Opportunistic Navigation with Doppler Measurements

from Iridium Next and Orbcomm LEO SatellitesMohamad Orabi

Department of Electrical Engineeringand Computer Science

University of California, IrvineIrvine, CA 92697orabim@uci.edu

Joe KhalifeDepartment of Mechanicaland Aerospace Engineering

University of California, IrvineIrvine, CA 92697khalifej@uci.edu

Zaher M. KassasDepartment of Mechanical and Aerospace Engineering

Department of Electrical Engineering and Computer ScienceUniversity of California, Irvine

Irvine, CA 92697zkassas@ieee.org

Abstract—A framework for opportunistic navigation with multi-constellation low Earth orbit (LEO) satellite signals is pro-posed. A receiver architecture suitable for processing bothtime division (TDMA) and frequency division multiple access(FMDA) signals from Orbcomm and Iridium NEXT satellitesis presented to produce Doppler frequency measurements frommulti-constellation LEO satellites. An extended Kalman filter(EKF)-based estimator is formulated to solve for a stationaryreceiver’s position using the resulting Doppler measurements.Experimental results are presented showing receiver positioningwith one Orbcomm satellite and four Iridium NEXT satellitewith an unprecedented final position error 22.7 m.

TABLE OF CONTENTS

1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

2. RECEIVED SIGNAL MODEL AND LEO RECEIVER

ARCHITECTURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2

3. MULTI-CONSTELLATION LEO SATELLITE-BASED

NAVIGATION FRAMEWORK . . . . . . . . . . . . . . . . . . . . . . . .3

4. OVERVIEW OF THE IRIDIUM NEXT AND ORB-COMM LEO CONSTELLATIONS . . . . . . . . . . . . . . . . . . . .4

5. EXPERIMENTAL RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . .6

6. CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7

ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7

1. INTRODUCTION

As cyber-physical systems move towards full autonomy,the need for accurate and resilient positioning, navigation,and timing (PNT) is now more critical than ever. Thisneed is also nourished by emerging technologies such asautonomous vehicles [1]. Furthermore, PNT has becomeentangled with critical infrastructure that could affect thenational and economic security of the entire Nation [2]. Ona similarly important front, PNT is envisioned to enablehigh-rate, low-latency communication systems, particularlyby enabling beam-forming for fifth-generation (5G) cellularnetworks [3, 4]. Global navigation satellite systems (GNSS)have been the leading providers of PNT solutions. However,they are vulnerable to unintentional interference, intentionaljamming, and malicious spoofing [5,6]. These vulnerabilities

978-1-7281-7436-5/21/$31.00 ©2021 IEEE

could results in large-scale disruptions and millions of dollarsworth of losses [7], especially that jamming and spoofingcapabilities are becoming alarmingly accessible to the masses[8]. While some signal processing techniques have beendeveloped to detect and mitigate such attacks [9–11], theydo not provide full protection against jamming or spoofing.Instead of relying mainly on GNSS, which makes them asingle point of failure, a more robust way to address theirvulnerabilities is by exploiting other sources for navigation,such as signals of opportunity (SOPs).

SOPs are abundant and span wide frequency bands, whichmakes them far more robust than GNSS signals against jam-ming and spoofing attacks. Previous work has demonstratednavigation solutions for both (i) terrestrial SOPs, such asAM/FM radio [12–15], cellular [16–26], and digital televi-sion signals [27–31], as well as (ii) non-terrestrial signalsfrom low Earth orbit (LEO) satellites [32–36]. AlthoughSOPs were not designed with PNT in mind, they are still ca-pable of providing submeter-level accuracy on aerial vehiclesas was shown in [37–39]. What is more, the exploitation ofcellular SOPs for resilient navigation in GPS-denied environ-ments under GPS jamming conditions has been shown to beeffective in [40].

In addition to cellular SOPs, LEO broadband communicationsatellite signals have been considered as possible reliablesources for navigation by various theoretical and experimen-tal studies [41–47]. Tens of thousand of LEO satellites will belaunched for broadband communication in the next five years.These signals have desirable attributes for opportunistic nav-igation, namely: (i) their location in LEO provides higherreceived signal power than that of GNSS satellites whichreside in medium Earth orbit (MEO); (ii) LEO satellites aremore abundant due to the larger number of satellites requiredto provide full earth coverage; and (iii) LEO satellites aredeployed into unique constellations and are transmitting indifferent frequency bands, providing both spatial and spectraldiversity.

