AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus PublicationsGöttingen, Germany10.5194/amt-10-15-2017Open-loop GPS signal tracking at low elevation angles from a ground-based observation siteBeyerleGeorggbeyerle@gfz-potsdam.dehttps://orcid.org/0000-0003-1215-2418ZusFlorianGFZ German Research Centre for Geosciences, Potsdam, GermanyGeorg Beyerle (gbeyerle@gfz-potsdam.de)3January2017101153423February201618April201630September201617November2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://amt.copernicus.org/articles/10/15/2017/amt-10-15-2017.htmlThe full text article is available as a PDF file from https://amt.copernicus.org/articles/10/15/2017/amt-10-15-2017.pdf
A 1-year data set of ground-based GPS signal observations aiming
at geometric elevation angles below +2∘ is analysed. Within the
“GLESER” measurement campaign about 2600 validated setting events were
recorded by the “OpenGPS” open-loop tracking receiver at an observation
site located at 52.3808∘ N, 13.0642∘ E between January and
December 2014. The measurements confirm the feasibility of open-loop signal
tracking down to geometric elevation angles of -1 to -1.5∘
extending the corresponding closed-loop tracking range by up to 1∘.
The study is based on the premise that observations of low-elevation events
by a ground-based receiver may serve as test cases for space-based radio
occultation measurements, even if the latter proceed at a significantly
faster temporal scale. The results support the conclusion that the open-loop
Doppler model has negligible influence on the derived carrier frequency
profile for strong signal-to-noise density ratios above about 30 dB Hz. At
lower signal levels, however, the OpenGPS receiver's dual-channel design,
which tracks the same signal using two Doppler models differing by 10 Hz,
uncovers a notable bias. The repeat patterns of the GPS orbit traces in terms
of azimuth angle reveal characteristic signatures in both signal amplitude
and Doppler frequency with respect to the topography close to the observation
site. Mean vertical refractivity gradients, extracted from ECMWF
meteorological fields, correlate weakly to moderately with observed signal
amplitude fluctuations at geometric elevation angles between +1 and
+2∘. Results from multiple phase screen simulations support the
interpretation that these fluctuations are at least partly produced by
atmospheric multipath; at negative elevation angles diffraction at the ground
surface seems to contribute.
Introduction
For more than a decade the existing Global Navigation Satellite System (GNSS)
infrastructure is exploited in meteorological applications and climate
studies. Ground-based GNSS observations reveal valuable information on the
tropospheric water vapour content integrated along the signal path
see e.g.and references therein. Furthermore, space-based platforms
equipped with GNSS receivers allow for the derivation of vertical profiles of
atmospheric refractivity, dry pressure and temperature see e.g.and
references therein. GNSS data products
derived from these ground-based, as well as space-based, observations are
being used by meteorological centres for assimilation into numerical weather
prediction models see e.g.and references therein. In
addition, climate studies increasingly take advantage of validated GNSS and
GNSS-RO data sets see e.g.and references therein.
A number of past and current spacecrafts carry GNSS-RO payloads, e.g. the
satellites GPS/Met , CHAMP , GRACE
, COSMIC , Metop
, TerraSAR-X
and TanDEM-X . Already the proof-of-concept mission GPS/Met
revealed the difficulties of retrieving dual-frequency carrier phase data,
when the ray tangent point enters the lower troposphere .
More specifically, noticed a significant negative
refractivity bias in the lower troposphere at tropical latitudes. At low
altitudes the GNSS signals experience multipath beam propagation see
e.g.. The resulting optical path length differences
lead to signal scintillations and these amplitude fluctuations increase the
probability of an early loss of tracking lock. To address these issues new
signal tracking methods were developed and implemented. Whereas the “fly
wheeling” tracking method of JPL's “Blackjack” GPS receivers mounted on
CHAMP and GRACE showed some progress, significant
improvements with respect to probing of the planetary boundary layer (PBL),
in particular at low latitudes, were obtained with the introduction and
implementation of open-loop (O/L) tracking (or raw-sampling) techniques
see e.g..
The open-loop signal tracking mode successfully resolves the problem of
premature loss of signal in the lower troposphere at low latitudes
. In contrast to closed-loop (C/L)
tracking, a receiver operating in open-loop mode partially or completely
disregards the tracking loop feedback values from the carrier and code
discriminators, but instead steers the corresponding numerically controlled
oscillators (NCOs) using a priori parameters. In the following, these O/L
parameters, which are usually derived from an atmospheric climatology, are
referred to as “O/L model”. The time duration, which the receiver operates
in open-loop tracking mode, may be controlled by predetermined threshold
values in terms of tangent point altitude, elevation angle and/or
signal-to-noise ratio (SNR). While these general considerations apply to all
open-loop and raw-sampling implementations, the specific realisations vary in
detail (see e.g. US patents US6731906 B2 and US6720916 B2).
A key requirement for the adoption of O/L signal tracking in operational
GNSS-RO missions is the insensitivity of derived carrier phase paths and code
pseudoranges on the particular choice of O/L model. According to
the requirement is met, provided the true atmospheric
Doppler profile deviates by not more than half of the sampling frequency from
the O/L Doppler model. With a typical sampling rate of fs=50 Hz
this requirement translates into a maximum frequency deviation of 25 Hz.
Recently, claimed, on the basis of GNSS-RO observations
recorded by the “IGOR” receiver aboard the TerraSAR-X spacecraft, that the
O/L Doppler model may influence the derived refractivity values for low
signal amplitudes below about 25 V/V and potentially contribute to the
negative refractivity bias. In order to substantiate this hypothesis they
proposed to track each GNSS-RO signal with two O/L models, separated in
frequency space by a predefined offset. We note, however, that other causes
certainly contribute to the observed refractivity bias as well see
e.g.and references therein. Since IGOR firmware
modification aboard TerraSAR is unfeasible, two indirect methods were
investigated. First, a measurement campaign was conducted in late 2012 with
the GNSS-RO receivers aboard the TerraSAR-X and TanDEM-X satellites recording
signals from the same setting GPS satellites, but using different O/L models
. Second, within the framework of the GLESER (GPS low-elevation
setting event recorder) measurement campaign a ground-based experiment was
devised and established at an observation site on the “Albert Einstein”
science campus in Potsdam, Germany (52.3808∘ N,
13.0642∘ E) in December 2010. The GLESER campaign targets signals
from GPS satellites at low elevations as they set beyond the horizon at
elevation angles below +2∘. The measurement hardware, the
single-frequency “OpenGPS” receiver, is an in-house development based on
C. Kelley's “OpenSourceGPS” concept .
The occurrence of multiple signal paths
(“multipath”) connecting transmitter device and receiver instrument
distinguishes ground-based from space-based GPS measurements. Local
multipath, caused by signal reflections in the direct vicinity of the
receiving antenna, cannot be avoided in most ground-based observations
see e.g.; on a spaceborne platform,
however, these local reflections may be eliminated to a large extent by
careful spacecraft design and suitable antenna placement
cf.. Within the framework of space-based radio
occultation the term “multipath” assumes an alternative connotation and
generally refers to tropospheric signal propagation close to the ray tangent
point, thousands of kilometres away from the receiver. Local multipath, i.e.
reflections in the vicinity surrounding the antenna, can be described using
geometric optics see e.g.;
tropospheric multipath is a diffraction phenomenon and requires wave optical
methods to analyse quantitatively see
e.g.. In the following, however, we
will argue that for elevation angles below about +2∘ wave optical
effects may contribute in ground-based observations as well.
