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, USA†Institute 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.SenSys’05,November 2–4, 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 onaccurate—typically acoustic—ranging 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 use—acoustics and radio signal strength—donot 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 πλ

π 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 δ = (f1 − f2)/2, δ � f2, and 2δ < fcut. Furthermore,assume that a node receives the radio signal

s(t) = a1 cos(2πf1t + ϕ1) + a2 cos(2πf2t + ϕ2) + 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 ϕ1 − ϕ2.

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

sIF(t) = a1 cos�2π(fIF + δ)t + ϕ1

�+ a2 cos

�2π(fIF − δ)t + ϕ2

�. (1)

To obtain the signal power:

s2IF(t) = a2

1 cos2�2π(fIF + δ)t + ϕ1

�(2)

+ a22 cos2

�2π(fIF − δ)t + ϕ2

�+ 2a1a2 cos

�2π(fIF + δ)t + ϕ1

�cos

�2π(fIF − δ)t + ϕ2

�.

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) = (a2

1 + a22)/2 (3)

+a21

2cos

�4π(fIF + δ)t + 2ϕ1

�+

a22

2cos

�4π(fIF − δ)t + 2ϕ2

�+ a1a2 cos

�4πfIFt + ϕ1 + ϕ2

�+ a1a2 cos

�4πδt + ϕ1 − ϕ2

�where (a2

1 + a22)/2 is the DC component.

2

Due to the nonlinear logarithmic distortion applied tos2IF(t), the resulting signal contains several new frequency

components. They are the linear combinations of the fre-quency components i · 2δ + 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(a2

1 + a22)/2 + n(t)

+ a1a2 cos�2π(2δ)t + ϕ1 − ϕ2

�i(4)

where n(t) is band-limited Gaussian white noise and k issome constant. Thus, the fundamental frequency of r(t) is2δ = f1 − f2. As the logarithm does not change the phase,its absolute phase offset is ϕ1−ϕ2. Note that the amplitudeof the harmonics are significantly smaller than that of thefundamental component.

We will use capital roman letters to denote nodes. Thedistance between nodes X and Y will be denoted by dXY .The speed of light is c.

Theorem 2. Assume that two nodes A and B transmitpure sine waves at two close frequencies fA > fB such thatfA − fB < fcut, and two other nodes C and D measure thefiltered RSSI signal. Then the relative phase offset of rC(t)and rD(t) is

2π�dAD − dAC

c/fA+

dBC − dBD

c/fB

�(mod 2π).

Proof. Let X be either A or B, and Y be either C or D.Let tX denote the time when node X starts to transmit, andaXY denote the amplitude of the attenuated signal transmit-ted by X and received by Y . The received composite signalat node Y is

sY (t) = aAY cos�2πfA(t− tA − dAY /c)

�(5)

+ aBY cos�2πfB(t− tB − dBY /c)

�+ n(t)

= aAY cos�2πfAt− 2πfA(tA + dAY /c)

�+ aBY cos

�2πfBt− 2πfB(tB + dBY /c)

�+ n(t)

after sufficient amount of time, that is when t is greater thantA +dAY /c and tB +dBY /c. Using Theorem 1, the absolutephase offset of the envelope signal rY (t) is

ϑY = −2πfA(tA + dAY /c) + 2πfB(tB + dBY /c). (6)

Now consider the two receivers C and D. The relativephase offset between rC(t) and rD(t) is

ϑC − ϑD = −2πfA(tA + dAC/c) + 2πfB(tB + dBC/c) (7)

+ 2πfA(tA + dAD/c)− 2πfB(tB + dBD/c)

= 2πfA/c · (dAD − dAC) + 2πfB/c · (dBC − dBD).

From this the statement of the theorem immediately fol-lows.

For wireless sensor nodes, due to their limited range andhigh carrier frequency relative to their cutoff frequency, theformula of the measured relative phase offset can be sim-plified. This gives the precursor of the definition of rangefollowing the next theorem.

Theorem 3. Assume that two nodes A and B transmitpure sine waves at two close frequencies fA > fB, and twoother nodes C and D measure the filtered RSSI signal. IffA−fB < 2 kHz, and dAC , dAD, dBC , dBD ≤ 1 km, then therelative phase offset of rC(t) and rD(t) is

2πdAD − dBD + dBC − dAC

c/f(mod 2π),

where f = (fA + fB)/2.

Proof. Using δ = (fA − fB)/2 we can rewrite ϑC − ϑD

from the conclusion of Theorem 2 as

ϑC − ϑD = 2πdAD − dAC + dBC − dBD

c/f(8)

+ 2πdAD − dAC − dBC + dBD

c/δ(mod 2π).