The potential of these future LEO megaconstellations hastriggered a renaissance of research in LEO-based PNT. Theapproaches in the literature can be grouped into three cate-gories: (i) LEO GNSS, (ii) GNSS augmentation with LEOsatellite signals, or (iii) opportunistic navigation exclusivelywith LEO satellite signals. In the first approach, LEOsatellites are assumed to be equipped with navigation pay-loads to provide PNT services similar to traditional GNSS

1

[41, 43]. While GNSS-like performance can be achieved insuch approaches, the additional cost of navigation payloadsis imposed on the LEO broadband companies and the users.In the second approach, LEO satellite signals are fused withGNSS signals, such as in [48], where simulated pseudorangemeasurements from Iridium NEXT satellites were used toaugment the pseudoranges from GPS satellites with the goalof reducing the dilution of precision. The third approach isfully opportunistic, either in a simultaneous tracking and nav-igation (STAN) framework that estimates both the receiver’sand satellites’ states using Doppler and/or pseudorange mea-surements from real LEO satellite signals [35], or in a differ-ential framework using LEO carrier phase differential (CD-LEO) measurements [49]. These opportunistic frameworkswere experimentally demonstrated on ground vehicles andunmanned aerial vehicles (UAVs) using exclusively signalsfrom two Orbcomm LEO satellites (without GNSS), achiev-ing position root mean-squared errors (RMSEs) of (i) 416 mfor a ground vehicle using the STAN framework after travers-ing a 7.5 km trajectory in 258 seconds, the last 228 seconds ofwhich without GNSS signals [35], (ii) 5.3 m for a UAV usingthe STAN framework after traversing a 1.53 km trajectoryin 155 seconds, the last 30 of which without GNSS signals[47]; (iii) 14.8 m for a UAV using the CD-LEO frameworkand traversing a 1.14 km trajectory in 2 minutes [36], all ofwhich without GNSS signals []; and (iv) 21.2 m for a UAVusing a blind Doppler tracking approach within the CD-LEOframework after traversing a 782 m trajectory in 90 seconds,all of which without GNSS signals [50]. Experimental resultswith Iridium NEXT satellite signals using an opportunisticapproach were presented in [51], where a 22 m RMSE wasachieved for a stationary receiver over a 30-minute period.One challenge in using LEO satellite signals opportunisticallyis the unknown nature of the LEO satellite positions andvelocities. While two-line element (TLE) files and orbitdetermination software (e.g., simplified general perturbation4 (SGP4)) could be used to predict LEO satellite positionsand velocities, the resulting estimates could be off by a fewkilometers and a few meters per second, respectively [35,52].

Despite these errors in the predicted LEO satellite orbits, theaforementioned experimental results have shown remarkablepotential for opportunistic navigation with LEO satellites.However, the experiments therein only utilized signals froma single LEO constellation, which does not exploit the spatialand spectral diversity of LEO constellations. Moreover, LEOsatellites are designed to cover as much of the Earth’s surfacewith as few satellites as possible, making it improbable tolisten to a large number of satellites (6 or more) from the sameconstellation simultaneously. This is illustrated in Figure1, which shows the percentage of time L or more satellitesare simultaneously visible over a period of 2 days. TheLEO satellite trajectories were generated using TLE filesand SGP4 software [53]. Figure 1 shows the importance ofbeing able to exploit multi-constellation LEO satellites forPNT. Currently, the literature presenting experimental resultswith multi-constellation LEO-based PNT is rather sparse. Asopposed to [51], which investigated opportunistic navigationusing only Iridium NEXT satellites, this paper uses bothIridium Next and Orbcomm satellite signals to investigatemulti-constellation LEO satellite-based opportunistic navi-gation. This paper makes three contributions. First, anextended Kalman filter (EKF)-based full opportunistic frame-work for navigating with Doppler measurements from multi-constellation LEO satellite signals is developed. Second,a receiver architecture capable of producing such Dopplermeasurements from multi-constellation LEO satellite signalsis provided. Third, experimental results are presented, show-

ing stationary receiver positioning using Doppler measure-ments from the Iridium NEXT and Orbcomm constellationssimultaneously, with a final two-dimensional (2–D) position

error of 23 m. Next to [54] 1, this paper presents the firstexperimental results for multi-constellation LEO satellite-based opportunistic navigation.

1 2 3 4 5 6 7 8Number of visible satellites

0

20

40

60

80

100

Perc

enta

ge o

f tim

e

Orbcomm

Iridium NEXT

Multi-constellation

Figure 1. Percentage of time when L or more satellites arevisible simultaneously for Orbcomm and Iridium NEXTsatellite constellations for a simulated duration of 2 days.