Whilst ground-based observations of low-elevation setting events do not allow
to derive bending angle profiles for ray tangent points above the receiver
altitude , these measurements
nevertheless are useful to investigate receiver tracking behaviour under
multipath conditions with strongly fluctuating SNRs. In addition, the signal
excess phase paths have been shown to be sensitive to the local refractivity
field see e.g..
In the present study we focus on low-elevation setting events with geometric
elevation angles decreasing from +2∘ at the measurement start to
about -1 to -1.5∘ at the end of the observation. Here,
geometric elevation angle is defined as the line-of-sight elevation angle at
the receiver antenna disregarding atmospheric refraction effects. Setting
events last for about 10 to 15 min on average; hence their durations are
about an order of magnitude longer than typical space-based radio occultation
measurements see, e.g.. Even if a ground-based
observation does not lend itself to the derivation of bending angle profiles
, from the signal tracking
perspective we regard GLESER observations as useful for investigating
open-loop tracking of signals with strongly fluctuating SNR. The present
study is restricted to the observation and analysis of setting events; an
extension towards rising events, however, is technically feasible and may be
considered for future implementations.
The paper is sectioned as follows. First, closed-loop and open-loop tracking
methods are briefly reviewed and the capabilities of GFZ's OpenGPS
receiver are illustrated with some example profiles. Second, the measurements
conducted during the GLESER campaign are introduced, and the data processing
algorithms and analysis methods are discussed. In the main section of this
paper the measurement results are discussed and put into perspective using
results from multiple phase screen (MPS) simulations. Finally, the OpenGPS
hardware and software are described in the Appendix.
Closed-loop and open-loop signal tracking
The GLESER campaign utilises the OpenGPS instrument, a single-frequency
12-channel GPS receiver. Several copies of this device, which is based on
C. Kelley's OpenSourceGPS concept , were built at GFZ and used in various ground-based and airborne GPS
measurement campaigns (see e.g.
). In order to provide a self-consistent description
of the OpenGPS instrument and its O/L signal tracking implementation, we
begin with a brief review of C/L and O/L tracking techniques.
It is well known that inhomogeneities in the tropospheric water vapour field,
in particular at low latitudes, can produce multipath propagation of GNSS
signals at low elevation angles see e.g.. Space-based
RO observations show that under these conditions SNR values exhibit strong
fluctuations, which early GNSS-RO receivers were unable to track properly
. To address premature signal loss GNSS-RO receiver tracking
algorithms based on closed feedback loops were replaced by “open-loop”
techniques see
e.g.. If a receiver
operates in open-loop mode the feedback loop is opened and the NCO producing
the replica signal is steered (in part or fully) from model parameters. This
model takes into account the expected signal dynamics from both, the
transmitter and receiver orbits, clocks biases and drifts as well as the
signal propagation characteristics in the lower troposphere. The latter are
typically obtained from an atmospheric climatology
.
Schematic representation of closed-loop
(top panel) and open-loop (bottom) carrier signal tracking. In closed-loop
mode the input signal is correlated with two replica signals, sin and cos,
and the latter is phase-shifted by 90∘ with respect to the former.
The correlation sums are low-pass filtered and the output is examined for
phase deviations between input and replica signal. The discriminator
adjustments close the feedback loop. Open-loop tracking (bottom panel)
dispenses with the phase discriminator and the numerically controlled
oscillator (NCO) is solely steered from model values (Doppler model). The
observed carrier phase finally is assembled from the NCO phases and the
in-phase and quad-phase correlation samples.
The schematic in Fig. illustrates the two tracking
concepts for carrier phase tracking; corresponding considerations apply to
code tracking as well. In standard C/L tracking
(Fig. , top panel) the down-converted input signal
(“input”) is correlated with two internal replica signals (“sin” and
“cos”) generated by the NCO see e.g.. The result is
low-pass filtered (represented by the box labelled “average”); the carrier
phase discriminator determines phase deviations between the observed and
modelled replica and provides appropriate adjustments to the loop filter. The
sin and cos replica signals, the latter being phase shifted by a
quarter cycle, i.e. 90∘ with respect to the former, allow us to
distinguish phase advances from phase delays between observed and replica
signal. The phase discriminator output is digitally filtered (“loop
filter”) to prevent unstable loop behaviour see
e.g.. The receiver output samples (“carrier phase
output”) combine the NCO model phases and the phase residuals from the
discriminator to yield the observed carrier phase.
If signal amplitudes drop below certain threshold levels, the corresponding
phase residuals start to be dominated by noise and proper alignment between
replica and observed signal can no longer be maintained.
Figure shows exemplarily the signal-to-noise density
ratio C/N0 as a function of
geometric elevation angle for a setting event recorded in the morning of
1 January 2015. At elevation angles below about +1.5∘ the density
ratios C/N0 start to fluctuate. At about +1.19 and again at
+0.56∘ transient signal gaps with
C/N0≲ 30 dB Hz occur which last for less than about
0.5 s. During these time intervals the phase discriminator output is
dominated by noise, causing enhanced NCO Doppler frequency fluctuations as is
illustrated in Fig. (blue line). At about
-0.26∘ elevation low signal level conditions persist for a longer
time period and the carrier NCO frequency deviates by hundreds of hertz (blue
line in Fig. ). Correspondingly, C/N0
drops by about 20 dB down to the noise level (Fig. )
and never recovers during the last part of this setting event.
Observed signal-to-noise density ratio
C/N0 as a function of geometric satellite elevation angle.
Atmospheric bending amounts to about 1 to 2∘ at the observation
site and therefore the two open-loop channels (green and red) continue to
track the signal down to elevation angles of about -1.2∘. A strong
amplitude fluctuation at about -0.26∘ causes the closed-loop
channel (blue) to lose tracking lock much earlier than the open-loop channels
(green and red). A C/N0 value of about 17 dB Hz is marked in
black. Constructive interference produce high C/N0 values
exceeding 48 dB Hz at elevations below -1∘. This observation of
GPS PRN 7 was recorded on 1 January 2015 between 06:38 and 06:52 GPS time.
Carrier NCO frequency as a function
of geometric satellite elevation angle. For clarity, a constant frequency
value of fref=1.4071 MHz is subtracted. The transition between
closed-loop and open-loop tracking is depicted in the insert highlighting the
10 Hz offset between the two O/L channels. Same event as shown in
Fig. .
Open-loop tracking is immune to transient SNR gaps, even if these breaks
stretch across extended time periods. The bottom panel of
Fig. schematically illustrates the concept. In O/L
tracking mode the feedback loop is removed and the NCO is solely controlled
by model values. The correlation output values, produced by the cos and sin
branches, are denoted by “in-phase” and “quad-phase” correlation samples,
respectively . In low-SNR
conditions the in-phase and quad-phase samples are dominated by noise.
However, since no feedback is present in O/L tracking, these noisy samples
cannot produce erroneous control input to the NCO and transient signal gaps
do not cause loss of tracking lock as illustrated in
Figs. and . Red and green
lines show C/N0 (Fig. ) and the NCO carrier
frequency (Fig. ) recorded by the receiver's two
open-loop channels, respectively. In the following the two channels are
denoted by the letters A and B. Both channels are attached to the same
PRN
and therefore track the same transmitter. Their corresponding NCO frequencies
are derived from the same model, but on channel A's value an additional
-5 Hz, and on B an additional +5 Hz, is added, resulting in a 10 Hz
inter-channel offset. This 10 Hz shift can clearly be identified in
Fig. (insert); here, O/L tracking mode starts at
an elevation angle of -0.08∘ and reaches the nominal 10 Hz shift
after a brief initialization phase at -0.13∘ elevation.
