite signal. Mixing antenna types could introduce up to 10 cm uncertainty in height component. Signal coming down from satellite at varying elevations and azimuths; defined phase center moves up and down relative to direction of the incoming signal. 2 to 10 km separation between stations produce similar reception angle of satellite signal received at antennas and effects tend to cancel; 20 to 50 km reception angle is different and doesn’t tend to cancel.

Different Phase Patterns Antenna Type A Antenna Type B
SV 20 SV 20 SV 14 SV 14 Different Phase Patterns Note that SV elevation and varying phase patterns affect signal interpretation differently Antenna Type A Antenna Type B Example of different electronic phase patterns of different antenna types and how each interprets the satellite signal as a function of azimuth and elevation. Mixing antenna types could introduce up to 10 cm uncertainty in height component. Signal coming down from satellite at varying elevations and azimuths; defined phase center moves up and down relative to direction of the incoming signal. Azimuth is not as large an influence as elevation on the signal.

Analyses of Data from Pilot Projects
Northridge Earthquake Project 1994 GPS on leveling-derived bench marks Two 3-hour sessions On different days Different times of day Provided 2 cm results for short lines, i.e. 5 to 10 km Detailed analysis of data in specific GPS projects - developed to provide GPS derived heights; provide a definitive answer and available data to experiment with. Northridge Earthquake GPS Leveling Project leveling over large project areas is too expensive; GPS is the future. No guidelines at this time. General idea for project; generate a “good” GPS base network that can be monitored for changes - overkill but it will work. Concentrate leveling in areas of change. Compare with conventional leveling.

Northridge Earthquake Project
Pearblossom Santa Paula Palos Verdes Tidal B Norwalk Los Angles Castaic Short baselines, typically 5 to 10 km; 3 hour observations on 2 different days, different geometries; provided 2 cm results. Knew we would because we were collecting more data than necessary. Compared GPS derived heights with conventional leveling for check - good comparisons! Repeat baselines worked at Northridge.

Harris-Galveston Coastal Subsidence District’s CORS and PAMs 7 stations in a 25 km radius collecting data 24 hours a day for 2+ years Various length baselines 24, 6, 3, 2 and 1 hour solutions 20 minute to epoch-by-epoch solutions Real-life influences due to multipath, atmosphere, and satellite geometry Harris -Galveston Coastal Subsidence District - drastic subsidence created by pumping water; monitor, keep in check. NW Houston 5 cm per year subsidence area, SE Houston stopped subsidence due to stop pumping ground water, strictly enforced, use surface water only - storm surge was inundating coastal zone. Before long all Houston area will be forced to use only surface water. How to monitor and determine problem areas - extensometers to measure subsidence, extend below water table and embedded into stable strata long permanent pipe about 2000 feet deep; ground subsides around pipe, occasionally cut pipe due to enclosure building lowering around stable pipe; cost $500,000 to $750,000 each, immovable, expensive to install. CORS - Lake Houston controls; coast guard CORS in area is subsiding. Heights nationally are improved by CORS and HARN; then locally by local groups.

Harris-Galveston Coastal Subsidence District
P P1 P2 P3 P4 CORS PAM GPS Site ADDICKS NORTHEAST Edna LaGrange Riverside LAKE HOUSTON Network - 80 stations 8 min sessions 7 times in 24 hours - sample to remove systematic effects - like sampling circle on theodolite 16 positions for 1st, 8 for 2nd. Various base lengths - various times - important guidelines to get results 95%; not sometimes it works others not. Local users don’t see global picture. This works for me but they don’t realize this may not work elsewhere. Many users projects typically don’t include enough redundancy for analysis of true elevation – This analysis provides improved understanding of the determined heights in the project and can be given to the client at the 95% confidence level.

Port-a-Measure PAM PAMs (Port-A-Measures) - cheap to build, mobile, self-contained; solar powered, batteries, receiver, computer, modem, system turns itself on - computer uses cell phone calls and downloads data. 1 week at each site.

Std. Dev. (0.91 cm) CORS - LAKE HOUSTON to NORTHEAST – 24 hour data sets, “hands off”; automatic processing, editing only to obtain solution. Could “hand” process and get some outliers down to 2 cm.

24 - Hour Solutions Day Day Day Day Day Mean = -3.1 Day 302  = 0.5 Day 300 Mean = -7.5 Hands on processing for daily comparisons < 1 cm spread from truth over the 5 days selected. Truth derived from multiple 24 hour observations. Some multipath problems, but typically combined problems, averaging out in final position; tropospheric effects, big changes and continual problem in the Houston area. Typical outliers probably due to atmospheric conditions; showed high RMS, should be below 1.5 cm over short lines. Not bad data; abnormal conditions. About 6 cm spread using 6 hr data sets over 23 km baseline.  = 0.3 Day 304 Day 301 Day 303

1.3 0.9 0.8 0.6 Day 130 Mean (1.33 cm) / Std. Dev. (0.83 cm) Day 131
Days 301 & 302 same time, same geometry, similar results; 3 mm difference at -7.5 cm height and 5 mm difference at -3.1 cm; mean of two heights differ by 4 cm; both about 2 cm from the truth. Can see similar results; different days but with same geometry, good precision, bad accuracy. Mean of two days observations, different times and geometry; gives height very close to truth. Varying geometry not stated in guidelines for continuous observations (long sessions) but should be. Mean is better approximation of truth; shorter occupation times for shorter baselines. Outliers had high RMS as indicator; typically result of noisy data. 0.6

Same data processed with less session length. 2 hrs compared with 3 hr data sets; increased spread but mean very close to truth.

