6.S Multipath
9. Data processing
9.1 Data preprocessing
9.1.1 Data handling
180 9. Data processing in a session is marked by an asterisk. This table immediately shows during which sessions a certain site has been occupied, or, inversely, which sites have been included in a certain session. The latter question is more relevant, as it determines which baselines can be computed from a certain session. For this reason, computer storage based on sessions is preferable.
The header of each session file should contain the session identifier and a list of the occupied sites. The header is followed by data blocks. The first block could contain the information for all satellites tracked during that session. An additional block could be reserved to store the following data for each site:
1. Measured data (e.g., carrier phases, code ranges, meteorological data).
2. Intermediate results (e.g., navigation solution, diagnostic messages).
3. Supplementary information (e.g., site description, receiver unit, field crew).
Figure 9.1, for example, represents the file for the first session of the survey.
This type of storage is called a linear list after Knuth (1978) where the data are addressed by the use of pointers. To find the data for a certain site, one has simply to search in the header for the site identifier, and the correspond-ing data are accessed by the pointer.
Data exchange. Although the binary receiver data may have been converted into computer independent ASCII format during downloading, the data are still receiver dependent. In this case, the data management previously
de-Session: a Site: P1
Header P2
P5 P6 Satellite data P1 site data Data blocks P2 site data P5 site data P6 site data
Fig. 9.1. Data management by a linear list
9.1 Data preprocessing 181 Table 9.2. Contents of RINEX format
Observation Meteorological Navigation
data file data file message file
Header Header Header
Site Site Comments
Crew Observation types
Equipment Comments
Eccentricities Observation types Comments
Data Data Data
Epoch Epoch Epoch
Satellites Measurements SV clock parameter
Measurements SV orbital parameters
Flags Ionospheric correction
Flags
scribed is appropriate only when (in each session) one receiver type is used.
Also, each GPS processing software has its own format which necessitates the conversion of specific data into a software independent format when they are processed with a different type of program.
From the preceding, one can conclude that a receiver independent format of GPS data would promote the data exchange. Such a common format should use standard definitions and should also be flexible enough to meet future requirements. To date, many formats have been proposed by various institutions but, for several reasons, they have not received wide acceptance.
A recent attempt has been made with the RINEX (Receiver Independent Exchange) format, d. Table 9.2. This format was first defined by Gurtner et al. (1989) and has been published in a second version by Gurtner and Mader (1990). The format consists of three types of ASCII files: (1) the observation data file containing the range data, (2) the meteorological data file, and (3) the navigation message file. The records of the files have variable lengths with a maximum of 80 characters per line. Each file is composed of a header section and a data section. The header section contains generic file information and the data section contains the actual data. The navigation message file is site independent, while the observation and meteorological data files must be created for each site of the session.
At present, RINEX is the most favored format. As a consequence, some
182 9. Data processing receiver manufacturers produce software for the conversion of their receiver dependent format into RINEX. The U.S. National Geodetic Survey (NGS) has acted as a coordinator for these efforts. For a detailed description of the RINEX format, the reader is referred to the cited literature. Table 9.2 gives an overview of the different file formats. For the satellites the abbreviation SV, meaning space vehicle, has been used.
RINEX uses the file naming convention "ssssdddf.yyt". The first four characters of the sequence are the site identifier (ssss), the next three the day of year (ddd), and the eighth character is the session number (f). The first two file extension characters denote the last two digits of the current year (yy), and the file type (t) is given by the last character. The satellite designation is in the form "snn". The first character (s) is an identifier of the satellite system and the remaining two digits denote the satellite number (e.g., the PRN number). Thus, the RINEX format enables the possible combination of different satellite observations such as GPS and TRANSIT.
