Tightly-Coupled Opportunistic Navigation forDeep Urban and Indoor Positioning

Kenneth M. Pesyna, Jr., Zaher M. Kassas, Jahshan A. Bhatti, and Todd E. HumphreysThe University of Texas at Austin

BIOGRAPHIES

Kenneth M. Pesyna, Jr. is pursuing a Ph.D. in the De-partment of Electrical and Computer Engineering at TheUniversity of Texas at Austin. He received his B.S. in Elec-trical and Computer Engineering from Purdue University.He is a member of the UT Radionavigation Laboratory andthe Wireless Networking and Communications Group. Hisresearch interests lie in the area wireless communicationand hybrid navigation.

Zaher M. Kassas is pursuing a Ph.D. in the Department ofElectrical and Computer Engineering at The University ofTexas at Austin. He received his B.E. in Electrical Engi-neering from The Lebanese American University, M.S. inElectrical and Computer Engineering from The Ohio StateUniversity, and M.S.E. in Aerospace Engineering from TheUniversity of Texas at Austin. He is a member of theUT Radionavigation Laboratory. His research interests in-clude estimation and filtering, control systems, intelligentautonomous systems (UAVs and UGVs), and navigation.

Jahshan A. Bhatti is pursuing a Ph.D. in the Departmentof Aerospace Engineering and Engineering Mechanics atthe University of Texas at Austin, where he also receivedhis M.S. and B.S. He is a member of the UT Radionavi-gation Laboratory. His research interests are in the devel-opment of small satellites, software-defined radio applica-tions, space weather, and GNSS security and integrity.

Todd E. Humphreys is an assistant professor in the depart-ment of Aerospace Engineering and Engineering Mechan-ics at the University of Texas at Austin and Director of theUT Radionavigation Laboratory. He received a B.S. andM.S. in Electrical and Computer Engineering from UtahState University and a Ph.D. in Aerospace Engineeringfrom Cornell University. His research interests are in esti-mation and filtering, GNSS technology, GNSS-based studyof the ionosphere and neutral atmosphere, and GNSS se-curity and integrity.

ABSTRACT

A strategy is presented for exploiting the frequency stabil-ity, transmit location, and timing information of ambient

radio-frequency “signals of opportunity” for the purpose ofnavigating in deep urban and indoor environments. Thestrategy, referred to as tightly-coupled opportunistic nav-igation (TCON), involves a receiver continually searchingfor signals from which to extract navigation and timinginformation. The receiver begins by characterizing thesesignals, whether downloading characterizations from a col-laborative online database or performing characterizationson-the-fly. Signal observables are subsequently combinedwithin a central estimator to produce an optimal esti-mate of position and time. A simple demonstration of theTCON strategy focused on timing shows that a TCON-enabled receiver can characterize and use CDMA cellularsignals to correct its local clock variations, allowing it tocoherently integrate GNSS signals beyond 100 seconds.

I. INTRODUCTION

Tightly-coupled opportunistic navigation (TCON) aimsto exploit ambient radio-frequency “signals of opportu-nity”(SOPs) to assist and enhance conventional globalnavigation satellite system (GNSS) navigation techniques.“Tightly-coupled” refers to a receiver architecture in whichthe SOPs are downmixed with the same oscillator andsampled in such a way that a nanosecond-accurate corre-spondence can be made between the various sampled sig-nal streams. Such coupling enables estimation algorithmsto optimally fuse SOP observables at the carrier phaselevel. “Opportunistic navigation” refers to the strategy ofcontinuously searching for opportune signals from whichto extract navigation and timing information, employingon-the-fly signal characterization as necessary. Becauseit must adapt to the available SOPs, a radionavigationreceiver implementing the TCON strategy (a TCON re-ceiver) can be considered a type of cognitive radio [1].

To make discussion and processing of SOPs as general aspossible, GNSS and non-GNSS signals are treated equiva-lently in the TCON framework: all ambient radio signalsare considered potential SOPs. Processing of SOPs canbe divided notionally into two stages: the characterizationstage and the exploitation stage. In the characterizationstage, a TCON receiver has recently acquired a new SOP.To optimally combine navigation and timing informationextracted from this SOP with information extracted fromother SOPs, the signal must first be characterized: trans-

Copyright c© 2011 by Kenneth M. Pesyna, Jr., Zaher M. Kassas,Jahshan A. Bhatti, and Todd E. Humphreys

Preprint of the 2011 ION GNSS ConferencePortland, OR, September 20–23, 2011

mitter position, timing offset from true time, timing offsetrate, and a measure of the carrier stability must all bedetermined by the receiver. TCON takes a collaborativeapproach to characterization. A TCON-enabled receiveror “node” wishing to characterize a new SOP can drawa priori signal information from an online database ofSOP characterizations. The database stores the freshestset of characterizations available for each SOP. Alterna-tively, SOPs can be characterized on-the-fly by each nodeindividually. Individual nodes may contribute recent SOPcharacterizations to the database for the benefit of othernodes. In the second SOP processing stage, the TCON re-ceiver exploits the SOP, extracting navigation and timinginformation provided by the SOP to assist its acquisitionand tracking of other SOPs. Once characterized, each SOPacts as a “pseudo-satellite,” allowing the TCON receiver toimprove its computed position, velocity, and timing (PVT)accuracy by combining all available SOPs. In an environ-ment when GNSS signals are impractically weak or un-available, navigation may still be possible. Within theTCON framework, receiver position and time can be con-strained by tracking the code and carrier phase of whateverSOPs are available.

