GPS data and computation

    There are two kinds of basic GPS observations: the pseudorange and the carrier phase. The pseudorange is generated by correlation between the satellite generated code and the identical copy of the code generated inside the receiver, while the carrier phase is generated by comparing the carrier frequency of the transmitted signal and the receiver generated replica [Hofmann-Wellenhof et al., 2001]. The pseudorange and carrier phase observations include error sources such as receiver clock offsets, satellite clock offsets, troposphere delay, ionospheric delay etc. Therefore, the complete equations for pseudorange (3-9) and carrier phase (3-10) observations are given by:

(3-9)

(3-10)

where P is the measured pseudorange in meters; is the measured carrier phase in meters; ρ is the true geometric range in meters; c is the speed of light in vacuum in m/s; dT is the satellite clock error in seconds; dt is the receiver clock error in seconds;

is the tropospheric delay in meters; is the ionospheric delay in meters; λ is the signal wavelength in m/cycle; N is the integer ambiguity in cycles; is the pseudorange measurement noise in meters and is the carrier phase measurement noise in meters.

When the GPS signal travels through the troposphere, its path will bend slightly due to the refractivity of the troposphere thus the signal is delay.  The tropospheric delay T at zenith is divided in a dry part and wet part therefore the tropospheric delay is given as [Saastamoinen, 1973]:

(3-11) The dry part can be estimated by following equation:   

0.0022768       (3‐12)  3.2.1 GPS observations and its error source

The signal of the GPS satellites is also delay when signal pass through the ionospheric. The first order approximation of the ionoshperic delay I is given as [Hofmann-Wellenhof et al., 2001]:

. (3-14) where TEC is the Total Electron Content along the signal path in units of electrons/m , and f is the L1 or L2 carrier frequency. Usually the ionoshperic delay can be eliminated by combining the observations into ionoshperic-free combination.

Finally the satellite clock error dT and the receiver clock error dt can be eliminated by applying double difference on observations. The satellite clock error can be eliminated and the orbital, tropospheric, ionospheric errors are also significantly reduced. The derived observations after differencing between receivers are known as the single difference. After differencing the single difference observations between different satellites, the double difference observations are derived and the receiver clock error eliminated.

In this study GPS observations include 168 GPS campaign-mode sites installed by the Central Geological Survey and 37 continuous-recorded GPS sites between 2002 and 2010 (Fig. 3-3). For GPS campaign-mode sites, observations are collected annually and three to ten stations are observed at the same time with dual-frequency geodetic receivers (Trimble 4000 SSE, Trimble 4700, Ashtech Z-XII, Ashtech Z-Extreme, Leica SR9500, Leica SR399, Leica GX1230, and Leica SR530) in each survey. Stations are usually observed more than two sessions and every session is about 6-14 hours with all available satellites rising higher than a 15° elevation angle being tracked. The sampling interval for data logging is 15 seconds. About 43% GPS data were collected more than 6 years. About 37% GPS data were collected between 2.5 and 6.0 years. Others were collected 1.0-2.5 years. The raw data for each station are transferred to the RINEX (Receiver INdependent EXchange) format by a transfer program for the use in post-processing.

As for the continuous-recorded GPS data, all sites are installed at least three year.

Most sites have been installed five or six years and the longest time spam is nine years.

All continuous-recorded GPS sites are receiving signals for 24 hours every day and the sampling intervals for data logging are 15 or 30 seconds. Most sites are installed by MOI (Minister of Interior), CGS (Central Geological Survey), CWB (Central Weather Bureau) and IES (Institute of Earth Sciences).

3.2.2 GPS data

Fig. 3-3: The distribution of GPS sites in southwestern Taiwan. Black triangles are campaign-mode sites. White triangles are continuous-recorded sites. Red dash lines are active fault. HCLF: the Houchiali fault, HKSF: the Hsiaokangshan fault, CHNF: the

All GPS data was processed session by session with Bernese software v.5.0 on the international terrestrial reference frame (ITRF2008) for acquiring daily coordinate solutions. The precise ephemerides are provided by International GNSS Service (IGS) and polar motion correction is using IERS Bulletin B values. After acquired a precise satellite orbit, observed codes are used to perform single point positioning and receiver clock correction. Triple difference of phase measurements are also used to compensate cycle-slips and detect blunder measurements before performing the relative positioning. The detected blunder measurement will not be used in following positioning procedures. In order to solve coordinate parameters, carrier-phase measurements form as double difference observations to perform relative positioning.

Ambiguities are solved by QIF (Quasi-Ionosphere-Free) algorithm which is capable to solve the and ambiguities without code observations [Steigenberger et al., 2006]. Tropospheric propagation effect is corrected by using Saastamoinen model with standard weather data including temperature, relative moisture and atmospheric pressure [Saastamoinen, 1973].

In order to promote the accuracy of solutions, whole computation process was divided into two parts. The first part is to compute positions and velocities of six local permanent stations (PKGM, S01R, KDNM, CKSV, LIUC and KMNM). Positions and velocities of six permanent stations are determined by four global IGS fiducial stations around Taiwan (TSKB, GUAM, PERT and IISC) by minimizing common-mode deviations from linear velocities. The second part is solving the coordinates of all GPS stations in SW Taiwan, all GPS stations were calculated from six local stations whose coordinates were derived from the a priori positions and velocities. Generally, the horizontal uncertainties of coordinates are 3 to 8 mm and the vertical uncertainties are approximately 10 to 20 mm for campaign-mode sites. As for continuous-recorded GPS sites, the horizontal uncertainties of coordinates are 2 to 5 mm and the vertical uncertainties are approximately 10 to 15 mm.

3.2.3 Computation strategies