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Exploring the Architecture Trade Space of NextGen Global Navigation Satellite Systems

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This paper studies the trade-offs between two metrics that play a key role in the design of Global Navigation Satellite System (GNSS) architectures: Dilution Of Precision (DOP) and cost. DOP is a multiplicative factor that quantifies the satellite-user geometric diversity and sets the limit on the achievable User Navigation Error (UNE). We focus on trade-offs between DOP and cost driven by satellite constellation architecture decisions-e.g., orbit altitude, number of satellites. For simplicity, we restrict the analysis to global constellations resulting in a worst-site Geometric DOP (GDOP) value less than 6. This GDOP value is considered a threshold above which the resulting system would add little value for most GNSS users. The cost metric is subdivided in flight unit production costs based on the satellite dry mass and the learning factor experienced when producing N identical flight units, as well as the launch costs. Satellite dry mass is derived from the estimated payload power required to close the navigation signal link budget at the target received signal power of-155dBW. User navigation error is inferred with the computed GDOP values and a typical GPS pseudorange measurement error budget for dual frequency signal processing. We identified orbit altitude regions of interest that can be used in the design of future GNSS and potentially outperform the current global constellation architectures. In particular, results show that several constellations in "low" Medium Earth Orbits (MEO),-approximately half the orbit altitude of current GNSS constellations-are on the UNE-Cost Pareto front. When compared with the current GPS and GALILEO architectures, these alternatives consist of larger constellations of smaller satellites and have the potential to achieve both better performance and lower costs. Our analysis indicates that Low Earth Orbit (LEO) constellations are significantly more expensive to deploy due to the larger number of satellites required. Finally, we assess the impact of operational costs, launch cost reduction, different end-of-life disposal strategies and transmit power on the overall results.
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1
Exploring the Architecture Trade Space of NextGen Global
Navigation Satellite Systems
Filipe Pereira
Cornell University
418 Upson Hall
Ithaca, NY 14850
607-261-0547
fmd43@cornell.edu
Daniel Selva
Texas A&M University
620C H.R. Bright Building
College Station, TX, 77843
979-458-0419
dselva@tamu.edu
Abstract This paper studies the trade-offs between two
metrics that play a key role in the design of Global Navigation
Satellite System (GNSS) architectures: Dilution Of Precision
(DOP) and cost. DOP is a multiplicative factor that quantifies
the satellite-user geometric diversity and sets the limit on the
achievable User Navigation Error (UNE). We focus on trade-
offs between DOP and cost driven by satellite constellation
architecture decisions - e.g., orbit altitude, number of satellites.
For simplicity, we restrict the analysis to global constellations
resulting in a worst-site Geometric DOP (GDOP) value less than
6. This GDOP value is considered a threshold above which the
resulting system would add little value for most GNSS users.
The cost metric is subdivided in flight unit production costs
based on the satellite dry mass and the learning factor
experienced when producing N identical flight units, as well as
the launch costs. Satellite dry mass is derived from the estimated
payload power required to close the navigation signal link
budget at the target received signal power of -155dBW. User
navigation error is inferred with the computed GDOP values
and a typical GPS pseudorange measurement error budget for
dual frequency signal processing. We identified orbit altitude
regions of interest that can be used in the design of future GNSS
and potentially outperform the current global constellation
architectures. In particular, results show that several
constellations in “low” Medium Earth Orbits (MEO), -
approximately half the orbit altitude of current GNSS
constellations- are on the UNE-Cost Pareto front. When
compared with the current GPS and GALILEO architectures,
these alternatives consist of larger constellations of smaller
satellites and have the potential to achieve both better
performance and lower costs. Our analysis indicates that Low
Earth Orbit (LEO) constellations are significantly more
expensive to deploy due to the larger number of satellites
required. Finally, we assess the impact of operational costs,
launch cost reduction, different end-of-life disposal strategies
and transmit power on the overall results.
TABLE OF CONTENTS
1. INTRODUCTION ....................................................... 1
2. METHODS ................................................................ 3
Decisions .......................................................... 3
Metrics .............................................................. 3
User Navigation Error .................................. 3
Total Space Segment Costs ........................... 4
3. RESULTS .................................................................. 8
Sensitivity analysis ........................................ 9
4. CONCLUSIONS ....................................................... 10
Limitations ................................................... 11
Future Work ................................................ 11