A TCON receiver’s centralized estimator characterizesSOPs and optimally fuses their observables together toproduce robust navigation and timing estimates. Severalchallenges must be addressed in the design of the esti-mator. First, the estimator must adapt to signals whichperiodically come and go, implying that the estimator’sdynamical model must be of variable state dimension. Sec-ond, the estimator must incorporate heterogeneous signals,some of which are more useful for navigation and tim-ing than others. This necessitates an adaptive estimationstrategy: the estimator must download SOP models froman online database or characterize these signals and refineits models of them in real-time.

Previous work in the area of hybrid navigation has in-cluded fusing together cellular and GPS signals [2], Wi-Fi and GPS signals [3], HDTV and GPS signals [4], andIridium and GPS signals [5]. Compared to these specificpairings, TCON is a generalization and an optimization:it is designed to optimally extract navigation and timinginformation from all available radio-frequency SOPs. Byincorporating measurements from a diverse signal set, aTCON receiver can robustly transition between differentenvironments (e.g., outdoor to indoor). By fusing signalmeasurements at the carrier phase level, a TCON receivermaximizes the navigation and timing-relevant informationthat it extracts from each signal. Moreover, carrier phase-level signal fusion enables synergistic feedback effects: theTCON receiver’s acquisition and tracking sensitivity androbustness for any particular signal is enhanced by observ-

ables gathered from other tracked signals. This synergismamong signals is the driving rationale behind vector track-ing architectures in GNSS receivers [6]. TCON is essen-tially an extension of vector tracking to include non-GNSSradio signals.

The paper is organized as follows. First, it describes indetail the TCON strategy. Second, it discusses signals ofopportunity and desirable characteristics they might have.Third, it presents a centralized estimator to fuse these sig-nal observables together. Finally, a simple TCON demon-stration is performed and the results are evaluated followedby conclusions.

II. TCON: A DETAILED DEFINITION

A. Tightly-Coupled

“Tightly-coupled” refers to a receiver architecture in whichsignals are downmixed and sampled with the same clockand signal observables are fused at the carrier phase level.Referencing all signals to the same clock ensures that iden-tical local clock variations are present in the samples of alltargeted signals. This commonality allows the receiver toestimate and remove the effects of its clock variations onits PVT solution. Analog-to-digital conversion of receivedSOPs must be done in such a way that the TCON re-ceiver can build up a tight correspondence between thesample timing among the various sampled signal streams,even though the sample rates may be different. In someprevious hybrid navigation work, GNSS and non-GNSSsignals have been downmixed, sampled, and tracked inseparate hardware, with timing correspondence providedonly by a low-bandwidth inter-hardware link, leading tomicrosecond-level rms errors in the relative timing of theGNSS and non-GNSS data streams [2]. Such timing uncer-tainty leads to hundred-meter-level errors when combiningpseudorange-type observables in a timing and navigationsolution. In contrast, a tightly-coupled architecture en-ables millimeter-level correspondence in carrier phase mea-surements among the various tracked SOPs and sub-meter-level correspondence in pseudorange-type measurements.Figure 1 shows a TCON-enabling hardware architecture inwhich the SOPs—in this case, GNSS, HDTV, and cellularsignals—are all signal conditioned and sampled coherently.

To avoid confusion, it should be noted that the notionof tight coupling in the present context does not refer tointegration of inertial measurement unit (IMU) measure-ments and SOP observables [7]. Although it shares manyprocessing similarities with this technique, tight couplinghere refers to the fusing of multiple ambient radio signalsrather than the fusing of signals with inertial sensors.

2

CellularHDTV

Signals of Opportunity

Central Estimator

Single Driving Clock

SignalJoint

ConditioningProcessing

GNSS

SOPA/D

Fig. 1. One implementation of a TCON-enabled receiver.

B. Opportunistic Navigation

“Opportunistic navigation” refers to a strategy in which aTCON receiver is continuously searching for ambient sig-nals from which to extract navigation and timing infor-mation. A receiver may choose to search out all availablesignals or concentrate on a specific subset. Section III willpresent and describe various potential SOPs. To make useof the available SOPs, a TCON receiver must character-ize the SOP by determining its carrier stability, timingoffset from true time, timing offset rate, transmitter loca-tion, and carrier-to-noise (C/N0) ratio. A TCON receivercan perform SOP characterization on-the-fly as a stand-alone process. Alternatively, for improved performance,the TCON receiver may draw from an up-to-date SOPcharacterization database to which it and other TCON re-ceivers contribute collaboratively. The database is “smart”in that it delivers upon request an SOP characterizationcomplete with SOP parameters and associated probabil-ity distributions that have been brought up-to-date by thedatabase’s internal SOP dynamics model. This networkedversion of TCON is an example of decentralized collabo-rative PVT estimation.