Same data processed with less session length. 1 hr compared with 3 and 2 hr results; increased spread but mean still very close to truth. How short of session will produce desired results. 0.3

Results from Pilot Project
24 hour solutions of data taken during “bad” atmospheric conditions may not always provide 2 cm results 1, 2, 3, and 6 hour solutions will repeat very well from day to day when observations are collected at about the same time on different days, but may produce significantly different results using data collected during different times of the days, i.e. having significantly different satellite geometry Increasing the elevation cut-off angle will decrease the effects due to multipath, but it will also decrease the number of available satellites which may significantly decrease accuracy of short observing sessions Different geometries and observation times provide closer approximation of truth; similar data, same geometry and multipath influences may produce similar results but disagree with truth. Outliers on one day repeated the next when compared with same geometry so they don’t look like outliers. Observations on different times of the day help detect and reduce the effects of outliers. Surveyors use 1/10 foot (±3 cm) 95% of time as standard height determination of accuracy; 2 cm criteria in guidelines is a small number and will yield 1/10 foot accuracy; typically absorbed in loops. Satellites selected for tests in project “windows” were always greater than 3 and almost always 4.

FGCS 48 Hour Pseudo-Kinematic Network, Gaithersburg, MD (June , 1995) 12 stations occupied in network Two TCORS and one rover 10 minute observing sessions at each site continuously over 48 hour time span 10 different occupations at each site Baselines ranged from 100 meters to 26.1 km FGCS 48 and 24 hour pseudo-kinematic tests - Gaithersburg, Maryland; 10 minute observations over two lines of stations spaced approximately 5 km to the north and to the west of NIST; over a 48 hour period in June and a 24 hour period in November Develop and test guidelines. “Truth” determined through the mean of 10 different solutions for each station.10 sessions - 10 answers - average = truth

FGCS 48 Hour Pseudo-Kinematic Network
WINGATE STRANGE REMONDI LOVE ANDERSON NBS 102 NBS 5 (TCORS) TS19977 SURVEY KINEMATIC STATIC HOLDAHL RAPID DICKERSON (TCORS) Investigate how each session differs from the truth. 2 answers for each occupation, 2 different length baselines to 2 project temporary continuously operating stations (TCORS); NIST and DICKERSON. 2 occupations at each station; attempt to use and analyze results for guidelines.

Distances to Stations from TCORS
WINGATE 25.1 km STRANGE 19.9 km REMONDI 14.9 km LOVE 9.9 km ANDERSON 4.5 km NBS 102 0.1 km NBS 5 (TCORS) TS19977 5.1 km SURVEY 10.1 km KINEMATIC 15.0 km STATIC HOLDAHL 16.1 km RAPID 25.0 km DICKERSON (TCORS) 9.3 km 6.9 km 9.2 km 12.2 km 16.8 km 19.4 km 15.9 km 15.2 km 17.8 km 21.5 km 8.3 km 26.1 km 2 different length baselines to 2 project temporary continuously operating stations (TCORS); NIST and DICKERSON.

H - RMS value greater than 1.5 Summary:
F * F * H F * * H F F - Could not fix integers - (FLOAT solution) - Not included in statistics RMS should be below 1.5 cm level; integer count must be known, must fix integers in all short baselines (< 10 km), if not something’s wrong. Compare standard deviations; single’s fair, repeat is better. Evaluate weather influences. High RMS show large differences - float solutions show large differences. Averaging of solutions tend towards truth - second 24 hr test could not repeat solutions in bad weather. Averaging around geometry window gives better results. Average the influences of GPS positions/heights; 10 minutes minimal occupations or 15 minutes to help average the affects of multipath, etc. H - RMS value greater than 1.5 Summary: * - Difference greater than 5 cm FLOAT Solutions - Large Residuals High RMS Values - Large Residuals

FGCS 24 Hour Pseudo-Kinematic Network, Gaithersburg, MD (November , 1995) 12 stations occupied in network Two TCORS and two rovers Simultaneous 10 minute observing sessions between rovers continuously over 24 hour time span 8 different occupations each site Baselines ranged from 100 meters to 26.1 km 24 hour test results - repeat test in other season. This test has 2 rovers observing simultaneously and produce values between the adjacent points; 10 minute occupations - 8 occupations at each station over 24 hour period.

FGCS 24 Hour Pseudo-Kinematic Network
WINGATE STRANGE REMONDI LOVE ANDERSON KIN C NBS 5 (TCORS) TS19977 SURVEY KINEMATIC STATIC RAPID DICKERSON (TCORS) NBS 102 Investigate how each session differs from the truth. 2 answers for each occupation, 2 different length baselines to 2 project temporary continuously operating stations (TCORS); NIST and DICKERSON. Plus simultaneous occupations between adjacent points. 2 occupations at each station; attempt to use and analyze results for guidelines.