The rest of the paper is organized as follows. Section2 describes the received signal model and LEO receiverarchitecture. Section 3 presents an EKF-based frameworkto navigate with the Doppler measurements estimated bythe multi-constellation LEO receiver. Section 4 gives anoverview of the Iridium NEXT and Orbcomm LEO satelliteconstellations. Section 5 presents experimental results. Sec-tion 6 gives concluding remarks.

2. RECEIVED SIGNAL MODEL AND LEORECEIVER ARCHITECTURE

This section presents the received multi-constellation LEOsignal model and the proposed receiver architecture.

Received LEO Satellite Signal Model

This paper considers a stationary receiver that listens to bothcontinuous signals and burst signals from multi-constellationLEO satellites on various channels. Let L denote the totalnumber of visible LEO satellites and U the total number ofconstellations to which these satellites belong. Furthermore,let Lu denote the number of visible satellites in the u-th constellation, where u = 1, 2, . . . , U . It follows that∑U

u=1 Lu = L. The baseband received signal for the u-thconstellation at the input of an opportunistic LEO receivercan be modeled as

ru(i) =

Lu∑

lu=1

slu(i) +nu(i), i = 0, 1, . . . , u = 1, 2, . . . , U,

(1)

where nu(i) , nIu(i) + jnQu(i), with nIu and nQu

aremodeled as zero-mean white Gaussian noise with varianceN0

2Ts; Ts is the sampling time; i represents time ti , t0 + iTs

1The results in this work were achieved independently from [54], whichwas published shortly after the first submission of this manuscript, whichachieved a 2–D position error of 132 m.

2

for some initial time t0; slu(i) is given by

slu(i),√

Clualu(i)exp {j2π[fD,lu(i)+fIF,lu ]iTs+jθlu(i)},

where Clu is the received signal power of the lu-th satel-lite; alu is the transmitted symbol at time i; fD,lu(i) andθlu(i) are the time-varying Doppler frequency and carrierphase of the lu-th satellite, respectively; and fIF,lu is theintermediate frequency of the lu-th satellite. It is assumedthat the symbols alu are drawn from an M -ary phase shift

keying (M -PSK) constellation, i.e., alu , exp[

j(

q2πM

)]

for

q ∈ {0, 1, . . . ,M − 1}.

It is important to note that (1) holds for both continuouslytransmitted and burst signals. The difference between thesesignals is the domain of the time index i. For continuoussignals, i goes from zero to infinity. For burst signals, i isdefined only over burst intervals, which requires knowledgeof the burst start-time, period, and duration. The burst periodand duration are known for the signals of interest (IridiumNEXT), and the start-time can be acquired through an energydetector.

Multi-Constellation LEO Receiver Architecture

The navigation receiver architecture in Figure 3, which oper-ates on the samples of ru(i) from (1), was designed to accountfor both time-division multiple access (TDMA) schemes(used by Iridium NEXT) and frequency-division multipleaccess (FDMA) schemes (used by both Iridium NEXT andOrbcomm). The receiver performs recursively the stepsdiscussed next to obtain an estimate of the Doppler frequency

for the lu-th satellite, denoted fD,lu . An extra step is requiredfor TDMA signals at initialization to acquire the burst starttime, which can be done using an energy detector. To thisend, it is assumed that an initial Doppler frequency estimate

fD,lu(0) and the burst start time tburstlu (0) and associatedindex i0lu are given.

1. The receiver first wipes-off the intermediate frequencyfIF,lu to obtain

dlu(i) , ru(i) exp[−j2πfIF,luiTs]. (2)

2. Next, the receiver groups samples of dlu(i) into datablocks of size Nu, denoted by

dklu = [dlu(kNu + i0lu ), dlu(kNu + 1 + i0lu ), . . . ,

dlu((k + 1)Nu − 1 + i0lu )],

where k = 0, 1, . . . , is the data block index. These datablocks have a duration Tblocku

= NuTs, which is equalto that of the burst for satellites that employ TDMA, orthat is an integer multiple of the symbol period Tsymb

ufor

continuously transmitting satellites. For TDMA schemes,only samples of the burst signal are chosen to form the datablocks. For a burst duration Tburstu and period Pburstu ≥Tburstu , the samples between two bursts are dumped by thereceiver. The duration of the dumped samples is given byTdump

u= Pburstu − Tburstu , as shown in Figure 2.

It is clear that Pburstu > Tburstu for TDMA signals, whichmakes Tdump

ustrictly positive, and Pburstu = Tburstu for

continuous signal transmission, which implies Tdumpu= 0.

