The RSGPS program andOPUS - 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

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

ROVERROVER

CORSCORS

• 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.

•.

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

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

NGS OPUS-RS SOLUTION REPORT ========================

USER: rick.foote@noaa.gov DATE: March 16, 2007RINEX 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/ 64.08ARP 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 1106727.888Easting (X) [meters] 287042.763 3597320.710Convergence [degrees] -1.45603091 0.66616871Point Scale 1.00015868 0.99994631Combined Factor 1.00016029 0.99994793

OPUS-RS Datasheet

US NATIONAL GRID DESIGNATOR: 18STG8704329746(NAD 83)

BASE STATIONS USEDPID DESIGNATION LATITUDE LONGITUDE DISTANCE(m)AF9635 RIC1 RICHMOND 1 CORS ARP N373216.429 W0772546.775 27622.4DI0878 DRV5 DRIVER 5 CORS ARP N365731.135 W0763323.903 83669.7DH7133 NCJA JACKSON NC CORS ARP N362430.563 W0772615.309 97871.3DG5940 VALY MASSIE CORS ARP N372232.071 W0790735.675 153094.0AI3289 VIMS VIRGINIA INSTITUT CORS ARP N373630.045 W0754113.207 155838.3DF8715 NCWI WILLIAMSTON CORS ARP N354948.750 W0770204.932 165293.6

NEAREST NGS PUBLISHED CONTROL POINTDH5858 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 = (∑dxi

2)(∑dyi2) – (∑dxidyi)2

andQ = nR + 2(∑dxi)(∑dyi)(∑dxidyi) – (∑dxi)2(∑dyi

2) – (∑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

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

POBPOB