# Presentation: 731226

## The RSGPS program andOPUS - RS

- Getting There Faster –

## OPUS-RS

- Uses RSGPS program instead of PAGES
- Uses P1 and P2, as well as L1 and L2, observations
- Resolves all ambiguities with LAMBDA

**Notes:**
Although the front page looks just like regular OPUS, OPUS-RS is actually a major new program. Internally it uses the RSGPS program rather than the PAGES program NGS has used for baseline processing for many years.

RSGPS is a new program, based on research done by the SPIN group at OSU (see paper on this subject at the ION meeting Friday afternoon).

NGS is still accumulating experience on its behavior.

Tgese are its major features

## OPUS-RS search algorithm

- Sort stations in CORS network by distance from rover. Select up to nine CORS that are less than 250 km from rover and that have suitable data.
- No solution is attempted if fewer than three CORS selected.
- No solution attempted if distance from rover to polygon                    enclosing selected CORS is greater than 50 km.

- 250 km limit

- <50 km

**ROVER**

**CORS**

## OPUS-RS uses RSGPS in two modes:
		Network and Rover

In network mode, at least one hour of data from the selected CORS are used to solve for ambiguities, tropospheric refraction, and double difference ionospheric delays at these CORS.  The positions of the CORS are held fixed.

In rover mode, ionospheric delays and troposphere parameters are interpolated (or extrapolated) from the selected CORS to rover.  Then the delays at the rover are constrained to solve for the position of the rover.  Again, the positions of the CORS are held fixed.

- 		Network and Rover
- In network mode, at least one hour of data from the selected CORS are used to solve for ambiguities, tropospheric refraction, and double difference ionospheric delays at these CORS.  The positions of the CORS are held fixed.
- In rover mode, ionospheric delays and troposphere parameters are interpolated (or extrapolated) from the selected CORS to rover.  Then the delays at the rover are constrained to solve for the position of the rover.  Again, the positions of the CORS are held fixed.

- .

**Notes:**
RSGPS has two modes.

When used in OPUS-RS, RSGPS is run first in the network mode, using selected nearby CORS (or IGS) stations as reference stations. This determines the behavior of the troposphere and ionosphere delays in the local area for the time span of the observations. 

RSGPS is then run in rover mode, where the observations from the rover station are now included. Tropospheric and ionospheric delays are now interpolated to the rover, and the data from all stations are adjusted simultaneously.

## OPUS-RS

- Produces solution with as little as 15 minutes of data (vs. 2 hours for current OPUS)
- To improve accuracy and reliability:
- 		- Collect observations for more than 15 			minutes (OPUS-RS accepts up to
-                  4 hours of data)
- 		- perform multiple observation sessions

**Notes:**
These are some of the properties of OPUS-RS

## OPUS-RS

- User interface is identical to regular OPUS, including Options page
- Output report is similar to regular OPUS, but with quality indicators based on the W-ratio from the LAMBDA validation tests
- The normalized RMS is a unitless measure of the scatter in the data misfits
- No peak-to-peak variations

**Notes:**
OPUS-RS will look a lot like regular OPUS

## OPUS-RS Datasheet

-                               NGS OPUS-RS SOLUTION REPORT
-                               ========================
-       USER: rick.foote@noaa.gov                     DATE: March 16, 2007
- RINEX FILE: vari045a.07o                            TIME: 11:40:07 UTC
-   SOFTWARE: rsgps  1.06 RS26.prl                   START: 2007/02/14 00:00:30
-  EPHEMERIS: igs14143.eph [precise]                  STOP: 2007/02/14 00:59:30
-   NAV FILE: brdc0450.07n                        OBS USED:  2784 /  2994   :  93%
-   ANT NAME: TRM41249.00                      QUALITY IND.  21.91/ 64.08
- ARP HEIGHT: 2.0                           NORMALIZED RMS:       0.295
-  REF FRAME: NAD_83(CORS96)(EPOCH:2002.0000)            ITRF00 (EPOCH:2007.12086)
-          X:      1108081.771(m)  see                 1108081.069(m)  see
-          Y:     -4958243.092(m)  accuracy           -4958241.626(m)  accuracy
-          Z:      3843038.534(m)  note                3843038.407(m)  note
-        LAT:   37 17 23.88604                      37 17 23.91389
-      E LON:  282 35 51.40742                     282 35 51.39258
-      W LON:   77 24  8.59258                      77 24  8.60742
-     EL HGT:          -10.287(m)                          -11.624(m)
-  ORTHO HGT:           23.244(m)            [Geoid03 NAVD88]
- UTM COORDINATES    STATE PLANE COORDINATES
-                          UTM (Zone 18)         SPC (4502 VA S)
- Northing (Y) [meters]     4129746.071          1106727.888
- Easting (X)  [meters]      287042.763          3597320.710
- Convergence  [degrees]    -1.45603091           0.66616871
- Point Scale                1.00015868           0.99994631
- Combined Factor            1.00016029           0.99994793