It is assumed the Doppler frequencies are approximatelyconstant during a data block duration, i.e.,

fD,lu(i) = fD,lu [k], kNu ≤ i < (k+1)Nu, k = 0, 1, . . . .(3)

{Data Block 1

M-PSK Burst No Signal M-PSK Burst No Signal

{Data Block 2

Tburstu Tdumpu

Pburstu

Figure 2. TDMA data block.

3. The data blocks dklu are then raised to the M -th power to

wipe off the M -PSK symbols, resulting in a pure tone at afrequency of M · fD,lu(i).4. A Fast Fourier Transform (FFT) of the signal is then taken,which results in an impulse-like peak at the next Doppler

frequency MfD,lu(k), which will be around MfD,lu(k− 1).

Therefore, the search for the FFT peak is limited to [fD,lu(k−

1)−∆f, fD,lu(k−1)+∆f ], where∆f is chosen to be greaterthan the maximum expected frequency deviation in a periodof Tblocku

. The Doppler estimates are then normalized by M .5. In order to successfully track a burst signal, it is importantto update the burst start time acquired at the initializationof the receiver. This is due to the change in the distanceand hence delay between the satellite and the receiver. Thedelay can be predicted from the estimated Doppler frequencyaccording to

tburstlu (k) = tburstlu (k − 1)−fD,lu(k)

fc,u + fIF,luPburst, (4)

where fc,u is the carrier frequency of the u-th constellation.The burst start time index is then updated accordingly. Com-pensating for the change delay using (4) results in slightvariations in the value of Tdump

lu.

The receiver architecture is summarized in Figure 3.

(.)M

fIF,2

fD,2 EKF

fIF,l

fD,l

fD,1(.)M FFT

(.)M

Dumped

SamplesPeak

Detection

FFT

FFT

Data Block dklu

Dumped

SamplesData Block dklu

Dumped

SamplesData Block dklu

Peak

Detection

Peak

Detection

fIF,1

Figure 3. Block diagram for the mutli-constellation receiverarchitecture presented in this paper. The dashed lines

represent optional feedback of the estimated Doppler toupdate Tdump

u.

3. MULTI-CONSTELLATION LEOSATELLITE-BASED NAVIGATION

FRAMEWORK

This section develops an EKF-based framework to navigatewith the Doppler measurements estimated by the multi-constellation LEO receiver discussed in Section 2. The goalis to estimate the receiver’s three dimensional (3–D) position

vector rr , [xr , yr, zr]T

using the Doppler measurements

3

obtained from the receiver developed in the paper. In whatfollows, the pseudorange rate model is first described and theEKF model is then provided.

Pseudorange Rate Measurement Model

Given a Doppler measurement fD,lu(k), a pseudorange ratemeasurement can be formed according to

zleo,lu(k) , cfD,lu(k)

fc,u + fIF,lu, k = 0, 1, . . . , (5)

where lu = 1, . . . , Lu, u = 1, . . . , U , and c is thespeed of light. Let the pseudorange rate measurements{

{zleo,lu(k)}Lu

lu=1

}U

u=1for k = 0, 1, . . ., be re-indexed ac-

cording {zleo,l(k)}L

l=1 for compactness of notation. Hence,the pseudorange rate measurement of the l-th satellite pro-duced by the receiver could be expressed as

zleo,l(k) =rT

leo,l(k) [rr−rleo,l(k)]

‖rr−rleo,l(k)‖+c[δtr(k)− δtleo,l] (6)

+ c[

δtiono,l(k) + δttrop,l(k)]

+ vleo,l(k),

where rleo,l and rleo,l are the l-th LEO satellite’s 3–D po-

sition and velocity vectors, respectively; δtr and δtleo,l arethe receiver’s and l-th LEO satellite’s clock drifts, respec-

tively; δtiono,l and δttrop,l are the l-th satellite’s ionosphericand tropospheric delay rates, respectively; and vleo,l is themeasurement noise, which is modeled as a zero-mean whiteGaussian random sequence with variance σ2

leo,l. It is assumed

that the receiver’s clock drift δtr and the satellites’ clock

drifts{

δtleo,l

}L

l=1are constant within the 10-minute satellite

visibility window. Moreover, since it not necessary to esti-mate the receiver and satellite’s clock drifts individually, they

will be lumped into one term ∆δtl , δtr − δtleo,l. In case of

multiple passes,{

∆δtl

}L

l=1are re-initialized at the beginning

of each pass. Note that at any time-step k, the l-th satellite’sposition and velocity vectors can be obtained from the TLEfiles and SGP4 software. For the brief duration of LEOsatellite visibility, the ionospheric and tropospheric delay

rates are negligible; hence, δtionol and δttropl

are ignored inthe measurement, yielding the measurement model given by

zleo,l(k) ≈rT

leo,l(k) [rr − rleo,l(k)]

‖rr − rleo,l(k)‖+ c∆δtl + vleo,l(k).