REFERENCES ............................................................. 11
BIOGRAPHY ............................................................... 13
1. INTRODUCTION
The art of navigation has been an essential skill throughout
human exploration. Important progress in celestial navigation
tools enabled the Age of Discovery and the beginning of
globalization. Another breakthrough, the advent of
chronometers in the 18th century, enabled the determination
of longitude and since then navigation and timing
information have remained closely linked. In the late 20th
century however, satellite navigation and the Global
Positioning System (GPS), in particular, revolutionized the
way we obtain positioning and timing information reliably
and anywhere on the globe with unprecedented levels of
accuracy and reliability. What started as a military system
designed to address US Air Force and Navy needs, evolved
later to accommodate civilian needs and prevent accidents
due to human navigation error. One notable incident in 1983,
involving an airliner that was shot down after inadvertently
entered the Soviet Union’s air space [1], prompted President
Reagan to accelerate the timeline for the civilian use of GPS.
With the abolishment of Selective Availability (SA) in the
civil signal, performance improved and new services became
possible. According to the 2017 GNSS market report
produced by the European GNSS Agency (GSA) [2], in 2015
the GNSS market generated over 100 $B in revenue
worldwide (25.6% of those revenues in the US alone), and
added-value services leveraging on GNSS technology are
expected to grow at 20% annually until 2020. The economic
impact and the importance of GNSS technology for the
operation of critical infrastructure have justified the
development of new global and regional navigation systems.
The current GNSS space infrastructure, of nearly 100
satellites, integrates a multitude of global constellations and
augmentation systems that can be seen as a collaborative
system-of-systems. This will pose new opportunities and new
challenges for the next decades.
2
The GPS architecture has been used as a case study in the
systems architecting literature [3] as an example of reliability
and adaptability in space systems design. GPS’s success is in
part attributed to the significant spin-off value generated
(e.g., civil aviation) that was far beyond the original plans.
GNSS global constellations architected decades later (e.g.,
GALILEO and BEIDOU) largely adopted the same
measurement techniques, orbit design, and technology such
as atomic clocks and Code Division Multiple Access
(CDMA). Nevertheless, it makes sense to analyze the
rationale behind the original architecture decisions and
question whether or not there are reasons to revisit them, after
decades of operations. Specifically, we identify five factors
motivating a new architecture study on GNSS.
First, the initial GPS design in the 70s excluded LEO due to
the fact that satellites, at that time, had an expected lifetime
of only 3-5 years, which required ~100 satellites to be
launched every year. This result was driven by the
requirements for global coverage, satellite visibility to at least
4 satellites anywhere on the Earth’s surface, and good
geometric diversity (e.g., DOP < 6.0). LEO GNSS
architectures need hundreds of satellites to achieve this
functionality, in contrast to the 24 satellites envisioned in the
original GPS architecture in MEO. However, operational
lifetime of GPS satellites has, on average, more than doubled
their designed lifetimes. This suggests that GPS III satellites
(15-year design lifetime) have the potential to remain
operational for 30 years, thus making lower orbits more
feasible.
Second, there is now a growing concern about space debris.
The current end-of-life disposal plans of GNSS global
constellations make use of graveyard orbits, e.g., at 500km
higher than the nominal orbit altitude, for both non-
operational satellites and rocket upper stages. However,
studies [4] indicate that resonance effects induced by
Sun/Moon and J2 secular perturbations will cause long-term
growth in orbit eccentricity. The same study concludes:
These results directly impact the safety of future navigation
satellites in the altitude region from 19,000 to 24,000 km”.
This is because the disposed satellites are predicted to start
crossing the operational orbits in 40 years. Satellites in lower
orbit could integrate re-entry disposal strategies benefiting
from lower end-of-life V requirements and improving
sustainability in the long-term.
Third, advancements in the miniaturization of space-
qualified atomic clocks have the potential to lower the
payload power requirements and dry mass of future
navigation satellites, making larger GNSS constellations in
lower orbits more competitive.
Fourth, demand for increased GNSS signal performance in
challenging environments, such as in indoor positioning or in
the presence of jamming signals, has led to an increase in
GNSS transmit power levels. As an example, the current GPS
III satellites transmit civil signals that are 5x more powerful
(~250W), than the previous generation GPS II-R (~50W).
This results in a ~7dB increase in Received signal power. On
the other hand, the same performance improvement would
have been experienced, for example, by placing GPS II-R like
satellites in a low MEO orbit, such as the 8330 km orbit
altitude considered in this study. Given the cost difference
(GPS II-R satellites cost 75% less than a GPS III) and
assuming that payload power and satellite lifetime are driving
the costs, as suggested in [5], this poses interesting trade-offs