III. SIGNALS OF OPPORTUNITY

TCON treats all radio-frequency signals as potential sig-nals of opportunity. This includes GNSS signals such asGPS, Galileo, and Glonass; cellular signals such as CDMA,GSM, 4G LTE, and WiMAX; high-definition television(HDTV), Wi-Fi, and non-GNSS satellite signals such asbroadcast by the Iridium communication system.

A. Desirable SOP Characteristics

SOPs are most useful in the TCON framework if they havethe following desirable characteristics:

Known (or predictable) timing offset from truetime: Standard time-of-arrival (TOA)-based navigationdepends on one knowing—or being able to predict via some

deterministic model—the transmission time of features inreceived signals. For example, in the case of GPS signals,the true transmission time of the start of a spreading codesequence can be calculated based on timing parametersbroadcast in the navigation data. Because a transmitter-applied time stamp can usually be inferred from the re-ceived SOPs, knowing the transmit time of a particular sig-nal feature is equivalent to knowing the transmitter clock’soffset from true time.

Stable transmitter clock: The more stable the SOPtransmitter clock, the less often a corresponding clock errormodel needs to be updated in a TCON receiver. For exam-ple, to support long coherent integration of an SOP signaldriven by a low-cost temperature-compensated crystal os-cillator (TCXO), an update of the TCXO’s error modelparameters would be required every 100 milliseconds orso. In contrast, the parameters of GPS satellite clock er-ror models need only be updated every 2 hours.

Known (or predictable) location: TOA-based navi-gation also depends on one knowing—or being able topredict—the transmitter location at any given time.

High received signal power: The received signal powerdepends on the effective isotropic radiated power (EIRP),the signal wavelength, the receiver-transmitter distance,any intervening signal-attenuating material, and the re-ceiver hardware. Naturally, higher received power yieldsmore precise observables.

Wide bandwidth: Wider bandwidth signals offer betterprecision in TOA measurements and better immunity tomultipath effects.

Continuous carrier: A continuous carrier underlying anSOP permits long coherent integration and facilitatescarrier-based positioning.

Known signal structure: Generation of a local signalreplica for tracking purposes requires knowledge of theSOP signal structure. While it is true that the signalcarrier can be recovered without knowledge of the signalstructure (e.g., by squaring techniques), the penalty paidfor such techniques is increased squaring loss.

B. “Freestyle” Navigation

In practice, available SOPs will lack some of these desirablecharacteristics. This is especially true of communicationsignals, most of which were not designed with navigationin mind. As an illustration of this, consider the navigation-and-timing-relevant characteristics of the following exam-ple SOPs:

1. GPS Signals

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(a) Low received signal power (∼ –150 dBW)(b) High frequency stability (∼ 10−12)(c) Known transmitter location via broadcast ephemeris(d) Known transmitter timing offset via broadcast clock

model2. Code Division Multiple Access (CDMA) Cellular(a) High received signal power relative to GPS

(∼ –110 dBW)(b) Varying frequency stability from provider to provider

(∼ 10−10 to 10−11)(c) Static tower location, although not always known(d) Rough synchronization to GPS time (µs-level errors)

3. Iridium Satellite System(a) High received signal power relative to GPS

(∼ –130 dBW)(b) Good frequency stability (∼ 10−10 to 10−11)(c) Freely available ephemeris (via NORAD TLEs) with

rough accuracy (∼ 100m)(d) Unknown clock offset relative to true time(e) Non-continuous carrier due to TDMA structure(f) Ambiguous carrier phase from burst to burst

Despite the few unfavorable characteristics of the CDMAcellular and Iridium signals, a TCON receiver can makeeffective use of them. The same holds true for many otherSOPs. The key to dealing with less-than-ideal SOPs is anability to adapt, to characterize signals on-the-fly as theybecome available or to draw an applicable characterizationfrom an SOP characterization database, as described ear-lier. In this paradigm, which might be called “freestylenavigation,” a TCON receiver refines its estimate of SOPcharacterization parameters even while refining an esti-mate of its own PVT. The centralized estimator describedin the following section makes this simultaneous estimationpossible.

IV. CENTRALIZED ESTIMATOR

The purpose of the centralized estimator is to optimallycombine observables from all SOPs targeted by a TCONreceiver. In this work, the centralized estimator is imple-mented as an extended Kalman filter (EKF). The followingsubsections describe the filter’s state vector, measurementmodels, and dynamics models.

A. State Vector

The estimator’s state vector concatenates a receiver basestate xreceiver with a state xSOP for each SOP. The basestate

xreceiver =[rT δt rT δt

]T(1)

consists of the receiver’s three-dimensional position r, thereceiver’s three-dimensional velocity r, the time offset of

the receiver’s clock δt, and the time derivative of this offset,also known as receiver’s clock drift δt. The SOP state

xSOP =[rTSOP δtSOP δtSOP γSOP

]T(2)

consists of the SOP’s three-dimensional position rSOP, theSOP’s clock offset from true time δtSOP, the SOP’s clockdrift δtSOP, and the SOP carrier phase ambiguity termγSOP. As the TCON receiver discovers SOPs, the basestate vector is augmented with SOP states to match thenumber of SOPs being tracked. This augmented base stateforms the full state vector

x =[xT

receiver, xTSOP1

, xTSOP2

, . . . ,xTSOPN

]T(3)

For some SOPs with well-known parameters, only a sub-set of the usual elements will be included in xSOP. Forexample, if the SOP transmitter position is known, as isthe case with GPS satellites or, on occasion, with cellu-lar basestations, then the position rSOP can be omittedfrom the SOP’s state vector. Likewise, if the transmitterclock error parameters are provided to the receiver, as isthe case with GPS signals, then δtSOP and δtSOP can beomitted. In these cases of known SOP parameters, the fullxSOP state could be retained and the Kalman filter initial-ized with precise a priori estimates of the known quanti-ties, but this approach is more computationally demandingthan omitting the SOP parameters that can be accuratelypredicted by a deterministic model, whether the model isdrawn from broadcast data or from an online database.