According to our assumption δ ≤ 1 kHz, so c/δ ≥ 300 km.Therefore, the second term can be disregarded.

For any four nodes A,B,C and D we define

dABCD = dAD − dBD + dBC − dAC , (9)

and for any frequency f

ϑABCD(f) = 2πdABCD

c/f(mod 2π). (10)

By the previous theorem we can effectively measure ϑABCD(f),which equals dABCD modulo the wave length of the carrierfrequency. By making multiple measurements with differentcarrier frequencies, one can reconstruct the value of dABCD,which is the principal ranging data of RIPS. It is trivial toverify that the following identities hold

dABCD = −dBACD = −dABDC = dCDAB . (11)

Note that in Theorem 3 we explicitly assumed that fA >fB . If the opposite holds, then the frequency of the envelopesignal becomes |fA−fB | and its phase offset 2π−ϑABCD(f).This follows from the fact that dABCD = −dBACD.

Theorem 4. In a network of n nodes there are at most32(n− 2)(n− 3) independent interference measurements that

can be made.

Proof. We fix two nodes X and Y of the network andconsider the following two classes of ranges

(M1) dXUY V , where X, Y, U, V are all different nodes, and

(M2) dXY UV , where X, Y, U, V are all different nodes andU < V in some fixed linear order.

Clearly, there are (n − 2)(n − 3) ranges of the first typeand one half of this number in the second type. This gives32(n−2)(n−3) measurements. We claim that all other ranges

can be calculated from these.Take nodes A, B, C and D. Then it is not hard to verify

that

dXAY C − dXBY C + dXBY D − dXAY D

= (dXC − dAC + dAY − dXY )

− (dXC − dBC + dBY − dXY )

+ (dXD − dBD + dBY − dXY )

− (dXD − dAD + dAY − dXY )

= dAD − dBD + dBC − dAC = dABCD.

(12)

3

This proves that every range can be calculated from rangesof the form dXUY V where U and V are arbitrary nodes.However, not all these are directly measurable, because forexample X cannot be the same node as U or V . The twodegenerate cases are

dXXY U = dXU − dXU + dXY − dXY = 0, and

dXUY Y = dXY − dUY + dUY − dXY = 0. (13)

Therefore, dABCD can be calculated from ranges from class (M1)whenever X 6= C, D and Y 6= A, B.

Using the equation dABCD = dCDAB , we can rewriteequation (12) as

dXCY A − dXCY B + dXDY B − dXDY A = dABCD, (14)

which allows to calculate dABCD whenever X 6= A, B andY 6= C, D. If neither (12) nor (14) can be used to calculatedABCD then it must be the case that {X, Y } = {A, B} or{X, Y } = {C, D}. In these cases, however, dABCD can bedirectly obtained from a measurement in class (M2) usingequations (11).

Note that the previous theorem gives only an upper boundon the number of linearly independent set of measurableranges in an n-node network. Since the submission of ourpaper, Lambert Meertens significantly improved this boundto n(n− 3)/2, and proved that to be sharp [12].

Notice that any solution to the resulting system of equa-tions is invariant under translations, rotations and reflection.Therefore, the number of unknowns is 2n−3 in 2D and 3n−6in 3D. In a 6-node network there are 9 linearly independentmeasurements, using the sharp bound, just enough for the9 unknowns. However, we need at least 8 nodes in 3D toget more measurements (20) than the number of unknowns(18).

3. SOURCES OF ERRORThe goal of this section is to list and briefly discuss the

sources of error of RIPS. In most cases further research isnecessary to properly study these errors.

We will consider two nodes transmitting unmodulated ra-dio waves at two close frequencies and two receivers mea-suring the absolute phase offset of the received signal r(t).We assume that the absolute phase offset is measured at afixed time instant that is established between the receiversusing some form of time synchronization. The relative phaseoffset is then calculated by subtracting the absolute phaseoffsets of the two receivers.

The sources of error are the following:

Carrier frequency inaccuracy—the difference between thenominal and the actual carrier frequency of the transmittedsignal. According to Theorem 3, the phase measurementerror introduced by an average 1 kHz carrier frequency in-accuracy for ranges dABCD less than 1 km is����2π

dABCD

c/f− 2π

dABCD

c/(f + 1000)

���� ≤ 2π · 1 km

c/1 kHz= 0.33% · 2π,

independently of the value of f .