in GNSS architecture design.
Finally, we are interested in studying the effects that rocket
reusability a tenfold rocket reusability could reduce satellite
launch costs by ~40%- has on the attractiveness of different
GNSS orbit altitude regimes.
Past contributions have analyzed the potential for GNSS LEO
constellations in light of existing industrial initiatives (e.g.,
Iridium NEXT, SpaceX, OneWeb) [6] or the potential of
combining GPS and LEO satellite signals for robust
centimeter-level position [7]. However, most GNSS
architecture studies have been directed towards improving
functionality of existing constellations. For example,
Fernández studies the enhancement of orbit/clock prediction
accuracy and broadcast navigation data by inter-satellite
links, assuming the GALILEO system architecture as a
starting point [8]. Hastings and La Tour study the economic
impact of space asset disaggregation assuming the current
GPS orbit design [9]. However, we could not find recent
GNSS architecture studies that considered alternatives in a
large range of orbit altitude regimes, in particular lower orbits
in MEO.
We believe that complex GNSS architecture trade-offs can be
properly understood by adopting a design space exploration
or “design by shopping” paradigm [10]. In this frame, multi-
objective optimization tools are used to generate a large
number of design alternatives [11]. These design alternatives
are parameterized by a set of design variables and evaluated
by a model computing a set of performance, cost or risk
metrics based on the values of those design variables and
some endogenous model parameters. Thus, the design
process is approached as a shopping experience, during
which the decision maker simultaneously elicits his or her
preferences while observing the major feasible alternatives
and trade-offs between conflicting objectives.
Given all this background, the goal of the paper is to apply
this design by shopping framework to explore the space of
possible architectures for future GNSS systems. We aim to
identify promising architectures or families of architectures,
and explore the main sensitivities to model parameters.
The rest of the paper has the following structure. Section 2
describes the methods used for the enumeration, evaluation
and ranking of GNSS space segment architectures. We focus
on the derivation of performance and cost metrics and
underlying assumptions taken at each step. Section 3 presents
the results of the tradespace exploration and sensitivity
analysis performed on the design decisions and driving
parameters. Finally, section 4 summarizes the main
3
contributions of the paper, discusses its limitations, and
suggests avenues for future work.
2. METHODS
We assume a bare-bones navigation satellite with a single
navigation payload transmitting three navigation signals in
L1, L2 and L5 frequencies, similarly to the GALILEO FOC
satellites without the Search And Rescue (SAR) payload. The
choice of triple frequency is based on the desire to obtain
performance metrics that are representative of modern
navigation satellites and signal processing techniques (e.g.,
removal of first-order ionospheric effects, triple carrier phase
ambiguity resolution)
The reference architectures for this work are GPS and
GALILEO, as shown in Table 1. We use formulas and
nomenclature used to routinely report on GPS Standard
Positioning Service (SPS) performance [12] and publicly
available information from the GALILEO project to model
satellite parameters, such as payload component power
consumption.
Table 1. Reference Architectures
Orbit
Altitude
[km]
Orbit
inclination
[deg]
#
Orbit
planes
# SV
per
plane
# SV
GPS
20,188
56
6
4
24
GAL
23,229
56
3
9
27
Decisions
Our architecture study is based on the following decisions
(one option to be chosen per decision): orbit altitude [km]
{780, 1250, 8330, 12525, 20188, 23229, 30967}, number of
satellites [#] {20, 24, 30, 48, 60, 84, 96, 360, 480, 600, 720,
840}, orbit inclination [deg] {87, 56, 64}, number of orbital
planes [#] {3, 4, 5, 6, 20, 24, 30} and satellite lifetime [years]
{5, 10, 15}. The resultant full-factorial architectural
enumeration produced 5,292 architectures. We constrained
the constellation design framework to include only Walker
Delta type constellations that are representative of current
GNSS architectures. In doing so, we excluded 378
architectures that did not result in the same number of
satellites per plane (i.e., the total number of satellites was not
an integer multiple of the number of planes).
A significant portion of the 4,914 remaining architectures
were unreasonable in terms of cost (e.g., 840 satellites at
30967km altitude) or performance (e.g. 20 satellites at 780
km altitude). Thus, we only considered architectures
consisting of polar orbits with more than 360 satellites and
with at least 20 orbital planes in LEO, and architectures
consisting of non-polar orbits with less than 96 satellites and
at most 6 orbital planes in MEO. For the remaining 810
architectures, we computed the Geometric Dilution of
Precision (GDOP) and eliminated those with a value greater
than 6.0 (typical value in GPS performance assessment). The
constrained full-factorial enumeration produced a total of 498
architectures that were subsequently evaluated.
Metrics
The evaluation of feasible architectures was based on the
following performance and cost metrics: User Navigation
Error (UNE) [m] and total space segment cost over 30 years
[FY2018 $B] respectively. These objective variables, were
normalized according to Equation 1, taking the minimum and
maximum values from the dataset:
 

