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

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

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

Ellipsoid, Geoid, and Orthometric Heights “Geoid” POPO P H (Orthometric Height) = Distance along plumb line (P O to P) Earth’s Surface Ocean Ellipsoid “h = H + N” N h Q N (Geoid Height) = Distance along ellipsoid normal (Q to P O ) h (Ellipsoid Height) = Distance along ellipsoid normal (Q to P) Plumb Line Mean Sea Level

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

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

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

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

Available “On-Line” at the NGS Web Site:

Table Summary of Guidelines

Sample Project Showing Connections CS1 PB2 SB2 LN4 LN3 LN2 LN5 LN1 LN7LN6 SB1 SB3 SB5 SB4 PB4 PB1 PB3 CS2 CS4 CS3

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

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

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

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

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. BCR4: This requirement is not applicable because project is not in a mountainous region. BCR Example 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.

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

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

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.

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

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.

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

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.

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.

Elevation published to centimeters. Orthometric height determined by GPS.

GPS-Derived Orthometric Heights Project

Baltimore County Maryland, NAVD88 GPS-Derived Orthometric Height Project

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

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

HYDES HARN LINE 81 MELSAGE HARN SAUTER RESET Baltimore City KEY 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 6D 5B 6D 5B 6D 5B 6D 5A 6C 6C, 5A 5A 6C 6C 5A 4E 6B 4E 4E 6B 4D 6B 6A 4E 4D 6A 4C 5E 4C 4D 5E 6A 4D 6A 4C 5E 4A 5C 4A 5C 4A 5C 4B 5D 4B 5D 5D 4B 4C 5E

Repeat Baseline Differences

Repeat Baseline Differences (Baselines less than 10 KM)

Height Differences (du) 5 Hour Sessions

Height Differences (du) 45 Minute Sessions

Height Differences (du) 45 Minute Sessions (continued)

Vertical Free Adjustment Results GEOID96

Vertical Free Adjustment Results G96SSS

Vertical Free Adjustment Results GEOID93

Baltimore County GPS-Derived Orthometric Height Project

Station Name GPS-derived Orthometric height relative to MELSAGE from minimally constrained adjustment (m) GPS-derived Orthometric height from final constrained adjustment (m) C=Constrained Minimally constrained minus final constrained adjustment (cm) GIS C-1.5 GIS GIS GIS GIS GIS GIS GIS GIS C-0.4 Final Set of GPS-Derived Orthometric Heights

Station Name GPS-derived Orthometric height relative to MELSAGE from minimally constrained adjustment (m) GPS-derived Orthometric height from final constrained adjustment (m) C=Constrained Minimally constrained minus final constrained adjustment (cm) GIS C-0.6 GIS GIS GIS GIS C-0.9 HYDE LINE C0.5 MELSAGE C0.0 SAUTER RESET Final Set of GPS-Derived Orthometric Heights (cont.)

Data Processing and Analysis of Repeat Base Line Results

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

Washington Monument Survey

From To Session DX (m) DY (m) DZ (m) Vector 1st - Next 1st - Next 1st - Next Length (m) 000A WASH 231B B B A A H WASH 229A B B A A B JEFF WASH 231B A A B B 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 229A A B B B H WASH 229A B B B A A JEFF WASH 230A B B B A 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 229B B A A B H WASH 229A B A B B A JEFF WASH 230A B B B A L1, Float Solution, Recorded Weather

Analysis of the Data Processing Fixed solutions / low RMS Repeatability of measurements Analysis of loop misclosures Be aware that repeatability and loop misclosures do not disclose all problems

From To Session dh Diff Dist RMS Solution Station Station Meters cm Meters Type BR13 BR * L1 float double L1 fixed double L1 fixed double BR13 K L1 fixed double L1 fixed double L1 fixed double BR14 GR L1 fixed double * L1 fixed double * L1 fixed double BR19 CL * L1 fixed double L1 fixed double * L1 fixed double BR20 BR Iono free fixed Iono free fixed Iono free fixed BR20 VINT HILL Iono free fixed Iono free fixed Iono free fixed *NOTE - Reprocess all vectors which have difference greater than 2 cm. Repeat Vector Analysis