B. Carrier Phase Measurement Models

The TCON central estimator is designed to ingest bothcarrier phase and pseudorange-type SOP measurements.Models for these measurements are similar to standardGPS carrier phase and pseudorange models, with someimportant distinctions. To illustrate these distinctions thefollowing subsections present GPS, CDMA, and Iridiumcarrier phase measurement models.

B.1 GPS Carrier Phase Measurement Model

The GPS beat carrier phase φG(tR), in cycles, at receivertime tR can be modeled as [8]

φG(tR) =1λ||r(tR)− rSV (tR − δt(tR)− δtTOF )||

+c

λ[δt(tR)− δtSV (tR − δt(tR))] + γG

+ εiono(tR) + εtropo(tR) + νφG(tR)

(4)

The terms that are underlined are initially unknown andthus are included in the SOP state vector. For GPS signals,this includes the receiver position r(tR), the receiver clock

4

offset δt(tR), and the carrier phase constant γG. Otherterms such as the satellite position rSV and the satelliteclock offset δtSV can be accurately predicted based on thebroadcast navigation data. A substantial component of theionospheric and tropospheric phase errors εiono(tR) andεtropo(tR) can also be eliminated by the broadcast model,by dual-frequency measurements, or by ionospheric andtropospheric models available on the Internet. νφG

(tR)represents additive white thermal noise introduced by thereceiver front end. Constants representing the speed-of-light c and the GPS-signal wavelength λ are present toconvert all terms to units of cycles, and the GPS-signaltime-of-flight δtTOF is present to refer the satellite positionrSV to the time of signal transmission.

B.2 CDMA Carrier Phase Measurement Model

The beat carrier phase measurement model of CDMA cel-lular signals is similar to that of the GPS carrier phasemodel. The CDMA beat carrier phase φC(tR), in cycles,at receiver time tR can be modeled as

φC(tR) =1λ||r(tR)− rC ||+ c

λ[δt(tR)

− δtC(tR − δt(tR))] + γC + νφC(tR)

(5)

The CDMA carrier phase model is different from the GPScarrier phase model in three respects: First, the constantCDMA transmitter (basestation) position rC may not beknown to the receiver. In this case rC must be includedin the corresponding xSOP and estimated on-the-fly. Typ-ically, however, an accurate estimate of rC could be drawnfrom the SOP characterization database and thus rC couldbe omitted from xSOP. Second, the transmitter’s clockoffset δtC may not be known to the receiver. Althougha model for δtC may be drawn from the SOP characteri-zation database, the model may not be sufficiently accu-rate to omit δtC from xSOP. Third, the CDMA carrierphase model does not include ionospheric or troposphericerror terms, as these are negligible for ground-based cellu-lar transmissions.

B.3 Iridium Carrier Phase Measurement Model

The Iridium satellite system is a constellation of 66 lowEarth orbit (LEO) satellites which provide global commu-nication coverage. There has been significant research inthe use of Iridium as a complement to GPS in jammingand otherwise GPS-denied environments, such as deep in-doors [5]. The beat carrier phase φI(tR), in cycles, of an

Iridium signal at receiver time tR can be modeled as

φI(tR) =

1λ ||r(tR)− rI(tR − δt(tR)− δtTOF )||+ c

λ [δt(tR)− δtI(tR − δt(tR))] + γI

+ 1M η(tR − δt(tR)− δtTOF ) + εiono(tR)

+εtropo(tR) + νφI (tR), within a burst0, between bursts

(6)

The Iridium carrier phase model has two key differencesfrom that of the GPS carrier phase model. The first is thepiecewise nature of φI(tR). The Iridium signal is transmit-ted as a time division multiple access (TDMA) waveform.These waveforms are burst-like, with the signal on duringa burst and off between bursts. Within a burst, the carrierphase is observable as shown in Eq. (6); between bursts, nopower is transmitted. The second key difference is the 1

M ηterm, which is present to model the random fractional-cycle phase ambiguity introduced by the satellite at thebeginning of each burst.

To make use of the Iridium signal within the TCONframework, a continuous carrier phase time history canbe stitched together from the glimpses of this time historyprovided within each burst. As part of this processing,the random fractional-cycle ambiguities can be resolved.This phase-stitching and ambiguity resolution process canbe done within the Kalman filter if η, the integer part ofthe ambiguity, is added to the SOP state, and the filteris modified to estimate both real-valued states and thisinteger-valued ambiguity. This phase-stitching and ambi-guity resolution algorithm has been the subject ongoingresearch by the authors and will be the topic of a futurepaper.