H - RMS value greater than 1.5
F H H H H H H H H H H H H H H F H H H H H H H H H H H F H H H H H H F H H Bad weather results - float solutions and high RMS; sometimes solutions work others don’t . Without redundancy there’s no way to know how well a solution fits. Bad weather produces different standard deviation. F - Could not fix integers - (FLOAT solution) - Not included in statistics H - RMS value greater than 1.5 “Bad” Weather High RMS Values

Base lines with high RMS produced outliers Base lines where integers could not be fixed produced outliers Standard deviation of a single 10 minute occupation during “good” atmospheric conditions was 2.1 cm Standard deviation of the mean of two 10 minute occupations during “good” atmospheric conditions was 1.4 cm Standard deviation of a single 10 minute occupation during “bad” atmospheric conditions was larger than a single 10 minute occupation obtained during “good” atmospheric conditions, i.e. 3.0 cm versus 2.1 cm How do you write guidelines - insure redundancy, strict GPS operation procedures, etc. Develop confidence. GPS has only been rigorously used about a decade, heights by GPS have only really been possible about 3 yrs. New system and uses - change guidelines as appropriate. Control network guidelines; have to be right, with station densification guidelines are and can be loosened; you have to understand where the pitfalls are. Single 10 minute occupations show differences; guidelines say mean should improve results, mean of 4 occupations improved results even more.

San Francisco Bay Demonstration Project Test of guidelines and modifications based on results Phase I: Static survey test for 2 cm accuracy Mixture of base line lengths; 2 to 50 km Long observing sessions; minimum of 3 hours Phase II: Kinematic survey test for 5 cm accuracy Short base line lengths; less than 5 km Short observing sessions; 15 minutes “Real-world” conditions, i.e., traffic, trees, buildings San Francisco Bay Demonstration Project - height modernization initiative; funded to NGS by congress. Mixture of long and short sessions; realistic observing conditions; varying baseline lengths; different observation scenarios; repeat observations on different days and times. 7 and 3 hour observations, Demonstrate GPS heights; show that guidelines work, also occupy tidal stations. 2 phases in project - 2nd phase photo control; low altitude, 2000 to 3000 feet, used in softcopy digital analyzer to show that system utilizing this photogrammetric technique works to 10 cm in height. Adjacent stations observations want better than 2 cm. Longer observations (15 minutes) worked pretty well under real life conditions; not good site but realistic; produced some outliers, possibly too short of sessions and definitely some bad sites. More points than required for photo control but adds checks to the system. Results from processing various scenarios - follow guidelines to check how results compare; “truth” determined from the mean of two 7 hour sessions at each station.

San Francisco Bay Demonstration Project
TIDAL 17 MOLATE TIDAL 5 BRIONE RV 223 CORS PT. BLUNT TIDAL 32 YACHT GPS Site N ASFB PORT 1 S 1320 KM TIDAL 7 M 554 CHABOT San Francisco Bay project area. U 1320 M 148 L 1241 N 1197 WINTON

Ah, the good life. A clear day in San Francisco
Ah, the good life. A clear day in San Francisco. Positioning pier corners. Once control with good heights have been brought into project area GPS connections to this control require shorter session lengths due to shorter baselines.

Individual solutions shown on scatter plot - good solutions for longer lines 30 minute observations.
Repeat vector comparisons. All comparisons in the ellipsoid height component fall within 2 cm except one and the base line distance exceeds the average 10 km spacing detailed in the guidelines.

Two Days/Different Times -10.254 > -10.275 -10.295
Two Days/Same Time > Difference = 0.3 cm “Truth” = Difference = 2.3 cm Two Days/Different Times > Difference = 4.1 cm “Truth” = 2 days same geometry close to each other but far from the truth; 2 days at different times (geometries) not so close to each other but their mean is closer to the truth. Don’t see problems due to good repeatability under the same conditions. Experts suggest about 3 hours difference in window for significant change in satellite geometry. Difference = 0.1 cm

Two Days/Different Times 20.660 > 20.637 20.614 Difference = 4.6 cm
Two Days/Same Time 20.660 > 20.662 Difference = -0.2 cm “Truth” = Difference = 4.6 cm Two Days/Different Times 20.660 > 20.614 Difference = 4.6 cm “Truth” = 2 days same geometry close to each other but far from the truth; 2 days at different times (geometries) not so close to each other but their mean is closer to the truth. Don’t see problems due to good repeatability under the same conditions. Difference = 2.3 cm

Need a Network! Two Days/Different Times -9.184 > -9.185 -9.185
Difference = 0.1 cm “Truth” = Difference = 3.3 cm Need a Network! Line is greater than 10 km Even following guidelines there’s still outliers - need network to find problems; adjustment with enough redundancy will put residuals where they belong.