(7)

EKF Model

From (7), it can be seen that the state vector to be estimated

is x ,

[

rT

r , c∆δt1, . . . , c∆δtL

]T

. Subsequently, an EKF is

designed to produce an estimate x(k|m) of x(k) using allpseudorange rate measurements from time-step 1 to m ≤ k.

The estimation error is denoted x(k|m) , x(k) − x(k|m).The EKF also calculates the estimation error covariance

P(k|m) , E

[

x(k|m)xT(k|m)]

. Given a prior x(0|0) and

P(0|0), the standard EKF equations are iterated. Since thestate vector x is constant, the EKF state and estimation error

covariance time-update equations are given by

x(k + 1|k) = x(k|k), P(k + 1|k) = P(k|k) +Q,

where Q is the process noise covariance. Note that Q shouldtheoretically be a zero matrix; however, in order to preventthe estimation error covariance from converging to zero, Qis chosen to be Q ≡ ǫI(3+L)×(3+L), where ǫ is a very small

positive number. Given an innovation vector ν(k + 1), thestate and covariance measurement update equations are givenby

x(k + 1|k + 1) = x(k + 1|k) +K(k + 1)ν(k + 1),

P(k + 1|k + 1) = [I−K(k + 1)H(k + 1)]P(k + 1|k),

where K(k+1) is the standard Kalman gain, H(k+1) is themeasurement Jacobian given by

H(k + 1) = [hleo,1(k + 1) . . . hleo,L(k + 1)]T,

hleo,l(k + 1) ,[

hT

r,l(k + 1), eTl

]T

where el is the standard L×1 basis vector whose l-th elementis 1 and the remaining elements are 0,

hr,l(k) ,rleo,l(k + 1)

‖rr(k + 1|k)− rleo,l(k + 1)‖

− [rr(k + 1|k)− rleo,l(k + 1)]

×rT

leo,l(k + 1) [rr(k + 1|k)− rleo,l(k + 1)]

‖rr(k + 1|k)− rleo,l(k + 1)‖3 ,

and rr(k + 1|k) is the receiver’s position prediction at time-step k+1. The innovation vector ν(k+1) is formed accordingto

ν(k + 1) = [νleo,1(k + 1), . . . , νleo,L(k + 1)]T,

where νleo,l(k + 1) = zleo,l(k + 1)− zleo,l(k + 1), such that

zleo,l(k + 1) =rT

leo,l(k + 1) [rr(k + 1|k)− rleo,l(k + 1)]

‖rr(k + 1|k)− rleo,l(k + 1)‖

+ c∆ˆδtl(k + 1|k).

It is important to note that the altitude of the receiver isassumed to be known. Therefore, the initial estimate ofzr is set to the known altitude and its corresponding initialuncertainty is set to be very small.

4. OVERVIEW OF THE IRIDIUM NEXT AND

ORBCOMM LEO CONSTELLATIONS

This section provides an overview of the two LEO constel-lations used in the experimental results: Iridium NEXT andOrbcomm.

Iridium NEXT System Overview

The Iridium NEXT constellation is the next-generation Irid-ium constellation which provides voice and data informa-tion coverage to satellite phones, pagers, and integratedtransceivers over the entire Earth surface on the L-band [55].

4

Iridium NEXT LEO Satellite Constellation— The IridiumNext constellation consists of 75 active satellites that orbitthe Earth in 6 different orbital planes spaced 30◦ apart [55],as shown in Figure 4. The planes are near-polar orbitswith 86.4◦ inclination angle and 780 km orbital altitude.Originally, the Iridium constellation was designed to incor-porate 66 satellites (gathered in 6 groups of 11) in order toprovide coverage for the entire Earth surface. Later, Iridiumdecided to enlarge the initial constellation (referred to as theNEXT campaign) by launching 12 extra satellites in order toprovide 24/7 real-time coverage, which would add two extrasatellites on each of the original orbital planes. Unfortunately,3 of them are not active since they experienced technicaldifficulties once they were launched and thus the currentconstellation remains at 75 satellites.

Plane 1 Plane 2

Plane 3

Plane 4

Plane 5

Plane 6

Orbital

direction

Equator

Seam

Seam

0 ◦

60 ◦

70 ◦

80 ◦

50 ◦

40 ◦

20 ◦

30 ◦

10◦

Latitude linesCommunicationlink

Latitude cutoff forcommunication link

Satellite

Figure 4. Polar view of the Iridium NEXT Constellation.