C. Dynamics Model

The state dynamics for the TCON extended Kalman filtercan be modeled as

x(k+1) = Φ(k)x(k)+Γ(k)w(k), w(k) ∼ N (0,Q(k)) (7)

where x is the system state, w is the process noise, Φ isthe state transition matrix, Γ is the process noise coeffi-cient matrix, and Q is the process noise covariance matrix.The state dynamics are governed by a simple polynomialmodel, as shown below for an example case in which asingle SOP is present:

The estimator has the full state vector

x =[xT

receiver,xTSOP

]T

=[rT, δt, rT, δt, rT

SOP, δtSOP, δtSOP, γSOP

]T(8)

5

the state transition matrix

Φ(k) =

I3×3 0 T · I3×3 0 0 0 0 00 1 0 T 0 0 0 00 0 I3×3 0 0 0 0 00 0 0 1 0 0 0 00 0 0 0 I3×3 0 0 00 0 0 0 0 1 T 00 0 0 0 0 0 1 00 0 0 0 0 0 0 1

(9)

where T represents the amount of time between consecu-tive filter updates; the process noise coefficient matrix

Γ(k) = I14×14, (10)

and the process noise covariance matrix

Q =

[σr2] 0 0 0 0 0 0 0

0 σ2δt 0 σ2

δtδt0 0 0 0

0 0 [σr2] 0 0 0 0 0

0 σ2δtδt

0 σ2δt

0 0 0 00 0 0 0 [σrS

2] 0 0 00 0 0 0 0 σ2

δtSσ2

δtS˙δtS

00 0 0 0 0 σ2

δtS˙δtS

σ2˙δtS

00 0 0 0 0 0 0 σ2

γS

(11)

The process noise w(k) accounts for any unmodeled dy-namics in the state and is assumed to be Gaussian dis-tributed with mean 0 and covariance Q. Q defines thenoise covariances for each component of the state. [σ2

r ]and [σ2

rSOP] refer to the noise covariance matrices for the

position of the receiver r and the position of the SOP rS.The covariance values within these matrices are sized toaccount for any unmodeled position changes. Most SOPsare assumed static (e.g. cellular basestations) or are as-sumed to have known trajectories (e.g. GPS satellites).Additionally, any changes in the receiver’s position is as-sumed to be well modeled by its velocity. As a result, theseposition process noise covariances can be kept much lessthan 1 m2. The noise covariance matrix of the receiver’svelocity [σ2

r ] accounts for any unmodeled changes in thevelocity of the receiver between consecutive filter updates.Since acceleration is not part of the state, the covarianceswithin this matrix should be sized to account for the ex-pected level of randomness in velocity.

The remaining terms, σ2δt, σ2

δt, σ2

δtδt, σ2

δtS, σ2

δtS, and σ2

δtS˙δtS

account for receiver and SOP clock noise. Often a receiverhas a good estimate of the variations of its own clock, andthus the receiver clock terms σ2

δt, σ2δt

, and σ2δtδt

are well-known in advance. However, the SOP clock terms σ2

δtS,

σ2δtS

, and σ2δtS

˙δtSwill either need to be downloaded from a

database as new SOPs are acquired or determined on-the-fly. This on-the-fly calibration, if performed, motivates the

need for an adaptive dynamics model where the processnoise covariance associated with the SOP clocks is refinediteratively as explained in the next section.

D. Adaptive Dynamics Model: Process Noise Co-variance

To process SOP observables correctly, the Kalman filterneeds a good estimate of the SOP clock dynamics to in-clude as part of its process noise covariance matrix Q.But if the receiver has no knowledge about the SOP, howis it to provide the filter with a good a priori model of itsclock dynamics? The receiver could draw from an onlineSOP characterization database as discussed in sec. II-B orit could perform a standalone characterization on-the-fly.For on-the-fly characterization, the receiver must providean initial guess of the model to the filter and then itera-tively converge on a more accurate estimate through theapproach presented in Fig. 2.

Fig. 2. The filter characterizes the SOP by iteratively estimatingthe SOP clock dynamics and updating the process noise covariancematrix Q with new clock model parameters.

In this approach, the Kalman filter starts with an initialguess of Q. Using this guess, the filter begins to processobservables, outputting an estimate phase-time history ofthe SOP clock offset δSOP(t) as part of its state estimate.Under conditions of strong observability (e.g., ≥ 4 GPSsatellites tracked and a known transmitter location for thetarget SOP), δSOP(t) will be close to the true SOP clockoffset δSOP(t) despite the presence of modest modeling er-rors in Q. The accuracy of δSOP(t) under these conditionsimplies that improved clock model parameters for the tar-get SOP can be obtained by an analysis of δSOP(t). Theseparameters are fed into a refined Q and the process is re-peated until convergence.

Although this iterative approach has been shown to workunder conditions of strong observability, it is not statisti-cally rigorous and does not degrade gracefully under condi-tions of weak observability. Future implementations of theTCON central estimator will adopt the adaptive approachof Ref. [9], in which Q is refined by combining weighted

6

candidate models that are tested simultaneously in a mul-tiple model framework.