Base lines with high RMS produced outliers Base lines where integers could not be fixed produced outliers Standard deviation of a 30 minute session for short lines, i.e. less than 10 km, was 1.2 cm Standard deviation of the mean of two 30 minute occupations on two different days and different times of day was 0.8 cm Standard deviation of a 10 minute session for short lines, i.e. less than 10 km, was 1.7 cm Standard deviation of the mean of two 10 minute occupations on two different days and different times of day was 1.1 cm Compare 30 min solutions from same data sets to show how they compare over the varying length lines. Note that standard deviation of 1.2 cm does not meet the 2 cm guidelines but a standard deviation of 0.8 cm does. Maybe need to observe longer to achieve results. Short lines provided good solutions for short observation times; take enough observations to produce good results; 1 observation is close but 2 observations improves results. Improvements in equipment, software, error reduction modeling for multipath, more available satellites; possibly up to 30 in the near future, 3 rd freq, geostationary satellites, will improve GPS derived heights even further. Federal role is to produce a document that works (probably not followed explicitly as people need to make money). Do the best job possible in good faith and realize potential pitfalls.

Establish / Monitor Project Control
CORS Continuously operating reference stations (CORS) provide data for test processing. National and state networks provide continuous GPS data for analysis over varying baseline length and session duration.

National CORS map at NGS web site
National CORS map at NGS web site. Availability of GPS data and National Spatial Reference System (NSRS) control position/ellipsoid height information.

Precision With CORS How GPS positioning is affected by baseline length
Minimum occupation time required to meet established specifications Twice the ±2 cm for horizontal components Twice the ±4 cm for vertical components Twice the rms being approximately equal to a 95% confidence region Varying length baselines formed from 19 CORS 10 days data from each site; various session lengths Sample project using CORS data to assess relationship of distance between stations and length of time data collected. We know our results with 24 hour data sets achieve consistent positional repeatability. What happens when we look at shorter observation times over the various baseline lengths.

Design of Research 6 - 4 hour sessions  10 days  12 baselines = 720
Sessions Processed 6 - 4 hour sessions  10 days  12 baselines = 720 “ “ “ “ = 480 “ “ “ “ = 360 “ “ “ “ = 240 “ “ “ “ = 120 (Total # of Sessions) hour data sets broken down into 12, 8, 6, and 4 hour data sets and processed for all 12 different baseline lengths.

Processing One station constrained Second station computed
ITRF97 (X, Y, and epoch January 1, 1999 X, Y, and Z position of second station is source of results Automatic integer fixing (on) Tropospheric model (on) Antenna phase patterns (ant_info.001) Precise ephemerides (NGS ephemeredes) Processing parameters. Use published ITRF97 position at “from” station and process new position at “to” station.

Differences from “processed” positions to published positions over varying baseline lengths and session times in the north component. Note jump at 250 km is there are two stations, one with baseline length of 252 km and the other with 253 km.

Differences from “processed” positions to published positions over varying baseline lengths and session times in the east component. Note jump at 250 km is there are two stations, one with baseline length of 252 km and the other with 253 km.

Differences from “processed” positions to published positions over varying baseline lengths and session times in the up (height) component. Note jump at 250 km is there are two stations, one with baseline length of 252 km and the other with 253 km.

Time Scatter Plots (Horizontal)
Scatter plot northing and easting at 160 km (100 mi) baseline length for the various session times. Clearly 4 hours of data is producing consistent results at this distance. Time Scatter Plots (Horizontal)

Observation Time in Hours
Observation Time in Hours Scatter plot up (height) component at 160 km (100 mi) baseline length for the various session times. 6, 8 and 12 hour results are very consistent at this baseline length and don’t show improved results from using more data. 4 hours of data is producing reasonable results at this distance.

RMS plot of the up (height) component for the various baseline lengths at the various session times.
Trend is more data produces improved heights but even 4 hours produces results below 2 cm over baselines shorter than 160 km.

Multiple Occupation Estimates
Averaging results from multiple sessions produce final positions/heights that are a closer approximation of “truth.”

60 Day time series for a CORS station as part of the products available from the NGS web site.
Indicators of how well a particular CORS is performing in the different components.

Comments About Results With CORS Data
Majority of time you are less than 300 km from CORS (continental U.S.) Baseline length has little effect on positional accuracy No setup error or antenna measurement blunders < 300 kilometers Using NGS’ PAGES software Precise ephemeris, Tropo models, and antenna patterns Horizontal and vertical specifications can be met in one 4-hour session Note: The is no station setup error associated with a CORS as they are permanently mounted.

Recommendations to Guidelines Based on These Tests
Must repeat base lines Different days Different times of day Detect, remove, reduce effects due to multipath and having almost the same satellite geometry Must FIX integers Base lines must have low RMS values, i.e., < 1.5 cm Recommendations - no low RMS; short data sets using a small piece of satellite visibility can cause high RMS; delete suspect satellites and reprocess - can’t fix integers - something’s wrong. Single frequency receivers will work - fix integers - short baselines - longer data sets. Different days - schedule 2nd observation on different day if reasonable. It’s just a matter of scheduling.