From To Session dh Diff Dist RMS Solution Station Station Meters cm Meters Type BR13 BR L1 fixed double L1 fixed double L1 fixed double BR13 K L1 fixed double L1 fixed double L1 fixed double BR14 GR L1 fixed double L1 fixed double L1 fixed double BR19 CL L1 fixed double L1 fixed double L1 fixed double BR20 BR Iono free fixed Iono free fixed Iono free fixed BR20 VINT HILL Iono free fixed Iono free fixed Iono free fixed Repeat Vector Analysis After Re-Processing

Adjustment Procedures to Obtain GPS-Derived NAVD’88 Orthometric Heights

Least Squares Adjustments The adjustment minimizes the effects of random errors A least squares adjustment computes a single network solution, even with redundant vectors Least squares will highlight blunders and large errors It will provide estimates on the precision of the coordinates for the stations

Errors All real observations contain errors  Two types of errors » Random errors which mean to zero » Systematic errors which do not Least squares will only give improved results if your errors are predominantly random Random error Systematic error

Least Squares Least squares is a mathematical procedure that takes a series of survey measurements  which must contain some extra or redundant measurements and calculates a single set of coordinates for the stations that will satisfy all of the measurements while minimizing the sum of the squares of the misfit (or residuals) Least Squares Condition v Critical value Outliers

SEUW =   (estimated errors) 2   (residuals) 2 Standard Error of Unit Weight If the residuals from a least squares adjustment are equal to the errors expected for the order of survey we have performed  The standard error of unit weight will have a value of unity If the residuals are lower than we would expect given our initial estimates of the errors  SEUW will be less than 1 If they are too high  SEUW will be greater than 1 Often used as a rough indication of whether a survey meets specifications

Minimally Constrained Adjustment Hold the minimum number of control points fixed to allow the least squares process to work  One fixed point for GPS  2 for triangulation survey without distance measurements The purpose of this adjustment is to  Check the internal consistency of the network  Detect blunders or ill-fitting observations  Obtain accurate error estimates How big do you make the bolt holes?

Constrained Adjustment Hold all control points in the network fixed at values from the NGS database  Minimum of 2 for GPS surveys  3 for triangulation survey without distance measurements The purpose of this adjustment is to  Reference the network to existing control and develop final coordinates for the new control points that are being established  Verify existing control. If any control points are wrong the standard error of unit weight and the residuals will increase compared to the minimally constrained adjustment

Adjustment of Primary Network Stations Horizontal Adjustment (Latitude, Longitude, Ellipsoid Heights) Minimum Constrained [One fixed station]  Fix latitude, longitude and ellipsoid height at one station  Resolve all blunders and large residuals  Determine which Control and known Primary Base Station coordinates should be fixed Constrained [All suitable stations fixed]  Fix latitude, longitude, and ellipsoid heights at Control and known Primary Base Stations  Make sure the constraints did not distort the project NOTE - Geoid model NOT applied at this time

CORS HARN NAVD’88 BM New Station 121°40’W 122°35’W 37°50’N 38°20’N LATITUDE LONGITUDE Primary Base Station Adjustment of Primary Base Stations MOLA MART LAKE 10CC D km 25.8km 38.7km 19.0km 28.7km 25.7km 38.3km 31.6km CORS, Control Points (known Primary Control) horizontal latitude, longitude, and ellipsoid heights No NAVD88 orthometric heights constrained at this time

Adjustment of Local Network Stations Horizontal Adjustment (Latitude, Longitude, Ellipsoid Heights) Minimum Constrained [One fixed station]  Fix latitude, longitude and ellipsoid height at one station  Resolve all blunders and large residuals  Evaluate coordinates at Control and Primary Base Station » should not be greatly affected by Local Station baselines Constrained [All suitable stations fixed]  Fix latitude, longitude, and ellipsoid heights at Control and Primary Base Stations  Make sure the constraints did not distort the project NOTE - Geoid model NOT applied at this time