Iridium NEXT Downlink Signals—Iridium NEXT signals aretransmitted over the 1616–1626.5 MHz band, which is partof the L-band. There are 252 carriers in both the uplinkand downlink channels, with carrier spacings of 41.6667 kHzwith a required bandwidth of 35 kHz [55]. These carrierfrequencies are grouped into sub-bands of 8 carriers, withthe 32nd group containing 4 carriers. A small portion ofthe Iridium NEXT spectrum, namely 1626–1626.5 MHz isassigned for paging and acquisition [55]. On this part ofthe spectrum are 5 simplex downlink channel with the samefrequency spacing as the standard channels and with 35 kHzof bandwidth. Doppler measurements are extracted from thesimplex downlink channels.

Iridium NEXT uses a TDMA scheme for downlink chan-nel multiplexing. The signal structure over the uplink anddownlink channels consists of signal bursts that are sentperiodically over the TDMA frame. Each burst is composedof an unmodulated tone, succeeded by a unique word and theinformation data. On the simplex channel, Iridium NEXTsatellites transmit the ring alert as well as paging/acquisitionmessages, which have the same burst structure as the standardcarriers. As such, the pure tone transmitted at the beginningof each burst can be used to extract Doppler measurements.However, the burst duration is 2.56 ms and the burst periodis about 1700 times longer at 4.32 seconds. This largescaling will yield poor Doppler frequency measurements ifnot accounted for, as discussed in Section 2.

Orbcomm System Overview

The Orbcomm system is a wide area two-way communicationsystem that uses a constellation of LEO satellites to provideworldwide geographic coverage for sending and receivingalphanumeric packets [56].

Orbcomm LEO Satellite Constellation—The Orbcomm con-stellation, at maximum capacity, has up to 47 satellites in7 orbital planes A–G, illustrated in Figure 5. Planes A, B,and C are inclined at 45◦ to the equator and each contains8 satellites in a circular orbit at an altitude of approximately815 km. Plane D, also inclined at 45◦, contains 7 satellites ina circular orbit at an altitude of 815 km. Plane E is inclinedat 0◦ and contains 7 satellites in a circular orbit at an altitudeof 975 km. Plane F is inclined at 70◦ and contains 2 satellitesin a near-polar circular orbit at an altitude of 740 km. PlaneG is inclined at 108◦ and contains 2 satellites in a near-polarelliptical orbit at an altitude varying between 785 km and 875km.

Equator

Plane A (45◦)

Plane C (45◦)

Plane E (0◦)

Plane F (70◦)

Plane G (108◦)

Plane D (45◦)

Plane B (45◦)

Existing Satellites

Future Satellites

Note: Drawing not to scale

Planes A, B, and C: 8 satellites

each with orbital altitude 815 km

Plane D: 7 satelliteswith orbital altitude 815 km

Plane F: 2 satelliteswith orbital altitude 740 km

Plane G: 2 satelliteswith orbital altitude 785{875 km

Plane E: 7 satelliteswith orbital altitude 975 km

Figure 5. Orbcomm LEO satellite constellation. Map data:Google Earth.

Orbcomm Downlink Signals— Orbcomm uses an FDMAscheme for downlink channel multiplexing. Satellite radiofrequency (RF) downlinks are within the 137–138 MHz VHFband. Downlink channels include 12 channels for transmit-ting to users and one gateway channel, which is reserved fortransmitting to the ground stations. Each satellite transmits tousers on one of the 12 subscriber downlink channels througha frequency-sharing scheme that provides four-fold channelreuse. The Orbcomm satellites have a subscriber transmitterthat provides a continuous 4800 bits-per-second (bps) streamof packet data using symmetric differential-quadrature phaseshift keying (SD-QPSK). Each satellite also has multiplesubscriber receivers that receive short bursts from the usersat 2400 bps.

Note that Orbcomm satellites are also equipped with a spe-cially constructed 1-Watt ultra high frequency (UHF) trans-mitter that is designed to emit a highly stable signal at 400.1MHz. The transmitter is coupled to a UHF antenna designedto have a peak gain of approximately 2 dB. The UHF signal isused by the Orbcomm system for user positioning. However,experimental data shows that the UHF beacon is absent.Moreover, even if the UHF beacon was present, one wouldneed to be a paying subscriber to benefit from positioningservices. Consequently, only downlink channel VHF signalsare exploited for navigation.