Available On-Line at the NGS Web Site: www.ngs.noaa.gov
Guidelines - will eventually become routine; not so much explanation of why its done but provides background information. Repeat baselines, station spacing, fixed height antenna setups, identify and control all error sources, tie local networks together, etc.. NOS NGS-58 GPS-Derived Ellipsoid Heights Guidelines will lay the foundation for GPS-Derived Orthometric Heights Guidelines. Produce 2 cm ellipsoid heights to be able to obtain 2 cm orthometric heights.

Station Selection and Reconnaissance
Assure accurate connections to control stations NGS approved CORS TCORS (temporary or project CORS) HPGN / HARN Federal Base Network (FBN) Cooperative Base Network (CBN) User Densified Network (UDN) NAVD 88 Bench Marks NGS Database and data sheets Identify GPS-usable stations Control stations provide accurate connections to the National Spatial Reference System (NSRS). Identify and use stations that exist in or are adjacent to the project area. Determine which stations have clear, unobstructed satellite visibility. Set offset stations and perform level ties to existing NAVD88 bench marks that are not good for GPS observations.

NGS Internet Page www.ngs.noaa.gov
NGS web page for access to CORS data, station data sheets, interactive tools, software, etc.

NGS CORS web page for access to CORS data.

Map of the NGS CORS coverage.

Regional map of the NGS CORS coverage showing site ownership, data collection rate, and spacing,

Location map of the specific site and links to data.

Map of the National A and B Order, HPGN/HARN monumented station coverage as of 1999.

Status map of FBN re-surveys. Improved ellipsoid heights.

Primary or Secondary Station Selection Criteria
1. HPGN / HARN either FBN or CBN Level ties to A or B stability bench marks during this project 2. Bench marks of A or B stability quality Or HPGN / HARN previously tied to A or B stability BMs 3. UDN stations 4. Bench marks of C stability quality Special guidelines for areas of subsidence or uplift Hierarchy of control stations to provide connection relative to the National Spatial Reference System (NSRS). Station stability is essential to provide accurate tie to control network. A stability – expected to maintain position/elevation well through time, not influenced by local subsidence or other conditions. Massive outcrop, very large deep foundation structures, deep sleeved rod marks driven to refusal. B stability – probably maintain position/elevation well through time, not influenced by local subsidence or other conditions. Large structures, rod marks driven to refusal. C stability – may maintain position/elevation well through time, but of the type commonly subject to surface motion and local conditions. Substantial concrete posts set below local frost level, smaller structures. Obviously, if there are local conditions affecting the position/elevations of control stations in the area special procedures will be required to provide consistent connection to NSRS.

Four Basic Control Requirements
BCR-1: Occupy stations with known NAVD 88 orthometric heights Stations should be evenly distributed throughout project BCR-2: Project areas less than 20 km on a side, surround project with NAVD 88 bench marks i.e., minimum number of stations is four; one in each corner of project BCR-3: Project areas greater than 20 km on a side, keep distances between GPS-occupied NAVD 88 bench marks to less than 20 km BCR-4: Projects located in mountainous regions, occupy bench marks at base and summit of mountains, even if distance is less than 20 km This same information is required by the GPS-derived Orthometric heights guidelines. Producing ellipsoid heights at the 2 cm level of accuracy is essential to producing accurate GPS-derived orthometric heights. Surrounding project areas will be difficult in many instances with existing NAVD88 bench marks. Level ties may be necessary to provide this requirement. Extra bench marks allow independent analysis through the adjustment process and may help identify potential bench marks with questionable stability or poor published elevations. Bench marks at base and top of mountains may help identify/rectify issues that are not otherwise apparent in the geoid model.

Obstruction Visibility
Diagram The station is at the center of this diagram and the horizon is the outer circle. All obstructions in the direct line of site to the satellites are plotted and identified by azimuth and elevation from the horizon.

Equipment Requirements
Dual-frequency, full-wavelength GPS receivers Required for all observations greater than 10 km Preferred type for ALL observations regardless of length Geodetic quality antennas with ground planes Choke ring antennas; highly recommended Successfully modeled L1/L2 offsets and phase patterns Use identical antenna types if possible Corrections must be utilized by processing software when mixing antenna types Guideline requirements in attempt to reduce/eliminate potential GPS error sources. Single frequency equipment produce very consistent results over short baselines, I.e., < 10 km. L1/L2 receivers may work better under certain atmospheric conditions even for shorter baselines. Reduce errors by using equipment that has been demonstrated to reduce effects of potential error sources. Error sources tend to cancel when using identical equipment/antenna types.

NGS monitors and determines antenna phase patterns at their test facility is at Corbin, Virginia and provides this information over the Internet. Phase patterns derived at this site work well at this site but each site is different, grass, gravel, dirt, scrub, etc., so derived phase patterns may perform differently under different conditions.

Trimble Geodetic L1/L2 Antenna (TRM 22020.00)
Ashtech Geodetic III Antenna U.S.C.G. V Antenna (ASH A1) Different antenna types may be dramatically different or visually similar. Phase patterns need to be derived for each antenna type and configuration such as adding a cover.

The NGS site also illustrates the different antenna type configurations with offsets from antenna reference point (ARP) to L1 and L2 mechanical phase centers.