Carrier frequency drift and phase noise—the phase noiseand drift of the actual carrier frequency of the transmittedsignal during the measurement. Theorem 1 relies on thefact that the frequencies of the emitted signals are stable.Any phase noise or carrier frequency drift will be directly

observable in the measured phase offset of the envelope sig-nal. This source of error can be minimized by shorteningthe length of a single phase measurement, and by minimiz-ing the chance of mechanical, electrical and other kinds ofshocks the RF chip is subjected to. In our implementationone measurement lasts for 29 ms so frequency drift is likelynegligible. Phase noise, on the other hand, may have a sig-nificant effect on phase measurement accuracy.

Multipath effects—the RF signal takes different paths whenpropagating from a transmitter to a receiver, causing am-plitude and phase fluctuations in the received signal. InTheorem 3 we assumed that the radio signal travels from Ato C for exactly dAC/c seconds, but this assumption doesnot hold in the presence of multipath fading. We expect thatin many cases higher level algorithms can filter out incon-sistent phase offset measurements corrupted by multipatheffects.

Antenna orientation—the change of the time of flight fromthe transmitter to the receiver introduced by the differentorientation or shape of the antennas used. Regardless of theorientation of antennas, the received radio signal componentin Equation (5) originating from A and received by C isalways

aAC cos�2πfA(t− tA − dAC/c)

�.

The frequency fA and transmission time tA are constants,and by Theorem 1 the amplitude aAC of the signal does notinfluence the phase offset of the signal strength. It is theo-retically possible that the time of flight component dAC/c isinfluenced by the orientation, but this was not empiricallyverified.

RSSI measurement delay jitter—the jitter of the delay be-tween the antenna receiving the radio signal and the RFchip delivering the RSSI signal to the signal processing unit.This jitter introduce a relative phase offset error at the tworeceivers. According to our experiments, the jitter is notnoticeable.

RSSI Signal-to-Noise Ratio—the signal strength relativeto noise of the rC(t) signal. The SNR mainly depends onthe physical distance between transmitters and receiver, asthe amplitudes of the transmitted signals are exponentiallydecreasing in space. The SNR value also depends stronglyon the hardware implementation of the RSSI detector circuitat the receiver.

Signal processing error—the error introduced by the sig-nal processing algorithm that calculates the phase offset ofrC(t). This is a noisy, logarithmically distorted, low fre-quency sinusoid, that can be approximated by a sine wavewith additive noise. The frequency and phase estimationof sine waves is a well-studied problem (see e.g. [13, 14]).The theoretical Cramer-Rao bound can be approximated byvarious signal processing algorithms for a given SNR.

Time synchronization error—the time synchronization er-ror of the time instance when the receivers measure theirabsolute phase offset of the received signal strength. Onrepresentative hardware it is possible to establish a timesynchronization point with better than 2 µs precision uti-lizing a single radio message (see [15]). Assuming a 2 kHzinterference frequency, this translates to %0.4 ·2π phase off-set error.

4

4. IMPLEMENTATIONWe have used the MICA2 mote platform with the TinyOS

operating system [16, 17] for our prototype implementation.As stated in Section 2, the primary objective is to havetwo nodes transmit sinusoid waves at close frequencies toproduce the interference signal and at least two receivers tocalculate the phase offset difference of the observed signals.It is necessary to measure phase offset differences at multiplefrequencies to be able to calculate the range. Specifically,our prototype RIPS implementation consists of the followingsteps:

(1) selecting a pair of transmitters from a group of motesparticipating in the localization and scheduling theirtransmission times,

(2) fine-grain calibration of the radios of senders to trans-mit at close frequencies,

(3) transmission of a pure sine wave by the two senders atmultiple frequencies,

(4) analysis of the RSSI samples of the interference signalat each of the receivers to estimate the frequency andphase offset of the signal,

(5) calculation of the actual dABCD range from the mea-sured relative phase offsets for each pair of receivers,and

(6) the localization algorithm.

Currently, the selection and scheduling of the transmittingpairs, part of the frequency calibration process, the calcula-tion of the dABCD range from multiple phase offset readingsand the localization itself are running on the base station.The software components running on the motes include acustom driver for the Chipcon CC1000 radio that allowspure sine wave transmission at a particular frequency, a ra-dio engine component that coordinates and synchronizes theparticipating nodes and handles the transmission and recep-tion of the interference signal, and a signal processing com-ponent that estimates the frequency and phase offset of thesampled RSSI signal.

