sensors
Article
Standalone GPS L1 C/A Receiver for Lunar Missions
Vincenzo Capuano *, Paul Blunt, Cyril Botteron, Jia Tian, Jérôme Leclère, Yanguang Wang,
Francesco Basile and Pierre-André Farine
École Polytechnique Fédérale de Lausanne (EPFL), Electronics and Signal Processing Laboratory (ESPLAB),
Rue de la Maladière 71b, CH-2002 Neuchâtel 2, Switzerland; paul.blunt@epfl.ch (P.B.);
cyril.botteron@epfl.ch (C.B.); jia_epfl_tian@163.com (J.T.); jerome.leclere@lassena.etsmtl.ca (J.L.);
wggaily@163.com (Y.W.); basile.fran1989@gmail.com (F.B.); pierre-andre.farine@epfl.ch (P.-A.F.)
* Correspondence: vincenzo.capuano@epfl.ch; Tel.: +41-21-6954-537
Academic Editor: Vittorio M. N. Passaro
Received: 13 January 2016; Accepted: 26 February 2016; Published: 9 March 2016
Abstract: Global Navigation Satellite Systems (GNSSs) were originally introduced to provide
positioning and timing services for terrestrial Earth users. However, space users increasingly rely
on GNSS for spacecraft navigation and other science applications at several different altitudes from
the Earth surface, in Low Earth Orbit (LEO), Medium Earth Orbit (MEO), Geostationary Earth Orbit
(GEO), and feasibility studies have proved that GNSS signals can even be tracked at Moon altitude.
Despite this, space remains a challenging operational environment, particularly on the way from
the Earth to the Moon, characterized by weaker signals with wider gain variability, larger dynamic
ranges resulting in higher Doppler and Doppler rates and critically low satellite signal availability.
Following our previous studies, this paper describes the proof of concept “WeakHEO” receiver; a
GPS L1 C/A receiver we developed in our laboratory specifically for lunar missions. The paper also
assesses the performance of the receiver in two representative portions of an Earth Moon Transfer
Orbit (MTO). The receiver was connected to our GNSS Spirent simulator in order to collect real-time
hardware-in-the-loop observations, and then processed by the navigation module. This demonstrates
the feasibility, using current technology, of effectively exploiting GNSS signals for navigation in
a MTO.
Keywords: GNSS; GPS; orbital filter; space navigation; Kalman filter; lunar mission; signal processing
1. Introduction
GNSS receivers have been successfully adopted as key elements of the navigation systems for
many space borne missions. Typically, they are used in LEO where the availability of the GNSS
signals is very good and high accuracy positioning can be achieved. Using a GNSS receiver as the
core navigation system enables greater autonomy of a spacecraft and reduces the burden and costs of
network operations [1]. For this reason, the autonomous navigation capabilities of GNSS are extremely
appealing, not only for LEO but for higher altitude Earth orbits as well. It is even possible for spacecraft
orbiting at altitudes beyond the GNSS constellations to receive weak signals from the opposite side of
the Earth. These receivers are picking up the spillover of the main lobe of the GNSS transmit antenna
pattern around the Earth mask and also signals from the weaker side lobes of the antenna pattern.
Research presented in [2–8] shows feasibility studies of GNSS as navigation system for space missions
in High Earth Orbits (HEO) and beyond up to Moon altitude. Other research work, such as [9–12]
and [13] has proposed GNSS receivers designed for such missions and the demonstration of a receiver
positioning in HEO is detailed in [14]. In [15–17] experimental demonstrations are described that show
the GNSS signals availability even at higher orbits than GEO. Research continues to investigate the
potential of using GNSS for lunar missions, in particular for Earth-Moon transfer orbits.
Sensors 2016, 16, 347; doi:10.3390/s16030347
www.mdpi.com/journal/sensors
Sensors 2016, 16, 347
2 of 21
In this paper, we describe the GPS L1 C/A hardware receiver, named “WeakHEO” receiver,
which we have designed and developed as a proof of concept for lunar missions at the ESPLAB
EPFL. Firstly, the hardware architecture of the receiver is presented followed by a description of
the defined mission and expected GNSS signal environment in which the receiver has to operate.
The high-sensitivity acquisition and tracking algorithms of the receiver are then described before
concluding with navigation test results from the receiver.
2. The WeakHEO Receiver Architecture
The architecture of the WeakHEO receiver is shown in Figure 1. The system comprises of three
main elements as follows.
‚
‚
‚
A tri-band (L1, L2, L5) RF front end, which amplifies, filters and down converts the GNSS signals
to an intermediate frequency (IF) where they are sampled. The reported initial implementation is
focused on processing and utilisation of the GPS L1 C/A code signal. However, a triple frequency
L1, L2, L5 front end (an early version of the front end in [18]) was selected to allow future
expansion to these frequencies. A high sampling rate is used to enable the receiver to support
precision tracking architectures and additional wider bandwidth signals in the future. A common
IF frequency of 53.78 MHz is used for all three bands and signals are sampled at 40.96 MHz with
4-bit resolution. The RF front is driven by a stable, low-phase noise Oven Controlled Crystal
Oscillator (OXCO).
A DE3 FPGA platform. An FPGA platform was required to allow custom designs of the
acquisition and tracking engines within the receiver. The WeakHEO receiver uses the same
development platform and builds on the FPGA-based architecture of the “Signature” receiver
developed by ESPLAB in EPFL [19]. Its core component is a Stratix III FPGA (Field Programmable
Gate Array) receiving the parallel sampled data from the RF front end. The FPGA contains a
softcore NIOS II (32bit RISC) processor and performs all the high sensitivity acquisition, tracking
and navigational data decoding processes. Raw measurements (pseudoranges, pseudorange rates,
signal parameters, time, etc.) are passed to the PC through a UART interface at a rate of 0.1 Hz.
Note that this rate has been chosen in order to allow the real-time processing of the navigation
solution on the PC (currently programmed in Matlab). In the next version of the receiver, a faster
update rate will be selected. An external memory (DDR2 SDRAM) connected to the FPGA is also
used as buffer for the acquisition.
A PC, The PC then performs the navigation solution in real time or can record and compute the
orbital filter calculations offline.
Sensors 2016, 16, 347
3 of 21
Sensors 2016, 16, 347
3 of 21
DDR2 SDRAM
OCXO
RF Frontend
Decimation
& down
conversion
I
Q
Buffer & I
DDR2
control Q
Acquisition
Nios II
softcore
processor
Acquisition
control
GPS tracking
channel 1
I
Q
Cos
Sin
Carrier
NCO
correlator
E
P
I
E
P
L
PC
Raw measurement
data
Navigation
Algorithm
Serial
port
L
Code NCO
GPS tracking channel 2
Tracking
control
GPS tracking channel N
Navigation data Decode
Decode
Assistance
data
Stratix III FPGA
Figure
Figure 1.
1. Architectural
Architectural components
components of
of the
the WeakHEO
WeakHEO receiver.
receiver.
2.1.
2.1. Operations
Operations of
of the
the Receiver
Receiver
The
operations
of the
the receiver
receiver are
are performed
performed in
in several
several steps
steps as
as follows:
follows:
The operations of
(1) The navigation software on the PC determines which GPS satellites are visible and estimates the
(1) The navigation software on the PC determines which GPS satellites are visible and estimates the
Doppler for each satellite. This information is then sent to the FPGA through the UART interface.
Doppler for each satellite. This information is then sent to the FPGA through the UART interface.
This allows a reduction of the frequency search space for the acquisition thus a reduction of the
This allows a reduction of the frequency search space for the acquisition thus a reduction of the
acquisition time.
acquisition time.
(2) The acquisition searches the satellites in view within a frequency search space around the coarse
(2) The acquisition searches the satellites in view within a frequency search space around the coarse
Doppler given. Once a satellite is acquired, there is a transition phase before the tracking to
Doppler given. Once a satellite is acquired, there is a transition phase before the tracking to
determine the position of the bit edge. Following this, tracking is started and the Time Of Week
determine the position of the bit edge. Following this, tracking is started and the Time Of Week
(TOW) is decoded from the received navigation data.
(TOW) is decoded from the received navigation data.
(3) The measurements (pseudoranges, pseudorange rates, satellite PRN, estimated C/No and TOW)
(3) are
Thesent
measurements
(pseudoranges,
pseudorange
satellite
PRN,solution
estimated
C/No and TOW)
to the computer
by the FPGA
at a rate ofrates,
0.1 Hz
and a PVT
is computed.
are sent to the computer by the FPGA at a rate of 0.1 Hz and a PVT solution is computed.
2.2. Description of the Mission Scenario
2.2. Description of the Mission Scenario
The reference trajectory for our study is a direct Earth-Moon Transfer Orbit (MTO). The initial
The reference trajectory for our study is a direct Earth-Moon Transfer Orbit (MTO). The initial
position and velocity with the respect to the Earth Centered Inertial frame (ECI) are reported in Table
position and velocity with the respect to the Earth Centered Inertial frame (ECI) are reported in Table 1,
1, as well as some characteristics assumed for the host spacecraft. The full trajectory is propagated
as well as some characteristics assumed for the host spacecraft. The full trajectory is propagated from
from the initial conditions by the PosApp software of our Spirent GSS8000 simulator, taking into
the initial conditions by the PosApp software of our Spirent GSS8000 simulator, taking into account
account gravitational effects from the Earth, Sun and Moon, atmospheric drag and the solar radiation
gravitational effects from the Earth, Sun and Moon, atmospheric drag and the solar radiation pressure.
pressure. The reference trajectory is represented by the blue portion of the MTO shown in Figure 2.
The reference trajectory is represented by the blue portion of the MTO shown in Figure 2. The reference
The reference orbit has been validated using the System Tool Kit (STK) [20]. Figure 3 shows the
orbit has been validated using the System Tool Kit (STK) [20]. Figure 3 shows the relation between
relation between altitude and time during the considered MTO and also the GPS satellites altitude.
altitude and time during the considered MTO and also the GPS satellites altitude.
Sensors 2016, 16, 347
4 of 21
Sensors 2016, 16, 347
4 of 21
Table
Initial
Sensors1.2016,
16,, xposition and velocity of the considered receiver trajectory and spacecraft parameters.
4 of 21
Table 1. Initial position and velocity of the considered receiver trajectory and spacecraft parameters.
Table 1. Initial position
and velocity of the considered receiver trajectory
and spacecraft parameters.