The NGS site also illustrates the different antenna type configurations with offsets from antenna reference point (ARP) to L1 and L2 mechanical phase centers

Referencing the antenna where satellite signals are acquired to the mark on the ground. Height above the mark to the antenna reference point (ARP), typically the base of the antenna mount, provides the necessary height relationship of the antenna to the mark on the ground. Processing software includes the constant antenna relationship information, i.e., ARP to bottom/top of ground plane, and to L1/L2 phase centers.

Additional information relating ARP to various antenna components.

Data Collection Parameters
VDOP < 6 for 90% or longer of 30 minute session Shorter session lengths stay < 6 always Schedule travel during periods of higher VDOP Session lengths > 30 minutes collect 15 second data Session lengths < 30 minutes collect 5 second data Track satellites down to 10° elevation angle Vertical element critical relative to Sat geometry – position/elevation derived by averaging of all signals - key to accurate heights is to average all affects. Outliers with low VDOP values- may have multipath at site. When bad multipath detected; raise mask but pay close attention to VDOP values. Maybe required to record more data. Increased masks - time vs. mask - can’t observe above indicated line due to VDOP cutoff of 6. Same data sets using different masks sometimes produce 5 cm differences - pay attention to VDOP. Session lengths to average affects. Longer sessions to average affects of longer baselines whereas shorter sessions get by with shorter baselines as affects at each station are similar. 10 degree mask for data collection allows the receiver to “cleanly” lock on to low elevation satellites providing strong, continuous satellite lock when processing at 15 degrees. Collecting data down to 10 degrees typically does not require much additional storage space.

Meteorological Data Weather data must be collected at control, primary, and secondary base stations at height of antenna PC Wet and dry temperatures, atmospheric pressure Sessions > 2 hrs; record beginning, midpoint, ending Sessions < 2 hrs > 30 min; record beginning and ending Sessions < 30 min; record at midpoint Note on obs log where recorded and unusual conditions Stabilize equipment to ambient conditions Check equipment prior to observations Averaging weather conditions throughout the session by recording barometric pressure, temperature, and relative humidity and noting on observation logs. Equipment that is not stabilized to the local ambient conditions will produce inaccurate weather measurements which will not be useful in data reduction. Make sure all weather equipment are monitoring conditions consistently. Monitor and record weather data accurately and consistently or it will be of no use for future data reduction. Tropospheric models provide reliable, consistent corrections for delays caused by the lower atmosphere (troposphere). Ground recorded weather conditions provide correction for the final distance traveled by the satellite signals which may vary from station to station, i.e., stations at different elevations or where weather fronts are moving through an area affecting stations differently.

Antenna Setup Fixed-height tripods required for 2 cm standard
Shade plumbing bubbles at least 3 min prior to plumbing Check perpendicularity of poles at beginning of project Fixed-height poles preferred for 5 cm standard Alternate tripod setups; antenna heights MUST be measured carefully and accurately Check measuring system before project Check and adjust tribrachs at beginning of project Perform totally independent meter and feet measurements Have measurement computations checked by someone else Fixed-height tripods provide several things in a survey. They eliminate uncertainty in measurements from the station mark to the antenna reference point (ARP). Places all antennas at the same relationship (height) above their surroundings which minimizes affects of ground reflections as all antennas are at the same height. Alternate tripod setups must be measured as accurately as possible and all measurements must be verified by separate measuring device and units. Note depth of dimple on disk/survey mark so corrections may be applied to all antenna height measurements, including fixed height poles. Orthometric elevations determined by conventional leveling was derived at the top of the disk/survey mark.

“Fixed” Height Tripod Example of fixed height pole with antenna.
Macrometer V1000 antenna with 3 foot ground plane; about 45 pounds.

“Slip-leg” Tripod and Slant Height Measurement
Measuring a tripod set up using the slant-height method. Macrometer V1000 GPS receiver with antenna pictured. Note – it takes two geodesists to accurately measure a set up such as this.

Table 1. -- Summary of Guidelines
Summary of the guidelines broken down into columns indicating 2 cm or 5 cm standards with the rows identifying key elements discussed in the NOS NGS-58 GPS-Derived Ellipsoid Heights Guidelines. Guidelines - will eventually become routine; not so much why they work but will provide background information. Repeat baselines, station spacing, fixed height antenna setups, etc. Control all error sources, tie local networks together.

Appendix B. - - GPS Ellipsoid Height Hierarchy
HARN/Control Stations (75 km) Primary Base (40 km) Secondary Base (15 km) Local Network Stations (7 to 10 km) Appendix B. Guidelines guarantee proper ties and provide acceptable relative accuracies. HARN not better than 5 cm vertical accuracy absolute. CORS getting down to 3 cm vertical accuracy absolute. Basic concepts - nutshell overview - if errors are not large they’re probably not visible; requires redundancy and a network. 5 cm accuracy - ties to the net at least to 5 cm (network) and internally to 2 cm (local). Layering of control to produce local network stations. Shorter baseline lengths, shorter observation times.