Measurements
The GLESER measurement campaign started in December 2010 and since then
data acquisition of low-elevation setting events operates almost
continuously. Gaps of up to several days occurred and are caused by hardware
or software problems, operator errors or other technical reasons. The
following discussion is restricted to observations recorded in 2014. The
instrument provided on average 8.3 observations per day throughout this year
with three data gaps (29 January to 1 February, 29–31 August and
18–22 December 2014). Between 15 July and 6 September the OpenGPS
receiver malfunctioned due to an operator error and 437 observations from
that time period are removed from the data set, leaving 2581 low-elevation
events.
The instrument is housed on the top floor of the former water tower on the
“Albert Einstein” science campus in Potsdam, Germany
(52.3808∘ N, 13.0642∘ E). An active L1(1575.42 MHz) GPS antenna (NovAtel/ANTCOM 2G15A-XTB) is mounted on the
tower's observation deck and tilted by about 45∘ towards the
western horizon to increase recorded signal strength at very low elevation
angles. The antenna includes a low-noise amplifier with 33 dB gain and is
sensitive to right hand circular polarisation only. A 10 m low-loss signal
cable connects the antenna to the OpenGPS receiver. According to the
manufacturer's documentation the cable loss is 14 dB per 100 m at 1 GHz.
View towards west from the observation platform.
The picture was taken about 2–3 m behind the receiver's GPS antenna, which
is tilted by about 45∘ towards west (the antenna and its mounting
pole is visible at about 290∘ azimuth angle). The metal structure
at about 220∘ is part of a lightning protection system and does not
block the antenna's field of view, which ranges from 200 to 340∘.
Throughout the observation period a satellite with a given PRN sets beyond
the horizon at almost the same azimuth angle. The angles of those nine PRNs
discussed in the present study are marked in red.
Figure depicts the panoramic view of the western horizon
from the observation deck between azimuth angles of 180 (south) and
360∘ (north). The azimuth angles are marked in black at the top
side of the photograph. Thick red lines indicate the azimuth angles of those
PRNs, which are analysed in the present study. The picture was taken a few
metres east of the receiving patch antenna, which is visible to the right of
the 290∘ azimuth tick mark.
Data acquisition is activated once a satellite enters the observation window
which ranges from 200 to 340∘ in azimuth (thin broken red lines
in Fig. ) and from +2 to -2∘ in elevation. Any
additional satellite entering the observation window during this time period
is disregarded and not tracked in O/L mode. Raw observables stored on disk
include pseudoranges ρC/L,n, carrier
phases φC/L,n and time tags tn for all C/L channels.
In addition, raw O/L measurements (in-phase and quad-phase correlation sums
Ĩn and Q̃n; NCO ranges ρNCO,n and NCO
carrier frequencies fNCO,n from both O/L channels) are written
to separate files. Here, the subscript n=1,2,… enumerates the
successive TIC events (for an explanation of TIC event, see
Appendix ) recurring every 20 ms. The correlation sums
Ĩn and Q̃n are not sampled at TIC instants but are
coherently integrated over a time period of 20 ms preceding the TIC
event. The corresponding time offset between Ĩn, Q̃n and
φNCO,n is disregarded in the following analysis. Raw
data accumulation rate is about 360 MB day-1 or
about 2.5 GB week-1.
Open-loop performance in terms of the
gain or loss in elevation angle range compared to closed-loop tracking. The
end elevations ϵoffO/L and
ϵoffC/L are defined as the lowest angle
with C/N0 still exceeding 30 dB Hz. In general, O/L tracking
lowers the final elevation angle by about 0.11∘ on average.
However, in about 14 % of the measurements C/L tracking outperforms the O/L
channels, in a few cases by up to 1∘. Red markers refer to O/L
channel A and green to channel B.
In order to quantify the performance gain of O/L in comparison to C/L
detection we compare in Fig. the lowest
elevation angles observed in the two tracking modes,
ϵoffO/L and
ϵoffC/L. They are defined as the minimum
elevation in a given setting event with the smoothed density ratio
C/N0 still exceeding 30 dB Hz. Smoothing is performed by a
running mean filter of 1 s width. We find that out of a total of
2581 setting events 2368 and 2366 were recorded by the O/L channel A and B,
respectively. In the remaining 8 % of the observations closed-loop tracking
stopped too early and O/L was never activated. With active channels A and B,
however, in about 86 % of the O/L measurements (2017 out of 2368
and 2069 out of 2366 for channel A and B, respectively) end elevation angles
from O/L tracking yielded smaller values compared to the C/L results. Additionally, in
21 % of the measurements (499 out of 2368 and 505 out of 2366 for channel A
and B, respectively) O/L tracking extended more than 0.25∘ further
down than the corresponding C/L observation.
Data processing and analysis
Data processing is performed on an event-by-event basis. Typically, setting
events last about 700–900 s; however, measurements extending over a time
period of up to 1400 s are occasionally observed. During the initial stage
OpenGPS, raw data files are converted to
MATLAB® binary format to facilitate the
subsequent processing steps. First, the observed in-phase and quad-phase
samples sums are demodulated:
In=DnĨn;Qn=DnQ̃n.
This done to allow calculation of the
residual phase samples:
φres,n=atan2Qn,In.
Here, the four-quadrant arctangent atan2(x,y) denotes the
principal value of the angle of the complex number x+iy.
The literature discusses two methods for the determination of the data bits
Dn, “internal” and “external” demodulation. On the one hand, Dn can
be extracted from the observations Ĩn and Q̃n themselves
. On the other hand, external demodulation extracts Dn
from independent observations, such as GFZ's NavBit data base, registered
under 10.1594/GFZ.ISDC.GNSS/GNSS-GPS-1-NAVBIT. In
the following, external demodulation is used since in low-elevation events the
modulus of the difference between adjacent the carrier phase residuals,
φres,n-φres,n-1,
frequently reaches and exceeds ±90∘. In these cases a clear
separation between propagation-induced phase fluctuations and phase changes
due to a sign change of Dn is difficult to achieve.
Accumulated residual carrier phase samples Φres,n then
follow from
Φres,n≡φres,n+Cn=atan2Qn,In+Cn
with the unwrapping term Cn defined by
Cn=Cn-1+2πatan2Qn,In-atan2Qn-1,In-1<-πCn-1-2πatan2Qn,In-atan2Qn-1,In-1>+πCn-1else
if n>1 and Cn=1=0. In addition, during
this first processing stage the receiver's 1 Hz navigation solution, which
includes an estimate of the receiver's clock bias, is retrieved as well.
Observed carrier
frequencies fobs, reconstructed from NCO and residual
frequencies (Eq. ), using external data bit
demodulation as a function of elevation angle (red and green). In addition,
the closed-loop result is plotted in blue. For clarity, a constant offset
fref=1.4071 MHz is subtracted. Same event as shown in
Figs. and .
Second, elevation and azimuth angles for each tracked satellite are
calculated from broadcast ephemeris data using the bias-corrected receiver
clock time and linearly interpolated from 1 to 50 Hz. From the bit-corrected
phase samples Φres,n the observed carrier frequencies
fobs,n(A,B)≡fNCO,n(A,B)+fres,n(A,B)≈fNCO(A,B)+12πΦres,n(A,B)-Φres,n-1(A,B)tn-tn-1
are derived with superscript A and B, indicating the corresponding O/L
channel. Figure shows
fobs,n(A,B) (Eq. ) corresponding to
the event plotted in Fig. using external data
bit demodulation (red and green lines). The C/L channel (blue line) loses
lock at about -0.3∘ elevation and its carrier frequency output
leaves the scale. Incidentally, at about -1.2∘ the C/L frequency
briefly crosses the displayed frequency range again. Below about
-1.2∘ elevation Earth's limb completely shadows the signal from
PRN 7 (see Fig. ) and from there on O/L and C/L outputs
contain noise only.