9.1.2 Cycle slip detection and repair
Definition of cycle slips. When a receiver is turned on, the fractional beat phase (i.e., the difference between the satellite transmitted carrier and a receiver generated replica signal) is observed and an integer counter is ini-tialized. During tracking the counter is incremented by one (1) whenever the fractional phase changes from 27r to O. Thus, at a given epoch the observed accumulated phase !:J.<p, d. Remondi (1984) or Remondi (1985), is the sum of the fractional phase <p and the integer count n. The initial integer number N of cycles between the satellite and the receiver is unknown. This phase ambiguity N remains constant as long as no loss of the signal lock occurs.
In this event, the integer counter is reinitialized which causes a jump in the instantaneous accumulated phase by an integer number of cycles. This jump is called cycle slip which, of course, is restricted to phase measurements.
A graphical representation of a cycle slip is given in Fig. 9.2. When the measured phases are plotted versus time, a fairly smooth curve should be obtained. In the case of a cycle slip, a sudden jump appears in the plotted curve.
Three sources for cycle slips can be distinguished. First, cycle slips are caused by obstructions of the satellite signal due to trees, buildings, bridges, mountains, etc. This source is the most frequent one. The second source for cycle slips is a low signal-to-noise ratio due to bad ionospheric conditions, multipath, high receiver dynamics, or low satellite elevation. A third source is a failure in the receiver software, d. Rein (1990b), which leads to incorrect signal processing. Cycle slips could also be caused by malfunctioning satellite
9.1 Data preprocessing 183 phase
' - -_ _ - ' -_ _ _ _ - ' -_ _ _ _ ...l..-_ _ _ time Fig. 9.2. Graphical representation of a cycle slip oscillators, but these cases are rare.
As seen from Fig. 9.2, cycle slip detection and repair requires the loca-tion of the jump (Le., cycle slip) and the determinaloca-tion of its size. Repairs are made by correcting all subsequent I,hase observations for this satellite and this carrier by a fixed amount. Det,~ction is accomplished by a testing quantity. In the example given, this is the measured raw phase. The deter-mination of the cycle slip size and the correction of the phase data is often denoted as cycle slip "fixing".
Testing quantities. The formulation of -,;esting quantities is based on mea-sured carrier phases and code ranges. For a single site, the testing quantities are phases, phase combinations, or combinations of phases and code ranges.
Single receiver tests are important because they enable in situ cycle slip de-tection and repair by the receiver's internal software. When two sites are in-volved, single-, double-, and triple-differences, d. Sect. 8.2.1, provide testing quantities. Table 9.3 summarizes a number of candidate testing quantities.
The measured phase cI>i(t) can be modeled by
j ( _ j ( ) j j
Ai(
t)AcI>i t) - [!i t +ANi +c.6.8i (t)-
-y+ ...
(9.1)where i and j denote the site and the satellite, respectively. The term
Ai(
t) has been substituted for (40.3 TEe/cos z') according to Eq. (6.59). Note that the phase model contains a number of time dependent terms on the right-hand side which may prevent cycle slip detection.The model for the dual frequency phase combination is developed con-sidering a single site and a single satellite. Thus, the sub- and superscripts
184 9. Data processing Table 9.3. Testing quantities to detect cycle slips
Required data Testing quantity
Single site Two sites
Single frequency U ndifferenced phase Single-differen ce
phase (L1 or L2) Double-difference
Triple-difference Dual frequency Phase combination
phases (L1 and L2) (ionospheric residual) Single frequency Phase / code range phase (L1 or L2) combination and code range
in Eq. (9.1) can be omitted; whereas, the frequency dependency is shown explicitly by L1 and L2 :
A(t) ALl 'PLl(t) = !>(t)
+
ALl NL1+
C ~6(t) - -f2+ ...
L1 A(t)
AL2 'PL2(t)
=
!>(t)+
AL2 NL2+
C ~6(t) - -f2+ ....