4.1 CC1000 characteristicsOur sensor nodes are equipped with the Chipcon CC1000

radio chip configured to transmit in the 433 MHz frequencyband. The following features provided by the radio chipwere essential to the implementation of our interferometricalgorithm:

(1) capability to transmit an unmodulated sine wave ina reasonably wide frequency band (between 400 MHzand 460 MHz), as well as the ability to tune the fre-quency of the transmitter in fine-grain steps (65 Hz),

(2) short-term stability of the frequency of the unmodu-lated sine wave (for less than 29 ms time period),

(3) relatively precise capture of RSSI with only a smalldelay jitter, and

(4) capability to transmit at different power levels.

The relatively wide frequency band is necessary for calcu-lating the actual range from the phase offset differences (seeSection 5). The fine-grained frequency tuning is needed toachieve the separation of the two transmitters as required byTheorem 3 in Section 2. We require the short-term stabil-ity of the carrier frequency because the frequency and phaseoffset analysis at the receivers uses averaging over multi-ple periods to increase the SNR. The timing precision ofthe measured RSSI signal is also critical because the RSSImeasurement delay affects the relative phase offset error asdiscussed in Section 3. Finally, transmission at differentpower levels is required since the distance of the two trans-mitters from a receiver can vary up to the point where thecloser transmitter completely overwhelms the signal fromthe more distant one.

Even though the radio chip is highly configurable withmany favorable properties, it has certain limitations thatwe had to overcome:

(1) the time required to calibrate the radio chip has a largejitter of up to 5 ms,

(2) the frequency synthesizer is not accurate enough, wehave seen carrier frequency deviations that dependedon the temperature and voltage levels,

We cope with the radio timing fluctuations by using atime synchronization scheme, which is external to the radiochip (Section 4.2). It is also important to overcome the car-rier frequency inaccuracy because the interference frequencyneeds to fall within a small range. We implemented an al-gorithm (Section 4.3) that determines the radio parametersfor the transmitters corresponding to a frequency separationof close to 0 Hz. We run the this algorithm frequently (i.e.,once for each transmitter pair) to overcome the dependencyof the generated frequency on the current temperature andvoltage.

4.2 Time synchronizationIn order to measure the relative phase offset of the RSSI

signals between different receivers, the nodes need to syn-chronize and measure the absolute phase offsets relative toa common time instant. After collecting the absolute phaseoffsets from the receivers, the relative phase offsets can becalculated by subtracting them from each other. In this sec-tion we discuss the necessary synchronization strategy. Wedo not use network-wide time synchronization. Instead, wesynchronize the nodes participating in the current ranginground only and only for the duration of a single measure-ment.

Before a node can transmit or receive a radio signal ata particular frequency, it needs to acquire the radio chipfrom the standard MAC layer and calibrate it to that fre-quency. Once the chip is acquired, no further inter-nodecommunication is possible, so the participating nodes haveto follow a predefined schedule starting from a precise timeinstant to stay synchronized. This scheduling is challengingbecause the time required to perform most operations withthe radio, such as acquire and calibrate, have a significantvariance. The crucial operation is the sampling of the RSSIsignal that needs to be aligned with a couple of microsecondsprecision across the receivers.

The timing uncertainties in the radio chip are mitigatedby imposing an external synchronization protocol depicted

5

Sender1

Receiver

Time

Sender2

send sync msg

TS1

TS2

TR

Timers fire

receive sync msg

receive sync msg

TS1+t1

TS2+t1

TR+t1

acquire()

acquire()

acquire()

Timers fire

TS1+t2

TS2+t2

TR+t2

calibrate()

calibrate()

calibrate()

Timers fire

TS1+t3

TS2+t3

TR+t3

transmit()

receive()

transmit()

Figure 2: The synchronization schedule that alignsthe start of the transmission and reception at mul-tiple nodes.

in Figure 2. In this protocol, the master node initiates themeasurement by broadcasting a radio message, which identi-fies the other sender node, the type of measurement (tuningor ranging) and the transmit powers. The message also spec-ifies a time instant in the future—in the local time of themaster—when the measurement must be started. Finally,the radio stack attaches a precise timestamp to the packet,when it is sent from the mote. Each receiver converts thesynchronization point to its local time by using the arrivaltimestamp of this message. The converted value is usedto set up a local timer and is re-broadcasted. This simpleprotocol enabled us to extend interferometric measurementsbeyond the data communication range. It was shown in [15]that it is possible to set up synchronization points this waywith microsecond accuracy on the MICA2 platform. Westart calibration and signal transmission/reception at fixedtimes after the synchronization point. The combined errorof synchronization and clock skew over a time period of lessthan 1 second is still just a few microseconds.

The external synchronization ensures that the receiversand transmitters send the receive and send commands to theradio chip at the same time. This does not necessarily meanthat the receivers start receiving data from the ADC at thesame time. To compensate for this, each receiver recordsthe times when the RSSI samples arrived and adjusts themeasured absolute phase accordingly.