In addition, with the observed in-phase and quad-phase correlation sums,
Ĩn and Q̃n (Eq. ), the
signal-to-noise density ratio C/N0, in units of dB Hz, is
calculated according to , and
:
C/N0dBHz=10⋅logĨ2+Q̃22⋅VarQ̃C/L⋅Tc.
Here, 〈x〉 is the mean value of x and Tc=0.02 s denotes the coherent integration time.
VarQ̃C/L is the variance of
the observed quad-phase correlation sums of the associated master channel
running in C/L mode between 0 and +2∘ elevation angle.
If no GPS signal is present and the receiver input signal is pure noise,
Ĩ and Q̃ are uncorrelated and
Ĩ2+Q̃2=2⋅Q̃2=2⋅VarQ̃≈2⋅VarQ̃C/L
since Q̃=0. Under these conditions the
density ratio C/N0(dBHz) decreases to a value of
10⋅log1Tc≈17dBHz
using Eq. () (dashed black line in
Fig. ).
Simulations
In order to interpret the observed C/N0 fluctuations we performed
a series of MPS simulations
. The propagation of a plane wave through
the lower troposphere is modelled by a series of 500 non-equidistant phase
screens covering the range from the receiver to a distance of 500 km. On
each phase screen the wave suffers a phase delay determined by the
inter-screen distance Δz and the refractivity height profile
N(h)=400exp-hhs1-0.052πatanh-htphzn,
with height h, scale height hs=8 km, PBL top height htp and PBL top transition zone
hzn=50 m. The interaction of the wave with the ground surface
is modelled by applying a raised-cosine filter with a 6 dB steepness of
25 m (i.e. within 25 m the filter weight decreases by 6 dB) at zero
altitude. The phase screens extend vertically from -20 to +20 km with a
5 km wide raised-cosine filter applied at the upper and lower boundary to
suppress spurious diffraction effects; the receiver altitude is taken to be
50 m. The variation of elevation angle between -2 and +2∘ is
modelled by tilting the ground surface and its overlying atmosphere
correspondingly.
Normalised signal amplitudes as a function of
elevation angle derived from several MPS simulations.
Refractivities on the individual phase screens are calculated from an
exponential profile furnished with a planetary boundary layer in the lower
troposphere. Signal absorption at the surface is taken into account (red and
blue lines); green and black lines show the result without ground absorption.
Two boundary layers are modelled: a horizontal boundary layer top at 2 km
altitude (red and black) and a layer top increasing from 1 to 2 km between
30 and about 60 km distance from the receiver (blue and green). For
legibility the red, green and blue lines are shifted by an additional +1,
+2 and +3 dB offset, respectively. For details see text.
Results from four simulation runs are shown in Fig. ; it
displays the normalised signal amplitude as a function of elevation angle.
Signal absorption at the ground surface produces characteristic diffraction
patterns for elevation angles below
0∘ (red and blue lines). Without ground absorption the diffraction
patterns almost disappear and the profiles approximate step functions
expected from geometric optics (green and black). The MPS simulations did not
produce C/N0 fluctuations for horizontally oriented PBL tops
(parameterised by the parameter htp in
Eq. ). However, if the top layer tilts towards the
receiver, substantial signal deviations at elevation angles
above 0∘ are observed. Figure illustrates this
phenomenon for a PBL top layer ascending from 1 km at 30 to 2 km at about
60 km distance (green and blue lines); at distances below 30 and above
60 km htp remains fixed at 1 and 2 km, respectively.
The MPS simulation results, plotted in Fig. , highlight
ground diffraction effects below about 0∘ elevation angle (blue and
red) and PBL-induced C/N0 variations above about 0∘
(blue and green). The results suggest that these C/N0 fluctuations
are independent from each other and tend to be separated in elevation angle
space. Finally, we note that the addition of irregularities on spatial scales
characteristic for turbulence to the refractivity profiles did not produce
significant C/N0 changes.
Discussion and interpretation
We begin the discussion of the GLESER results by comparing the
performance of internal versus external data bit demodulation and define the
quantity as
EnX≡DnX,int-Dn-1X,int-Dnext-Dn-1ext.
Here, |x| denotes the modulus of x, the superscript X=A or X=B
indicates the O/L channel and “int” or “ext” characterises the demodulation
method. The quantity EnX is sensitive to differences between
sign changes from one sample to the next, rather than differences between the
bit values, since only the former affect the derived carrier frequency. We
note that EnX=1 for randomly chosen
DnX,int and Dnext.
Failure rate of internal navigation
bit retrieval in terms of averaged performance parameter 〈E〉
(Eq. ) as a function of elevation angle for signal
density ratios C/N0≥ 30 dB Hz (blue, left axis). The
corresponding number of observations per elevation bin is plotted as well
(red, right axis). The statistics is based on 242 observations recorded in
January 2014.
For 242 observations in January 2014 with signal density ratios
C/N0≥30 dB Hz the parameters En
(Eq. ) are grouped into an elevation grid with
0.1∘ bin size and averaged. The result is shown in
Fig. . At elevation angles just
below 0∘ there is good agreement between internal and external data
bit retrieval; at lower elevations, however, the failure rate increases
significantly. Results for elevation angles below -1.2∘ are
statistically not significant due to the strongly decreasing number of
observations (red line). To eliminate potential errors caused by internal
data bit removal, we restrict the following discussion to data processed
using external demodulation.
Table lists all 19 PRNs recorded during the 311-day
observation period in 2014 and the corresponding number of setting events.
The third column gives the mean azimuth angle and its 1σ standard
deviation at 0∘ elevation. Enhanced changes in azimuth angle of
PRN 8 are most likely related to the decommissioning of GPS space vehicle
number 38 in October 2014. The last column in Table
shows the fractions of profiles in which O/L tracking reached a lower
elevation angle than the corresponding C/L result. For example, a value of 70 %
indicates that in 30 out of 100 observations the C/L channel tracked to a
lower elevation than the corresponding O/L channels. The low O/L enhancement
values for PRN 28 might be caused by signal reflections at the water surface
of Templiner Lake (see Fig. at about 260∘ azimuth
angle). As described in the Appendix (Sect. ), the O/L model
is initialised within the elevation angles range between 0 and
+2∘. It appears feasible that surface reflections induce
C/N0 fluctuations at these elevation angles see
e.g., degrading the quality of the O/L model and
thereby causing poor O/L performance.
Number of low-elevation events and azimuth
angle at zero elevation for all 19 PRNs recorded during 311 days in 2014.
Azimuth angle is given as mean and 1σ standard deviation. The last
column lists the percentages of observation in which O/L tracking reached a
lower elevation angle than the corresponding C/L detection. The first number
refers to O/L channel A, the second to channel B.
The panorama photograph Fig. shows the view to the local
horizon within the 140∘ wide observation window ranging
from 200 to 340∘ and centred at 270∘ azimuth
(west). It exhibits a substantial variation of surface properties in azimuth
angle with enhanced building densities of the city of Potsdam in a westerly to
north-westerly direction (about 280 to 350∘), mostly forests at
azimuth angles below 270∘ and water surfaces from Templiner Lake
between about 250 and 260∘. Also indicated in
Fig. are the approximate zero-elevation azimuth angles of
setting GPS satellites (red marks). Due to the specific geometry of the GPS
constellation the orbit traces exhibit a characteristic azimuth angle repeat
pattern when viewed from a fixed ground-based location
, i.e. a specific PRN sets at the same azimuth angle
with small deviations of less than 1 ∘ (see centre column of
Table ).