Parameters
Values
Parameters
Parameters
ECI Initial position (km)
ECI Initial position (km)
ECI Initial
(km)
ECIposition
Initial velocity
(km/s)
ECI Initial velocity (km/s)
Departure
ECI Initial velocity
(km/s) date
Departure date
Mass ofdate
the spacecraft (kg)
Departure
Mass of the spacecraft (kg)
(m2 )
Mass of theReference
spacecraftsurface
(kg)
2)
Reference surface (m
Radiation
pressure
Reference
surface
(m2) coefficient
Radiation pressure coefficient
Radiation pressure coefficient
`
˘
Values
Values
2395.52
´5298.28 ´3022.82
2395.52 ` −5298.28 −3022.82˘
(2395.52 −5298.28
10.19 3.58
1.72 )
−3022.82
10.19 3.58 1.72
(10.192 July
)
3.582005,
1.7200:34:18
2 July 2005, 00:34:18
1000
2 July 2005, 00:34:18
1000
1000 20
20
1
20
1
1
Figure 2. STK representation of the considered MTO.
altitude (km)
Figure
2.2.STK
considered
Figure
STKrepresentation
representation ofof
thethe
considered
MTO.MTO.
Figure 3. Relation between altitude and time during the considered MTO and GPS constellation
altitude.
Figure 3. Relation between altitude and time during the considered MTO and GPS constellation
2.3. GNSS
Characteristics
Figure
3. Signal
Relation
between altitude and time during the considered MTO and GPS
altitude.
constellation altitude.
2.3.1. Simulation Models and Assumptions
2.3. GNSS Signal Characteristics
In our simulations we have modelled a GPS constellation consisting of 32 GPS satellites,
2.3. GNSS Signal Characteristics
allocated
in the six
orbital
planes
according to [21]. Realistic GPS L1 C/A signals are generated by our
2.3.1.
Simulation
Models
and
Assumptions
Spirent GSS8000 full constellation simulator, where the signal power level at the receiver
is
2.3.1. Simulation
andweAssumptions
In ourasModels
simulations
have modelled a GPS constellation consisting of 32 GPS satellites,
modelled
[22]:
allocated in the six orbital planes according to [21]. Realistic GPS L1 C/A signals are generated by our
In our simulations we have modelled a GPS constellation consisting of 32 GPS satellites, allocated
in the six orbital planes according to [21]. Realistic GPS L1 C/A signals are generated by our Spirent
GSS8000 full constellation simulator, where the signal power level at the receiver Pr is modelled as [22]:
ˆ
Pr “ PICD ` OG ` 20 ˆ log10
R0
R
˙
´ Ltx ´ Lrx
(1)
Sensors 2016, 16, 347
5 of 21
where:
PICD “ ´128.5 dBm
OG “ `3 dB
R0
R
Ltx
Lrx
is the guaranteed minimum signal level for the GPS L1 C/A signals on
the Earth according to [21].
is the global offset, chosen to obtain in simulation the performance
obtained when real signals are received. Typically, the transmitted signal
power levels are from 1 to 5 dB higher than the minimum received
ones [23], for this reason an intermediate value of 3 dB has been chosen.
is the reference range used for inverse-square variation calculation and
equal to the range from a receiver to the GNSS satellite at zero elevation.
is the range from GNSS satellite to the receiver.
is the loss from the GNSS satellite transmit antenna in the direction of the
receiver. 3D GPS antenna patterns have been modelled, as described in
our previous study [24,25].
is the loss from the receiver antenna in the direction of the GNSS satellite.
2.3.2. Signal Power and Dynamics
In this section we report some significant simulation results from our previous studies [13,24],
and [26] used to define the main receiver characteristics. Figure 4 shows the received power levels of
all the GPS L1 C/A signals as a function of the time, during the full considered trajectory. As shown
in Figure 5, the fourth strongest GPS L1 C/A signal (at least four ranges are required to compute the
3D position) at receiver antenna reaches approximately a minimum power level of ´168.5 dBm. For
this reason, a very high sensitivity receiver architecture is required. Moreover, the carrier frequency is
affected by Doppler shifts and Doppler rates (see Figures 6 and 7 respectively) of up to 20 kHz and up
to 4 Hz/s respectively at the Moon altitude (where the signals are weaker) and of up to 60 kHz and up
to 65 Hz/s at the beginning of the MTO (where the signals are stronger), requiring a certain robustness
against high dynamics for the receiver.
The identified minimum power level of ´168.5 dBm of the fourth strongest signal during the
full considered MTO can be seen as a power sensitivity value required for the receiver to acquire and
track at least four signals (and then provide the navigation solution) with a certain probability. Then,
assuming a receiver antenna gain of 10 dBi, we have targeted a sensitivity of at least ´159 dBm, slightly
higher than the minimum required.
According to [27], it is possible to calculate the carrier-to-noise density ratio C/N0 (in dB-Hz)
from the received power Pr (in dBm) by using the following formula, valid for a front-end noise figure
of 2 dB and an effective antenna temperature of 130 K:
C{N0 “ Pr ` 174
(2)
A received signal level of ´159 dBm then corresponds to a C/N0 of 15 dB-Hz.
However, when a GNSS simulator is used, the effective antenna temperature is the room
temperature, which increases the noise. In that case, the carrier-to-noise ratio can be obtained as
C{N0 “ Pr ` 172
(3)
A received signal level of ´157 dBm then corresponds to a C/N0 of 15 dB-Hz for testing with the
GNSS simulator.
Sensors 2016, 16, 347
Sensors
Sensors
2016,
16,,
x
Sensors2016,
2016,16,,
16, x
347
6 of 21
666of
of21
21
of
21
Figure 4.
4. Received
Received power
power levels
levels of
of the
the GPS
GPS L1
L1 C/A
C/A signals
signals
as aaa function
function of
of the
the time,
time, during
during the
the full
full
Figure
Figure
4.
Received
power
levels
of
the
GPS
L1
C/A
signals
as
function
of
the
time,
during
the
full
Figure
4.
Received
the
GPS
L1
C/A
signalsas
considered
trajectory,
by
assuming
a
0
dBi
receiver
antenna
gain.
considered
dBi
receiver
antenna
gain.
trajectory,by
byassuming
assumingaaa000dBi
dBireceiver
receiverantenna
antennagain.
gain.
considered trajectory,
trajectory,
by
assuming
Figure 5. First, second, third and fourth highest received power levels of the GPS L1 C/A signals as a
function
thesecond,
time,
during
considered
by assuming
0the
dBi
receiver
antenna
Figure
5.
First,
second,
third
and
fourth
highest
received
power
levels
GPS
L1
signals
as
Figure
5.
First,
third
and
fourth
highest
received
levels
of
the
GPS
L1
C/A
signals
as
Figure
5.of
First,
second,
thirdthe
andfull
fourth
highesttrajectory,
receivedpower
power
levelsof
ofathe
GPS
L1C/A
C/A
signalsgain.
asaaa
function
of
the
time,
during
the
full
considered
trajectory,
by
assuming
dBi
receiver
antenna
gain.
function
functionof
ofthe
thetime,
time,during
duringthe
thefull
fullconsidered
consideredtrajectory,
trajectory,by
byassuming
assumingaaa000dBi
dBireceiver
receiverantenna
antennagain.
gain.
Figure 6. Doppler shift of received GPS L1 C/A signals across the MTO.
Figure
Figure6.
6.Doppler
Dopplershift
shiftof
ofreceived
receivedGPS
GPSL1
L1C/A
C/Asignals
signals
across
the
MTO.
Figure
6.
Doppler
shift
of
received
GPS
L1
C/A
signalsacross
acrossthe
theMTO.
MTO.
Sensors
Sensors 2016,
2016,16,
16,,347
x
77ofof21
21
Figure
signals across
across the
Figure7.7. Doppler
Doppler rates
rates of
of received
receivedGPS
GPSL1
L1C/A
C/A signals
the MTO.
MTO.
2.4.
2.4. Geometric
Geometric Dilution
Dilution of
of Precision
Precision (GDOP)
(GDOP) and
and Ranging
Ranging Errors
Errors
As
As described
described in
in [24]
[24] in
in detail,
detail, the
the achievable
achievable navigation
navigation accuracy
accuracy at Moon
Moon altitude
altitude is strongly
strongly
limited
limited by
by aa very
very poor
poor relative
relative geometry
geometry between
between the
the receiver
receiver and
and the
the transmitters
transmitters (very
(very large
large GDOP
GDOP
values)
errors.
ForFor
instance,
at Moon
altitude,
simulations
in [26]inshow
values
values)and
andlarge
largeranging
ranging
errors.
instance,
at Moon
altitude,
simulations
[26] GDOP
show GDOP
much
higher
than
1000
for
an
acquisition
sensitivity
of
15
dB-Hz.
Due
to
the
very
low
carrier
to
noise
values much higher than 1000 for an acquisition sensitivity of 15 dB-Hz. Due to the very low carrier
ratio
C{Nratio
processing
GPS L1 C/A
signals,
thesignals,
code tracking
thermal
range
jitter σ
to noise
𝐶/𝑁when
when processing
GPS
L1 C/A
the code
tracking
thermal
range
0 values,
tDLL
0 values,
can
values
larger
than larger
6 m [24].
A6detailed
characterization
of GDOP and
ranging
for
jitterachieve
σ𝑡𝐷𝐿𝐿 can
achieve
values
than
m [24]. A
detailed characterization
of GDOP
anderror
ranging
different
sensitivity
values
and
different
GNSS
signals
is
provided
in
[24].
error for different sensitivity values and different GNSS signals is provided in [24].
2.5.
2.5. GPS
GPS Acquisition
Acquisition
2.5.1. Acquisition Strategy
2.5.1. Acquisition Strategy
The three main acquisition methods for GNSS signals are the serial search (SS), the parallel
The three main acquisition methods for GNSS signals are the serial search (SS), the parallel
frequency search (PFS), and the parallel code-phase search (PCS) [28]. Compared to the PCS and
frequency search (PFS), and the parallel code-phase search (PCS) [28]. Compared to the PCS and the
the PFS methods, the acquisition time of the SS method is extremely long, therefore, the SS was
PFS methods, the acquisition time of the SS method is extremely long, therefore, the SS was not
not considered. Compared to PCS, PFS has two main drawbacks. Firstly, an extra loss due to the
considered. Compared to PCS, PFS has two main drawbacks. Firstly, an extra loss due to the
integration before the fast Fourier transform (FFT) and secondly a loss due to the mismatch between
integration before the fast Fourier transform (FFT) and secondly a loss due to the mismatch between
the replica code chipping rate and the received code chipping rate, especially important for long
the replica code chipping rate and the received code chipping rate, especially important for long
integration times [28]. Since the sensitivity is of prime importance in high altitude space applications,
integration times [28]. Since the sensitivity is of prime importance in high altitude space applications,
these additional losses are not acceptable, and therefore the PCS technique was selected.
these additional losses are not acceptable, and therefore the PCS technique was selected.
