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Radio Interferometric Geolocation

Miklos Maroti

Peter Volgyesi

Sebestyen Dora

Branislav Kusy

Andras Nadas

Akos Ledeczi

Gyorgy Balogh

Karoly Molnar

{miklos.maroti, branislav.kusy, akos.ledeczi}@vanderbilt.edu

ABSTRACTWe present a novel radio interference based sensor local-ization method for wireless sensor networks. The techniquerelies on a pair of nodes emitting radio waves simultaneouslyat slightly different frequencies. The carrier frequency of thecomposite signal is between the two frequencies, but has avery low frequency envelope. Neighboring nodes can mea-sure the energy of the envelope signal as the signal strength.The relative phase offset of this signal measured at two re-ceivers is a function of the distances between the four nodesinvolved and the carrier frequency. By making multiple mea-surements in an at least 8-node network, it is possible toreconstruct the relative location of the nodes in 3D. Ourprototype implementation on the MICA2 platform yieldsan average localization error as small as 3 cm and a range ofup to 160 meters. In addition to this high precision and longrange, the other main advantage of the Radio Interferomet-ric Positioning System (RIPS) is the fact that it does notrequire any sensors other than the radio used for wirelesscommunication.

Categories and Subject DescriptorsC.2.4 [Computer-Communications Networks]: Distrib-uted Systems; C.3 [Special-Purpose and Application-Based Systems]: Real-time and Embedded Systems; J.2[Physical Sciences and Engineering]: Engineering

General TermsAlgorithms, Design, Experimentation, Measurement, The-ory

Department of Mathematics, Vanderbilt University, 1326Stevenson Center, Nashville, TN 37240, USAInstitute for Software Integrated Systems, Vanderbilt Uni-versity, 2015 Terrace Place, Nashville, TN 37203, USA

Permission to make digital or hard copies of all or part of this work forpersonal or classroom use is granted without fee provided that copies arenot made or distributed for profit or commercial advantage and that copiesbear this notice and the full citation on the first page. To copy otherwise, torepublish, to post on servers or to redistribute to lists, requires prior specificpermission and/or a fee.SenSys05,November 24, 2005, San Diego, California, USA.Copyright 2005 ACM 1-59593-054-X/05/0011 ...$5.00.

KeywordsSensor Networks, Localization, Location-Awareness, RadioInterferometry, Ranging

1. INTRODUCTIONMany applications of wireless sensor networks (WSN) re-

quire the knowledge of where the individual nodes are lo-cated [1, 2, 3]. Yet robust sensor localization is still an openproblem today. While there are many approaches in exis-tence, they all have significant weaknesses that limit theirapplicability to real world problems. Techniques based onaccuratetypically acousticranging have limited range [4,5, 6]. They need an actuator/detector pair that adds to thecost and size of the platform. Furthermore, a considerablenumber of applications require stealthy operation makingultrasound the only acoustic option. However, ultrasonicmethods have even more limited range and directionalityconstraints [7, 8]. Methods utilizing the radio usually relyon the received signal strength that is relatively accuratein short ranges with extensive calibration, but imprecise be-yond a few meters [8, 9, 10]. The simplest of methods deducerough location information from the message hop count [11].In effect, they also use the radio signal strength, but theyquantize it to a single bit. Finally, many of the proposedmethods work in 2D only. For a recent summary of local-ization methods and their performance refer to [8].

In summary, existing WSN localization methods todayhave either adequate accuracy or acceptable range, but notboth at the same time. Furthermore, the very physical phe-nomenon they useacoustics and radio signal strengthdonot show any promise of achieving the significant improve-ment that is necessary to move beyond the current stateof the art. Our novel method, on the other hand, uses ra-dio interferometry and attains high accuracy and long rangesimultaneously.

Traditional radio interferometry has many applications inphysics, geodesy and astronomy. The method is based ontwo directional antennas measuring the radio signal from asingle source and performing cross correlation. The resul-tant interference signal can be further analyzed to createradio images of distant celestial objects, determine the rel-ative location of two receivers very precisely, or conversely,determine the location of a radio source when the locationof the two receivers are known. A radio interferometer isan expensive device requiring tunable directional antennas,very high sampling rates and high-precision time synchro-nization. Hence, it is not directly applicable to WSNs.