In the following the observations are grouped PRN-wise. The azimuth angle
repeat pattern implies that these subsets refer to almost the same azimuth
angles. For example, settings of PRN 18 invariably take places at lake
Templiner Lake, whereas PRN 32 sets across the urbanised area of Potsdam
throughout the year. The non-uniform topography most likely contributes to
the observed variability in C/N0 (see e.g.
Fig. ) and, as will be discussed below, Doppler
frequency with respect to azimuth angle. The occurrence time of the setting
event, however, shifts by about 4 min day-1, which corresponds to
24 h per average year (365.25 days). Thus, the statistical analysis
performed in the present study essentially averages out any potential diurnal
variation. The investigation of these temporal variations is left to future
research.
Carrier signal-to-noise density ratio,
averaged over the two O/L channels, as a function of elevation angle. The
panels show observations from nine PRNs sorted row-wise according to
increasing azimuth angle (see Fig. ). Mean and
1σ standard deviations, calculated from 0.2∘ elevation bins,
are marked in dark blue. Once the signal is completely blocked by the
horizon, C/N0 drops to about 17 dB Hz (see
Eq. ).
Figure provides a general overview of the observed
mean signal density ratios
C/N0avg[dBHz]≡12C/N0A[dBHz]+C/N0B[dBHz]
as a function of elevation angle. We note that by expressing C/N0
in units of dB Hz, Eq. () constitutes in effect a geometric
mean value in terms of the ratios Ĩ2+Q̃22⋅Var(Q̃C/L)⋅Tc (see Eq. ).
Figure shows C/N0 for PRNs 2, 7, 13, 14,
17, 18, 22, 23 and 32. The following analysis is focused on this set of nine
PRNs; they were selected according to data availability and azimuth angle
coverage. The individual panels in Fig. and the
following figures are arranged row-wise according to increasing azimuth angle
(see Fig. ). In Fig. also the mean
and 1σ standard deviations are plotted with an elevation bin size
of 0.2∘ (blue). The overall features are similar in all nine panels
with C/N0≈40–45 dB Hz at the start of the setting event,
decreasing to about 15 dB Hz at the lower end. At about 0∘
elevation, at the transition between C/L and O/L tracking, signal
propagation over the urban area (PRNs 23, 13 and 32 corresponding to azimuth
angles of 305, 317 and 318∘) appear to exhibit stronger
C/N0 attenuations and fluctuations compared to signals arriving
from more southerly directions across forest areas.
Examining density ratio averages (Eq. ) in lieu of
C/N0A and C/N0B is justified, since the two
values agree in the majority of observations. As a matter of principle,
however, significant deviations are conceivable, because the density ratio
depends on frequency offset Δf(A,B) between the O/L NCO
frequency fNCO(A,B) and the signal's true carrier
frequency f0,
Δf(A,B)≡fNCO(A,B)-f0.
Provided the observed and replica signal are perfectly aligned in the
pseudorange domain, the amplitude loss induced by Δf(A,B) is
given by
LΔf(A,B)≡sinπΔf(A,B)TcπΔf(A,B)Tc
with a coherent integration time of Tc. For illustration
Fig. shows the normalised C/A code correlation
function as a function of code lag and frequency offset in the vicinity of
the correlation maximum and the loss function L(Δf(A,B)) at zero
delay (red line).
Normalised C/A code correlation
function as a function of delay and Doppler frequency offset. At zero delay
the code correlation function corresponds to the frequency response (solid
red line). It closely matches the modulus of the normalised sinc function
(dotted red line, shifted by +2.5 chips for clarity).
Thus, in the absence of other factors affecting C/N0A and
C/N0B individually, the density ratios of channel A and B will
differ by
ΔC/N0≡C/N0A-C/N0B=20logΔf(B)Δf(A)sinπΔf(A)TcsinπΔf(B)Tc.
The statistics of ΔC/N0 is plotted in
Fig. as a function of elevation angle. Mean
density ratio values, grouped in steps of 0.2∘, are marked in blue
with error bars indicating the 1σ standard deviation. The mean values
of ΔC/N0 are zero within the statistical uncertainties;
individual observations, however, differ by more than 10 dB Hz. While in
general the largest deviations occur below 0∘ elevation, i.e.
during O/L tracking, also C/L tracking results exhibit non-zero values of
ΔC/N0. Finally, in the panels for PRNs 7, 22 and 23
characteristic features between -1 and 0∘ elevation are evident.
Their most likely explanation are multipath signal propagation at azimuth
angles between about 270 and 300∘.
Same as Fig. ,
however, showing ΔC/N0, the difference of the two O/L density
ratios, as a function of elevation angle.
The observed density ratio difference ΔC/N0 can be analysed
quantitatively. For this purpose the observation fobs(A,B)≈f0 is assumed to be a valid approximation for the true carrier
frequency f0. Using the defining Eq. () we obtain
fobs(A)-fobs(B)=fNCO(A)+fres(A)-fNCO(B)+fres(B)≈0
and
ΔC/N0(fres(A))≈20logfres(A)+10Hzfres(A)sinπfres(A)Tcsinπfres(A)+10HzTc
or, alternatively,
ΔC/N0fres(B)≈20logfres(B)fres(B)-10Hzsinπfres(B)-10HzTcsinπfres(B)Tc.
Figure shows the correlation between the
observed density ratio differences ΔC/N0 and
fres(A) (gray data points). Here, the data set is restricted
to the subset of typically 210 000 (PRN 2) to 370 000 (PRN 7) samples
tracked in O/L mode. The expected result derived from
Eq. () is overlaid in dark blue; dashed lines mark the
residual frequency of -5 Hz.
Same as
Fig. , however, showing the residual frequency in O/L
channel A as a function of ΔC/N0, the difference of the two O/L
density ratios (gray points). The theoretically expected result
(Eq. ) is shown in dark blue; light blue lines are the
theoretical result shifted by ±50 Hz highlighting the occurrence of
frequency aliasing. The horizontal dashed lines mark the -5 Hz residual
frequency.
The resulting patterns exhibit a marked dependence on PRN, i.e. on azimuth
angle. Whereas the observations of PRN 14 (azimuth angle at
about 226∘) indicate only moderate excursions in terms of residual
frequency with most data points clustered at -5 Hz (dashed line), the
signals from PRN 32, arriving from an azimuth angle of 318∘, show
strong deviations causing residual frequencies exceeding the Nyquist value of
fs/2=25 Hz. Here the agreement with the theoretical results
(blue line, Eq. ) is evident. A substantial number of
observations deviate from the O/L model by more than fs/2 and are
therefore affected by aliasing. The light blue curves, which are derived from
Eq. () but shifted by ±50 Hz, show good
agreement with the observations and substantiate this interpretation. The
aliasing effect is stronger for negative fres(A) since
channel A is shifted with respect to the O/L model by an additional -5 Hz.
Same as
Fig. , however, showing the corresponding
results from O/L channel B.
Correspondingly, aliasing for positive residual frequencies is stronger for
channel B since this channel is shifted with respect to the O/L model by
+5 Hz as illustrated by Fig. , which
shows the corresponding result derived O/L channel B data. Again, the dark
blue lines (and the aliased curves in light blue) mark the theoretical result
derived from Eq. ().