The acquisition structure of receiver is illustrated in Figure 8. In acquisition, the receiver uses
The acquisition structure of receiver is illustrated in Figure 8. In acquisition, the receiver uses
coherent accumulations, which are the length of a full navigation data-bit (20 ms for GPS C/A code).
coherent accumulations, which are the length of a full navigation data-bit (20 ms for GPS C/A code).
The results are then non-coherently accumulated to gain further sensitivity. To reduce the effect of
The results are then non-coherently accumulated to gain further sensitivity. To reduce the effect of
the data-bit transitions a number of different accumulations are formed with different starting points.
the data-bit transitions a number of different accumulations are formed with different starting points.
Ideally, for GPS C/A code we would have 20 accumulations spaced 1 ms apart. However, to limit the
Ideally, for GPS C/A code we would have 20 accumulations spaced 1 ms apart. However, to limit the
impact on the FPGA resources we form 10 accumulations spaced 2 ms to achieve a balance between
impact on the FPGA resources we form 10 accumulations spaced 2 ms to achieve a balance between
performance and the available resources.
performance and the available resources.
Following the results of Section 2.3.2, the sensitivity targeted is 15 dB-Hz, slightly higher than
Following the results of Section 2.3.2, the sensitivity targeted is 15 dB-Hz, slightly higher than
the minimum required to acquire at least four signals. Using the methodology proposed in [27], the
the minimum required to acquire at least four signals. Using the methodology proposed in [27], the
theoretical analysis of the acquisition parameters is presented in Table 2. This is used to estimate
theoretical analysis of the acquisition parameters is presented in Table 2. This is used to estimate the
the total required integration time required for a successful acquisition. In acquisition, the receiver’s
total required integration time required for a successful acquisition. In acquisition, the receiver’s
sampling rate of 40.96 MHz is decimated to 4.096 MHz as a compromise to improve processing
sampling rate of 40.96 MHz is decimated to 4.096 MHz as a compromise to improve processing
performance. The resolution in the code search is one sample so this results a resolution around ¼
performance. The resolution in the code search is one sample so this results a resolution around ¼ of
of a chip. A higher sampling frequency requires more samples to be processed but results in a fine
a chip. A higher sampling frequency requires more samples to be processed but results in a fine
resolution in the code search domain. A lower frequency means less samples to process but poorer
Sensors 2016, 16, 347
8 of 21
Sensors 2016, 16, 347
8 of 21
resolution in the code search domain. A lower frequency means less samples to process but poorer
resolution
with
fromtracking
the codefrom
misalignment.
In tracking
the fullAsample
rate of
40.96
MHz
MHz is used
tohigher
allow losses
precision
narrow correlator
spacings.
frequency
step
of 25
Hz
is
used
to selected,
allow precision
tracking
from narrow
spacings.
A frequency
step tolerable
of 25 Hz has
been
has
been
again as
compromise
for the correlator
performance.
Finally,
the maximum
Doppler
selected,
again
as compromise
for the performance.
maximum
Doppler
rate error
rate error
is defined
as the Doppler
rate, which Finally,
implies the
a shift
of onetolerable
frequency
bin during
the
is
defined
as
the
Doppler
rate,
which
implies
a
shift
of
one
frequency
bin
during
the
integration
time.
integration time.
Read data
from
SDRAM
Coherent
accumulator
Carrier
mixer
Complex
multiplier
FFT
Incoherent
accumulator
Peak
extraction
FFT
Carrier
generator
Code
generator
Magnitude
calculator
FFT
Determina
tion
module
Control
module
output
conj
Coherent
accumulator
Magnitude
calculator
Incoherent
accumulator
Peak
extraction
Figure 8.
8. Block
Block scheme
scheme of
of the
the acquisition
acquisition module.
module.
Figure
Table 2. Theoretical acquisition parameters.
Table 2. Theoretical
acquisition parameters.
Quantity
Value
C/N0 (dB-Hz)
15
Quantity
Value
Sampling rate (MHz)
4.096
C/N0 (dB-Hz)
15 4
Quantization (bit)
Sampling rate (MHz)
4.096
Quantization loss (dB)
0.05
Quantization (bit)
4
Coherent
integration
time
(ms)
Quantization loss (dB)
0.0520
Coherent integration
timegain
(ms)(dB)
20 46
Coherent
Coherent
gain (dB)
46 25
Frequency
search step (Hz)
Frequency search step (Hz)
25
Worst case frequency mismatch loss (dB)
0.91
Worst case frequency mismatch loss (dB)
0.91
Code
search
step
(chip)
0.25
Code search step (chip)
0.25
Worst
case
code alignment
1.16
Worst case
code
alignment
loss (dB) loss (dB)
1.16
Data bitData
alignment
loss
(dB)
0.92
bit alignment loss (dB)
0.92
SquaringSquaring
loss (dB) loss (dB)
5.73
5.73
Final desired SNR (dB)
16
Final desired SNR (dB)
16
Non-coherent gain required (dB)
26.77
Non-coherent
required (dB)
26.77
Number of
non-coherent gain
integration
475
Total
accumulation
time (s)
9.5475
Number
of non-coherent
integration
Maximum tolerable
Doppler
rate error (Hz/s)
2.639.5
Total
accumulation
time (s)
Maximum tolerable Doppler rate error (Hz/s)
2.63
2.5.2. Acquisition Hardware Implementation
2.5.2. Acquisition Hardware Implementation
The FPGA implementation of the acquisition is shown in Figure 9. The Nios II processor is used to
manage
configure
the different
blocks
(e.g., theisacquisition
configured
with parameters
Theand
FPGA
implementation
of the
acquisition
shown in module
Figure 9.isThe
Nios II processor
is used
such
as Doppler
code, number
of integrations,
etc.), and to
analyzeisthe
data provided
to manage
and frequency,
configure PRN
the different
blocks
(e.g., the acquisition
module
configured
with
by
the acquisition
module
to decide
if a signal
been
detected.
The acquisition
module
parameters
such as
Doppler
frequency,
PRNhas
code,
number
of integrations,
etc.),
and toprocesses
analyze the
the
input
data usingby
thethe
PCS
method asmodule
shown in
provides
statistics
value,
data provided
acquisition
to Figure
decide8 ifand
a signal
hasacquisition
been detected.
The(peak
acquisition
mean
value,
standard
deviation,
etc.) tothe
thePCS
Nios
II processor.
Since
the integration
time isacquisition
very long
module
processes
the input
data using
method
as shown
in Figure
8 and provides
(9.5
s), the(peak
amount
of data
to save
is significant
39 etc.)
M samples).
Therefore,
a DDR2Since
SDRAM
statistics
value,
mean
value,
standard (around
deviation,
to the Nios
II processor.
the
external
to the
FPGA
is used
save
thisamount
data. of data to save is significant (around 39 M samples).
integration
time
is very
long to
(9.5
s), the
Therefore, a DDR2 SDRAM external to the FPGA is used to save this data.
Sensors 2016, 16, 347
9 of 21
Sensors 2016, 16, 347
9 of 21
NIOS II Processor
Acquisition Reset
Manager
Input Data
Data Buffer
Manager
DDR2 SDRAM
Controller
Acquisition Module
DDR2 SDRAM
Figure 9. Global structure of the acquisition implementation.
Figure 9. Global structure of the acquisition implementation.
In high sensitivity acquisition, the acquisition time can be very long and the transition between
In high sensitivity
the acquisition
timeThus,
can bewe
very
long and
transition
between
the
the acquisition
and theacquisition,
tracking becomes
difficult.
propose
to the
acquire
the signal
twice,
acquisition
and
the tracking
becomes
difficult.
Thus,
we propose to acquire the signal twice, reducing
reducing the
frequency
search
space after
the first
step.
the frequency
search
space
after
the
first
step.
The time spent to search one frequency bin is defined as:
The time spent to search one frequency bin is defined as:
fSTI 4.096 106 9.5
TFB  f TI  4.096 ˆ 106 ˆ6 9.5 237.5 ms
“ 163.84 10 6 “ 237.5 ms
TFB “ fSFPGA
(4)
(4)
f FPGA
163.84 ˆ 10
where fS is the sampling rate, TI is the total integration time, and fFPGA is the clock frequency of the
where fS is the sampling rate, T I is the total integration time, and fFPGA is the clock frequency of the
FPGA. For the first acquisition, the frequency search space considered is ±35 kHz. With a frequency
FPGA. For the first acquisition, the frequency search space considered is ˘35 kHz. With a frequency
step of 25 Hz, there are NFB,1 = 2801 frequency bins, thus the time to search the entire frequency search
step of 25 Hz, there are NFB,1 = 2801 frequency bins, thus the time to search the entire frequency search
space is:
space is:
3 ´3 “ 674.5 s
TA,1 “
2801ˆ
237.5
(5)
T TI`T NFB,1
N TTFB “99.5
.5`2801
237
.51010
674.5s
(5)
A,1
I
FB,1 FB
According to Figure 7, the Doppler rate is less than 4 Hz/s after the initial few hours of the MTO.
According to Figure 7, the Doppler rate is less than 4 Hz/s after the initial few hours of the MTO.
Therefore, during the first acquisition the frequency of the received signal may have shifted by up to
Therefore, during the first acquisition the frequency of the received signal may have shifted by up to
2700 Hz (4 Hz/s ˆ 675 s). For the second acquisition, the frequency search space is then ˘2700 Hz,
2700 Hz (4 Hz/s × 675 s). For the second acquisition, the frequency search space is then ±2700 Hz,
which corresponds to NFB,2 = 217 frequency bins. The time to search the frequency search space of the
which corresponds to NFB,2 = 217 frequency bins. The time to search the frequency search space of the
second step is:
second step is:
TA,2 “ TI ` NFB,2 TFB “ 9.5 ` 217 ˆ 237.5 10´3 « 61 s
(6)
3
TA,2 TI ofNthe
217237
.510
 61
s by up to 244 Hz, which
(6)
FB,2T
FB  9.5signal
During this time, the frequency
received
could
have
shifted
is still too large to start correctly the tracking. However, provided we recorded the time between the
During this time, the frequency of the received signal could have shifted by up to 244 Hz, which
two consecutive acquisitions, the Doppler rate can been estimated by looking at the evolution of the
is still too large to start correctly the tracking. However, provided we recorded the time between the
Doppler frequency, or from the evolution of the code delay. From Figure 7, we can assume the Doppler
two consecutive acquisitions, the Doppler rate can been estimated by looking at the evolution of the
rate is constant during a short time interval and therefore it is possible to initialise the tracking from
Doppler frequency, or from the evolution of the code delay. From Figure 7, we can assume the
these results.