HARN/Control Stations
CS1 Control stations are the existing CORS, HPGN/HARN surrounding the project area. CS2 75 km CS3

Primary Base Stations CS1 PB1 PB2 40 km PB3 CS3 CS2
Primary control - establishes controlling stations at 5 cm level within project area; could be existing HARN. Primary base - bridge gaps; establish control for future surveys; provides 40 km knowns; some stations in each project used for ties between local projects at 2 cm. 3 or 4 primary bases; 4 allow extra check; establish accurate ellipsoid heights between primary bases to control project; everything within area based on primary base stations. CS3 CS2

Primary Base Stations Basic Requirements: 5 Hour Sessions / 3 Days
Spacing between PBS cannot exceed 40 km Each PBS must be connected to at least its nearest PBS neighbor and nearest control station PBS must be traceable back to 2 control stations along independent paths; i.e., base lines PB1 - CS1 and PB1 - PB2 plus PB2 - CS2, or PB1 - CS1 and PB1 - PB3 plus PB3 - CS3 Requirements for primary base stations.

Secondary Base Stations
CS1 PB1 SB1 SB2 SB3 15 km SB4 PB2 PB3 Secondary control - to eliminate systematic errors in the shorter segments. Still need to establish internal primary control unless HARN is within 40 km; helps in connecting local networks together. Secondary base - bridges gaps also; detects long wavelength error sources between stations; serve as jumps and place holders to reach/surround local stations; establishes local control in some areas; longer observations, provide better statistical differences to help minimize local errors; builds network and increases loop closure potential for searching for errors. CS3 CS2

Secondary Base Stations
Basic Requirements: 30 Minute Sessions / 2 Days /Different times of day Spacing between SBS (or between primary and SBS) cannot exceed 15 km All base stations (primary and secondary) must be connected to at least its 2 nearest primary or secondary base station neighbors SBS must be traceable back to 2 PBS along independent paths; i.e., base lines SB1 - PB1 and SB1 - SB3 plus SB3 - PB2, or SB1 - PB1 and SB1 - SB4 plus SB4 - PB3 SBS need not be established in surveys of small area extent Requirements for secondary base stations.

Local Network Stations
CS1 PB1 LN1 SB1 SB2 LN2 LN3 LN5 LN4 LN6 7 km LN7 SB3 SB4 PB2 PB3 Local stations - where you want control; actual project stations. Must be realistic and not densify beyond accuracy limitations (i.e. third order levels at 7 km is 6 mm × o7.0 = mm) Trying to get 2 cm results! Local control - ultimate goal of survey; secondary helps bring in control and act as local control. Establish network; create short loop closures; include redundancy; and lots of triangles. CS3 CS2

Local Network Stations
Basic Requirements: 30 Minute Sessions / 2 Days / Different times of the day Spacing between LNS (or between base stations and local network stations) cannot exceed 10 km All LNS must be connected to at least its two nearest neighbors LNS must be traceable back to 2 primary base stations along independent paths; i.e., base lines LN1 - PB1 and LN1 - LN2 plus LN2 - SB1 plus SB1 - SB3 plus SB3 - PB2, or LN1 - PB1 and LN1 - LN3 plus LN3 - SB2 plus SB2 - SB4 plus SB4 - PB3 Requirements for local control stations.

Sample Project Showing Connections
CS2 CS1 LN4 LN1 LN3 LN2 PB2 PB1 LN5 SB2 SB1 SB3 SB5 SB4 Creating the network to position local control stations which are the goal of this project. Primary base stations connect to the NSRS though direct traceable ties to control stations and to each other. These are the long observations sessions and will be adjusted together with the control stations. These adjusted positions will then be constrained in the adjustment of the secondary and local network stations. From the primary base stations baselines are shorter and observation sessions are shorter in duration. Additional connections between secondary stations used in this illustration provide network points for a possible future project in that area. Loop misclosures are an important analysis tool. Keep loops short in total distance and minimize number of stations included. Extra observations may be necessary to close smaller loops and directly tie adjacent stations. PB3 PB4 CS3 CS4

Sample Project

Project Information Area: East San Francisco Bay Project
Latitude ° 50” N to 38° 10” N Longitude 121° 45” W to 122° 25” W Receivers Available: 5 Standards: 2 cm GPS-Derived Heights Northeastern part of San Francisco Bay and continuation of the San Francisco Bay Demonstration Project. All planning requires pertinent information like how many receivers are going to be used and to what standards is the survey being performed.

GPS-Usable Stations CORS HARN NAVD’88 BM New Station Spacing Station
Primary Base Station LATITUDE 8.2km Project planning- what stations are being created and which available GPS usable stations will be used for control. Observation logistics – can I get there from here? This project had several “gaps” where initial planed local control stations were not selected. To maintain a consistent average 10 km spacing several “filler” stations were included in the project. 4 NAVD88 bench marks surround the project area. Primary base stations were selected from the existing HPGN and two other stations that surround the project area, one a vertical control station. 37°50’N 122°35’W LONGITUDE 121°40’W

Primary Base Stations LATITUDE LONGITUDE 38°20’N CORS HARN NAVD’88 BM
New Station D191 10CC 19.0km Primary Base Station 28.7km 25.7km LATITUDE 38.3km 31.6km 38.7km 25.8km LAKE 29.6km MART MOLA Primary base stations are observed for 3 sessions of 5 hour duration using the two HPGN and one CORS as control. Baseline lengths indicate that the spacing between primary base stations is less than the required 40 km. An adjustment is performed on these sessions to produce positions/ellipsoid heights for the two new primary base stations, MART and D191. 37°50’N 122°35’W LONGITUDE 121°40’W