(1)
and ranked using a Pareto sorting algorithm, in order to find
the non-dominated solutions.
User Navigation Error
The UNE equation (combining both 3D position and receiver
timing errors) was derived from the navigation solution error
covariance expression obtained in a least squares process,
when processing pseudorange measurements. Assuming zero
mean and uncorrelated pseudorange measurement errors,
UNE is given by:

(2)
where User Equivalent Range Error (UERE) determines the
uncertainty in the ranging signal, and the GDOP quantifies
user-satellite geometric diversity. For the purposes of this
study, we assumed a UERE value typical of a range error
budget obtained in dual-frequency signal processing, 0.6 m,
as computed in Table 10.3 of [13]. In doing so, we assumed
that the quality of the satellite orbit and clock determination
products was independent of the orbit altitude regimes. This
makes sense when considering a large-scale GNSS ground
tracking network such as the one used by the International
GNSS Service (IGS). We have not assessed the impact of
using the current GPS control segment (with 16 monitoring
stations) in the orbit determination process, for all the
proposed constellations.
For a typical GNSS user located on the earth’s surface,
GDOP is mainly a function of satellite constellation design
parameters. Intuitively, we can think of the receiver-satellite
unit vectors forming a tetrahedron in space. The GDOP value
is found to be highly correlated with the tetrahedron’s volume
[14]. In order to evaluate GDOP, a grid of equidistant points
was generated with a spacing of 111km x 111km, which
corresponds to roughly one-degree longitude at the Equator.
At each point, GDOP was computed over 24h for all satellites
above elevation angle. The satellite orbit propagation
simulation was done using MATLAB and the orbit
determination toolbox (ODTBX [15]), with the following
force models: Joint Gravity Model 2 with degree and order
20, Sun & Moon Perturbations using JPL DE405
ephemerides, NRL-MSISE2000 global atmospheric model
with a drag coefficient of 2.2, and solar radiation pressure
4
with a coefficient of reflectivity of 0.8. Given the time-
consuming nature of the GDOP computation, we performed
it a priori and stored the results, assuming a satellite mass of
700Kg and cross-sectional area of 3m2. These satellite data
are characteristic of GALILEO FOC satellites. The global
average GDOP over the day at the worst site, <GDOP>worst,
was determined by computing the average over a day for each
unique latitude/longitude point and taking the worst value as
the result [12].
Part of the GNSS orbit design process (e.g., the choice of
orbit inclination) takes GDOP variations into account, since
these can be significant at different latitudes. The desire to
have better DOP performance at higher latitudes partly
explains the fact that the Russian GLONASS uses an orbit
inclination of 64 degrees (instead of 56 degrees used on the
other GNSS global constellations). An example of how
GDOP varies by latitude is shown in Figure 1.
Figure 1. Maximum values of the Average Geometric
Dilution of Precision (GDOP) over one day as a function
of latitude for GPS and two candidate architectures
Total space segment costs
In order to evaluate the feasibility of the proposed GNSS
space segment architectures, we introduced a cost metric that
considers the satellite constellation production
costs,as well as the launch costs,
, over a period of 30 years. The impact of
operational cost/satellite was not considered at this stage, but
its contribution is taken into account in the sensitivity
analysis section. Thus, the total space segment cost reported
in FY2018 Billion U.S. dollars is:


 

(3)
The choice of time period is justified for being a multiple of
all considered satellite lifetime options (arch. decision #7),
and for increasing the sensitivity of the cost metric to this
decision. Next, we present the derivation of the two cost
components.
Satellite constellation costs
Spacecraft development costs are estimated based on the
satellite dry mass. Table 2 shows satellite unit costs,  for
satellites that we consider representative of the orbit altitude
regimes and dry mass values of interest in this study. These
values are derived from publicly available data and converted
to FY2018 U.S. dollars, considering inflation and euro to
dollar conversions, when appropriate.
Table 2. Reference data for satellite unit cost estimation
Sat.
mission
Sat.
bus
Orbit
alt.
[km]
Sat.
dry
mass
[Kg]
Sat.
unit
cost
[M$]
Ref.
Globalstar
ELiTe
1000
1,414
350
23.11
[16]
GIOVE-A
SSTL
600
23,222
540
39.90
[17]
GALILEO
FOC
OHB
Smart
MEO
23,222
660
45.70
[18]
O3B
ELiTe
1000
8,063
800
49.72
[19]
GPS IIF
AS-
4000
20,188
1453
59.94
[20]
GPS III
A2100
20,188
2269
209.47
[21]
The number of flight units required over the 30-year time
span (N) is computed taking into account the number of
satellites () in the constellation (arch. decision #1) and
the satellite lifetime () (arch. decision #7):


(4)
Productivity gains obtained through increased efficiency are
captured by assuming a learning factor (S) of 85%. The total
satellite constellation cost is given by:

  
 
(5)
Satellite dry mass
We estimated the spacecraft dry mass using a power law
relationship with payload power as derived in [22]. This
empirical formula was obtained by analyzing FCC filling
data from non-geosynchronous communication satellites that
we consider similar in nature to GNSS satellites.
5


(6)
Based on the data in [22], we have estimated the standard
error of the estimate (SEE) to be 45.8% for a range of satellite
dry mass values between 566 and 2778 kg. In order to have a
good estimate of the payload power consumption, we
gathered available data from the GALILEO FOC satellite.
This satellite constitutes a good example of a navigation
satellite architecture given the absence of other NAV-
unrelated payloads in contrast with a modern GPS satellite,
which has 7 different payloads. Based on the block diagram
produced by the satellite manufacturer [23] and ignoring the
SAR functionality, we identified the core components in
Table 3. Data from the referenced sources was used to
produce the payload power budget.
Table 3. Payload Power Consumption
Payload
component
Units
[#]
Maximum power
consumption [W]
Ref.
Phase Hydrogen
Maser (PHM) atomic
clock
2
54
[24]
Rubidium Atomic
Frequency Standard
(RAFS)
2
39
[25]
TWTA amplifier
1


[26]
Navigation Signal
Generation Unit
(NSGU)
1
35
[27]
Frequency
Generation and Up
conversion Unit
(FGUU)
1
22
[28]
Remote Terminal
Unit (RTU)
1
12
[29]
Payload thermal
subsystem
1
15% of total
payload power
consumption
We assumed a RF signal amplification using Travelling
Wave Tube Amplifiers (TWTA) with an efficiency of 68%
[26] and a payload thermal subsystem consuming 15% of the
total payload power. Using the maximum power
consumption values per component, we obtained a
conservative estimate of the total payload power
consumption:


(7)