Doppler rate is constant during a short time interval and therefore it is possible to initialise the
tracking from these results.
Sensors 2016, 16, 347
10 of 21
2.5.3. Acquisition Aiding from Navigation
For a standalone receiver, some aiding can still be obtained from the navigation result. The a priori
knowledge consists of:
-
Position (from the last known position stored in memory),
Time (from the real-time clock),
Reference frequency (since the receiver oscillator offset is determined by the navigation solution)
Approximate GNSS satellite positions and velocities (calculated from the almanac data stored
in memory).
Therefore, the frequency search uncertainty for the acquisition mainly depends on the time
uncertainty, receiver velocity and position uncertainties, and almanac uncertainty, which will be
discussed below.
Time Uncertainty
By time, we mean the time of week (TOW) from the navigation data. This can be delivered as
the GPS week and seconds of the week. Provided the receiver is tracking at least one satellite above
15 dB-Hz the time can be decoded and considered to be known within 1 s. The rate of change of
the Doppler frequency is up to 4 Hz/s according to Figure 7. Therefore, for 1 s of error in time, the
corresponding error in the Doppler estimation is up to 4 Hz. Once a navigation fix is achieved, as we
are using a stable OCXO our time knowledge will not drift quickly in periods of poor GNSS visibility
(around 1 ms/day) and so is likely to be much better.
Receiver Velocity Uncertainty
According to our post processing simulations, whose assumptions are described in [25], when
the GPS solution is not filtered through any orbital forces model, the receiver velocity uncertainty
can reach approximately 700 m/s at Moon altitude, that means that the corresponding frequency
uncertainty is 700 m/s/0.19 m = 3684 Hz (0.19 m being the wavelength of the L1 C/A signal).
Receiver Position Uncertainty
According to our simulations, when the GPS solution is not filtered through any orbital forces
model, the receiver position uncertainty can reach peaks of 80 km at Moon altitude (neglecting a very
few higher peaks). Using the equations given in Section 3.6.5 of [27], the corresponding frequency
uncertainty is (3800 m/s ˆ 80 km)/(380 000 km ˆ 0.19 m) = 4.2 Hz, where 3800 m/s is the GPS satellite
speed, 380,000 km is the distance between the Earth and the Moon, and 0.19 m is the wavelength of
the L1 C/A signal.
Almanac Uncertainty
The precision of the ephemeris is very high, so the frequency uncertainty induced by the ephemeris
can be ignored. According to Section 3.6.6 of [27], if the almanac data are used for frequency assistance,
the frequency uncertainty is 60 Hz.
Total Search Uncertainty
According to the analysis above, the total frequency uncertainty is about ˘3692 Hz. Note that
for the position and velocity uncertainty, to be conservative we have considered the worst case that is
obtained at Moon altitude; in fact it is the highest altitude of the trajectory and it corresponds to the
highest GDOP and accordingly to the highest position and velocity errors.
Sensors 2016, 16, 347
11 of 21
Sensors 2016, 16, 347
11 of 21
2.6. GPS Tracking
2.6. GPS Tracking
2.6.1. Bit Synchronisation and Navigation Data Decoding from very Weak Signals
2.6.1. Bit Synchronisation and Navigation Data Decoding from very Weak Signals
Following the acquisition stage, the acquisition engine passes its estimates of Doppler, Doppler
stage,
thetracking
acquisition
engine
estimates
rate, Following
code offsetthe
andacquisition
bit position
to the
channel
andpasses
is thenitsfree
to look of
forDoppler,
the next Doppler
satellite.
rate,
code
offset
and
bit
position
to
the
tracking
channel
and
is
then
free
to
look
for
the
satellite.
The position of the navigation data bit edge must be located and confirmed. This is next
necessary
as
The
position
of
the
navigation
data
bit
edge
must
be
located
and
confirmed.
This
is
necessary
as
although the acquisition uses full navigation data bit length accumulations of 20 ms, it only computes
although
the spaced
acquisition
fulltonavigation
data bit length
accumulations
of 20 ms,
it only computes
10
branches
2 msuses
apart
reduce complexity.
In the
tracking channel
20 branches,
spaced
10
branches
spaced
2
ms
apart
to
reduce
complexity.
In
the
tracking
channel
20
branches,
spaced
1
1 ms apart are then formed and accumulated to confirm the bit edge position. During this process the
ms
apart
are
then
formed
and
accumulated
to
confirm
the
bit
edge
position.
During
this
process
the
tracking channel operates a low bandwidth FLL (0.2 Hz) initialised with the estimation of Doppler,
tracking
operates
a low
FLL the
(0.2 acquisition
Hz) initialised
with Following
the estimation
of Doppler,
Doppler channel
rate, code
offset and
bitbandwidth
position from
engine.
confirmation
of
Doppler
rate,
code
offset
and
bit
position
from
the
acquisition
engine.
Following
confirmation
of
the
the bit edge position, decoding of the navigation data bits is started. The theoretical probability of a
bit
edge position,
of C/A
the navigation
bits iscarrier
started.
Thetracking
theoretical
probability
navigation
data bitdecoding
error of the
code signaldata
assuming
phase
is given
by [23]:of a
navigation data bit error of the C/A code signal assuming carrier phase tracking is given by [23]:
¯
´a
1
PB “ 1 er f c
c{n0 τa
(7)
(7)
⁄
=2
2
where
error
function,
c{n0⁄is the
carrier
to noise
density
ratioratio
(scalar)
and
where er f c isisthe
thecomplementary
complementary
error
function,
is the
carrier
to noise
density
(scalar)
τ
is
the
accumulation
time
(20
ms
for
C/A
code).
The
probability
of
a
bit
error
is
0.13
at
a
C{N
a
and
τ is the accumulation time (20 ms for C/A code). The probability of a bit error is 0.13 at a ⁄0 of
15
dB-Hz
and
0.056
at at
1818
dB-Hz.
AA
C{N⁄0 of 27.5
dB-Hz
is required
to give
a probability
of of
bitbit
error
of
of 15
dB-Hz
and
0.056
dB-Hz.
of 27.5
dB-Hz
is required
to give
a probability
error
´6 .−6As each subframe is 300 bits long, this probability would result in less than one contaminated
10
of 10 . As each subframe is 300 bits long, this probability would result in less than one contaminated
subframe in
every 3000.
3000. However,
However, as
shown in
in [29,30],
[29,30], the
the fact
fact that
that the
the message
message is
is regularly
regularly repeating
repeating
subframe
in every
as shown
can be
be exploited
exploited to
to effectively
effectively increase
increase the
the accumulation
accumulation time
time and
and reconstruct
reconstruct the
the message
message at
at weaker
weaker
can
signal
levels.
signal levels.
The data
procedure
can be
divided
into two into
steps,two
the first
stepthe
is frame
The
datadecoding
decoding
procedure
can
be divided
steps,
first synchronization
step is frame
(finding
the preamble),
thethe
second
step is to
decode
thestep
desired
from
multiple
repetitions.
synchronization
(finding
preamble),
the
second
is to data
decode
the
desiredsubframe
data from
multiple
As
depicted
in
Figure
10,
each
GPS
frame
contains
5
sub-frames.
Every
sub-frame
has
6
s
duration.
It
subframe repetitions. As depicted in Figure 10, each GPS frame contains 5 sub-frames. Every substarts with
8 bit
preamble
consists
10 words.
Each
wordofhas
30 bits. Each
The preamble
frame
has 6as known
duration.
It starts
with and
a known
8 bitofpreamble
and
consists
10 words.
word has
marks
the
beginning
of
each
sub-frame
and
is
repeated
every
6
s.
30 bits. The preamble marks the beginning of each sub-frame and is repeated every 6 s.
TLM(8+14)
22 bits
TLM(8+14)
22 bits
TLM(8+14)
22 bits
TLM(8+14)
22 bits
TLM(8+14)
22 bits
Par
HOW(TOW+ID)
Par
6bits
19+3 bits
6bits
Par
HOW(TOW+ID)
Par
6bits
19+3 bits
6bits
Par
HOW(TOW+ID)
Par
6bits
19+3 bits
Par
HOW(TOW+ID)
6bits
19+3 bits
Par
HOW(TOW+ID)
6bits
19+3 bits
6bits
Par
6bits
Par
6bits
NAVI data
NAVI data
NAVI data
NAVI data
NAVI data
Par
6bits
Par
6bits
Par
6bits
Par
6bits
Par
6bits
NAVI data
NAVI data
NAVI data
NAVI data
NAVI data
Par
6bits
Par
6bits
Par
6bits
Par
6bits
Par
6bits
Figure
Figure 10.
10. GPS
GPS frame
frame structure.
structure.
The following steps are used to find out the position of the preamble from received data (see
The following steps are used to find out the position of the preamble from received data (see
also Figure 11).
also Figure 11).
(1) Store 20 frames (i.e., 20 × 30 s, or 100 sub-frames, i.e., 30,000 bits) of original demodulated data
(1) in
Store
20 frames
a vector
A. (i.e., 20 ˆ 30 s, or 100 sub-frames, i.e., 30,000 bits) of original demodulated data in
a
vector
A.
(2) Search for all the preamble-like sequences. Find all the likely preambles of vector A, and store
(2) these
Search
for all thevalues
preamble-like
Find
all the180°
likely
preambles
of vector
A, and
store
correlation
in vectorsequences.
B. Due to the
possible
phase
ambiguity
induced
by phase
˝ phase ambiguity induced by phase
these
correlation
values
in
vector
B.
Due
to
the
possible
180
tracking and the chance of cycle slips with weak signals, positive and negative correlations are
tracking and
searched
for. the chance of cycle slips with weak signals, positive and negative correlations are
searched
for.generated by reshaping the correlation vector B into sub-frame length rows. Each
(3) Matrix C is
(3) column
Matrix C
is generated
reshaping
the correlation
into sub-frame
length
rows.
Each
then
representsby
a possible
preamble
locationvector
in the B
sub-frame.