4.3 TuningThe CC1000 radio chip needs to perform internal calibra-

tion of the frequency synthesizer PLL to adjust it to thefrequency and compensate for supply voltage and temper-ature variations. The self-calibration is a time consumingprocess that takes up to 34 ms according to the Chipcondatasheet [18]. Moreover, since the PLL can generate onlya limited scale of frequencies, it is advised to recalibrateit for frequencies more than 1 MHz apart. We found ituseful to index the available frequency band (400 MHz to460 MHz) by frequency channels, so that transmitting on adifferent channel mandates recalibration. We define chan-nel 0 to be at 430.1 MHz and the channel separation to beapproximately 0.526 MHz.

A key benefit of CC1000 chip is that the PLL can gener-ate different frequencies at a very fine frequency resolution(65 Hz) once calibrated to a particular channel. We indexthese fine-grained frequencies with frequency tuning and re-quire no recalibration when changing the tuning parameter.The nominal frequency f can be then obtained from the

channel and tuning parameters the following way:

f = 430.1 + 0.526 · channel + 65 · 10−6 · tuning.

One of the limitations of the chip is that the actual fre-quency for a specific channel can differ from the nominalvalue by up to 2 kHz. Since the frequency range where wecan measure the interference accurately is limited by thetime constraint for a measurement (29 ms) as well as thelimited sampling rate of the RSSI signal on MICA2 plat-form (9 kHz), we need to ensure that the difference betweenthe transmission frequencies is in the range of 200 Hz to800 Hz.

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

-3.9

0-3

.58

-3.2

5-2

.93

-2.6

0-2

.28

-1.9

5-1

.63

-1.3

0-0

.98

-0.6

5-0

.33

0.00

0.33

0.65

0.98

1.30

1.63

1.95

2.28

2.60

2.93

3.25

3.58

3.90

Radio tuning parameter (kHz)

Inte

rfer

ence

freq

(kH

z)

.

ideal tuning parameter

interference has too high frequency

Figure 3: A receiving node observes the frequency ofinterference of two transmitters. The first transmit-ter changes the carrier frequency in 325 Hz steps.

We implemented a frequency tuning algorithm that deter-mines the radio settings for the transmitters correspondingto the same frequency. Let the transmitters be set to thesame channel and f1, f2 be the actual signal frequencies.We found the maximum carrier frequency error to be lessthan 2 kHz, so we can assume that |f1 − f2| < 2 · 2 kHz =4 kHz. The first transmitter emits a sine wave at frequen-cies f1(i) = f1 + i · 325 Hz, i = −15,−14, . . . , 15 usingthe tuning capability of the radio chip, while the secondtransmitter keeps transmitting at frequency f2. A receivernode analyzes the frequency of the interference signal whichis |f1(i) − f2| (see Figure 3). Using the known step size(325 Hz), the receiver can filter out the noise and faulty fre-quency measurements and determine the value of i for whichthe interference frequency is close to 0. The receiver prop-agates this information back to the first transmitter whoconsequently determines the settings for the radio chip suchthat the interference frequency is in the required range.

It should be noted that the frequency error for two nodesdoes not stay constant for different channels. Observing itat two channels 50 MHz apart, we have seen up to 300 Hzchange. However, as the frequency error is mainly caused bythe imprecision of the crystal that drives the radio chip, it isapproximately linear in frequency. Therefore, we can mea-sure the correct tuning parameter for two different channelsand interpolate these values to obtain the radio parametersfor the other channels.

4.4 Frequency and phase estimationDue to the limited communication bandwidth the sam-

pled RSSI values need to be processed on the motes. Thesignal processing algorithm estimates the frequency and thephase of the RSSI signal and transmits these and a qualityindicator of the measurement to the base station. The al-gorithm is divided to online and post-processing parts. The

6

online part is executed upon each A/D converter interruptfor 256 consecutive samples. Afterwards, more extensivepost-processing is performed on the data computed in theonline phase.

Hardware limitations on the mote make computationallyexpensive signal processing techniques prohibitive. The ADCsampling rate (9 kHz) and the clock frequency of the 8 bitmicrocontroller (7.4 MHz), allows roughly 820 CPU cyclesper sample for online processing. Post processing is lim-ited by a somewhat less strict deadline: several measure-ments are made between time synchronization points, leav-ing around 10,000 cycles per measurement for post-process-ing. The lack of floating point hardware support and mem-ory space limitations further restrict the domain of feasiblealgorithms. The use of standard, but computationally ex-pensive solutions, such as Fourier analysis or autocorrela-tion, is not feasible.