1

The novel idea behind the proposed Radio InterferometricPositioning System (RIPS) is to utilize two transmitters tocreate the interference signal directly. If the frequencies ofthe two emitters are almost the same then the composite sig-nal will have a low frequency envelope that can be measuredby cheap and simple hardware readily available on a WSNnode. Trying to use this signal to deduce information on thepositions of the two transmitters and the receiver directlywould require tight synchronization of the nodes involvedmandating hardware support. Instead, we use the relativephase offset of the signal at two receivers which is a func-tion of the relative positions of the four nodes involved andthe carrier frequency. By making multiple measurements inan at least 8-node network, it is possible to reconstruct therelative location of the nodes in 3D.

The key attribute of this method is that the phase offsetof a low frequency signal is measured, yet it corresponds tothe wavelength of the high-frequency carrier signal. Hence,we can use low precision techniques that are feasible on thehighly resource constrained WSN nodes, yet we still achievehigh accuracy.

The rest of the paper is organized as follows. In the nextsection we provide the theoretical background behind ra-dio interferometric positioning. The subsequent section an-alyzes the different sources of error affecting the overall ac-curacy. Then we describe our prototype implementation onthe MICA2 platform. It is followed by a discussion of thetechnique used to get a distance metric out of noisy phaseoffset measurements. In the subsequent section we present acentralized localization algorithm that determines the nodelocations from the ranging data. We conclude the paperwith an analysis of the data we gathered at field experi-ments.

D

A

B

C

dAC

dBC

dAD

dBD

)2 mod( 2offset phasecarrier

ACBCBDAD

dddd +=

Figure 1: Radio interferometric ranging technique.

2. INTERFEROMETRIC POSITIONINGRadio interferometric positioning exploits interfering ra-

dio waves emitted from two locations at slightly differentfrequencies to obtain the necessary ranging information forlocalization. The composite radio signal has a low beat fre-quency and its envelope signal can be measured with lowprecision RF chips using the received signal strength indica-tor (RSSI) signal. The phase offset of this signal depends onmany factors, including the time instances when the trans-missions were started. However, the relative phase offsetbetween two receivers depends only on the four distancesbetween the two transmitters and two receivers and on thewavelength of the carrier frequency. By measuring this rel-ative phase offset at different carrier frequencies, one cancalculate a linear combination of the distances between thenodes, and ultimately infer their relative position. First wewill prove these claims and then study the minimum numberof measurements necessary in order to be able to resolve thephase ambiguities and localize the participating nodes.

We model the radio RSSI circuitry in the following way.The RSSI signal is the power of the incoming signal mea-sured in dBm after it is mixed down to an intermediate fre-quency fIF. It is then low pass filtered with cutoff frequencyfcut (fcut fIF). Let r(t) denote this filtered signal.

Theorem 1. Let f2 < f1 be two close carrier frequencieswith = (f1 f2)/2, f2, and 2 < fcut. Furthermore,assume that a node receives the radio signal

s(t) = a1 cos(2f1t + 1) + a2 cos(2f2t + 2) + n(t),

where n(t) is Gaussian noise. Then the filtered RSSI sig-nal r(t) is periodic with fundamental frequency f1 f2 andabsolute phase offset 1 2.

Proof. If the noise is temporarily neglected then themixed down intermediate frequency signal is

sIF(t) = a1 cos2(fIF + )t + 1

+ a2 cos

2(fIF )t + 2

. (1)

To obtain the signal power:

s2IF(t) = a21 cos

2 2(fIF + )t + 1 (2)+ a22 cos

2 2(fIF )t + 2+ 2a1a2 cos

2(fIF + )t + 1

cos

2(fIF )t + 2

.

Using the following trigonometric identities

cos2(x) =1

2+

cos(2x)

2

cos(x) cos(y) =cos(x + y)

2+

cos(x y)2

we obtain

s2IF(t) = (a21 + a

22)/2 (3)

+a212

cos4(fIF + )t + 21

+

a222

cos4(fIF )t + 22

+ a1a2 cos

4fIFt + 1 + 2

+ a1a2 cos

4t + 1 2

where (a21 + a

22)/2 is the DC component.

2

Due to the nonlinear logarithmic distortion applied tos2IF(t), the resulting signal contains several new frequencycomponents. They are the linear combinations of the fre-quency components i 2 + j 2fIF in equation (3), where iand j are non-negative integers.

The low pass filter eliminates all high frequency compo-nents (j > 0). Hence,

r(t) = k logh(a21 + a

22)/2 + n(t)

+ a1a2 cos2(2)t + 1 2

i(4)

where n(t) is band-limited Ga