The size
of this
matrix
is
column
then
possible
preamble
location
in the sub-frame.
The
of thisto
matrix
300
× 100.
Therepresents
absolutes avalues
of matrix
C are
then accumulated
down
thesize
columns
form is
a
300
ˆ
100.
The
absolutes
values
of
matrix
C
are
then
accumulated
down
the
columns
to
form
a
vector D.
vector
D. largest correlations of vector D are recorded. The largest value should be the correct
(4) The
three
position of the preamble, however, with weak signals other possible locations may need to be
checked.
(5) The first position is assumed correct, the vector A reshaped into a matrix of sub-frame length
rows and the sub-frame number from each successive sub-frame is checked after column wise
Sensors 2016, 16, 347
12 of 21
The three largest correlations of vector D are recorded. The largest value should be the correct
position of the preamble, however, with weak signals other possible locations may need to
Sensors 2016, 16,, x
12 of 21
be checked.
(5)
(5) The
The first
first position
position is
is assumed
assumed correct,
correct, the
the vector
vector A
A reshaped
reshaped into
into aa matrix
matrix of
ofsub-frame
sub-framelength
length
rows
rows and
and the
the sub-frame
sub-frame number
number from
from each
each successive
successive sub-frame
sub-frame is
is checked
checked after
after column
columnwise
wise
accumulation.
If
the
sub-frame
number
is
incrementing
correctly,
this
position
is
declared
correct
accumulation. If the sub-frame number is incrementing correctly, this position is declared correct
and
used in
in subsequent
subsequentprocessing.
processing.Otherwise,
Otherwise,the
the
other
probable
positions
of the
preamble
and used
other
probable
positions
of the
preamble
are
are
checked.
checked.
(4)
A
True
preamble
locations
B
30000
Data bits
C
D
Figure 11. GPS preamble location.
Figure 11. GPS preamble location.
Assuming
the signal
signalis is
tracked
consistently
throughout,
after preamble
correlation
and
Assuming the
tracked
consistently
throughout,
after preamble
correlation
and column
column
wise accumulation,
the right
position of
preamble
andwill
thebe
sub-frame
will
wise accumulation,
the right position
of preamble
will
be foundwill
and be
the found
sub-frame
synchronized.
be synchronized.
Once the subframe is synchronised it is possible to reconstruct the desired data items from the
Once
the
is synchronised
it is possible
reconstruct
desired
items
stored
data
bysubframe
accumulation
down the column.
The to
parity
of each the
word
in thedata
matrix
canfrom
thenthe
be
stored
data
by
accumulation
down
the
column.
The
parity
of
each
word
in
the
matrix
can
then
be
checked individually. If the parity check is passed, the word is decoded and its position marked. The
checked
If the parity
check
is passed,
thesub-frames
word is decoded
and be
its repeated
position marked.
choice ofindividually.
20 entire navigation
frames
is made
so that
1 to 3 will
20 times
−6 atbe
The
choiceinofa20
entire navigation
frames
is accumulated
made so that data
sub-frames
1 to 310will
resulting
probability
of bit error
in the
of less than
15repeated
dB-Hz. It20
is times
likely
´
6
resulting
a probability
bit error in
thebeaccumulated
of less than
15 dB-Hz.
It is likely
that timein
and
ephemeris of
parameters
can
provided bydata
the platform
and10
onlyatframe
synchronisation
that
time andTherefore,
ephemeriswe
parameters
be provided
by of
thethe
platform
frame synchronisation
is required.
have onlycan
decoded
the time
week inand
ouronly
hardware
implementation
istorequired.
Therefore,
we have only decoded the time of the week in our hardware implementation to
demonstrate
the principle.
demonstrate
the principle.
The success
rate of the acquisition engine with signals of different carrier to noise density ratios
Theissuccess
of the12.
acquisition
engine
with
signals ofat
different
carrier
to noise
density
ratios
(C/No)
shown rate
in Figure
Here 25 trials
were
performed
each signal
level
and the
success
rate
(C/No)
is
shown
in
Figure
12.
Here
25
trials
were
performed
at
each
signal
level
and
the
success
rate
recorded for the acquisition, bit synchronization, and data decoding stages. The signals were
recorded
forwith
the acquisition,
synchronization,
and the
dataoutput
decoding
stages.
The signals
generated
generated
our Spirentbit
GSS800
simulator and
power
is displayed
inwere
Figure
12. The
decoding of the time of the week is used to determine if frame synchronisation was successful. Using
typical derivations from [23,31] the detection threshold is chosen such that the probability of
detection is theoretically 0.95 at 15 dB-Hz and probability of false alarm is 10−3.The acquisition results
of Figure 12 are slightly worse but within 1 dB of the expected values. Clearly, the receiver is limited
by its ability to synchronise and decode the navigation data before the acquisition limit is
Sensors 2016, 16, 347
13 of 21
with our Spirent GSS800 simulator and the output power is displayed in Figure 12. The decoding
of the time of the week is used to determine if frame synchronisation was successful. Using typical
derivations from [23,31] the detection threshold is chosen such that the probability of detection is
theoretically 0.95 at 15 dB-Hz and probability of false alarm is 10´3 .The acquisition results of Figure 12
are slightly worse but within 1 dB of the expected values. Clearly, the receiver is limited by its ability
Sensors 2016, 16,, x
13 of 21
to synchronise and decode the navigation data before the acquisition limit is encountered. Despite this,
at 15 dB-Hz the
receiver
is at
still
to acquire
and decode
the navigational
data
with the
a success
rate of
encountered.
Despite
this,
15able
dB-Hz
the receiver
is still able
to acquire and
decode
navigational
around
60%
for eachrate
attempt.
data
with
a success
of around 60% for each attempt.
Figure
Figure 12.
12. Sucess
Sucess rate
rate of
of acquisition
acquisition stages
stages with
with varying
varying signal
signal levels.
levels.
2.6.2. Weak Signal Tracking
2.6.2. Weak Signal Tracking
The WeakHEO receiver is assumed to be a stand-alone receiver with a low rate communication
The WeakHEO receiver is assumed to be a stand-alone receiver with a low rate communication
interface to the spacecraft platform. Therefore, knowledge of the full navigational data sequence is
interface to the spacecraft platform. Therefore, knowledge of the full navigational data sequence
not assumed and data wipe-off is not used. Data wipe-off allows the use of pure (non-squaring) PLL
is not assumed and data wipe-off is not used. Data wipe-off allows the use of pure (non-squaring)
discriminators to be used in tracking for lower jitter and a larger pull-in range compared to CostasPLL discriminators to be used in tracking for lower jitter and a larger pull-in range compared to
type discriminators.
Costas-type discriminators.
Typical expressions for the jitter of conventional GNSS tracking loop can be found in [23,32].
Typical expressions for the jitter of conventional GNSS tracking loop can be found in [23,32].
Figure 13a shows the expected PLL jitter and a conservative loss of lock threshold for a third order
Figure 13a shows the expected PLL jitter and a conservative loss of lock threshold for a third order
Costas PLL, assuming thermal and oscillator noise (based on the WeakHEO OCXO) are the only error
Costas PLL, assuming thermal and oscillator noise (based on the WeakHEO OCXO) are the only error
sources and an integration time of 20 ms. This indicates that in the presence of navigation data flips
sources and an integration time of 20 ms. This indicates that in the presence of navigation data flips we
we need to use bandwidth as low as 1 Hz to operate at 15 dB-Hz. The code tracking loop of the
need to use bandwidth as low as 1 Hz to operate at 15 dB-Hz. The code tracking loop of the receiver
receiver is a first order loop aided by the carrier loop and uses a bandwidth of 0.1 Hz. Figure 13b
is a first order loop aided by the carrier loop and uses a bandwidth of 0.1 Hz. Figure 13b shows
shows the DLL jitter for the dot-product power discriminator with a 0.1 Hz, a 20 ms integration time
the DLL jitter for the dot-product power discriminator with a 0.1 Hz, a 20 ms integration time and
and different early-to-late correlator spacing d. Correlator spacings of 0.25 chip or greater are required
different early-to-late correlator spacing d. Correlator spacings of 0.25 chip or greater are required to
to maintain code tracking at 15 dB-Hz. If an adaptive spacing is used, smaller correlator spacings can
maintain code tracking at 15 dB-Hz. If an adaptive spacing is used, smaller correlator spacings can be
be used at higher signal levels to reduce the pseudorange jitter. It should be noted that using such
used at higher signal levels to reduce the pseudorange jitter. It should be noted that using such low
low bandwidths to improve the performance in weak signal environments lengthens the time
bandwidths to improve the performance in weak signal environments lengthens the time between
between statistically independent measurements from the code and carrier loops [32]. This is not
statistically independent measurements from the code and carrier loops [32]. This is not critical for this
critical for this application. These low bandwidths are suitable for operation at altitudes significantly
application. These low bandwidths are suitable for operation at altitudes significantly above the GNSS
above the GNSS constellation; however, during the first part of the MTO the line-of-sight jerk can ´
be
constellation; however, during the first part of the MTO the line-of-sight jerk can be as high as 6 ms 3 .
as high as 6 ms−3. The received signal strength is far greater at this point but still requires a carrier
The received signal strength is far greater at this point but still requires a carrier loop PLL bandwidth
loop PLL bandwidth of around 5 Hz to tolerate this jerk [32]. Therefore, when conventional
approaches to GNSS tracking are used for this application the carrier loop bandwidth will need to be
adjusted during the MTO.
Sensors 2016, 16, 347
14 of 21
of around 5 Hz to tolerate this jerk [32]. Therefore, when conventional approaches to GNSS tracking
are used
Sensors
2016,for
16,,this
x application the carrier loop bandwidth will need to be adjusted during the MTO.
14 of 21
(a)
(b)
Figure
Figure 13.
13. (a)
(a) PLL
PLL jitter;
jitter; (b)
(b) DLL
DLL jitter
jitter versus
versus C/No.
C/No.
Conventional tracking models the incoming system as having deterministic dynamics by
Conventional tracking models the incoming system as having deterministic dynamics by typically
typically using fixed tracking loop bandwidths. An alternative method, which provides more
using fixed tracking loop bandwidths. An alternative method, which provides more flexibility is based
flexibility is based on Kalman filter theory. Rather than assuming deterministic dynamics, the
on Kalman filter theory. Rather than assuming deterministic dynamics, the Extended Kalman Filter
Extended Kalman Filter (EKF) assumes that the signal dynamics follow a linear stochastic model.