**OPUS-RS Datasheet**

## US NATIONAL GRID DESIGNATOR: 18STG8704329746(NAD 83)

-                               BASE STATIONS USED
- PID       DESIGNATION                        LATITUDE    LONGITUDE DISTANCE(m)
- AF9635 RIC1 RICHMOND 1 CORS ARP            N373216.429 W0772546.775   27622.4
- DI0878 DRV5 DRIVER 5 CORS ARP              N365731.135 W0763323.903   83669.7
- DH7133 NCJA JACKSON NC CORS ARP            N362430.563 W0772615.309   97871.3
- DG5940 VALY MASSIE CORS ARP                N372232.071 W0790735.675  153094.0
- AI3289 VIMS VIRGINIA INSTITUT CORS ARP     N373630.045 W0754113.207  155838.3
- DF8715 NCWI WILLIAMSTON CORS ARP           N354948.750 W0770204.932  165293.6
-                  NEAREST NGS PUBLISHED CONTROL POINT
- DH5858      ED SNIDER CORS ARP             N371723.886 W0772408.592       0.0
- This position and the above vector components were computed without any
- knowledge by the National Geodetic Survey regarding the equipment or
- field operating procedures used.

## OPUS results: independent of reference station geometry and distances 

- Recall that the accuracies of the OPUS-derived positional coordinates do not depend on the geometry of the reference stations.
- Also, the accuracies of the OPUS-derived psitional coordinates depend only slightly on the distances from the rover to the reference stations (perhaps less than 0.01 ppm, that is, less than 1 mm per 100 km).

## OPUS-RS results: Depend on both reference station geometry and distances

- In contrast, the accuracy of OPUS-RS-derived positional coordinates depend both on the geometry of the reference stations and the distances from the rover to the reference stations, because OPUS-RS interpolates (or extrapolates) the atmospheric conditions (tropo- and iono-delays) measured at the reference stations to predict the atmospheric conditions at the rover.

## Interpolative Dilution of Precision (IDOP)

- Suppose z = f(x,y) can be adequately approximated by the equation, z = ax + by + c, and suppose there is a set of independent observations zi at the point (xi , yi) for i = 1,2,3,...,n where n is the number of reference stations.
- If the standard error of each observation equals σ, then the predicted value of z at the point (x0 , y0) has a standard error σ0 given by the expression
-           σ0 = (R/Q)0.5σ
- where
-           R = (∑dxi2)(∑dyi2) – (∑dxidyi)2
- and
- Q = nR + 2(∑dxi)(∑dyi)(∑dxidyi) – (∑dxi)2(∑dyi2) – (∑dyi)2(∑dxi2)
- Here dxi = xi – x0   and  dyi = yi – y0 for i = 1,2, 3,...,n.
- The term (R/Q)0.5 is a unitless quantity called the “interpolative dilution of precision” or IDOP.

## IDOP VALUES AS A FUNCTION OF LOCATION EXAMPLE FOR THE CASE OF 4 CORS 

**BEST IDOP =  **1/**√ N**
**THEREFORE, WITH 9 CORS, THE IDOP AT THE CENTROID WOULD BE .33, **
**WITH 4 CORS IT WOULD BE .5 AT THE CENTROID**

**Notes:**
IDOP – Interpolative Dilution of Precision is a measure of the suitability of the geometry between the network stations and the rover (or the VRS). It tells us how well we can interpolate quantities such as tropospheric refraction from know values at the network stations to the rover (or the VRS). The best situation occurs when the network stations are evenly spaced and the rover falls exactly in the middle. The value of IDOP grows progressively larger as the rover moves away from the centroid of the network stations, becoming quite large when the rover is outside the polygon enclosing the reference stations. Unfortunately, this can happen when the surveyor is working close to the coast and all the reference stations are inland. 

## Slide 14

## Accuracy depends on IDOP & RMSD

- RMSD = Root mean square distance
- 	RMSD = [ ( ∑ di2 ) / n ]0.5
- where di is the distance between the rover and the i-th CORS,
- and n equals the number of CORS being used.
- Sigma = [ (a*IDOP)2 + (b*RMSD)2 ]0.5
- where a and b are constants.

## Values for a and b

- East-west:  a = 1.87 ± 0.26 cm     b = 0.047 ± 0.010 ppm
- North-south:  a = 1.77 ± 0.21 cm     b = 0.05 ± 0.008 ppm
- Up-down:   a = 6.69 ± 0.71 cm      b = 0.151 ± 0.028 ppm
- Note that the north-south values are statistically indistinguishable from the east-west values.
- Also note that the up-down values are about 3.7 times larger than either the north-south values or the east-west values.

## Vertical standard error achievable when a user submits 15 minutes of GPS data to OPUS-RS

## POB

**POB**