Figure 4 shows a representative RSSI signal recorded bya mote. Peak detection is performed on-line in the ADC in-terrupt routine eliminating the need for large sample buffersand shortening the post-processing time. First, the raw sam-ples are filtered by a moving average component in order toenhance the SNR. Next the minimum and maximum signalvalues—essential parameters to our adaptive peak detectionalgorithm—are acquired from the leading 24 samples. Thisfirst part of the data series is long enough to contain at leastone full period. The acquired amplitude value serves as aquality indicator of the measurement. Later on, samplesabove (below) a threshold currently set at 20% of the am-plitude from the maximum (minimum) value are identifiedas high (low) amplitudes in the filtered signal. Peaks are de-fined as center points of two consecutive high level thresholdcrossings (non-high → high, followed by a high → non-highstep). Peaks are discarded in this phase if the signal has notcrossed the low threshold since the last peak, minimizingthe risk of false positive detections.

0 0.005 0.01 0.015 0.02 0.025 0.03120

140

160

180

200

220

240

260

Time (s)

Am

plitu

de

RSSI raw signalFiltered signalMinimumMaximumLow thresholdHigh thresholdFalse peaksFiltered peaks

Figure 4: Peak detection and filtering.

The post-processing phase works exclusively on peak in-dexes, identified and stored by the online algorithm. Afterit determines the shortest period between subsequent peaks,it accumulates the sum of the periods that are not longerthan 130% of the shortest one (to compensate for the veryrare false positive detections in the first phase). Peaks onboth ends of an outlier period are marked as false peaks anddiscarded. This simple and draconian rule might throw out

good peaks, a small price to pay for rejecting false peaks,which could significantly impair the phase calculation. Fre-quency is calculated as the reciprocate of the average periodlength.

The phase of the RSSI signal is estimated by the av-erage phase of the filtered peaks. Since small errors inthe frequency estimation can result in a significant errorin the phase calculation, we compute the phases relative tothe center of the sample buffer, thereby reducing the ac-cumulated phase error due to an inaccurate frequency es-timate [13]. The algorithm also employs a basic phase un-wrapping method to average values near 0 and 2π properly.

Since floating point calculations are prohibitive on themote, hand optimized fixed point arithmetic is used through-out the frequency and phase computations. The estimatedfrequency, phase and amplitude tuple is finally sent back tothe base station.

4.5 SchedulingThere are two levels of scheduling involved in the inter-

ference measurement process:

A) High level scheduling is responsible for selecting thepair of transmitters and should minimize the numberof interference measurements while producing enoughindependent measurements to localize nodes uniquelyin 3-dimensions. As given at the end of Section 2, fora group of n nodes that form a single hop network, wehave at most n(n − 3)/2 choices for the independentinterference measurements. The number of unknownsis 3n−6 in 3-dimensional localization, so for groups ofnodes larger than 8 we get an over-determined systemof equations. In our current implementation, the basestation selects all possible pairs of transmitters whileall other nodes within their range act as receivers.

B) Low level scheduling coordinates the activities of thetwo transmitters and multiple receivers. The frequencytuning algorithm and the phase offset estimation proc-ess described earlier in this section both involve mul-tiple steps that require proper frequency calibrationand timing. Currently, 13 different frequency chan-nels 5 MHz apart are used between 400 and 460 MHz.Furthermore, the scheduler executes the phase offsetmeasurement with the same pair of transmitters, butdifferent radio power settings to compensate for theeffect of one transmitter being much closer to a re-ceiver than the other. Currently, three combinationsare used: full power/full power or the two combina-tions of full power/half power.

5. RANGE CALCULATIONFrom a set of phase measurements for the frequencies

f1, . . . , fk the following Diophantine equations can be for-mulated

dABCD = λini + γi = λjnj + γj , (15)

where λi = c/fi is the wave length, γi = λiϑi2π

is the phaseoffset relative to the wave length, ϑi is the measured phaseoffset, and ni is an integer. We need a set of λi’s so that theirleast common multiple is larger than the possible domain ofdABCD. In case of the 433 MHz band, having 5 MHz sepa-ration means that three different measurements are enough

7

assuming perfect phase estimation. The concept is illus-trated in Figure 5.

dABCDλi

2pi

solution

Figure 5: Calculating the range from phase offsets.

Unfortunately, the phase measurements are noisy, so theDiophantine equations become invalid. They can be refor-mulated into inequalities

|(λini + γi)− (λjnj + γj)| < ε, (16)

where ε is a fraction of the wavelength determined by thephase measurement accuracy. This inequality set can besolved and the dABCD solution defined as the mean of theindividual di = λini + γi values. However, there may bemultiple solutions resulting in more than one dABCD val-ues differing by small integer multiples of the wavelengthapproximately.

