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Class 27: 28 April 2008 Planning and Analysis of a Height Modernization Survey using TM 58/59

Class 27: 28 April 2008 Planning and Analysis of a Height Modernization Survey using TM 58/59. GISC3325 28 April 2007. GPS-Derived Heights Part II. Planning and Evaluating a GPS Vertical Survey. NOAA, NOS, National Geodetic Survey. Topics To Be Discussed. Review of heights and accuracies

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Class 27: 28 April 2008 Planning and Analysis of a Height Modernization Survey using TM 58/59

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  1. Class 27: 28 April 2008 Planning and Analysis of a Height Modernization Survey using TM 58/59 GISC3325 28 April 2007

  2. GPS-Derived Heights Part II Planning and Evaluating a GPS Vertical Survey NOAA, NOS, National Geodetic Survey

  3. Topics To Be Discussed • Review of heights and accuracies • A Guide for Establishing GPS-derived Orthometric Heights • Sample project following NGS’ guidelines • Discussion on base line processing and analysis of repeat base line results • Discussion of adjustment procedures and analysis of results • Height Modernization Initiative • NGS web site and services

  4. Ellipsoid, Geoid, and Orthometric Heights “h = H + N” Earth’s Surface P Plumb Line Ellipsoid h Q N Mean Sea Level “Geoid” PO Ocean 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)

  5. GPS - Derived Ellipsoid Heights Z Axis P (X,Y,Z) = P (,,h) h Earth’s Surface Zero Meridian Reference Ellipsoid Y Axis   Mean Equatorial Plane X Axis

  6. Simplified Concept of ITRF 00 vs. NAD 83 h83 h00 Earth’s Surface ITRF 00 Origin 2.2 meters NAD 83 Identically shaped ellipsoids (GRS-80) a = 6,378,137.000 meters (semi-major axis) 1/f = 298.25722210088 (flattening) Origin

  7. Expected Accuracies • GPS-Derived Ellipsoid Heights • 2 centimeters (following NOS NGS-58 Guidelines) • Geoid Heights (GEOID03) • Relative differences typically less than 1 cm in 10 km • 2.4 cm RMS about the mean nationally • Leveling-Derived Heights • Less than 1 cm in 10 km for third-order leveling

  8. Recommendations to Guidelines Based on Tests and Sample Projects • 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

  9. Available “On-Line” at the NGS Web Site: www.ngs.noaa.gov

  10. Table 1. -- Summary of Guidelines

  11. Sample Project Showing Connections CS2 CS1 LN4 LN3 LN1 LN2 PB2 PB1 LN5 SB2 SB1 LN6 LN7 SB3 SB5 SB4 PB4 PB3 CS3 CS4

  12. A Guide for Establishing GPS-Derived Orthometric Heights (Standards: 2 cm and 5 cm)

  13. A Guide for Establishing GPS-Derived Orthometric Heights(Standards: 2 cm and 5 cm) • Three Basic Rules • Four Basic Control Requirements • Five Basic Procedures 3-4-5 System

  14. Three Basic Rules • Rule 1: • Follow NGS’ guidelines for establishing GPS-derived ellipsoid heights (Standards: 2 cm and 5 cm) • Rule 2: • Use latest National Geoid Model, i.e., GEOID03 • Rule 3: • Use latest National Vertical Datum, i.e., NAVD 88

  15. 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

  16. BCR Example BCR1: Sketch indicates that the 20 km rule was met. BCR2: This requirement is not applicable because the project is greater than 20 km on a side. BCR3: Circled bench marks are mandatory. Analysis must indicate bench marks have valid NAVD 88 heights. Other BMs can be substituted but user must adhere to 20 km requirement. BCR4: This requirement is not applicable because project is not in a mountainous region.

  17. Five Basic Procedures • BP-1: Perform 3-D minimum-constraint least squares adjustment of GPS survey project • Constrain 1 latitude, 1 longitude, 1 orthometric height • BP-2: Analyze adjustment results from BP-1 • Detect and remove all data outliers

  18. BP2: After performing minimum constraint adjustment, plot ellipsoid height residuals (or dU residuals) and investigate all residuals greater than 2 cm.