 
The transmit power level, necessary for the transmission
of three navigation signals (L1, L2 and L5) at the target
received signal power () was determined with
the link budget equations. Under the assumptions of
maximum satellite-user range 
@ minimum elevation
angle,  ), antenna polarization loss: 
, excess loss (beyond free-space loss):  ,
receiver antenna gain:  and transmit antenna gain:
 , the received signal power can be expressed by
the following equation [30]:


(8)
where the maximum satellite-user range, 
 was derived
by the law of cosines as described in [30]:

  
(9)
The corresponding transmitted power level, (using
the same symbols for all quantities in dB as in the linear
domain) was obtained as follows:
  





(10)
where 


The satellite dry mass estimate given by the power law
relationship in Equation 6 does not account for the impact of
satellite lifetime. Satellites with longer design lifetime
typically have higher levels of redundancy in critical
subsystems. In our study, we assumed additional redundancy
in the TT&C subsystem [31], which accounts for 5% of the
total spacecraft mass according to subsystem mass
distributions from historical spacecraft data [32] , as shown
in Table 4.
Table 4. NAV Spacecraft Subsystem Mass Distribution
Percentage of satellite dry mass (standard deviation)
EPS
P/L
Struct.
AOCS
TT&C
Prop
Therm
32
21
23
6
5
3
10
(3)
(2)
(3)
(0.5)
(1)
(0.5)
(1)
In order to capture the level of redundancy dependency with
satellite lifetime, the number of redundant elements was
computed according to the expression suggested in [31],
assuming a reference reliability   at a reference
lifetime   as reported by the GALILEO FOC
6
satellites [23]:


 
(11)
Thus, the satellite dry mass estimate considering redundant
components,  was obtained as follows:
 
(12)
Radiation Environment
The radiation environment where existing navigation
satellites operate, i.e. MEO, is very hazardous when
compared to LEO or GEO orbits. Thus, it is important to
estimate the total radiation dose and add-on shielding
required at different orbit altitude and inclination. Assuming
a maximum radiation dose of 30kRad at the center of an
Aluminum (Al) sphere, -appropriate for “careful COTS”
components-, the necessary Al thickness was determined
using ESA’s SPENVIS database. Radiation sources and
effects considered in the simulation are shown in Table 5. The
required Al sphere thickness obtained for the reference GPS
and GALILEO architectures, as shown in Table 6, was 8 and
7 mm respectively.
Table 5. Radiation sources and model parameters
Radiation source
Model parameters
Trapped proton and
electron fluxes
Proton model AP-8, solar
minimum
Electron model AE-8, solar
maximum
Long-term solar
particle fluences
ESP-PSYCHIC (total fluence)
Ion : H
Confidence level: 80%
Galactic cosmic ray
fluxes
Ion range: H to U Magnetic
shielding
Ionizing dose for
simple geometries
SHIELDOSE-2 model
Center of Al spheres
Silicon target
In order to compute a mass penalty due to add-on shielding,
we assumed a bulk satellite density of 
(derived
from GALILEO FOC volume and mass data) and computed
the corresponding satellite volume for our satellite dry mass
estimates. The Al thickness values were added to the radius
of a sphere of equivalent volume and the volume of the
resultant spherical shell was then converted to a mass penalty,
, using a mean Al density of 2700 kg/m3. The final
satellite dry mass quantity was updated as follows:
 
(13)
Table 6. Required aluminum thickness for careful COTS
components
Satellite lifetime
5
10
15
Orbit Altitude
[km]
Orbit
Inclination []
Aluminum Thickness
[mm]
780
87
2
3
4
1250
87
4
7
17
8330
56
7
8
9
64
7
8
9
12525
56
8
9
9
64
8
9
9
20188
56
8
8
9
64
8
8
9
23229
56
7
8
8
64
7
8
8
30967
56
5
6
7
64
5
6
6
Propellant mass
The propellant mass derivation was based on the required
for satellite orbit correction maneuvers, ADCS and End-of-
Life (EOL) disposal. Orbit correction maneuvers are required
for the conservation of the overall satellite constellation
geometry. Using  data from AIUB CODE [36] and GPS
outage information retrieved from Notice Advisory for
Navigation Users (NANU) messages, we estimated a
required 0.17m/s every ~500 days. Given the deep 2:1
resonance effects experienced by GPS orbits, the required
for most architectures is likely to be less than this value. The
final expression accounting for the satellite lifetime is the
following:
  
(14)
Table 7. GPS SVN45 Maneuver history
SVN45 (PRN21)
YEAR
DOY
GPS
WEEK

(mm/s)
Duration
(days)
2009
205
1541
129.8
--
2011
46
1623
155.2
571
2012
241
1703
173.4
560
2014
39
1778
182.7
528
2015
156
1847
161.5
482
2016
267
1915
212.1
476
2017
349
1979
191.8
447
Mean
172.4
511
EOL orbital disposal  requirements are computed
7
assuming a Business as Usual (BAU) strategy. For the MEO
constellations, we used of a graveyard orbit located 500km
higher than the operational altitude: ,
while in LEO we assumed a circular disposal orbit at 500km
altitude -ensuring a re-entry in less than 25 years for typical
GNSS satellite mass and area to mass ratios. EOL orbital
disposal  was obtained by the following equation:



(15)
Rather than assuming a  value for attitude control, we
derived this value from available mass history data from the
GALILEO FOC satellite [37], as shown in Table 8. In the
absence of orbit maneuvers, the changes in mass can be
attributed to the thruster propellent required for ADCS.
Table 8. GALILEO Sat E203 Mass History
SVN
Year
DOY
Mass [kg]
E203
2015
86
706.162
253
705.688
Thus, we estimated the consumed propellant for ADCS to be
 in Nominal mode. In Sun Acquisition Mode
(SAM), however, the propellant mass consumption,
was reported as  or  [38], so we
decided to adopt this value for the purposes of this study. The
corresponding per year amounts to , assuming
hydrazine monopropellant with a specific impulse 
 and a satellite weight of 700kg. The final  expression
is given by:

(16)
The propellant mass was derived from the rocket equation
assuming hydrazine monopropellant and the satellite dry
mass estimate
 


(17)
Launch costs
The total constellation launch costs,
 , were
calculated by determining the minimum number of rocket
launches needed for full constellation deployment over a time
horizon of 30 years. The prime rocket/upper stage
configuration chosen for this analysis was the Soyuz-
2/Fregat, given that it has been extensively used for
Navigation satellite orbit insertions, both in the GLONASS
and GALILEO programs. Based on data from [33], we
considered a fixed cost per launch:
 . In
cases where the satellite wet mass exceeded the Soyuz-2
performance to the desired orbit altitude, we assumed the use
of SpaceX’s Falcon 9 with a fixed cost per kg, 

. This value was derived from the recent launch cost
of GPS III satellite (wet mass= 3880kg) valued at $96.5
million [34]. This constitutes the BAU case, which did not
account for first-stage rocket reusability. The impact of lower
launch costs was considered in the sensitivity analysis
section, as shown in the results section. This aims to capture
the projected savings of rocket first-stage reusability that,
according to SpaceX, can amount to 40% for a tenfold
reusability [35]. Equation 19 was used in the determination
of the total constellation launch costs, derived from the
minimum number of rocket launches required to deploy the
entire satellite constellation, , as computed in the next
section. The satellite wet mass was computed by adding the
satellite dry mass and the propellant mass:
 
(18)

 

  

 
(19)
Rocket Performance
Rocket performance was derived from available Soyuz 2-1B
rocket data. Data extracted from the user manual [39] and
other sources [40] was used to perform a 2nd order polynomial
regression, in order to calculate the LV performance,
, for all orbit altitudes, , considered in this
study.
Figure 2. Soyuz 2-1B performance data


(20)
Given the satellite dry mass and rocket launcher performance
we computed the maximum number of satellites per launch
vehicle as follows:

 

(21)
Furthermore, we added the constraint of a single orbit plane
per launch vehicle, given that maneuvers other than orbit
phasing require a large amount of . The resulting
expression is given in Equation 22.
0
1000
2000
3000
4000
5000
6000
010000 20000 30000 40000
LV performance [kg]
Orbit altitude [km]
8
 


 

(22)
where 
 is the number of satellite generations / 30 years,
 is the number of orbital planes (arch decision #4),