E. Importance of Backward Smoothing

Within the TCON framework, there is a need to imple-ment backward-smoothing in addition to regular forwardfiltering. New measurements create innovations within a(causal) filter which introduce abrupt dynamics in the fil-tered state estimates. These abrupt dynamics may notconform to the filter’s state dynamics model, even whenthe filter’s assumed dynamics and measurement models arean accurate reflection of reality [10]. Backward smoothingremoves the abrupt dynamics introduced by innovationsin forward-pass filtering. In other words, smoothing moreaccurately recreates the actual signal dynamics, allowingthe state variations to conform more closely to the a pri-ori dynamics model. There are certain state elements forwhich smoothing is critically necessary. The receiver clockoffset δt is one such element. An accurate estimate of δtis needed to perform long coherent integrations in weak-signal environments for purposes of signal detection. Asmoothed δt(tR) time history eliminates the need for ad-hoc frequency stability transfer techniques such as the oneadvanced in [11].

Figure 3 shows the effects of smoothing versus filtering onthe time history of the receiver clock estimate δt(tR) for asingle run of the Kalman filter and backward-smootherwhile ingesting carrier phase observables from six GPSsatellites. It is apparent from this figure that the fil-

0 50 100 150 200 250−2.5

−2

−1.5

−1

−0.5

0

0.5

1

Time (seconds)

Rec

eive

r C

lock

Offs

et (

cycl

es)

Filtered Rx Clock EstimateSmoothed Rx Clock Estimate

Fig. 3. Filtered and smoothed estimates of δt produced by theKalman filter while ingesting carrier phase observables from six GPSsatellites.

tered estimate of δt(tR) varies much more wildly than thesmoothed estimate. Consequently, the filtered estimatedoes not conform to expected clock variations modeled inQ whereas the smoothed estimate does.

V. SIMPLE TCON DEMONSTRATION

This section describes a simple demonstration designed toshow the benefits of TCON. Although one of the main usesof TCON is for navigation, this demonstration will focuson timing. The goal of this demonstration is to show howa TCON receiver calculates its receiver clock variationsusing two types of SOPs: GPS signals and cellular CDMAsignals.

A. Experimental Setup

The experimental setup is presented in Fig. 4. Two Na-tional Instruments RF Vector Signal Analyzers (RFSAs)were used to simultaneously downmix and sample bothGPS and CDMA signals. Both RFSAs were driven by thesame external reference clock and sampled synchronously,in compliance with the tightly-coupled requirement of theTCON framework. The samples were stored to a redun-dant array of independent disks (RAID). Next, the Gen-eralized Radionavigation Interfusion Device (GRID) soft-ware receiver [12, 13] was augmented to simultaneouslytrack both the GPS L1 C/A and CDMA cellular pilot sig-nals. The receiver was programmed to produce simulta-neous pseudorange and carrier phase observables at a rateof 10 Hz for 6 of the GPS satellites in view as well as twoCDMA basestations. Finally, these observables were fedinto a centralized estimator, a MATLAB-based extendedKalman filter, where they were optimally fused to estimatethe elements of the full state presented in Eq. (12).

x =[xT

rec.,xTGPS1

, . . . ,xTGPS6

,xTCDMA1

,xTCDMA2

]T(12)

The SOP state vector for each tracked GPS signal xGPS isa subset of the full SOP state vector xSOP. As discussedin section IV-A, rSOP, δtSOP, and δtSOP can be omittedfrom xSOP for GPS signals since they can be accuratelypredicted from models drawn from the GPS broadcastdata. The only unknown state element for GPS signalsthat needs to be estimated by the filter and is thus con-tained in xGPS is the GPS carrier phase ambiguity termγGPS. The SOP state vector for each tracked CDMA sig-nal xCDMA consists of a subset of xSOP as well. In thisdemonstration, is is not necessary to know or estimate thepositions of the CDMA transmitters. Thus rCDMA is omit-ted from xCDMA. The other three CDMA SOP state pa-rameters δtCDMA, δtCDMA, and γCDMA must be estimatedand thus are included in xCDMA.

B. Wardriving for Signals of Opportunity

Signals for this demonstration were captured during awardriving effort in downtown Austin, Texas. The Na-tional Instruments equipment and the RAID (Fig. 4.(1))were placed into a vehicle (Fig. 5), and two antennas

7

Fig. 4. The TCON experimental setup: (1) Sample CDMA and GPS signals using two National Instruments RFSAs and store the sampleddata to a RAID. (2) Track both signals and produce observables using the GRID software receiver. (3) Fuse these observables together withina MATLAB-based EKF.

were placed on the roof of the vehicle (Fig. 6). One an-tenna was designed to capture GPS signals and the otherCDMA signals. Signals were recorded in static, dynamic,

Fig. 5. The National Instruments RFSAs, RAID, reference clock,and computer placed in the back of the wardriving vehicle.

“open sky,” and “dense urban” situations. For this timingdemonstration, the data from one of the “static, open sky”situations were used. Specifically, the vehicle was parkedalong the side of the road (Fig. 7) and signals from twocell basestations, a Sprint and a Verizon basestation, wererecorded simultaneously along with signals from all GPSsatellites in view.

Fig. 6. Wardriving antennas placed on the roof of the vehicle.