  19. BP2: Station pairs with large residuals, i.e., greater than 2.5 cm, also have large repeat base line differences. NGS guidelines for estimating GPS-derived ellipsoid heights require user to re-observe these base lines. Following NGS guidelines provides enough redundancy for adjustment process to detect outliers and apply residual on appropriate observation, i.e., the bad vector.

  20. Five Basic Procedures(continued) • BP-3: Compute differences between GPS-derived orthometric heights from minimum-constraint adjustment in BP-2 and published NAVD88 BMs

  21. BP3: All height differences are under 5 cm and most are less than 2 cm. Almost all relative height differences between adjacent station pairs are less than 2 cm. However, most of the height differences appear to be positive relative to the southwest corner of the project.

  22. Five Basic Procedures(continued) • BP-4: Determine which BMs have valid NAVD88 height values from results from BP-3 • Differences need to agree 2 cm for 2 cm survey • Differences need to agree 5 cm for 5 cm survey • May detect systematic tilt over large areas • Solve for geoidal slope and scale • BP-5: Perform constrained adjustment with results from BP-4 • Constrain 1 latitude, 1 longitude, all valid orthometric height values • Ensure final heights not distorted in adjustment

  23. BP4: To detect and remove any systematic trend, a tilted plane is best fit to the height differences (Vincenty 1987, Zilkoski and Hothem 1989). After a trend has been removed, all the differences are less than +/- 2 cm except for one and almost all relative differences between adjacent station are less than 2 cm.

  24. BP5: After rejecting the largest height difference (-2.4 cm), of all the closely spaced station pairs only 3 are greater than 2 cm, 1 is greater than 2.5 cm and none are greater than 3 cm.

  25. Elevation published to centimeters. Orthometric height determined by GPS.

  26. GPS-Derived • Orthometric Heights • Project

  27. Baltimore County Maryland, NAVD88GPS-Derived Orthometric Height Project

  28. Baltimore County, Maryland, NAVD88 GPS-derived Orthometric Height Project Project Horizontal and Vertical Control

  29. Observation Sessions; Primary Control HYDES HARN 1A, 2A, 3A 92 1A, 2A, 3A 1A, 2A, 3A 1A, 2A, 3A MELSAGE HARN 1A, 2A, 3A 1A, 2A, 3A KEY Existing HARN New Primary Control Baltimore City 43 Day 263 = Project Day 1 Day 264 = Project Day 2 Day 268 = Project Day 3 Session A for all days; 5 hour observations

  30. Observation Sessions; Local Control Day 269 = Project Day 4 Day 270 = Project Day 5 Day 271 = Project Day 6 Session =A, B, C, D, E; 45 minute observations 82 81 6C, 5A HYDES HARN 97 92 80 4E 6B 4D 6A 4C 4D 5B 78 6D 5E 6A 4E 6B 5B 6D 6B 4A 5B 5A 6C 4C 4D 5B 107 6D 5C 94 6D 79 5A 6C 6C 4A 5C 4D 4E LINE 5E 6A 6B 5A 6A 4A 4E 98 5C 91 84 5C MELSAGE HARN 4C 4A 4B 5D KEY 90 5E 5D 4C 4B 4B 5D 5E Baltimore City 5D 4B 43 SAUTER RESET

  31. Repeat Baseline Differences

  32. Repeat Baseline Differences(Baselines less than 10 KM)

  33. Height Differences (du) 5 Hour Sessions

  34. Height Differences (du) 45 Minute Sessions

  35. Height Differences (du) 45 Minute Sessions (continued)

  36. Height Differences (du) 45 Minute Sessions (continued)

  37. Vertical Free Adjustment Results GEOID96

  38. Vertical Free Adjustment Results G96SSS

  39. Vertical Free Adjustment Results GEOID93

  40. Baltimore County GPS-DerivedOrthometric Height Project H GPS - H Leveling(88) (Units = cm) -0.5 -0.6 -0.7 82 81 HYDES HARN 97 92 80 78 107 79 94 LINE 0.0 -2.1 -0.1 -0.4 -0.9 98 MELSAGE HARN 91 0.5 84 -0.3 -1.2 0.0 0.3 KEY 0.0 90 0.0 GEOID93 -0.2 GEOID96 -1.5 -1.0 G96SSS Baltimore City 43 SAUTER RESET