Same as Fig. ,
however, showing the difference between the two observed frequencies obtained
from O/L channel A and B as a function of the mean signal-to-noise density
ratio (Eq. ). Mean and 1σ standard deviations,
calculated from C/N0 bins 2.5 dB Hz wide, are marked in green.
The fraction of data points exceeding Δfobs>+40 Hz is
indicated as ρ40Hz. The result of the statistical analysis
excluding this subset still exhibits a positive bias if C/N0≲30 dB Hz (red).
The preceding discussion is based on the assumption
fobsA=fobsB.
Referring to Fig. , however, we deduce that
Eq. () is not strictly fulfilled, in particular for
low signal-to-noise density ratios. The panels of
Fig. show the observed frequency difference
Δfobs≡fobs(A)-fobs(B) as a function of mean density ratio for the selected
nine PRNs. Their mean values and 1σ standard deviations, sorted into
2.5 dB Hz bins, are superimposed on the individual data points (gray dots)
as green lines.
In all panels a small fraction of the data set, denoted by
ρ40Hz in Fig. , populates the
frequency band Δfobs≳+40 Hz with a mean value of
about +50 Hz and signal levels ranging from 10–20 dB Hz to more than
40 dB Hz. Again, this +50 Hz offset is caused by aliasing. If the true
signal frequency f0 occurs within the frequency range between +20 and
+25 Hz, it is correctly tracked by channel A but aliased to the -30 to
-25 Hz frequency window by channel B, since channel B's NCO is shifted by
-10 Hz with respect to channel A's NCO and therefore its frequency range
extends from -30 to +20 Hz. Thus, the frequencies observed by channel A
and B differ by +50 Hz. Conversely, signals appearing at frequencies
between -20 and -25 Hz are properly recorded by channel B but suffer
aliasing in channel A again, producing a +50 Hz offset in Δfobs. Formally, the observed frequency difference Δfobs as a function of true frequency f0 is
Δfobs(f0)=fNCO(A)+fres(A)(f0)-fNCO(B)+fres(B)(f0)=0Hz-20Hz<f0<+20Hz+50Hzelse.
We note that in both cases the offset is +50 Hz and therefore signals
differing from f0 by integer multiples of 50 Hz cannot be distinguished
using dual-channel O/L tracking.
Even though the fraction ρ40Hz remains below 4 %, the
corresponding samples bias the mean value (green lines in
Fig. ) towards positive frequencies, but they are
not the sole cause for the observed bias. If all observations with Δfobs≥+40 Hz are removed from the data set, the
corresponding mean values are still biased, albeit significantly less (red
lines in Fig. ).
Mean and standard deviations of Δfobs (centre column) for nine values of the carrier
signal-to-noise density ratio C/N0 between 10 and 50 dB Hz;
averaging bin size is 5 dB Hz. The statistics is based on all PRNs shown in
Fig. . The third column lists the corresponding
result, neglecting frequency deviations larger than 40 Hz.
Table summarises the results shown in
Fig. . The centre column lists the mean and
1σ frequency differences averaged over all nine PRNs displayed in
Fig. . The corresponding results for the frequency
differences excluding the fraction ρ40Hz are given in the
last column.
The magnitude of the observed frequency bias can be motivated in the
following way. In the limit of vanishing signal levels the residual
frequencies are dominated by noise and thus
fres(A)≈0≈fres(B).
Under these circumstances the observed frequency difference between channel A
and B becomes
limC/N0→noiseΔf=limC/N0→noisefobs(A)-fobs(B)=fNCO(A)-fNCO(B)=10Hz.
The mean values observed in Fig. are consistent
with this estimate. However, the figure also shows that for
C/N0≳ 30 dB Hz the frequency difference Δfobs is
bias free; the deviations occur solely at signal levels C/N0≲ 30 dB Hz.
We note that this bias is independent from the sampling
frequency fs. The numerical values of C/N0, however,
which characterise the transition zone between biased and bias-free samples,
depend on the antenna gain and other receiver-specific parameters. They
cannot be directly compared to observations from space-based GNSS-RO payloads
which typically are equipped with higher-gain antennas.
Apart from clusters appearing at +50 Hz, Fig.
indicates the presence of frequency offsets at about +25 Hz for PRN 7, 13,
17 and 23. A convincing cause for the presence of these +25 Hz clusters
could not be identified; most likely they are related to atmospheric effects
on the propagating signal and not receiver induced, since the effect strongly
depends on PRN, i.e. azimuth angle. This issue requires further
investigations.
Standard deviation of C/N0
at elevation angles between +1 and +2∘ versus mean refractivity
gradient for nine PRNs extracted from ECMWF (March to mid-July 2014). For
PRN 13, 14 and 23 one data point exceeds the axis limit of 4.2 dB Hz; its
respective mean refractivity gradient is marked by an arrow. (Of course,
these observations are included in the statistical analysis.) In the upper
left corner of each panel correlation coefficients are given (top: Pearson's
coefficient; bottom: Spearman's coefficient). The corresponding significance
parameters are stated in brackets. Results from O/L channel B (green points)
very closely agree with channel A data (red) and therefore almost completely
mask the latter.
The occurrence of strong SNR fluctuations during the last phase of most
setting events (see Fig. ) independent of azimuth angle
suggests propagation-induced causes in addition to topographic, i.e. surface
interaction effects. Hypothetically we relate these fluctuations to multipath
ray propagation within the PBL.
The MPS simulations (Fig. ) suggest that at negative
elevation angles diffraction effects caused by the ground surface dominate
the observed C/N0 fluctuations; at higher elevations atmospheric
multipath seems to be more relevant. This hypothesis is tested for the
4.5-month time period from March to mid-July 2014 by correlating the standard
deviation of C/N0 between elevation angles of +1 and
+2∘ with the mean refractivity gradient 〈dN/dz〉. The calculation of 〈dN/dz〉 is restricted to the altitude range from
1 to 3 km. Figure shows the results for nine
PRNs.
The vertical refractivity profiles N(z) are extracted from European Centre
for Medium-Range Weather Forecasts (ECMWF) meteorological fields. Their
horizontal resolution is 1∘×1∘ (about 110 km in
meridional and 69 km in zonal direction at the receiver location)
with 137 height levels ranging from 0 to about 80 km; the averaging interval
of 1 to 3 km corresponds to about 13 vertical height levels. For signal
azimuth angles less than 270∘ (west to south-west) the refractivity
profile is extracted from ECMWF grid point (52∘ N,
12∘ E), about 84.4 km south-west of the observation site
(240.2∘ true bearing). For azimuth angles greater than
270∘ (west to north-west) the ECMWF grid point (53∘ N,
12∘ E) is selected, which is located about 99.8 km in the
north-western direction (314.2∘ true bearing). The standard
deviation of the carrier signal-to-noise density ratio,
σ(C/N0), calculated within the elevation angle range
+1∘<ϵ<+2∘, is taken as proxy for the
signal amplitude fluctuation.
Same as
Fig. but the correlation analysis now
includes all observations at elevations between -2 and +2∘. With
the exception of PRN 7 (and the Pearson's coefficient for PRN 18) the derived
correlations are no longer significant. Note the change of scale with respect
to Fig. .
Each panel of Fig. includes information on the
correlation; the Pearson and Spearman coefficients are quoted in the top and
bottom line, respectively see e.g., the corresponding
significance parameters are given in brackets. The values indicate that
〈dN/dz〉 and the standard deviation of
C/N0 are weakly to moderately correlated. With the exception of
PRN 17 (top right panel) all calculated correlations are significant on the
5 % level. The (negative) correlations range from -0.17 to -0.40. We
note that ECMWF refractivity profiles below 1 km frequently exhibit strong
gradients. Their inclusion into the calculation of 〈dN/dz〉 significantly decreases the correlations
or even renders them insignificant.