CORS HARN NAVD’88 BM New Station Spacing Station 121°40’W 122°20’W 37°55’N 38°16’N LATITUDE LONGITUDE Primary Base Station 8. 2km Adjustment of Local Network Stations Existing and newly derived Primary Control horizontal latitude, longitude, and ellipsoid heights No NAVD88 orthometric heights constrained at this time

Combined Network Horizontal Adjustment Perform combined adjustment  Control and Primary Base network along with local network  Latitude, longitude, and ellipsoid height Use GEOID model to obtain geoid heights Make sure combined adjustment did not distort the project

Combined Horizontal Adjustment CORS HARN NAVD’88 BM New Station 121°40’W 122°35’W 37°50’N 38°20’N LATITUDE LONGITUDE Spacing Station Primary Base Station 8.2km CORS, Control Points and existing and new Primary Control horizontal latitude, longitude, and ellipsoid heights No NAVD88 orthometric heights constrained at this time

3-D Vertical Adjustment (Orthometric Heights) Minimum Constrained [One fixed station]  Fix latitude, longitude, and orthometric height at one station  Resolve all blunders and large residuals  Compare orthometric heights from adjustment with published NAVD 88  Determine which NAVD 88 bench marks should be fixed Constrained [All suitable orthometric heights fixed]  Fix latitude, longitude at one station  Fix orthometric heights at all suitable stations  Make sure the constraints did not distort the project Combined Network Vertical Adjustment

Constrained Vertical Adjustment CORS HARN NAVD’88 BM New Station 121°40’W 122°35’W 37°50’N 38°20’N LATITUDE LONGITUDE Spacing Station Primary Base Station 8.2km 1 horizontal latitude and longitude All valid NAVD88 orthometric heights

Topography A B C D E F GPS-Derived Heights from GEOID03 Separation = Published NAVD88 Orthometric Height= New Control Ellipsoid h h h h h h GEOID03 N N N N N N Hh-NHh-N Hh-NHh-N Hh-NHh-N Hh-NHh-N Hh-NHh-N Hh-NHh-N

Constrained Vertical Adjustment Topography A B C D E F h adj Adjusted Ellipsoid Ellipsoid Height Adjusted to Fit Constrained Orthometric Heights GPS-Derived Orthometric Heights = Published NAVD88 Orthometric Height= New Control H H H H Geoid GEOID03 N N N N N N Ellipsoid h h h h h h H GPS

Summary Mistakes and systematic errors must be removed before the adjustment A least squares adjustment handles random errors and provides a single solution The Minimally Constrained adjustment checks the internal consistency of the network The Constrained adjustment checks the existing control and references the network to the datum The vertical adjustment estimates GPS-derived Orthometric heights

Analysis of a Height Project The project consists of 3 different parts as follows: 1. Determine ellipsoid height of the two bridges using three different GPS receivers on the two bridges, one receiver at the pilot house, and a CORS site. 2. Determine the difference between Geoid96 with NAVD 88 by observing a minimum of four NAVD 88 bench marks including one primary bench mark at the tidal station. 3. Determine the height from the bottom of the bridges to each of the antenna mounts on the bridges using classical and trig leveling. This project plan is for measuring the vertical clearance for the Cooper River Bridges, known as the Grace Memorial Bridge and Silias Pearman Bridge.

Implementation of real-time, using GPS, sensors that will determine the maximum height of a vessel at the lowest point of a bridge. This project plan is for measuring the vertical clearance for the Cooper River Bridges. Vertical clearance is critical for ensuring safe navigation for the Port of Charleston, South Carolina.

MOUNTING THE ANTENNAS 1. Determine ellipsoid height of the two bridges using three different GPS receivers on the two bridges, one receiver at the pilot house, and a CORS site.