An error function can be defined as

error =qX

(dABCD − di)2. (17)

The solution with the minimum error value becomes the finaldABCD estimate. The more number of different frequenciesare used the better the estimate is. Instead of the necessarythree, we currently use around 10 different frequencies.

6. LOCALIZATIONSince the RIPS ranging method does not provide range

estimates between a pair of nodes directly, but a combi-nation of distances among four nodes, none of the existinglocalization methods is directly applicable. Solving the largenumber of nonlinear equations would be somewhat cumber-some and not scale well. Instead, as a first cut at the local-ization problem, we decided to use an optimization methodbased on genetic algorithms (GA). GA follows the idea ofDarwinian evolution and widely used as a general functionoptimization method. Our current approach is not meant asa comprehensive solution yet. In the limited time we had,our goal was to evaluate the ranging method in the con-text of overall localization accuracy and provide a baselinelocalization method.

Given a set of nodes with unknown locations and a set Mof dABCD ranges, our goal is to find the relative positionsof the nodes. An error function is defined over the nodelocations and a GA is used to find the node locations withthe smallest error. Here is the brief description of the appliedgenetic algorithm:

(1) Generate an initial population of populationSize ran-dom solutions.

(2) Select subpopulationSize solutions randomly from thepopulation.

(3) Evaluate each solution in the selected subset using theerror function.

(4) Sort the subset according to error.

(5) Remove the worst 20% of the individuals in the sub-set, then generate new individuals by selecting randomparents from the best 20% and applying genetic oper-ators on the parents.

(6) Go to step (2).

A solution here is a placement of nodes. The error of asolution s is defined as

error(s) =1

n

s XABCD∈M

(dABCD − dABCD(s))2, (18)

where dABCD is the measured range and dABCD(s) is thecalculated range in the solution s.

A node placement is represented directly by a vector of(x, y, z) coordinates of the nodes. The following genetic op-erators are used to create new solutions:

(1) Crossing over: each node position is inherited from oneof the two parents with even chance.

(2) Mutations (all cases have equal chance)

(a) Move one node by a Gaussian random numberwith a small ε variance.

(b) Move one node to a random position.

(c) Move all nodes by the same Gaussian randomnumber with a small ε variance.

The value of ε is set to the current value of the errorfunction. It makes it possible for the nodes to do bigger“jumps” if the error is larger. When the error gets small thenodes can fine tune their positions this way.

This algorithm uses all the given ranges and tries to mini-mize the difference between the input range and the range inthe solution. However, the input data has range estimateswith relatively large errors corresponding to integer multi-ples of the wavelength distorting the solution. We extendedthe genetic representation of the solution to include the setof used measurements and let the GA optimize this set aswell. This way the GA searches for the node positions and aset of good measurements simultaneously, making it possi-ble to eliminate all or most of the bad measurements. In ourexperiments this enhanced GA was able to reach the sameaccuracy as the one running on a data set where all rangeswith large errors were removed manually.

7. EVALUATION

7.1 Effective rangeDetermining the effective range of the radio interferomet-

ric ranging technique is not as straightforward as it is withmethods relying on direct pairwise ranging. There are fournodes involved here and not only are there constraints ontheir pairwise distances, but also restrictions on the geome-try of their arrangement. The maximum distance betweena transmitter and a receiver is clearly related to the ra-dio range. We have observed nice interference signals evenwhen the receiver was far beyond the communication rangeof the transmitters at 160 meters using somewhat elevatedmotes. In the same setup the communication range was only

8

80 meters. That means that the interferometric techniquecan have twice the range as the digital communication im-plemented on the MICA2 mote using the same radio. In theremaining discussion we’ll call this distance the interfero-metric radio range.

So far we have only talked about the maximum distancebetween a transmitter and a receiver. There is no directconstraint on the distance between the two transmitters orthe distance between the two receivers. However, by im-plication, they need to be within twice the interferometricradio range. Another important consideration is the ratio ofthe distances from a single receiver to the two transmitters.The received signal strength of one of the signals cannotbe much larger than the other to generate a good qualityinterference signal. Tuning the transmitter output powercan compensate for this, however. Note that this does notconstrain the range of the given geometric arrangement oftwo transmitters and a receiver, since the given transmitterhas to be close to the receiver if its signal can overwhelm theother signal. On the other hand, the same amplitude tuningneeds to work for two receivers at the same time. Therefore,the second receiver needs to be in an area where the interfer-ence signal quality using the given amplitude tuning is stillgood enough. Furthermore, obstructions, multipath effectsand other environmental conditions will adversely affect theeffective range.