  41. Final Set of GPS-Derived Orthometric Heights

  42. Final Set of GPS-Derived Orthometric Heights (cont.)

  43. Data Processing and Analysis • of Repeat Base Line Results

  44. Vector Processing Controls • Elevation Mask - 15 degrees • Ephemeris - Precise • Tropospheric Correction Model • Iono Corrections - All baselines longer than 5 km. • Fix Integers • Baselines less than 5 km: L1 fixed solution • Baselines greater than 5 km: Iono free (L3) solution • Looking for RMS - Less than 1.5 cm

  45. Washington Monument Survey 1934 1999

  46. L1, Float Solution, Predicted Weather From To Session DX (m) DY (m) DZ (m) Vector 1st - Next 1st - Next 1st - Next Length (m) 000A WASH 231B 23.3958 -101.5071 142.1077 176.198 230B -0.2463 -0.2060 -0.0313 0.060 229B -0.1140 0.1148 -0.0838 -0.149 229A 0.1718 -0.2620 0.2073 0.341 231A 0.1387 -0.2439 0.2101 0.328 868H WASH 229A 194.0185 -335.8332 -176.4013 426.080 230B -0.0135 0.2206 -0.2093 -0.093 229B -0.1019 0.1925 -0.1924 -0.119 231A -0.0053 0.0117 -0.0331 0.002 230A -0.0354 0.0883 -0.1207 -0.036 231B -0.0983 0.1579 -0.1745 -0.097 JEFF WASH 231B 146.1021 -129.6425 80.2985 211.189 231A 0.1341 -0.2111 0.1901 0.295 230A -0.0595 -0.0776 0.0688 0.033 229B -0.1014 0.1360 -0.1639 -0.216 230B 0.0961 0.0648 -0.0276 0.016

  47. L1, Partial Fixed Solution, Predicted Weather From To Session DX (m) DY (m) DZ (m) Vector 1st - Next 1st - Next 1st - Next Length (m) 000A WASH 229A 23.2992 -101.3609 141.9511 175.974 231A 0.0054 -0.0414 0.0020 0.026 230B -0.0435 0.1553 -0.1650 -0.228 229B -0.0236 0.0825 -0.0953 -0.128 231B -0.1005 0.1497 -0.1596 -0.228 868H WASH 229A 194.0163 -335.8572 -176.3620 426.082 229B -0.0323 0.1054 -0.0964 -0.058 230B -0.0366 0.1522 -0.1457 -0.076 231B -0.1028 0.1360 -0.1370 -0.097 231A -0.0302 0.0540 -0.0590 -0.032 230A -0.0070 0.0198 -0.0440 -0.001 JEFF WASH 230A 146.1764 -129.6260 80.2979 211.230 230B 0.1508 0.0315 -0.0017 0.084 229B -0.0509 0.1939 -0.2241 -0.239 231B 0.0809 0.0107 0.0039 0.051 231A 0.1914 -0.1280 0.1387 0.264

  48. L1, Float Solution, Recorded Weather From To Session DX (m) DY (m) DZ (m) Vector 1st - Next 1st - Next 1st - Next Length (m) 000A WASH 229B 23.4735 -101.5769 142.1521 176.284 231B 0.0349 -0.0099 -0.0105 0.002 231A 0.1006 -0.0148 0.0467 0.060 229A 0.1578 -0.0754 0.0643 0.116 230B 0.1569 -0.0359 0.0296 0.065 868H WASH 229A 194.1045 -336.0715 -176.2377 426.240 229B -0.0472 -0.0049 -0.0677 0.010 230A 0.0599 -0.0952 0.0204 0.094 231B -0.0604 -0.0141 -0.0716 0.013 230B 0.0733 -0.0290 -0.0379 0.072 231A 0.0061 -0.0184 -0.0120 0.022 JEFF WASH 230A 146.1589 -129.5715 80.2348 211.161 230B 0.1522 0.1006 -0.0685 0.018 231B 0.0187 0.1229 -0.1099 -0.104 229B 0.0319 0.0955 -0.1089 -0.078 231A 0.1027 0.1151 -0.0498 -0.019

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