GPS OCCUPATION CLASSICAL LEVELING 2. Determine the difference between Geoid96 with NAVD 88 by observing a minimum of four NAVD 88 bench marks including one primary bench mark at the tidal station.

TRIG-LEVELING 3. Determine the height from the bottom of the bridges to each of the antenna mounts on the bridges using classical and trig leveling.

Height Project C 69 TBM SILE ARP HOLLINS TIDAL 13 CBPA CHA1 CORS NAVD88 Bench Mark Temporary (Project) CORS (Mounted to each end of bridge) (Connection to water surface)

From To Session Length DX (m) DY (m) DZ (m) Vector ppm (Hrs) 1st - Next 1st - Next 1st - Next Length (m) 1001 TIDE 036A B CBPA CHA1 040A A A CHA1 SILE 034A A A CPBA TIDE 036A B HOLL SILE 034B C Repeat Vector Analysis

STATION NAME LAT / LON ELLIPSOID SHIFT (cm) SHIFT (cm) * CHARLESTON 1 CORS ARP TIDAL * No Published Ellipsoid Height Free Adjustment Horizontal Positions Compared to Published NAD83 Positions

Free Adjustment minus NAD83 Published 0.8cm Horiz 1.8cm Ellip. Ht. FIXED C 69 TBM SILE ARP HOLLINS TIDAL 13 CBPA CHA1 CORS NAVD88 Bench Mark Temporary (Project) CORS 32.8cm Horiz Residuals plotted to help determine inconsistencies

CJ0085 DESIGNATION TIDAL 13 CJ0085 ______________________________________________________________ CJ0085* NAD 83(1992) (N) (W) ADJUSTED CJ0085* NAVD (meters) 7.28 (feet) ADJUSTED CJ0085 ______________________________________________________________ CJ0085 ELLIP HEIGHT (meters) GPS OBS CJ0085 CJ0085 HORZ ORDER - FIRST CJ0085 VERT ORDER - FIRST CLASS I ****************************************************************************** CJ0578 DESIGNATION CJ0578 CJ0578 ______________________________________________________________ CJ0578* NAD 83(1986) (N) (W) ADJUSTED CJ0578* NAVD (meters) (feet) ADJUSTED CJ0578 ______________________________________________________________ CJ0578 CJ0578 HORZ ORDER - FIRST CJ0578 VERT ORDER - FIRST CLASS II NOTE - Different adjustments for the positions Sample Data Sheets

STATION NAME LAT / LON ELLIPSOID SHIFT (cm) SHIFT (cm) C HOLLINGS TIDAL TBM SILE ARP CHARLESTON POLIT HOUSE ARP TBM SILW ARP TBM GRAC ARP CHARLESTON 1 CORS ARP TBM SALAIS BOTTOM OF BRIDGE Adjusted Constrained Horizontal Compared to Free Horizontal Positions [Station Not Fixed] Minimum shifts between free and constrained adjustments Constraints did not adversely affect adjustment

STATION NAME LAT / LON ELLIPSOID SHIFT (cm) SHIFT (cm) C HOLLINGS TIDAL TBM SILE ARP CHARLESTON POLIT HOUSE ARP TBM SILW ARP TBM GRAC ARP CHARLESTON 1 CORS ARP TBM SALAIS BOTTOM OF BRIDGE Adjusted Constrained Horizontal Compared to Free Horizontal Positions [Station Fixed] A bad constraint in position also affects the ellipsoid heights

STATION NAME LAT / LON ORTHOMETRIC SHIFT (cm) SHIFT (cm) C HOLLINGS TIDAL TBM SILE ARP TBM SILW ARP Free Vertical Adjustment Compared to Published NAVD88 Elevations GPS-derived orthometric height does not agree with published orthometric height

Free Vertical Adjustment minus NAVD88 Published C 69 TBM SILE ARP HOLLINS TIDAL 13 CBPA CHA1 CORS NAVD88 Bench Mark Temporary (Project) CORS -8.2cm FIXED 0.6cm 0.1cm 0.9cm Residuals plotted to help determine trends or inconsistencies