L2
(9.2)
For the difference of the two equations
(9.3) the frequency independent terms (i.e., the geometric distance and the clock error) vanish. Dividing (9.3) by ALl provides
AL2 AL2 A(t) ( 1 1 )
'PLl(t) - - 'PL2(t)
=
NLl - - NL2 - - --2-ALl ALl ALl f Ll 1£2
(9.4) which may be slightly transformed using c = A
f
and from this one obtainsAL2 fLl
ALl h2 (9.5)
9.1 Data preprocessing 185 so that
(9.6) or
( ILl
hI
A(t)c)Ll t) - -I c)L2(t)
=
NLI - -I NL2 -.AP
L2 L2 Ll Ll
(9.7) which is the final form of the dual frequency combination. This model is often denoted as the ionospheric residual, cf. Goad (1986). The right-hand side of Eq. (9.7) shows that the ionospheric residual does not contain time varying terms except for the ionospheric refraction. In comparison to the influence on the raw phases in Eq. (9.1), the influence of the ionosphere on the dual frequency combination is reduced by a factor (1 - (fLl/
h2?)'
Substituting the appropriate values for
hI
andh2'
yields a reduction of 65%, cf. Goad (1986).If there are no cycle slips, the temporal variations of the ionospheric resid-ual would be small for normal ionospheric conditions and for short baselines.
Indicators of cycle slips are sudden jumps in successive values of the iono-spheric residual. The remaining problem is to determine if the cycle slip was on L1, L2, or both. This will be investigated in the next paragraph.
Note that the ionospheric residual c)Ll(t) - -I c)L2(t) ILl
L2
is a scaled difference of dual frequency phases just as the ionospheric-free linear combination
c)Ll(t) - -I c)L2(t)
h2
, Llcf. Eq. (6.79). These two expressions differ, essentially, by the reciprocal nature of the c) L2 coefficients.
Another testing quantity follows from a phase/code range combination.
Modeling the carrier phase and the code pseudoranges by .A c)1 (t) =
e1
(t)+
.A N!+
c Ll81 (t) - Ll1ono(t)+
LlTrop(9.8)
186 9. Data processing and forming the difference
(9.9) provides a formula where the time dependent terms (except the ionospheric refraction) vanish from the right-hand side. Thus, the phase/code range combination could also be used as testing quantity. The ionospheric influ-ence may either be modeled, cf. for example Beutler et al. (1987), or ne-glected. One might justify neglecting the ionospheric term since the change of fllono(t) will be fairly small between closely spaced epochs.
The simple testing quantity (9.9) has a shortcoming which is related to the noise level. The noise level is in the range of ten cycles for time series of the phase/code range combinations, cf. Bastos and Landau (1988). This noise is mainly caused by the noise level of the code measurements and to a minor extent by the ionosphere. The noise of code measurements is larger than the noise for phase measurements because resolution and multipath are proportional to the wavelength. Traditionally, the measurement resolution was A/100; today's receiver hardware are achieving improved measurement resolutions approaching A/lOOO. In other words, this would lead to (P-) code range noise levels of a few centimeters. Hence, the phase/code range combination would be an ideal testing quantity for cycle slip detection.
Many authors use single-, double- or triple-differences for cycle slip de-tection, cf. for example Goad (1985), Remondi (1985), Hilla (1986), Beutler et al. (1987). This means that, in a first step, unrepaired phase combinations are used to process an approximate baseline vector. The corresponding resid-uals are then tested. Quite often several iterations are necessary to improve the baseline solution. Note that triple-differences can achieve convergence and rather high accuracy without fixing cycle slips.
The list of testing quantities in Table 9.3 is not complete. Allison and Eschenbach (1989) use differences of integrated Doppler and Bock and Shi-mada (1989) propose the wide lane signal, cf. Eq. (6.16), as testing quantity.
Detection and repair. Each of the described testing quantities allows the location of cycle slips by checking the difference of two consecutive epoch values. This also yields an approximate size of the cycle slip. To find the correct size, the time series of the testing quantity must be investigated in more detail. Note that in case of phases, phase/code range combinations, single-, double-, and triple-differences the detected cycle slip must be an integer. This is not true for the ionospheric residual.
One of the methods for cycle slip detection is the scheme of differ-ences. The principle can be seen from an example given in Lichtenegger