5

5. EXPERIMENTAL RESULTS

An experiment was conducted to demonstrate the proposedreceiver architecture and navigation framework. To this end,two universal software radio peripherals (USRPs) Ettus E312were used to collect multi-constellation LEO satellite signals.One USRP was equipped with a VHF quadrifilar helix an-tenna to sample Orbcomm signals at a carrier frequency of137.5 MHz, which is the central frequency of the Orbcommband [56], and the other was equipped with an AT 1621-12Iridium antenna to sample Iridium NEXT signals at a carrierfrequency of 1626.2708 MHz, which is the central frequencyof the Iridium ring alert burst signal according to [51]. BothUSRPs were set to sample data at 2.4 Msps over a 410-secondperiod. The samples were stored for offline processing, anda software-defined radio (SDR) implementation of the afore-mentioned receiver architecture was used to post-process thecollected data. The experimental setup is illustrated in Figure6. Moreover, the M -PSK constellation size was set to 2 forthe Orbcomm signals and 1 for the Iridium signals, respec-tively. Note that Orbcomm satellites transmits quadraturePSK (QPSK) signals (M = 4); however, raising the signalto the second power yielded better results than M = 4. TheM -PSK constellation size was chosen to be 1 for IridiumNEXT since their satellites transmit a pure tone as part of theburst. Moreover, Tblock and Tdump, where set to 100 ms andzero, respectively, for the Orbcomm constellation. For theIridium constellation, they were set to Tblock = 2.56 ms andTdump = 4.3174 s, enabling burst processing for a signal witha period of Pblock = 4.32 s, equivalent to that of the ring alertburst signal. The SDR produced Doppler measurements forfive satellites, consisting of (i) one continuously transmittingOrbcomm satellite and (ii) four burst transmitting IridiumNEXT satellites. The Doppler measurements were providedat a rate of 100 ms for the Orbcomm satellite and 4.32 sfor the Iridium NEXT satellites. The satellites’ positionsand velocities were determined using a MATLAB-based SGP4propagation software and publicly available TLE files. Thepositions of the satellites along with the skyplot with respectto the receiver are shown in Figure 8.

Ettus E312

USRPVHF quadrifilar

helix antenna

Iridium Antenna

AT1621-12

MATLAB-Based Receiver

and Navigation Framework

Post-Processing

Laptop

Ettus E312

USRP

Figure 6. Experimental setup.

Figure 7 shows the true and estimated pseudorange ratesobtained from the TLE files and the receiver, respectively, foreach of the five satellites. The satellites were not all trackedfor the entire duration of their availability due to bad signalreception at low elevation angles. Figure 7 also illustratesthe availability of the satellites within the 410 s windowwhen the data was recorded. The Orbcomm satellite wasavailable throughout the entire window and was providingmeasurements every 100 ms. However, for the Iridiumconstellation, three satellites are tracked initially and are thenlost at 78, 118, and 217 s, respectively. The EKF continues toestimate the receiver’s position using one Orbcomm satellite

0 50 100 150 200 250 300 350 400

Time (s)

-6k

-4k

-2k

0

2k

4k

6k

Pse

ud

ora

ng

e r

ate

(m

/s)

TLE Measured

Iridium 119

Iridium 168

Iridium 122

Iridium 180

Orbcomm

FM 116

Figure 7. Pseudorange rates time history predicted usingTLE files for the satellites tracked by the proposed receiver

along with the actual measurements produced by thereceiver.

Receiver

Position

Figure 8. Skyplot and satellite positions of the trackedOrbcomm and Iridium NEXT satellites.

until the receiver starts extracting measurements from anotherIridium NEXT satellite at 304 seconds. Figure 7 illustratethe availability of Orbcomm and Iridium NEXT satellitesduring the experiment window as well as the actual numberof LEO satellites that were tracked by the receiver. It isworth mentioning that tracking an Iridium NEXT satellitefor 100 seconds only produces around 23 pseudorange ratemeasurements.

0 50 100 150 200 250 300 350 400

Time (UTC)

0

1

2

3

4

5

6

Num

ber

of vis

ible

sate

llite

s

Orbcomm Iridium NEXT Multi-constellation Tracked

Figure 9. Number of tracked and available satellites as afunction of time.