(EKF) assumes that the signal dynamics follow a linear stochastic model. This allows an adaptive
This allows an adaptive scheme where the response to dynamics is adjusted based on the signal
scheme where the response to dynamics is adjusted based on the signal conditions. Therefore, the
conditions. Therefore, the ranging processor is designed to adapt the tracking loop bandwidths as a
ranging processor is designed to adapt the tracking loop bandwidths as a function of the measured
function of the measured C/N0, to maintain the optimum trade-off between noise resistance and
C/N0 , to maintain the optimum trade-off between noise resistance and dynamics response. It should
dynamics response. It should be noted that this is not exclusively possible with the EKF based
be noted that this is not exclusively possible with the EKF based tracking and can be applied to
tracking and can be applied to conventional tracking. However, this is performed implicitly when
conventional tracking. However, this is performed implicitly when using the EKF approach as part of
using the EKF approach as part of its dynamic model.
its dynamic model.
A number of variations on EKF tracking have been developed for both code and carrier tracking
A number of variations on EKF tracking have been developed for both code and carrier
[29,33–35]. Comparing EKF tracking to conventional architectures is troublesome as the non-linear
tracking [29,33–35]. Comparing EKF tracking to conventional architectures is troublesome as the
models used in the EKF implementation are effectively constantly adapting its tracking bandwidth.
non-linear models used in the EKF implementation are effectively constantly adapting its tracking
Generally, jitter comparisons are made with conventional architecture under different dynamic
bandwidth. Generally, jitter comparisons are made with conventional architecture under different
conditions. However, this does provide to opportunity to choose scenarios and tracking loop settings
dynamic conditions. However, this does provide to opportunity to choose scenarios and tracking
to exaggerate the benefits of one technique over another. An attempt to compare the techniques by
loop settings to exaggerate the benefits of one technique over another. An attempt to compare the
experimentally determining the steady-state bandwidth of the EKF and finding the equivalent
techniques by experimentally determining the steady-state bandwidth of the EKF and finding the
performing PLL is found in [36]. Here, the EKF is demonstrated to be able to track the carrier phase
equivalent performing PLL is found in [36]. Here, the EKF is demonstrated to be able to track the
down to 10 dB-Hz, around a 7 dB improvement under equivalent conditions. Tests with software
carrier phase down to 10 dB-Hz, around a 7 dB improvement under equivalent conditions. Tests with
receiver implementations of conventional and EKF tracking in [37] show around a 4 dB to 7 dB
software receiver implementations of conventional and EKF tracking in [37] show around a 4 dB to
improvement in sensitivity for the EKF approach.
7 dB improvement in sensitivity for the EKF approach.
The EKF is well suited to applications such as the one considered here where the platform has
The EKF is well suited to applications such as the one considered here where the platform has
predictable dynamics and the receiver’s oscillator can be measured and modelled. For the WeakHEO
predictable dynamics and the receiver’s oscillator can be measured and modelled. For the WeakHEO
receiver we have implemented a first order EKF for carrier phase tracking as detailed in [29]. The
receiver we have implemented a first order EKF for carrier phase tracking as detailed in [29]. The EKF
EKF is only used for the carrier tracking and conventional tracking is used for the code loop to
is only used for the carrier tracking and conventional tracking is used for the code loop to minimise
minimise the computational load.
the computational load.
In [26] we show how Doppler and Doppler rate aiding from an integrated orbital filter can be
In [26] we show how Doppler and Doppler rate aiding from an integrated orbital filter can be used
used to improve sensitivity of conventional FLL tracking to around 11 dB-Hz. This is considered
to improve sensitivity of conventional FLL tracking to around 11 dB-Hz. This is considered suitable
suitable for a stand-alone receiver as the orbital filter can be integrated into the receiver’s navigation
for a stand-alone receiver as the orbital filter can be integrated into the receiver’s navigation software.
software.
Figure 14 shows double difference measurements of the WeakHEO DLL jitter taking with our
Figure 14 shows double difference measurements of the WeakHEO DLL jitter taking with our
GNSS simulator with varying carrier to noise density ratios. Reasonable agreement with the theoretical
GNSS simulator with varying carrier to noise density ratios. Reasonable agreement with the
values can be found.
theoretical values can be found.
Sensors 2016, 16, 347
Sensors 2016, 16,, x
15 of 21
15 of 21
Figure
Figure14.
14.WeakHEO
WeakHEODLL
DLLjitter
jitterversus
versusC/No.
C/No.
2.7. GPS Navigation
2.7.
An orbital
orbital filter
filter has
has been
been implemented
implemented that
that integrates
integrates the
the GPS
GPS observations
observations with
with an
an orbital
orbital
An
forces model,
model, by
by means
means of
of an
an adaptive
adaptive Extended
Extended Kalman
Kalman filter
filter (EKF).
(EKF). The
The EKF
EKF integrates
integrates the
the least
least
forces
square single-epoch
single-epoch position
position and
and velocity
velocity solutions
solutions that
that are
are computed
computed using
using the
the pseudoranges
pseudoranges and
and
square
the pseudorange
pseudorange rates output by the WeakHEO GPS receiver,
receiver, together
together with
with the
the position
position and
and velocity
the
predictedby
by an
an orbital
orbital forces
forces model.
model. The resultant filtered navigation
navigation solution
solution can efficiently
efficiently mitigate
mitigate
predicted
the
effect
of
the
very
high
GDOP
and
large
ranging
errors;
indeed,
it
is
significantly
more
accurate
the effect of the very high GDOP and large ranging errors; indeed, it is significantly more accurate
than the
the unfiltered
unfiltered least
least square
square single-epoch
single-epoch solution,
solution, as
as shown
shown in
in Section
Section 3.
3. Thus, it can
can be
be used
used to
to
than
aid the
the GPS
GPS receiver
receiver to
to acquire
acquire and
and track
track weak
weak GPS
GPS signals
signals while
while experiencing
experiencing high
high dynamics.
dynamics. A
aid
detailed description of
and
tracking
modules
cancan
be
detailed
of the
the orbital
orbitalfilter
filterand
andits
itsaiding
aidingtotothe
theacquisition
acquisition
and
tracking
modules
found
in in
[26].
InIn
a adifferent
can
be
found
[26].
differentconfiguration,
configuration,less
lesssimple
simplebut
butpotentially
potentiallymore
more efficient,
efficient, the EKF can
integrate
directly
pseudoranges
and
pseudorange
rates
provided
by
the
tracking
loops
together
with
integrate directly pseudoranges and pseudorange rates provided by the tracking loops together with
their prediction
prediction provided
provided by
by the
the orbital
orbital forces
forces model.
model. This has been
been investigated
investigated in our
our previous
previous
their
study [25],
[25], which
which also
also describes
describes the
the performance
performance of
of our
our orbital
orbital filter
filter when
when it
it uses
uses signals
signals transmitted
transmitted
study
by the GPS-Galileo combined
configurations
is is
described
in
by
combined constellation.
constellation.AAcomparison
comparisonofofthe
thetwo
two
configurations
described
[38].
in
[38].
As described
described in [24],
[24], during
during aa MTO,
MTO, once
once the
the receiver
receiver is
is above
above the
the GPS
GPS constellation,
constellation, the
the GPS
GPS
As
accuracy
strongly
decreases
with
the
altitude.
Both
pseudorange
error
and
GDOP
worsen
as
the
accuracy strongly decreases with the altitude.
the
receiver goes
goes further
further from
from the
the GPS
GPS constellation.
constellation. For this reason, if the covariance matrix of the
the
receiver
measurements
R
is
composed
of
constant
variance
values
over
time,
the
filter
cannot
be
tuned
measurements R is composed of constant variance values over time, the filter cannot be tuned properly
properly
the (Figures
full MTO6 and
(Figures
6 and
7 of the
[38]effect
shows
effect ofR modelling
as constant
during
theduring
full MTO
7 of [38]
shows
of the
modelling
as constantRmatrix).
matrix).
As described in [38], the covariance matrix R of the filter has to be adapted to the GPS
As described
in [38],
the covariance
R of as
thefunction
filter has
to GDOP
be adapted
to thebyGPS
measurements
accuracy.
Indeed,
the R matrixmatrix
is modelled
of the
multiplied
the
measurements
accuracy.
Indeed,
R matrix
is modelled
as function
of the
multiplied
the
estimated
pseudorange
error.
The the
adaptive
strategy
is illustrated
in Figure
15. GDOP
From the
estimatedbystate
estimated at
pseudorange
The adaptive
illustrated
in Figure
15.onFrom
estimated
computed
the previouserror.
time-step,
the filter strategy
estimatesisthe
GDOP and
the noise
boththe
pseudorange
statepseudorange
computed atrate
themeasures
previoustotime-step,
filter estimates
the GDOP and the noise on both
and
update thethe
covariance
matrix R.
pseudorange and pseudorange rate measures to update the covariance matrix R.
Sensors 2016, 16, 347
16 of 21
Sensors 2016, 16, 347
16 of 21
Estimated
state
tk-1
GDOP
Rk
EKF
Pseudorange and
pseudorange rate
error
GPS
measures
tk
Figure 15. Dynamic tuning of the covariance matrix of the measurements.
Figure 15. Dynamic tuning of the covariance matrix of the measurements.
3. WeakHEO Navigation Performance
3. WeakHEO Navigation Performance
In order to test the achievable performance in terms of position and velocity determination we
have
selected
twothe
representative
of the MTO,
eachofofposition
one-hourand
duration.
In
order
to test
achievable portions
performance
in terms
velocity determination we
The
first
portion
starts
approximately
at
36,000
km
of
altitude
(altitude
of the Geostationary
have selected two representative portions of the MTO, each of one-hour duration.
Earth
Orbit)
and
a
second
portion
starts
approximately
at
the
average
distance
of
theGeostationary
Moon from theEarth
The first portion starts approximately at 36,000 km of altitude (altitude of the
centre
of
the
Earth
of
384,400
km,
very
close
to
the
apogee
of
the
MTO.