East Bay Project Points
CORS HARN NAVD’88 BM New Station Spacing Station TIDD D191 10LC Primary Base Station X469 MONT Z190 DROU BM20 Q555 LATITUDE 04KU CATT TOLA TIDE 5144 ZINC PT14 R100 8.2km Local network stations that will be connected to the primary base stations. Secondary base stations were not necessary in this project because of local station density. P371 04HK LAKE MART 37°55’N 122°20’W LONGITUDE 121°40’W

Observation Sessions Session F Session E Session D Session G LATITUDE
CORS HARN NAVD’88 BM New Station Spacing Station Session E Session D Primary Base Station Session G LATITUDE Observation scenario planning – five receivers G number of sessions. Each session observed twice under different satellite geometry. Short baseline lengths, short observation sessions. Observation progression provides minimal move times between sessions enabling the crews to complete all sessions, A through G, in one day. Poor “windows” of satellite geometry planned during move times. Individual sessions overlap previous session providing good network configuration and redundancy. Session A started on known control station which allows coordinate seeding through the unknown stations. There are many number of observation scenarios to provide similar results. Session A Session C Session B 37°55’N 122°20’W LONGITUDE 121°40’W

Independent Base Lines
CORS HARN NAVD’88 BM New Station Spacing Station Primary Base Station LATITUDE 8.2km Non-trivial baselines determined from the scheduled observations. Each session was observed twice providing repeat vectors for height analysis. Adjacent stations are connected, loops are fairly short in length and involve separate sessions providing a good analysis tool. Additional sessions or different observation scenario could “strengthen” the network configuration in the west. 37°55’N 122°20’W LONGITUDE 121°40’W

Observation Schedule Observation schedule illustrating sessions observed on day 1 repeated on day 2 but using completely different satellite geometry. Day 1 starts on session A through G and day 2 starts with session D through C. 45 minutes per session provides the minimum 30 minute session requirement. 15 extra minutes on site provide a cushion of comfort if someone is late or other problem arises in the field. Rather have crews observe a little longer as opposed to sending them back because of a short session.

Field Observations Observation logs Obtain a clear station rubbing
Record complete receiver/antenna manufacturer, model part number, and serial numbers Record meteorological data and unusual conditions Record station and observer information Record height of antenna and measurement computations Obtain a clear station rubbing Rubbing for each occupation of station Make complete plan sketch of mark when rubbing not feasible Observations logs provide checks on station occupied, observer’s name, equipment used with part numbers and serial numbers, antenna height information, weather information, and other station occupation data. Station rubbings or photos identify which station was actually occupied by the observer. Many confusing situations can be encountered in the field, i.e., reference marks, azimuth marks, similar designated bench marks, etc., and clear station rubbings can solve many questions in the office when processing and adjusting data.

Sample Observation Log
(Front Side) Front side of NGS style GPS observation log.

Sample Observation Log
(Back Side) Reverse side of NGS style GPS observation log.

Sample Station Rubbing
NGS style station rubbing sheet with supporting stamping, agency, station description information.

Basic Concept of Guidelines
Stations in local 3-dimensional network connected to NSRS to at least 5 cm uncertainty Stations within a local 3-dimensional network connected to each other to at least 2 cm uncertainty Stations established following guidelines are published to centimeters by NGS Basic concepts - nutshell overview - if errors are not large they’re probably not visible; requires redundancy and a network. 5 cm accuracy - ties to the net at least to 5 cm (network) and internally to 2 cm (local). Local & network accuracy - accuracies identified for project (local or relative to adjacent stations) and network (relative to national datum or closer approximation of absolute). Local accuracy - uncertainty statement of coordinates/heights between adjacent stations. Leveling - we see slight accumulation 4-5 cm; good closures over large loops but not so good over short distances. Network accuracy - uncertainty statement of coordinates/heights to the geodetic datum; nationally the CORS network, known relatively to 2 to 3 cm. Control stations - KNOWN control; things that fit between should fit the control stations; CORS approach 2 cm and the HARN 5 cm.

Network / Local Accuracy
A project performed in southern South Carolina has local accuracy of 2 cm relative to the points in that project. A project performed in northern South Carolina and southern North Carolina has local accuracy of 2 cm relative to the points in that project. The project in southern South Carolina is relative to the project in northern South Carolina and southern North Carolina at the 5 cm network accuracy.

Points of Contact National Geodetic Survey NOAA, N/NGS Geodetic Services Division Bldg. SSMC3, Station East-West Highway Silver Spring, MD Phone: Fax: Internet Web Site: Curtis L. Smith Phone:

GPS-Derived Heights Part 1 Development and Description of NGS Guidelines Detailing heights, height systems, their relationships, and development through.

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GPS-Derived Heights Part 1 Development and Description of NGS Guidelines Detailing heights, height systems, their relationships, and development through.

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