Fig. 7. Vehicle and tower positions for the “static, open-sky” signalrecording.

C. Results: Estimating Receiver Clock Dynamics

The data from the wardriving effort were post-processedwithin the GRID software receiver (Fig. 4.(2)) to producecarrier phase observables for six GPS satellites and two

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Fig. 8. Three processing stages of the TCON demonstration: (1) Obtain a “truth” estimate of the local clock variations δt(t) by ingesting onlyGPS observables into the EKF. (2) Characterize CDMA SOPs by ingesting both CDMA and GPS observables. (3) Estimate δt(t) ingestingonly CDMA observables.

CDMA basestations. These observables were subsequentlyfed into an extended Kalman filter (EKF) implemented inMATLAB (Fig. 4.(3)).

The EKF was run in three stages. In the first stage, itingested GPS carrier phase observables from the six GPSsatellites. In the second stage, it ingested both the GPSobservables as well as carrier phase observables from thetwo cellular CDMA basestations. In the third stage, itingested only CDMA carrier phase observables. Thesethree stages are diagrammed in Fig. 8. In all three stagesthe forward-pass filter was run followed by the backward-smoother. As explained in section IV-E, the backward-smoother produces state estimates which conform moreclosely to the dynamics model.

During the first stage, the smoother estimated the carrierphase ambiguity term γGPS for each GPS satellite. As de-scribed in section V-A, this is the only SOP state param-eter that needs to be estimated for GPS signals. Duringthis stage, the smoother also estimated the receiver’s po-sition r as well as the receiver’s clock offset and drift, δtand δt. Given the strong observability afforded by trackingsix GPS signals, the smoother’s estimates of the receiver’sposition and clock dynamics were very accurate. For thesake of this demonstration and the results to come, thesmoother’s estimate of the receiver clock offset as a func-tion of receiver time δt(tR) is taken as the “truth” timehistory of δt.

During the second stage, while ingesting both GPS andCDMA measurements, the smoother was set to perform anon-the-fly characterization of signals from the two CDMAbasestations. The smoother iterated over the same seg-ment of data until it converged on a process noise modelfor each CDMA SOP clock. It also calculated the carrierphase ambiguity term γCDMA for each basestation.

During the final stage, the smoother was evaluated for itsability to estimate the receiver clock offset while ingestingonly CDMA observables. This shall be called the CDMA-only based estimate δtCDMA of δt. Here, the smootherexploited the characterization of the CDMA SOPs per-formed during stage 2. Because of this characterization thesmoother knew precisely how to weight the carrier phasemeasurements from each SOP. This is significant becauseit was found that the Verizon SOP was significantly morestable than the Sprint SOP.

Figures 9 and 10 show a comparison, at each stage, of thesmoother’s estimate of the receiver clock variations for twodifferent receiver clocks. Figure 9 shows the smoother’sperformance at estimating these variations with a highlystable oven-controlled crystal oscillator (OCXO) as the re-ceiver clock. Figure 10 shows the smoother’s performanceat estimating these variations with a temperature com-pensated crystal oscillator (TCXO) as the receiver clock.During the wardriving effort, an OCXO was used as thereceiver clock and thus the original wardriving data wereused for the OCXO-based demonstration. However, for theTCXO-based demonstration, the GPS and CDMA observ-ables were modified appropriately to simulate a TCXO asthe receiver clock. Specifically, common-mode phase andpseudorange variations commensurate with that caused bya mid-range TCXO were added across all channels.

When compared against the truth model δt (the GPS-onlycarrier phase-based estimate of the receiver clock varia-tions), Fig. 9 shows that the smoother had no trouble esti-mating the OCXO receiver clock variations while ingestingboth GPS and CDMA carrier phase measurements. How-ever, when ingesting only CDMA carrier phase measure-ments, the smoother performance degrades somewhat. Inreality, because the receiver clock (an OCXO) varied muchless than 1 cycle over the 4-minute segment, its variationswere not significantly observable by the smoother, par-

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ticularly since the smoother was ingesting measurementsfrom only two CDMA SOPs. The clocks within the CDMAbasestations are of OCXO-quality. As a consequence, withonly two of these SOPs being ingested during stage 3, thesmoother had trouble distinguishing variations of the re-ceiver’s clock from variations caused by the CDMA SOPclocks. Nonetheless, as section V-D, will argue, even thisseemingly poor estimate of the receiver’s variations will begood enough to allow a TCON-based receiver to extend itscoherent integration time beyond 100 seconds.

0 50 100 150 200 250−0.2

−0.15

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eive

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lock

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et (

cycl

es)

GPS Only EstimateGPS+CDMA EstimateCDMA Only Estimate

Fig. 9. Receiver clock offset estimates (OCXO).

0 50 100 150 200 250−8

−6

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2

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Time (seconds)

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eive

r C

lock

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et (

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GPS Only EstimateGPS+CDMA EstimateCDMA Only Estimate

Fig. 10. Receiver clock offset estimates (simulated TCXO).