Figures
16
and
illustrate
Orbit) and a second portion starts approximately at the average distance of the Moon17
from
the centre
the ECI 3D position and velocity accuracy, respectively, of a least square (LS) single-epoch solution,
of the Earth of 384,400 km, very close to the apogee of the MTO. Figures 16 and 17 illustrate the ECI
a pure propagated (Pp) solution (obtained only propagating the initial condition through the orbital
3D position and velocity accuracy, respectively, of a least square (LS) single-epoch solution, a pure
forces model), and the orbital filtered (OF) solution, which integrates by means of the developed
propagated
(obtained
propagating
condition
through
orbital
adaptive(Pp)
EKFsolution
the LS together
withonly
the Pp
solution. Thethe
LSinitial
solution
is as expected
verythe
noisy
due toforces
model),
and the
orbital
filtered
(OF) solution,
which and
integrates
by means
the developed
the noise,
which
affects
pseudorange
measurements
it increases
with theofaltitude
because ofadaptive
the
EKF the
LS together
the Pp18).
solution.
LSside,
solution
as expected
very
due to the
increasing
GDOPwith
(see Figure
On theThe
other
the Ppisposition
solution
hasnoisy
a significant
driftnoise,
to thepseudorange
error in the initial
condition; in
fact,
aboutwith
250 sthe
thealtitude
position because
error reaches
50increasing
m as
whichdue
affects
measurements
and
it after
increases
of the
expected
because
of On
the initial
0.2 m/s
error
the
initial velocity.
(0.2
m/s
× 250 s = 50 drift
m). The
OFto the
GDOP
(see Figure
18).
the other
side,
theinPp
position
solution
has
a significant
due
is several
times more
accurate;
GPS250
measurements
prevent
orbital50propagation
errorsolution
in the initial
condition;
in fact,
after the
about
s the position
errorthe
reaches
m as expected
solution
drifting,
the error
orbitalin
propagation
GPS
solution.
19–21
illustrate
the
because
of the
initial while
0.2 m/s
the initial smooths
velocity.the
(0.2
m/s
ˆ 250 Figures
s = 50 m).
The
OF solution
is
same quantities but for the MTO portion at Moon altitude. In this case as well, the benefit of the
several times more accurate; the GPS measurements prevent the orbital propagation solution drifting,
orbital filter is even more significant since the OF solution is more than one order of magnitude more
while the orbital propagation smooths the GPS solution. Figures 19–21 illustrate the same quantities
accurate than the LS solution.
but for the
MTO
at Moon
thistests
casehave
as well,
the benefit
orbital
filter
is even
Note
thatportion
the Hardware
in altitude.
the Loop In
(HIL)
not been
carried of
outthe
over
the full
MTO
moreduration
significant
since
the
OF
solution
is
more
than
one
order
of
magnitude
more
accurate
than
as it lasts almost 5 days and we currently do not have that simulation capability. Instead, the
LS solution.
the full MTO test has been performed in post processing by simulating pseudorange and
pseudorange
measurements
Figures
10 and
in [26])
assesscarried
the OF out
performance.
Note
that therate
Hardware
in the(see
Loop
(HIL)
tests11have
nottobeen
over the Then,
full MTO
several
tests
we performed
for the
portion
different
of thecapability.
full MTO allowed
duration
as HIL
it lasts
almost
5 days and
wesame
currently
doand
notforhave
that potions
simulation
Instead, the
us to test
determine
thatperformed
a 1 h test duration
is well enough
to let the OFpseudorange
converge. Afterwards,
we have rate
full MTO
has been
in post processing
by simulating
and pseudorange
performed
HIL
tests
for
several
representative
portions
of
1
h
durations
to
assess
the
acquisition,
measurements (see Figures 10 and 11 in [26]) to assess the OF performance. Then, several HIL tests we
tracking, data decoding, and finally navigation performance (as reported in this section) of the
performed for the same portion and for different potions of the full MTO allowed us to determine that
WeakHEO receiver for the signals encountered in a lunar mission. It is also important also to keep in
a 1 h mind
test duration
is well enough to let the OF converge. Afterwards, we have performed HIL tests for
that the current WeakHEO receiver is only a proof of concept and thus not the final device ready
several
representative
portions
h durations
assess
acquisition,
tracking,
data decoding, and
to operate in a lunar
mission,of
for1 which
clearly to
more
and the
longer
tests will be
required.
finally navigation performance (as reported in this section) of the WeakHEO receiver for the signals
encountered in a lunar mission. It is also important also to keep in mind that the current WeakHEO
receiver is only a proof of concept and thus not the final device ready to operate in a lunar mission, for
which clearly more and longer tests will be required.
Sensors 2016, 16, 347
17 of 21
Sensors 2016, 16,, x
Sensors 2016, 16,, x
Sensors 2016, 16,, x
17 of 21
17 of 21
17 of 21
Figure
position error
error for
portion
whichwhich
starts at
GEO at
altitude
the singleFigure
16. 16.
3D3Dposition
forthe
theconsidered
considered
portion
starts
GEOfor:
altitude
for: the
Figure least
16. 3Dsquare
position
error
for the(in
considered
portion
which
starts
at GEO
altitude
for:
theand
singleepoch
(LS)
solution
blue);
the
orbital
filtered
(OF)
solution
(in
red);
the the
single-epoch
square error
(LS) for
solution
(in blue);
the orbital
solutionfor:
(inthe
red);
and
Figure 16.least
3D position
the considered
portion
which filtered
starts at (OF)
GEO altitude
singleepoch least (Pp)
square
(LS) (in
solution
(in blue); the orbital filtered (OF) solution (in red); and the
propagated
solution
green).
propagated
(Pp) square
solution(LS)
(in solution
green). (in blue); the orbital filtered (OF) solution (in red); and the
epoch least
propagated (Pp) solution (in green).
propagated (Pp) solution (in green).
Figure 17. 3D velocity error for the considered portion which starts at GEO altitude for: the singleFigure least
17. 3Dsquare
velocity
error
for the(in
considered
portion
which
starts
at GEO
altitude
for:
theand
singleepoch
(LS)
solution
blue);portion
the
orbital
filtered
(OF)
solution
(in
red);
the
Figure
17. 3D
error
for
the
which
starts
at
GEO
altitude
for:
the
Figure
17.velocity
3D velocity
error
for considered
the considered
portion
which
starts
at
GEO
altitude
for:
thesingle-epoch
singleepoch
least
square
(LS)
solution
(in
blue);
the
orbital
filtered
(OF)
solution
(in
red);
and
the
propagated
(Pp)
solution
(in
green).
least epoch
squareleast
(LS) square
solution
(in solution
blue); the
(OF)filtered
solution
(in solution
red); and(inthered);
propagated
(LS)
(inorbital
blue); filtered
the orbital
(OF)
and the (Pp)
propagated (Pp) solution (in green).
propagated
(Pp) solution (in green).
solution
(in green).
Figure 18. GDOP during the MTO portion that starts at 36,000 km altitude.
Figure 18. GDOP during the MTO portion that starts at 36,000 km altitude.
Figure
GDOP
duringthe
theMTO
MTO portion
portion that
36,000
kmkm
altitude.
Figure
18. 18.
GDOP
during
thatstarts
startsatat
36,000
altitude.
Sensors 2016, 16, 347
18 of 21
Sensors 2016, 16,, x
18 of 21
Sensors 2016, 16,, x
18 of 21
Sensors 2016, 16,, x
18 of 21
Figure 19. 3D position error for the considered portion at Moon altitude for: the single-epoch least
Figure 19. 3D position error for the considered portion at Moon altitude for: the single-epoch least
square
solution
(inerror
blue);
filtered
(OF) at
solution
red); for:
andthe
thesingle-epoch
propagated least
(Pp)
Figure (LS)
19. 3D
position
forthe
theorbital
considered
portion
Moon (in
altitude
square (LS) solution (in blue); the orbital filtered (OF) solution (in red); and the propagated (Pp)
solution
(in 3D
green).
square
solution
(inerror
blue);
filtered
(OF) solution
red); for:
and the
thesingle-epoch
propagated (Pp)
Figure (LS)
19.
position
forthe
theorbital
considered
portion
at Moon (in
altitude
least
solution (in green).
solution
(in green).
square (LS)
solution (in blue); the orbital filtered (OF) solution (in red); and the propagated (Pp)
solution (in green).
Figure 20. 3D velocity error for the considered portion at Moon altitude for: the single-epoch least
square
(LS)
solution
(inerror
blue);
the
orbital
filtered
(OF) at
solution
(in red); for:
andthe
thesingle-epoch
propagated least
(Pp)
Figure
20. velocity
3D
velocity
theconsidered
considered
portion
Figure
20. 3D
error
forfor
the
portion
at Moon
Moonaltitude
altitude for:
the single-epoch
least
solution
(in
green).
square
(LS)
solution
(in
blue);
the
orbital
filtered
(OF)
solution
(in
red);
and
the
propagated
(Pp)
Figure
3D velocity
error for
considered
portion
Moon altitude
for:and
the single-epoch
least (Pp)
square
(LS) 20.
solution
(in blue);
thethe
orbital
filtered
(OF) atsolution
(in red);
the propagated
solution
(in green).
square (LS)
solution (in blue); the orbital filtered (OF) solution (in red); and the propagated (Pp)
solution (in green).
solution (in green).
Figure 21. GDOP during the MTO portion at Moon altitude.
Figure 21. GDOP during the MTO portion at Moon altitude.
Figure 21. GDOP during the MTO portion at Moon altitude.
Figure 21. GDOP during the MTO portion at Moon altitude.
Sensors 2016, 16, 347
19 of 21
4. Conclusions
Following our previous feasibility studies of GNSS as navigation system to reach the Moon,
this research paper describes the proof of concept of the GPS L1 C/A “WeakHEO” receiver for lunar
mission, wholly developed in our laboratory in the last two years. After highlighting the characteristics
of the GPS L1 C/A signals for the considered MTO, which have been identified in our previous
research work, the requirements and constraints in the receiver design are defined. Afterwards, the
general receiver architecture is described, providing a more detailed description of the acquisition,
tracking and navigation modules. These modules are specifically designed for use with the dynamic
environment and signal conditions seen in high altitude space applications, and the architecture
presented is capable of performing acquisition, tracking, data synchronization and demodulation
down to a level of 15 dB-Hz. This is verified on the hardware with tests using representative RF signals
produced by a GNSS simulator. The navigation module makes use of an adaptive orbital filter, which
exploits an orbital forces model to filter the noisy GPS least square single-epoch solutions and is able to
significantly increase the navigation accuracy to a few hundred meters at Moon altitude. The filtered
navigation solution can then be used to aid the acquisition and tracking modules allowing higher
sensitivities also in high dynamics.