The MPS simulations (see Fig. ) also suggest that the
(negative) correlation between σC/N0 and 〈dN/dz〉 weakens if elevation angles close to or
below the horizon are included. Figure confirms
this prediction. In contrast to Fig. in this
figure the elevation angle range, used for the calculation of
σC/N0, is extended downwards to -2∘.
With the exception of both correlation coefficients for PRN 7 and the Pearson
coefficient for PRN 18, the derived correlations are no longer significant;
i.e. based on these results the null hypothesis cannot be rejected on the
5 % significance level.
An investigation of the relationship between signal amplitude and frequency
fluctuations, the local atmospheric refractivity field and, potentially,
effects arising from surface topography is beyond the scope of this paper and
will be addressed with higher resolution meteorological data in future
studies.
Conclusions
For more than a decade the OpenGPS receiver is used at GFZ in several
ground-based and airborne measurement campaigns. Owing to its open hardware
and software architecture the device can be adapted to address specific
signal tracking issues in GNSS radio occultation, reflectometry,
scatterometry or related fields. Here, a subset of low-elevation events
recorded during the long-term GLESER campaign are introduced and
discussed. Between 1 January and 31 December 2014 the instrument
recorded 2581 validated setting events at an observation site located
at 52.3808∘ N, 13.0642∘ E. The OpenGPS receiver tracks
signals from setting GPS satellites simultaneously in both, closed-loop and
open-loop mode down to geometric elevation angles of -1 to
-1.5∘. These low-elevation events are characterized by fluctuations
of about 10–20 dB Hz in signal-to-noise density ratio and about 10–20 Hz
in carrier frequency. Tracking the same event with one closed-loop and two
open-loop channels in parallel allows for direct intercomparison of open-loop
versus closed-loop performance. Whilst open-loop tracking allows us to follow
strongly fluctuating signals to very low elevation angles, in about 14 % of
the observations closed-loop tracking outperformed the open-loop channels,
since fluctuations in the early phase of the setting event between +2 and
0∘ elevation angle prevented proper initialization of the open-loop
model.
The analysis of open-loop data is performed on demodulated in-phase and
quad-phase correlation samples. The present study suggests that navigation
message demodulation using external information, e.g. extracted from GFZ's
NavBit data base (10.1594/GFZ.ISDC.GNSS/GNSS-GPS-1-NAVBIT), is
preferable to internal demodulation. Open-loop signal tracking results are
insensitive to the receiver-internal Doppler model for carrier
signal-to-noise density ratios C/N0≳ 30 dB Hz; below
this value reconstructed Doppler frequencies gravitate towards the model
value and thus potentially constitute a bias source. The present study did
not address potential contributions of the ionospheric signal propagation
and/or local multipath to the observed C/N0 fluctuations. These
issues need to be addressed in future work preferably using dual-frequency
receivers.
MPS simulations suggest that the observed weak to moderate
correlations between mean vertical refractivity gradients within the mean
PBL and the C/N0 fluctuations at positive
elevation angles are related to multipath induced by tilted layers of
refractivity gradients. At lower elevation angles, below 0∘, signal
diffraction at the ground surface dominates the observed amplitude
variations.
Data availability
The GLESER campaign raw data files have been supplied with the digital
object identifier 10.5880/GFZ.2016.1.1.002 and are available from GFZ's
data archive at http://dx.doi.org/10.5880/GFZ.2016.1.1.002. The data
are supplemented with documentation describing the measurement data files and
an archive containing the OpenGPS receiver software used during the
measurement campaign. The OpenGPS receiver software is free software and
available at http://dx.doi.org/10.5880/GFZ.2016.1.1.002. You can
redistribute it and/or modify it under the terms of the GNU General Public
License as published by the Free Software Foundation, either version 3 of the
License or (at your discretion) any later version. This program is distributed
in the hope that it will be useful, but without any warranty. See the GNU
General Public License at http://www.gnu.org/licenses/ for more
details. Access to GFZ's NavBit data base
(10.1594/GFZ.ISDC.GNSS/GNSS-GPS-1-NAVBIT) is provided by the
Information System and Data Center (ISDC) at
http://dx.doi.org/10.1594/GFZ.ISDC.GNSS/GNSS-GPS-1-NAVBIT. Information
on access to ECMWF data is available at http://www.ecmwf.int.
OpenGPS receiver hardware
The OpenGPS instrument (a photograph of the PCI card is reproduced in
Fig. ) inherited its key design features from the
OpenSourceGPS project . It utilises the
NovAtel® Superstar 1 (formerly CMC
Electronics®) GPS module (outlined red in
Fig. ) and is based on the well-documented
Zarlink® (formerly Mitel
Semiconductor®) GPS chip set consisting of
the single-frequency front-end GP2015 and the hardware correlator GP2021
.
During signal acquisition and tracking the 12 detection channels of the
GP2021 hardware correlator provide in-phase and quad-phase correlation sums
at the end of each full C/A code sequence. The occurrences are
denoted DUMP events and repeat at a rate of about once every millisecond
. DUMP events are aligned to the individual
C/A code sequences and therefore are asynchronous events. A
real-time operating system (Linux OpenSUSE version 11.3 with RTAI (RealTime
Application Interface for Linux) version 3.8.1 kernel extension module)
ensures that the correlator registers are read and processed within these
time constraints.
In addition, the current values of the carrier and code NCOs are output as
well. In contrast to DUMP events, these TIC events occur simultaneously on
all active channels and can be triggered at a used-defined frequency. Linux
RTAI meets the necessary time constraints for correlator input and output
with latency times below about 3–5 µs as measured on the
OpenGPS hardware.
The OpenGPS hardware utilises a modified Superstar 1 circuit board.
Following the OpenSourceGPS concept the on-board
processing unit ARM7TDMI and memory chip are unsoldered from the board and
the modified module is mounted on a PROTO-3 (manufactured by KOLTER
ELECTRONIC®) prototyping board which plugs
into a PCI expansion slot of a standard PC.
The signal acquisition and tracking program runs on the host computer;
control, monitoring and readout of the GP2021 hardware correlator are
performed through the PROTO-3's PCI port. An interface module, which was
designed and built in-house using discrete TTL logic (outlined blue in
Fig. ), connects to the hardware correlator's input and
output registers and allows direct access to the correlator registers from
the host PC via the PCI interface bus.
GFZ's OpenGPS receiver board for PCI
interface bus. A PCI prototyping board carries a modified single-frequency
GPS module (red outline). Data cables connect the input/output ports of the
hardware correlator chip to the TTL logic board (blue) and the PCI
interface.
Compared to conventional GPS receivers with on-board processing units, the
OpenGPS design clearly has some disadvantages. Using a PCI expansion card
for signal front-end as well as down-conversion and performing signal
acquisition and tracking on a host PC implies larger size, mass and power
consumption. However, the CPU processing power of the host PC
surpasses the capabilities of the Superstar 1 onboard processor by a wide
margin. The OpenGPS instrument therefore allows us to operate the hardware
correlator at higher sampling rates, to extract additional data from the
correlation process (e.g. in-phase and quad-phase correlation samples from
both GP2021 delay branches) and to run a full-featured operating system with
network layer and graphical display capabilities in addition to the real-time
process.
During the GLESER measurement campaign a mini-PC
(Shuttle® XPC SB52G2) equipped with 760 MB
memory and an Intel Pentium 4 processor clocked at 1.8 GHz serves as host
PC. Despite this modest, by today's standards, hardware the instrument supports
sampling frequencies of up to 100 Hz; the observations described and
discussed in this study are recorded at 50 Hz.