is the number of satellites per plane and

 is the number of satellites per launch vehicle
3. RESULTS
In this section, we present results from tradespace exploration
and sensitivity analysis to the design decisions and key
parameters. The tradespace exploration is focused on three
different scenarios, as shown in Table 10. Scenario 1
incorporates all the assumptions described previously.
Scenario 2 and 3, however, consider operational costs of 4$M
per satellite per year, an increase of 10dBW in transmit power
levels, a decrease in 5% in the learning factor, a reduction of
40% in launch costs and different EOL disposal strategies.
These are meant to capture trends observed across successive
GPS satellite generations and other events such as rocket first
stage (tenfold) reusability.
Tradespace Exploration
The sorting algorithm identified 12 architectures in the Pareto
front for scenario 1. Table 9 presents the entire set of 12 non-
dominated architecture solutions with the corresponding sets
of decisions and performance/cost metrics, while Figure 3
shows the Pareto front. The following conclusions were
drawn from the resulting data: First, the “low MEO”
constellation at 12525 km altitude and MEO at 20188 km
altitude dominate the Pareto front in scenario 1. However, the
Low MEO constellations perform better overall in scenarios
2 and 3 as seen in Table 11. Second, the Pareto front is
dominated by architectures with the longest lifetime. This is
in part due to the fact that we did not consider the effects of
technology obsolescence, which would favor shorter satellite
lifetimes. Third, GALILEO seems to have a better design
than GPS in the sense that it has fewer number of alternative
architectures that outperform it (in terms of both UNE and
Cost metrics) in all three scenarios. Fourth, the architecture
that outperforms GALILEO in all scenarios, corresponds to a
48 satellite (15-year lifetime) constellation in an orbit at
8330km altitude, 64 deg inclination and consisting of 6
equally spaced orbital planes. This constitutes a good
example of potential high performing GNSS constellations in
Low MEO
Figure 3. Tradespace exploration (Scenario 1)
9
Table 9. Pareto front architectures (scenario 1)
Table 10. Simulation scenarios
Table 11. Scenario results
Sensitivity analysis
We used variance-based sensitivity analysis methods to
understand which input parameters are driving the
uncertainty in the output variables. In particular, we used
Sobol’s sensitivity indices to study the main effects of each
decision. The results are summarized in Table 12, and lead to
the following observations: SV lifetime has no impact on the
user NAV error (as expected), and the number of satellites is
the main contributor to both DOP and cost.
Table 12. Sensitivity Analysis - Main Effects
Decisions
Metrics
SV
orbit
alt
Orbit
Incl.
# Orbit
Planes
SV
life
time
NAV
Error
Total
Cost over
30 years
[B$]
S/C
Power
[W]
Dry
Mass
[Kg]
Wet
Mass
[Kg]
Flight
Unit
Cost
[M$]
Launch
Costs
[B$]
DOP
1250
87
30
15
0.56
25.10
431.30
599.22
654.17
45.70
11.64
0.94
8330
64
6
15
1.12
2.48
533.10
523.15
766.18
39.90
1.16
1.87
12525
56
3
15
1.35
1.63
624.00
573.31
595.36
45.70
0.58
2.25
12525
64
6
15
0.93
2.67
624.00
573.31
595.36
45.70
1.16
1.56
12525
64
6
15
0.81
2.95
624.00
573.31
595.36
45.70
1.16
1.36
12525
64
6
15
0.67
4.06
624.00
573.31
595.36
45.70
1.75
1.12
20188
56
3
15
1.19
2.31
848.40
686.08
709.59
49.72
1.16
1.98
20188
64
5
15
0.75
3.88
848.40
686.08
709.59
49.72
1.94
1.25
20188
64
4
15
0.67
5.23
848.40
686.08
709.59
49.72
2.72
1.12
20188
64
6
15
0.62
5.42
848.40
686.08
709.59
49.72
2.91
1.03
23229
64
6
15
0.61
6.59
958.50
713.23
737.07
49.72
4.07
1.02
30967
64
6
15
0.60
10.66
1292.30
797.91
822.35
49.72
8.15
1.00
Scenario
EOL Disposal
OPS Cost
[M$ /sat]
RX Signal Power
[dBW]
Learning Factor
[%]
Launch Cost
reduction [%]
1
BAU
0
-155
85
0
2
BAU
4
-145
80
40
3
Re-entry
4
-145
80
40
Scenario
Number of non-dominated architectures
Number of constellations that outperform
GPS / GALILEO
LEO
Low
MEO
MEO
High
MEO
LEO
Low MEO
MEO
High MEO
1
1
5
5
1
0/0
0/1
3/0
0/0
2
2
4
2
3
0/0
11/7
3/0
0/0
3
2
7
2
1
0/0
10/8
3/0
0/0
SV
orbit
altitude
# SV
Orbit
Incl.
# Orbit
Planes
SV
lifetime
UNE
0.042
0.139
0.010
0.036
0.000
Total
Cost
0.124
0.159
0.158
0.120
0.082
10
Furthermore, we analyzed the impact of operational cost per
satellite per year on the overall results. In Figure 4, we see
that as the operational costs increase, the relative advantage
of Low MEO constellations is reduced. This can be explained
by the fact that operational costs are assumed to increase
linearly (the effects of learning factor in operations are
ignored) with the number of satellites. Thus, large
constellations in Low MEO and specially in LEO will incur
heavy cost penalties. The number of LEO architectures on the
Pareto front does not reduce to zero because the constellation
that contains the lowest GDOP value overall (first row in
Table 9) is in LEO and always shows up in the Pareto front.
Figure 4. % Architectures in Pareto front (at different
orbit altitude regimes) vs operation costs/satellite/year
We also investigated the impact of increasing the received
signal power. In Figure 5, we observe an increasing
advantage of lower altitude constellations (LEO and Low
MEO). This can be explained by the higher transmit power
levels required at higher altitudes to achieve the same power
performance at the user end.
Figure 5. % Architectures in Pareto front (at different
orbit altitude regimes) vs received signal power increase
Finally, we looked at variations in the payload power, given
that it is an important variable driving the satellite dry mass
estimation. The uncertainty comes from the following facts:
First, we used maximum power consumption values, as
reported by the manufacturers, even so the average
consumption is lower; Second, we had doubts concerning the
accuracy of the power consumption estimate related to the
payload thermal subsystem; Third, power transmission losses
were ignored so the overall payload consumption is higher.
Figure 6 shows that for most values of payload power, Low
MEO and MEO constellations dominate the Pareto front,
with Low MEO performing better at the higher end of the
Payload power consumption.
Figure 6. % Architectures in Pareto front (at different
orbit altitude regimes) vs Payload Power variation
4. CONCLUSIONS
The main contribution of this paper was to explore alternative
GNSS space segment architectures, evaluate their
performance in terms of user and control segment