The horizontal position estimate was initialized around 200km away from the receiver’s true position, and the initialhorizontal uncertainty was set to 1010 m2. The receiver’s

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altitude was initialized according to Section 3, with a 0.1m2 initial uncertainty. Figure 10 shows the time evolutionof the EKF position errors in the east and north coordinatesalong with the ±3σ bounds, reaching a final position errorof 22.7 m. The small jumps seen in the EKF errors happenat a period of 4.32 s, which is the rate at which pseudorangerate measurements were produced from the Iridium NEXTsatellite signals. The receiver’s true and estimated positionsare shown in Figure 11. It is also worth noting that someof the position error could be attributed to errors in the LEOsatellites’ positions and velocities predicted by the TLEs andSGP4 orbit determination software.

0 50 100 150 200 250 300 350 400

Time (s)

-4

-2

0

2

4

East (k

m)

Error 3 bounds

0 50 100 150 200 250 300 350 400

Time (s)

-4

-2

0

2

4

Nort

h (

km

)

Figure 10. The time evolution of the EKF east and northposition estimation errors as a function of time.

22.7 m

California, USAInitial Estimate

Initial Uncertainty

Final Estimate

Final Uncertainty

True Position

UC Irvine

True RxEstimated

Rx

Figure 11. True position of the receiver along with theestimate produced by the EKF using pseudorange rate

measurements for one Orbcomm and four Iridium NEXTsatellites.

6. CONCLUSION

This paper proposed a framework for opportunistic naviga-tion with multi-constellation LEO satellite signals. A receiverarchitecture suitable for processing both TDMA and FDMA

signals from Orbcomm and Iridium NEXT satellites to pro-duced Doppler frequency measurements to LEO satelliteswas proposed. An EKF-based estimator was formulatedto solve for a stationary receiver’s position using Dopplermeasurements from multi-constellation LEO satellites. Un-precedented experimental were presented showing receiverpositioning with one Orbcomm satellite and four IridiumNEXT satellite with a final position error less than 23 m.

ACKNOWLEDGEMENTS

This work was supported in part by the Office of NavalResearch (ONR) under Grant N00014-19-1-2511 and in partby the U.S. Department of Transportation (USDOT) un-der University Transportation Center (UTC) Program Grant69A3552047138. The authors would also like to thankCarlos Acebes for his contributions to the paper and NadimKhairallah for his help with data collection.

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Mohamad Orabi is a graduate studentat the Department of Electrical Engi-neering and Computer Science at Uni-versity of California, Irvine and mem-ber of the Autonomous Systems Per-ception, Intelligence, and Navigation(ASPIN) Laboratory. He received aB.E. in Electrical Engineering from theLebanese American University (LAU).His research interest include opportunis-

tic navigation, software-defined radio, machine learning, anditerative learning control.

Joe Khalife is a postdoctoral fellowat the University of California, Irvineand member of the Autonomous Sys-tems Perception, Intelligence, and Nav-igation (ASPIN) Laboratory. He re-ceived a B.E. in Electrical Engineer-ing, an M.S. in Computer Engineeringfrom the Lebanese American University(LAU) and a Ph.D. in Electrical Engi-neering and Computer Science from the

University of California, Irvine. From 2012 to 2015, hewas a research assistant at LAU, and has been a memberof the ASPIN Laboratory since 2015. He is a recipientof the 2016 IEEE/ION Position, Location, and NavigationSymposium (PLANS) Best Student Paper Award and the 2018IEEE Walter Fried Award. His research interests include op-portunistic navigation, autonomous vehicles, and software-defined radio.

Zaher (Zak) M. Kassas is an asso-ciate professor at the University of Cal-ifornia, Irvine and director of the Au-tonomous Systems Perception, Intelli-gence, and Navigation (ASPIN) Labo-ratory. He is also director of the U.S.Department of Transportation Center:CARMEN (Center for Automated Vehi-cle Research with Multimodal AssurEdNavigation), focusing on navigation re-

siliency and security of highly automated transportation sys-tems. He received a B.E. in Electrical Engineering fromthe Lebanese American University, an M.S. in Electricaland Computer Engineering from The Ohio State University,and an M.S.E. in Aerospace Engineering and a Ph.D. inElectrical and Computer Engineering from The Universityof Texas at Austin. He received the 2018 National ScienceFoundation (NSF) Faculty Early Career Development Pro-gram (CAREER) award, and 2019 Office of Naval Research(ONR) Young Investigator Program (YIP) award. He is arecipient of the 2018 IEEE Walter Fried Award, 2018 Instituteof Navigation (ION) Samuel Burka Award, and 2019 IONCol. Thomas Thurlow Award. He is an Associate Editor forthe IEEE Transactions on Aerospace and Electronic Systemsand the IEEE Transactions on Intelligent Transportation Sys-tems. His research interests include cyber-physical systems,estimation theory, navigation systems, autonomous vehicles,and intelligent transportation systems.

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