STATION NAME LAT / LON ORTHOMETRIC SHIFT (cm) SHIFT (cm) C HOLLINGS TIDAL TBM SILE ARP CHARLESTON POLIT HOUSE ARP TBM SILW ARP TBM GRAC ARP CHARLESTON 1 CORS ARP TBM SALAIS BOTTOM OF BRIDGE Adjusted Constrained Vertical Compared to Free Vertical Elevations [Station Not Fixed] Minimum shifts between free and constrained adjustments Constraints did not adversely affect adjustment

STATION NAME LAT / LON ORTHOMETRIC SHIFT (cm) SHIFT (cm) C HOLLINGS TIDAL TBM SILE ARP CHARLESTON POLIT HOUSE ARP TBM SILW ARP TBM GRAC ARP CHARLESTON 1 CORS ARP TBM SALAIS BOTTOM OF BRIDGE Adjusted Constrained Vertical Compared to Free Vertical Elevations [Station Fixed] A bad constraint in orthometric height affects all orthometric heights

NGS Data Sheet GEOID03 H = =  (-32.60) - Nh GEOID96 = 0.17 m GEOID99 = 0.11 m GEOID03 = 0.05 m

NAVD ‘88 Relative to (h - N) GEOID03 San Francisco Bay Demonstration Project

GPS Site L 1241 (+3.6) U 1320 (+3.5) S 1320 (+4.5) TIDAL 32 (+0.4) RV 223 (+0.4) R 1393 (-1.3) N 1197 (+2.9) M 148 (+1.1) M 554 (-0.6) TIDAL 7 (-2.4) KM H = h - N Comparisons with Published Station Heights (Centimeters) H = Orthometric Height h = Ellipsoid Height N = Geoid Height GEOID03

“Real World”

“Mapping World”

8002 The Opus solution for your submitted RINEX file appears to be 8002 quite close to an NGS published control point. This suggests that 8002 you may have set your GPS receiver up over an NGS control point Furthermore, our files indicate that this control point has not 8002 been recovered in the last five years If you did indeed recover an NGS control point, we would 8002 appreciate receiving this information through our web based 8002 Mark Recovery Form at

First station : SURVEYOR 290 Second station : SURVEYOR 284 Delta height = Ellipsoidal distance =.0070 Mark to mark distance =.0231 DX =.0122 DN =.0068 DY =.0163 DE =.0015 DZ = DU = First station : SURVEYOR 290 Second station : SURVEYOR 278 Delta height = Ellipsoidal distance =.0089 Mark to mark distance =.0174 DX =.0114 DN =.0083 DY =.0122 DE =.0030 DZ = DU = First station : SURVEYOR 290 Second station : SURVEYOR 277 Delta height = Ellipsoidal distance =.0083 Mark to mark distance =.0115 DX =.0079 DN =.0080 DY =.0084 DE =.0022 DZ = DU = OPUS Processing Comparisons Day hr 7 min Day hr 23 min Day hr 14 min Day hr 7 min

= CORS = Base Receiver = Rover Receiver OPUS - Multiple CORS Providing Position to Base Receiver

P CORS 3 CORS 1 N CORS 2 P = Published Point N = New Point FINAL POSITION N Process Mean Position + N OPUS Mean Position 2 N Process+OPUS Position N Final Position N OPUS 1 + N OPUS 2 2 N O 1+2 N OPUS Mean Position How well OPUS 1 fits OPUS 2 P OPUS 1 + P OPUS 2 2 P O 1+2 P OPUS Mean Position How well OPUS 1 fits OPUS 2 P Published Position - P OPUS Mean Position How well OPUS fits Published P-N Process Mean Position - N OPUS Mean Position How well Process fits OPUS P-N Process 1 + P-N Process 2 2 P-N Process 1+2 P-N Process Mean Position How well Process 1 fits Process 2 Two 2+ Hour Sessions Two Receivers