independent metrics (DOP and space segment cost) and
propose specific architectures in Low MEO altitude regimes.
LEO constellations that require hundreds of satellites for
global coverage lead to substantially higher costs than the
current GNSS architectures. Additionally, considering the
proliferation of space debris in near-polar LEO orbits, these
large constellations raise safety and reliability concerns. Low
MEO altitude regmes have a much lower spatial density of
debris and could constitute a more sustainable and reliable
alternative to MEO orbits. Additionally, these orbit altitude
regimes require a modest increase in the number of satellites
and have the advantage of allowing the receiver power levels
to be increased at a fraction of the satellite mass/payload
power required at the GPS orbit. This is particularly
important as signal jamming mitigation efforts often require
higher transmit power levels. Specifically, the proposed
Walker constellation of 48 satellite in an orbit at 8330km
altitude, 64 deg inclination and consisting of 6 equally spaced
orbital planes, is an example of a promising family of future
GNSS architectures that is worth considering in more detail.
11
Limitations
There are several limitations in this study. First, we
considered only a limited set of possible satellite orbit
constellations, even if somewhat representative of a wide
range of orbit altitudes. Second, we have ignored the impact
of the control segment, namely the number and location of
monitoring stations, on the orbit determination quality and
overall system performance. Relying on the IGS Network is
appropriate for civilian users but it might not be for the
military. Third, we did not consider some of the traditional
GNSS performance metrics such as availability and
continuity that could be estimated by taking into account
satellite spares per orbit plane. Fourth, we have ignored the
timing user community and their needs. While this could be
addressed by computing a Time To First Fix (TTFF) metric,
it would be difficult if not impossible to estimate those values
on the basis of space segment design alone.
Future Work
We plan to extend the architecture design space to include
new decisions and more options. Also, we intend to construct
a more detailed model of UERE to account for the effects of
Doppler and Received Signal Power on the code / phase
tracking and multipath error components. By computing the
DOP metric at higher mask angles we can also assess the
robustness of the proposed architectures. Finally, with certain
assumptions, we think it would be possible to construct an
aggregate time and position utility metric that would better
capture the overall value of each GNSS architecture.
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13
BIOGRAPHY
Filipe Pereira is a Ph.D. candidate in
Systems Engineering at Cornell
University since 2017. He received the
M.Eng. degree in Aerospace
Engineering from Instituto Superior
Técnico, University of Lisbon,
Portugal, in 2002. After his
graduation, he worked at the Payload
Systems Laboratory at ESA/ESTEC in
support of the GALILEO and EGNOS programs. From
2006 to 2014 he worked at ESA/ESOC, where he joined
ROSETTA’s flight control team and later worked as a
Navigation Engineer at the Navigation Support Office.
From 2015 to 2017, he was the Comms lead for the
Cislunar Explorers mission (NASA’s CubeQuest
Challenge) at Cornell.
Daniel Selva is an Assistant Professor
of Aerospace Engineering at Texas
A&M University, where he directs the
Systems Engineering, Architecture,
and Knowledge (SEAK) Lab. His
research interests focus on the
application of knowledge engineering,
global optimization and machine
learning techniques to systems engineering and
architecture, with a strong focus on space systems. Before
doing his PhD in Space Systems at MIT, Daniel worked for
four years in Kourou (French Guiana) as an avionics
specialist within the Ariane 5 Launch team. Daniel has a
dual background in electrical engineering and aerospace
engineering, with degrees from MIT, Universitat
Politecnica de Catalunya in Barcelona, Spain, and
Supaero in Toulouse, France. He is a member of the AIAA
Intelligent Systems Technical Committee, and was recently
appointed to the European Space Agency's Advisory
Committee for Earth Observation.
... Among the above-mentioned complementary techniques, the standalone systems able to achieve the submeter accuracy currently offered by GNSS are the 5G-based and UWB-based solutions, but both have limited coverage and a relatively large energy consumption at the receiver side. In recent years, as more and more effort has been put to develop various Low Earth Orbit (LEO) constellations for communication purposes, researchers have also started to investigate the possibility of using existing LEO signals for PNT purposes as well as of designing novel LEO constellations with good properties for target PNT metrics [7], [8], [9], [10], [11]. For example, in [7] the authors explored how LEO constellations in use for communication purposes can be explored for navigation purpose, based on the premises that LEO satellite signals are received at a much higher power than GNSS signals, due to their closer proximity to Earth, and are thus more capable to penetrate indoors and to offer good coverage in deep urban canyons. ...
... The authors of [8] also explored alternative satellite systems structures to complement existing GNSS solutions and focused on low-MEO and some LEO architectures. A Pareto-based optimization approach was used, focusing on the deployment costs and payload power consumption. ...
... around 8300 km altitude) as a good tradeoff for the next generation of satellite-based positioning. Nevertheless, in the section dealing with limitations of the study of [8] it was emphasized that more orbits and constellations need to be taken into account for more robust conclusions, leaving therefore place for further deeper investigations of more satellite constellations. ...
... The mission was planned with at least a two-hour difference between repetitions using the respective GNSS corrections to reduce the effect of a particular constellation on the positioning accuracy [30]. Geometric Dilution of Precision (GDOP) values were under a maximum tolerance of six during the entire study [31]. Mission planning was conducted using the Trimble GNSS Planning Online website (https: //www.gnssplanning.com/, ...
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