When compared against the truth model of δt, Fig. 10shows that the smoother had no trouble estimating theTCXO receiver clock variations while ingesting the carrierphase measurements for both the GPS+CDMA and theCDMA-only situations (stage 2 and 3). Because the re-

ceiver clock (a simulated TCXO) varied many cycles overthe 4-minute segment, these variations were highly ob-servable by the smoother. This observability arises be-cause, compared with the OCXO-quality clocks withinthe CDMA basestations, the receiver clock variations wereeasy to distinguish from those caused by the basestations.Even with only two CDMA signals being ingested, thesevariations were accurately estimated as evident in Fig. 10.The next section discusses the importance of having a goodestimate of receiver clock variations.

D. Results Analysis

In this section, the time history of the CDMA-only receiverclock estimates δtCDMA(tR) will be analyzed for their accu-racy. The error in these estimates as a function of receivertime δt(tR) can be defined as the difference of CDMA-based estimate δtCDMA(tR) from the GPS-based “truth”estimate δt(tR):

δt(tR) = δt(tR)− δtCDMA(tR) (13)

Coherence time is one simple metric for evaluating theaccuracy of clock estimates. Roughly speaking, the co-herence time is the amount of time it takes for the phaseerror

φr(tR) = fc · δt(tR) (14)

(with linear trends removed) to drift more than one-half ofa cycle. Eq. (14) is a simple conversion from the receiverclock estimate error δt(tR) to the phase error φr(tR) wherefc represents the clock’s nominal center frequency. Here,fc = 1575.42 MHz, the GPS L1 C/A carrier frequency.More formally, the coherence time is defined as the timeat which the mean-squared coherence function 〈C2

coh(τ)〉drops below 0.5, where [11]

Ccoh(τ) =∣∣∣∣1τ

∫ τ

0

ejφ(t)r dt

∣∣∣∣ , 0 ≤ Ccoh(τ) ≤ 1. (15)

Figure 11 shows the mean-squared coherence of the esti-mate errors for both the OCXO and TCXO receiver clocks.〈C2

coh(τ)〉 could only be plotted out to 200 seconds here be-cause it is limited by the length of data with which it iscalculated. Nonetheless, it is apparent, from the figure,that both the OCXO and the TCXO estimate errors havecoherence times beyond 100 seconds, since neither tracehas by then dipped below 0.5.

As mentioned earlier, the coherence time is a good metricof how well the smoother was able to estimate the receiverclock variations. In fact, the coherence time of the esti-mate errors is a good measure of how long a receiver cancoherently integrate. A receiver provided with an estimateof its local clock variations can use this aiding information

10

10−1

100

101

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103

0.75

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0.95

1

Time (seconds)

Mea

n−S

quar

ed C

oher

ence

<C

2 coh>

OCXO ErrorTCXO Error

Fig. 11. Mean-squared coherence function calculated for bothOCXO and TCXO receiver clock estimate errors.

to remove these variations, allowing it to extend its coher-ent integration time beyond what its unaided local clockvariations would otherwise allow [11]. Because the CDMA-based estimate errors have a coherence time beyond 100seconds, this implies that post-characterized CDMA sig-nals can be used to supply a TCON-receiver with a coher-ent integration time beyond 100 seconds.

To acquire a GNSS signal under reasonable acquisitionstatistics, a receiver must integrate the signal such thatthe signal-to-noise ratio (SNR) of the coherent accumula-tions, known as the pre-detection SNR, or SNRPD, sur-passes an acquisition threshold of approximately 11 dB.The coherent integration time τ is related to SNRPD, thecarrier-to-noise ratio C/N0 of the received GNSS signal,and 〈C2

coh(τ)〉 by the following equation:

SNRPD(τ) = 〈C2coh(τ)〉 · τ · C/N0. (16)

Assuming an achievable coherent integration time of 100seconds (τ = 100), Fig. 11 can be used to approximatea mean-squared coherence lower bound C2

coh(100) ≈ 0.8for both clocks. With these values and an assumed tar-get SNRPD = 11 dB, Eq. (16) can be used to back-calculate a required C/N0 of at least –8 dB-Hz for reliableGNSS signal acquisition. This means that assuming allelse ideal, CDMA-only TCON (post-characterization) willallow GNSS acquisition of signals down to –8 dB-Hz. Ina real-world situation, of course, there are many limita-tions that prevent a receiver from acquiring GNSS signalsthis weak. Nonetheless, this demonstration has shown thatTCON can eliminate a receiver’s local clock variations asone of these limitations.

VI. CONCLUSION

A strategy referred to as tightly-coupled opportunisticnavigation (TCON) has been presented for exploiting thefrequency stability, transmit location, and timing informa-tion of ambient radio-frequency “signals of opportunity.”The strategy involves a collaborative framework for char-acterizing these signals and an optimal technique for fus-ing their observables together. A simple demonstration ofTCON on timing has shown that CDMA cellular signalsthat have been properly characterized by a TCON-enabledreceiver can be exploited by the receiver to estimate andremove the effects of its local clock variations, allowing it toextend its coherent integration time beyond 100 seconds.

ACKNOWLEDGMENTS

This work was generously supported in part by the De-partment of Defense through the National Defense Scienceand Engineering Graduate (NDSEG) Fellowship Program.Thanks also to Kyle Wesson and Andrew Higdon of TheUniversity of Texas at Austin Radionavigation Laboratoryfor their support in collecting the wardriving data.

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