5. Future Work
The performance will be further improved in the new “WeakHEO 2” version of our receiver, where
the available hardware resources will be increased, allowing the integration of the navigation module
into the processor within the FPGA. This will allow the orbital filter to provide aiding to the acquisition
and tracking modules at a high rate to improve performance as shown in [26]. The orbital filter of
the “WeakHEO 2” receiver will directly filter the raw pseudorange and pseudorange rate observations
instead of the single-epoch least square solution, with an expected higher navigation accuracy also
in case of less than four GPS observations available. In addition, the iteration rate of the navigation
output will be increased from 0.1 Hz to 1 Hz and the number of tracking channel increased from 6 to
at least 12 channels. Furthermore, in the future we will also consider processing other frequencies and
signals of other GNSS constellations to further improve the overall performance.
Author Contributions: The work presented in this paper was carried out in collaboration between all authors.
Cyril Botteron was leading the project and contributed together with Pierre-André Farine to the system
requirement and implementation definitions as well as to the overall design discussions. Vincenzo Capuano was
concerned with the definition the MTO scenario and system requirements, as well as with the design and the
implementation of the navigation module (adaptive orbital filter). He also contributed to carry out the simulation
tests and hardware-in-the-loop tests of the navigation performance. Paul Blunt contributed to the testing and
design verification detailed in this paper and is now responsible for the maintenance and development of the
WeakHEO and WeakHEO 2 receivers. Jia Tian and Yanguang Wang contributed respectively to the design and
the hardware implementation of the acquisition and of the tracking modules. Jérôme Leclère contributed to the
supervision of the overall FPGA design and implementation of the signal processing engine. Francesco Basile
contributed to the implementation of the orbital filter. All authors contributed to revisions of the manuscript.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
2.
3.
Miller, J. Enabling a fully interoperable GNSS space service volume. In Proceedings of the 6th International
Committee on GNSS (ICG), Tokyo, Japan, 5–9 September 2011.
Marmet, F.; Bondu, E.; Calaprice, M.; Maureau, J.; Laurichesse, D.; Grelier, T.; Ries, L. GPS/Galileo navigation
beyond low earth orbit. In Proceedings of the 6th European Workshop on GNSS Signals and Signal
Processing, Neubiberg, Germany, 5–6 December 2013.
Capuano, V.; Botteron, C.; Wang, Y.; Tian, J.; Leclère, J.; Farine, P.A. GNSS to Reach the Moon. In Proceedings
of the 65th International Astronautical Congress, Toronto, ON, Canada, 29 September–3 October 2014.
Sensors 2016, 16, 347
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
20 of 21
Braasch, M.S.; de Haag, M.U. GNSS for LEO, GEO, HEO and beyond. In Proceedings of the Advances in
the Astronautical Sciences, Rocky Mountain Guidance and Control Conference, Breckenridge, CO, USA,
31 January–4 February 2009.
Silva, P.F.; Lopes, H.D.; Peres, T.R.; Silva, J.S.; Ospina, J.; Cichocki, F.; Dovis, F.; Musumeci, L.; Serant, D.;
Calmettes, T.; et al. Weak GNSS signal navigation to the moon. In Proceedings of the ION GNSS+, Nashville,
TN, USA, 16–20 September 2013.
Palmerini, G.B.; Sabatini, M.; Perrotta, G. En route to the moon using GNSS signals. Acta Astronaut. 2009, 64,
467–483. [CrossRef]
Palmerini, G. GNSS software receiver as a navigation sensor in very high orbits. In Proceedings of the IEEE
International Workshop on Metrology for Aerospace, Benevento, Italy, 29–30 May 2014.
Manzano-Jurado, M.; Alegre-Rubio, J.; Pellacani, A.; Seco-Granados, G.; Lopez-Salcedo, J.; Guerrero, E.;
Garcia-Rodriguez, A. Use of weak GNSS signals in a mission to the moon. In Proceedings of the 7th ESA
Workshop on Satellite Navigation Technologies and European Workshop on GNSS Signals and Signal
Processing (NAVITEC), Noordwijk, The Netherlands, 3–5 December 2014.
Bamford, W.A.; Heckel, G.W.; Holt, G.N.; Moreau, M. A GPS receiver fot lunar missions. In Proceedings of
the ION NTM 2008, San Diego, CA, USA, 28–30 January 2008.
Bamford, W.; Naasz, B.; Moreaus, M. Navigation performance in high earth orbits using navigator
GPS receiver. In Proceedings of the American Astronautical Society Guidance and Control Conference,
Breckenridge, CO, USA, 4–8 February 2006.
Winternitz, L.; Moreau, M.; Boegner, G.; Sirotzky, S. Navigator GPS receiver for fast acquisition and weak
signal space applications. In Proceedings of the ION GNSS Conference, Long Beach, CA, USA, 21–24
September 2004.
Moreau, M.C.; Axelrad, P.; Garrison, J.L.; Wennersten, M.; Long, A. Test results of the PiVot receiver in
high earth orbits using a GSS GPS simulator. In Proceedings of the ION, Salt Lake City, UT, USA, 11–14
September 2001.
Capuano, V.; Botteron, C.; Farine, P.-A. GNSS performances for MEO, GEO and HEO. In Proceedings of the
64th International Astronautical Congress, Beijing, China, 23–27 September 2013.
Unwin, M.; van Steenwijk, R.D.V.; Blunt, P.; Hashida, Y.; Kowaltschek, S.; Nowak, L. Navigating above
the GPS constellation—Preliminary results from the SGR-GEO on GIOVE-A. In Proceedings of the 26th
International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2013),
Nashville, TN, USA, 16–20 September 2013.
Balbach, O.; Eissfeller, B.; Hein, G.; Enderle, W.; Schmidhuber, M.; Lemke, N. Tracking GPS above GPS
satellite altitude: First results of the GPS experiment on the HEO mission Equator-S. In Proceedings of the
IEEE Position Location and Navigation Symposium, Palm Springs, CA, USA, 20–23 April 1998.
Moreau, M.; Davis, E.P.; Carpenter, J.R.; Kelbel, G.D.P.A.D. Results from the GPS flight experiment on the
high earth orbit AMSAT OSCAR-40 spacecraft. In Proceedings of the ION GPS Conference, Tampa, FL, USA,
24–27 September 2002.
Davis, G.; Moreau, M.; Carpenter, R.; Bauer, F. GPS-based navigation and orbit determination for the AMSAT
AO-40 satellite. In Proceedings of the AIAA, Monterey, CA, USA, 5–8 August 2003.
Ruegamer, A.; Foerster, F.; Stahl, M.; Rohmer, G. A flexible and portable multiband GNSS front-end system.
In Proceedings of the ION ITM, Nashville, TN, USA, 17–21 September 2012.
Sheridan, K.; Wells, D.; Botteron, C.; Leclère, J.; Dominici, F.; Defina, A. An assisted-GNSS solution for
demanding road applications using the EGNOS Data Access System (EDAS). In Proceeedings of the Toulouse
Space Show, Toulouse, Franch, 8–11 June 2010.
AGI. Available online: http://www.agi.com/products/stk/ (accessed on 10 November 2015).
ICD-GPS-200F Navstar GPS Space Segment/User Segment Interfaces. 21 September 2011.
Spirent. SimGen Software User Manual. July 21 2015.
Kaplan, E.D.; Hegarty, C.J. Understanding GPS: Principles and Applications; Artech House: Norwood, MA,
USA, 2006.
Capuano, V.; Botteron, C.; Leclere, J.; Tian, J.; Yanguang, W.; Farine, P.A. Feasibility study of GNSS as
navigation system to reach the Moon. Acta Astronaut. 2015, 116, 186–201. [CrossRef]
Capuano, V.; Basile, F.; Botteron, C.; Farine, P.-A. Gnss Based Orbital Filter for Earth Moon Transfer Orbits.
J. Navig. 2015. [CrossRef]
Sensors 2016, 16, 347
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
21 of 21
Capuano, V.; Blunt, P.; Botteron, C.; Farine, P.-A. Orbital filter aiding of a high sensitivity GPS receiver
for lunar missions. In Proceedings of the International Technical Meeting of the Institute of Navigation,
Monterey, CA, USA, 25–28 January 2016.
Van Diggelen, F. A-GPS: Assisted GPS, GNSS and SBAS; Artech House: Norwood, MA, USA, 2009.
Leclère, J.; Botteron, C.; Farine, P.-A. Comparison framework of FPGA-based GNSS signals acquisition
architectures. IEEE Trans. Aerosp. Electron. Syst. 2013, 49, 1497–1518. [CrossRef]
Ziedan, N.I. GNSS Receivers for Weak Signals; Artech House: Norwood, MA, USA, 2006.
Duffett-Smith, P.J.A.R.P. Reconstruction of the satellite ephemeris from time-spaced snippets. In Proceedings
of the ION GNSS 2007, Fort Worth, TX, USA, 25–28 September 2007.
Musumeci, L.; Dovis, F.; Silva, P.F.; Lopes, H.D.; Silva, J. Design of a very high sensitivity acquisition. In
Proceedings of the Position, Location and Navigation Symposium—PLANS 2014, Monterey, CA, USA,
5–8 May 2014.
Groves, P.D. Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems; Artech House:
Norwood, MA, USA, 2013.
Ziedan, N.I.; Garrison, J. Extended Kalman filter-based tracking of weak GPS signals under high dynamic
conditions. In Proceedings of the ION GNSS 17th International Technical Meeting of the Satellite Division,
Long Beach, CA, USA, 21–24 September 2004.
Psiaki, M.L.; Jung, H. Extended Kalman filter methods for tracking weak gps signals. In Proceedings of the
ION GNSS, Albuquerque, NM, USA, 24–26 June 2002.
Jee, G.; Kim, H.; Lee, Y.; Park, C. A GPS C/A code tracking loop based on extended Kalman filter with
multipath mitigation. In Proceedings of the ION GPS 2002, Portland, OR, USA, 24–27 September 2002.
Salem, D.; O’Driscoll, C.; Lachapelle, G. Methodology for comparing two carrier phase tracking techniques.
In GPS Solutions; Springer: Berlin, Germany, 2012; Volume 16, pp. 197–207.
Petovello, M.; O’Driscoll, C.; Lachapelle, G. Carrier phase tracking of weak signals using different receiver
architectures. In Proceedings of the ION NTM 2008, San Diego, CA, USA, 28–30 January 2008.
Basile, F.; Capuano, V.; Botteron, C.; Farine, P.-A. GPS based orbital filter to reach the moon. Int. J. Space Sci.
Eng. 2015, 3, 199–218. [CrossRef]
© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons by Attribution
(CC-BY) license (http://creativecommons.org/licenses/by/4.0/).