Satellite Geometry: Satellites well spread out in the sky have a much stronger solution to the resection type problem (aka trilateration) then satellite that are grouped together. Since the position of satellite is well known software planning tools are available to assist in selecting the best times for GPS observations. Good Geometry (Strong) Poor Geometry (Weak) Dilution of Precision (DOP): Software for determining DOP is freely available on the Trimble web site. Low DOP values provide greater accuracy results. See: http://www.trimble.com/planningsoftware_ts.asp Lect 18 - Oct 29/07 Slide 1 of 8
GPS Error Summary: (Section 13.6). Direct code-based GPS observations can can locate absolute position (or point positioning). Point positioning errors include: 1) Clock Errors, 2) Atmospheric Refraction of EM radiation, 3) minor errors due to: i) satellite position accuracy, ii) multipath reflection, iii) receiver setup error, iv) satellite geometry, v) selective availability. These are summarized as: Error Source Size of Error (m) Satellite Clock 0-3 Satellite Perturbations 0-1 Ephemeris Error 1-5 Ionospheric Refraction 0-10 Troposperic Refraction 0-2 Receiver Noise 0-4.8 Other (multipath, etc) 0-0.5 Together these account for a 10-20 m error level. Error reduction can accomplished by modeling some of the errors (explained in Lect 17). However, significant error reduction can be achieved through: 1) Differential GPS - base station errors are broadcast to users (error 0.5-3 m) 2) Carrier Phase Relative Positioning - monitoring GPS phase at two locations (error mm cm) Lect 18 - Oct 29/07 Slide 2 of 8
Differential GPS: (Section 13.7). Involves locating a GPS receiver at a known location (base station)and broadcasting the error to user (rover) who receive the error and make corrections to code-based absolute positions. Locating the the base (A) at a known position allows a maority of the error sources for the satellite () can be evaluated: R A (t 0 ) = A (t 0 ) + A (t 0 ) + c (t 0 ) c A (t 0 ) Normally our goal is to find (X,Y,Z) A by observing R A from four satellite. However, in this case we know (X,Y,Z) A and we can determine A exactly. This allows a pseudorange correction to be determined for satellite (PRC ) as: PRC = R A (t 0 ) + A (t 0 ) = A (t 0 ) + c (t 0 ) c A (t 0 ) These corrections capture the atmospheric corrections. Because we cannot broadcast corrections for every millisecond code repetition, we generate PRC at reference times (t o ) and a rate of change from reference time to reference time called a range rate correction (RRC ). This allow a PRC to generated at any time t. The PRC and RRC are broadcast (radio or satellite) to user who use the information to correct there code-based pseudoranges as: R B corrected = R B + PRC = B + B A = B c + c + c[ B A ] Here we have assume the atmosphere between B is the same as B and the receiver clock error is removed by differencing with an addition satellite measurement. Lect 18 - Oct 29/07 Slide 3 of 8
Differential GPS Implementation: (Section 13.7). A number of private firms offer such as Omnistar provide subscripting based DGPS service anywhere in the world (~$2500/yr) through satellite broadcast. www.omnistar.com The Canadian Government has a service called CDGPS delivered via MSAT that can be used in the US and Canada. It is a free service that has recently expanded. www.cdgps.com These services were initially envisaged to allow SA (100 m errors) to be removed from GPS code-based signals since SA could be removed through differencing. While the need is less significant benefits over straight code-based solutions result (10 m for code-based GPS to 1 m for DGPS). Other services are offered through radio by the Canadian Coast Guard (www.ccg-gcc.gc.ca/dgps/) for ship navigation and the high availability WAAS system from the FAA for air navigation and zero visibility landings (en.wikipedia.org/wiki/wide_area_augmentation_system) Lect 18 - Oct 29/07 Slide 4 of 8
Relative Positioning: (Section 13.8-.9). Survey grade GPS solutions are made available by measuring the carrier phase angle of the GPS signal. The easy part is counting the number of full waves that change between the satellite and the receiver once a lock occurs. The hard part is determining the initial number of full waves between the satellite and the receiver. We start this process by correcting the code-based measurement using a Base Station set over a known location. This allows us to determine our gross error and make an estimate of the integer ambiguity or the base to the satellite. This estimate is improved further and further by making difference calculations. The more satellites, frequencies (L1 and L2), and observation time you have, the fast it is to resolve the integer ambiguity. We use our knowledge of (X,Y,Z) A together with difference equations to determine the location of (X,Y,Z) B Lect 18 - Oct 29/07 Slide 5 of 8
Differencing: (Section 13.8-.9). The process of determining the integer ambiguity involves differencing where satellite observations are subtracted from one another at multiple receive and satellite combinations over multiple time periods. Single Differencing Double Differencing Triple Differencing A f = 1 A + N A f A - A f = 1 A + N A f A i - = 1 AB + N AB f = 1 i i AB + N AB f i - (t 1 ) = 1 AB(t 1 ) + N AB (t 2 ) = 1 AB(t 2 ) + N AB = 1 AB + N AB f = 1 AB + N AB (t 12 ) = 1 AB(t 12 ) Satellite Clock Error Removed Receiver Clock Error Removed Ambiguity Removed Carried Phase Equation Lect 18 - Oct 29/07 Slide 6 of 8
Real-Time Kinematic (RTK) GPS: (Section 14.2.5). The modern survey grade GPS systems use radios to broadcast corrections and ambiguity tracking from the base station to rovers to determine initial ambiguity and ambiguity counts after satellite lock. RTK has the advantage over other (older) kinetic methods of being able to field check results because results are obtained instantaneously and require no office post-processing. These devices can monitor up to 40 channels of satellite data (20 satellites on L1 & L2) for either GPS and GLONSS systems. Error ±(10mm + 1 ppm) Horizontal ; ±(15mm + 1 ppm) Vertical Lect 18 - Oct 29/07 Slide 7 of 8
Elevations from GPS: (Section 13.4.3). It Is important to note that heights generated by GPS are those relative to the ellipsoid (WGS 84). This is different from the elevation derived from MSL benchmark propogation. What is measured by GPS is h the height of the GS antenna above the ellipsoid (or geodetic height). We can find the geoidual undulations (N) for a given location in Canada by going the NRCan web site for ellipsoid transformations and downloading software to make transformations to old CGVD28 orthometric heights. http://www.geod.nrcan.gc.ca/software/gpsht_e.php Alternatively, there is an on-line application. Lect 18 - Oct 29/07 Slide 8 of 8