Screenshot of a terminal window running
the OpenGPS user space application ogdspl. In the lower half
characteristic information on the 12 tracking channels is shown. Note that
ogdspl maps azimuth angles to the interval [-180,+180∘]
with -90 and +90∘ referring to west and east, respectively. At
the time of the measurement on 16 October 2015 channel 1 tracked PRN 28 at an
elevation angle of +1.64∘ (column 6 entitled “elev”). Its azimuth
value (-98.15∘) is within the selected observation window ([-160,-20∘]) and the O/L channels A and B, here listed as channel 11 and
12, are cloned from channel 1. In-phase and quad-phase samples as well as
parameters describing the alignment between master and clone channels are
listed at the very bottom of the screen. The top few lines list position and
clock solutions from to the real-time navigation solution.
OpenGPS receiver software
The OpenGPS signal acquisition, tracking and real-time processing
software originates from the OpenSourceGPS project as well
; it also draws from source code written by S. Esterhuizen
and S. van Leeuwen . The main tasks of the receiver
program are
search and acquisition in code and frequency space,
signal tracking using code delay and carrier phase-locked loops,
decoding of the navigation data modulation,
calculation of transmitter position and velocity from broadcast ephemeris,
calculation of receiver position and receiver clock bias from measured
pseudoranges,
output of raw data to disk.
See e.g. and . Since the timeliness requirements for
these tasks differ by several orders of magnitude these tasks are allocated
to two processes running in parallel, the kernel module
ogrcvr_mod.ko and the user space application ogrcvr. The
module ogrcvr_mod.ko executes tasks controlling the code and
carrier phase tracking loops. To maintain tracking lock the carrier phase and
code data have to be read from the GP2021 registers, and the necessary loop
adjustments have to be determined and written back to the correlator within a
time interval of less than 100–200 µs. The real-time extension
layer RTAI guarantees this latency performance even for high disk
reading and writing operations or network traffic. ogrcvr handles
deferrable tasks, such as determination of satellite positions and velocities
from ephemeris data, calculation of the navigation solution and data storage.
Communication between real-time module and user space process is accomplished
using shared memory and FIFO (first in, first out) buffers. Inspection and
modifications of relevant signal tracking parameters, such as loop bandwidths
and loop orders, O/L channel frequency and code offsets and sampling
frequencies, are performed via a proc-based command line interface.
A third process, ogdspl, can optionally be started to display
tracking and positioning information on the terminal screen
(Fig. ). In total, the source code of all kernel and
user space modules comprises about 20 000 lines of C code.
The OpenGPS receiver operates in two different observation modes. In
“monitor mode” up to 10 of the 12 correlator channels are assigned to PRNs
of visible GPS satellites. The O/L channels A and B, in
Fig. listed as number 11 and 12, remain unassigned.
When a satellite, tracked by channel number k, crosses the +2∘
elevation boundary from above, the receiver transitions to “measurement
mode”, channels A and B are assigned to this satellite's PRN and their code
and carrier NCOs are aligned to those of channel k as well. In the
following this process is called “cloning” of A and B from the “master”
channel k and A/B are referred to as “clone” channels.
In measurement mode code and carrier NCO data, in-phase and quad-phase
correlation sums from both GP2021 correlation branches (“prompt” and
“dither”) and position and clock bias results from the real-time
navigation solution are stored on the local hard disk. The delay between the
prompt and dither branch is fixed at 0.5 chips (about 150 m). Code, carrier
phases and correlation sums are written with a temporal resolution of
Ts=0.02 ms (corresponding to a sampling frequency of
fs=50 Hz); the navigation solution is provided once per
second. We note that the stored correlation sums are coherently integrated
over Ts, whereas the NCO code and carrier phase are instantaneous
values sampled at the corresponding TIC event.
Typically, measurement mode lasts for about 10–15 min and ends when the
satellite's elevation angle drops below -2∘. During an
initialization phase, for elevation angles above 0∘, the code and
carrier phase loop adjustments are collected at each TIC event and
stored. Thereafter, when elevation angles are below 0∘, the carrier
loop is opened and NCO input values are calculated by linear extrapolation of
the stored Doppler adjustments. For code O/L tracking a hybrid method is
employed; if C/N0≤30 dB Hz, the code NCO values are
calculated from a second-order polynomial extrapolation of the stored
adjustments. Otherwise, the code loop operates in C/L mode; in addition, the
difference between actual adjustments and model-derived values is saved and
added to the model. Thus, potential deviations between observations at
C/N0>30 dB Hz and the extrapolated loop adjustments are used
to update the model.
The OpenGPS receiver software determines geometric elevation angles from
GPS almanac information. Since the data post-processing analysis is based on
the more precise GPS ephemeris data, the elevation angles of the measurement
start and the end of the O/L initialization may deviate from the nominal
values of +2 and 0∘, respectively, by some tenths of a degree
(see e.g. insert in Fig. ).
Closer inspection of the O/L carrier NCO frequencies in
Fig. (red and green lines; the insert shows a
zoomed-in view) reveals residual deviation of the O/L channel from the target
Doppler model in addition to the nominal values of ±5 Hz. First, at the
start of O/L tracking mode (at about -0.08∘ elevation angle) the
two clone channels are gradually moved into phase alignment to the O/L model
by adjusting the corresponding NCO frequencies (OpenGPS's hardware
correlator GP2021 does not support carrier phase adjustments). For channel B
(+5 Hz) the duration of this initialization process is shorter, since its
initial phase happened to be closer to the model phase. Furthermore, even
after completion of the alignment process, small fluctuations on the order of
a few 100 mHz are still apparent. These fluctuations are caused by the
finite bandwidth of a dedicated feedback loop, which keeps the two O/L
channels separated by 10 Hz in Doppler space. (Accessing the GP2021's
MULTI_CHANNEL_SELECT registers led to adverse side effects in our
tests.)
Compared to O/L methods employed by space-based GNSS-RO receivers, which are
based on predetermined code and carrier parameters derived from atmospheric
climatologies , the
OpenGPS O/L technique creates a different O/L model during the
initialization phase (elevation angles between +2 and 0∘) for
each setting event. Thus, diurnal variations in the atmospheric refractivity
field may be better accounted for in the O/L model. However, under
high-humidity conditions strong refractivity gradients could lead to SNR
fluctuations and subsequent (transient) loss of tracking lock already during
the O/L initialization phase at positive elevation angles producing a faulty
O/L model. In this case it is possible that C/L tracking actually outperforms
the O/L results (see Fig. ).
Acknowledgements
Helpful discussions with Stefan Heise are gratefully acknowledged. Thoughtful
comments and valuable suggestions from two anonymous reviewers significantly
improved this paper. We thank Christian Selke and Martin König for the
design and assembly of the OpenGPS hardware and Potsdam Institute for
Climate Impact Research for access to the observation deck on building A31.
GPS broadcast ephemeris data were provided by GFZ's orbit processing group at
Oberpfaffenhofen, Germany. The OpenGPS receiver software is derived from
the GPL-licensed OpenSourceGPS code base written by Clifford Kelley with
contributions from Stephan Esterhuizen and Sam Storm van Leeuwen. The
European Centre for Medium-Range Weather Forecasts (ECMWF) is acknowledged
for access to meteorological analysis data. Trademarks are owned by their
respective owners. The article processing charges for this
open-access publication were covered by a Research
Centre of the Helmholtz Association. Edited by:
J. Joiner Reviewed by: two anonymous referees
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