RIPS works with dABCD range measures and not pairwisedistances. What are the possible values dABCD can take?Since all four terms in the equation are between 0 and themaximum interferometric radio range (r), it is easy to seethat

− 2r ≤ dABCD ≤ 2r. (19)

7.2 Experimental setupDue to the difficulties involved in establishing the ground

truth very accurately, so far we have only experimented withsmaller scale setups. The data we analyze in the followingsections were gathered using 16 nodes in a 4x4 grid deployedin a flat grassy area with no obstructions. The overall areacovered was 18x18 meters. In order to localize nodes in 2Dwe selected 3 anchor points. They were picked randomlywhile making sure that they did not fall in a line.

The grid was selected because of the relative ease of set-ting up the positions precisely. While measuring the edgeswith a tape measure can be done well enough, keeping allthe angles right is harder. We estimate that the accuracyof node placement is within 5cm. Note that we do not usethe fact that the nodes are arranged in a grid at any pointin our positioning method.

7.3 Frequency and phase accuracyThe performance of our frequency and phase detection

algorithm is comparable to a high resolution (1 Hz) DFT-based approach. The justification of DFT-based tone para-meter estimation and its relationship to the maximum like-lihood estimator can be found in [13].

Figure 6 shows frequency and relative phase offset resultsof frequency tuning observed on a pair of motes (one of thesenders changed its carrier frequency in small increments).The number of RSSI samples (measurement interval) limitsboth approaches at low frequencies. In the “normal oper-ating range,” however, the mote implementation performssurprisingly well. On the frequency diagram both methods

0 5 10 15 20 25 30 35 40 450

200

400

600

800

1000

Freq

uenc

y (H

z)

CC1000 tuning parameter

0 5 10 15 20 25 30 35 40 450

1

2

3

4

5

6

C-D

pha

se d

iffer

ence

(rad

)

CC1000 tuning parameter

FFTMote

FFTMote

Figure 6: Comparison of frequency and phase re-sults and high resolution DFT estimation at differ-ent interference frequencies.

closely reveal the ideal “v-shaped” curve. Phase differencemeasurements have significantly more noise (the ideal re-sponse would be a constant value flipped at 0 Hz), as weexpected in Section 4.4.

The average error of relative phase offset measurement isillustrated in Figure 7. In the experimental setup we fixedone pair of motes as transmitters and performed frequencytuning around 0 Hz interference. We repeated the sameexperiment 30 times. For all

�142

�pairs we calculated the

median phase and the average deviation at each frequency.Next, we calculated the average value of these deviations.By using the amplitude value as a quality indicator of mea-surements, the average error can be drastically reduced.

-1500 -1000 -500 0 500 1000 15000

0.2

0.4

0.6

0.8

1

1.2

Interference frequency (Hz)

Mea

n er

ror (

rad)

All measurementsAmplitude > 5Amplitude > 20

Figure 7: Mean deviation of phase measurementsusing different filtering thresholds.

7.4 Ranging accuracyThe error distribution of the calculated dABCD ranges can

be approximated by the superposition of a set of Gaussiandistributions with centers at integer multiples of the wave-length of the carrier frequency. Depending on the experi-mental setup, about half of the range estimates have lessthan one quarter wavelength error with the remaining val-ues shifted by one or two wavelengths as shown in Figure 8.The ratio of the good and shifted values can be significantlyimproved using simple filtering techniques while keeping thenumber of range estimates high enough to enable accuratelocalization of the nodes.

9

The algorithm measuring the interference signal frequencyand phase also determines the average amplitude of the sig-nal. The amplitude shows strong correlation with the errorof the range estimate. Currently, we use a constant am-plitude threshold (12% of maximum A/D range) to discardmeasurements with low SNR. This filtering can be carriedout locally on each mote acting as receiver, but currently itis done on the base station.

The interference signal is measured by all the nodes inradio range. Due to measurement errors, the frequency es-timates will vary at different motes. Nodes that measurethe frequency with a large error will likely have a bad phaseestimate also. Therefore, these measurements need to be fil-tered out as well. The filtering is carried out by identifyinga narrow frequency window that has the maximum numberof frequency estimates in it. All the measurements outsideof this window are discarded. This process can also be car-ried out on the motes, but it would require communicationamong the active receivers. Currently it is done on the basestation.

Finally, we calculate the range for a given pair of trans-mitter receiver pairs only if the number of frequency chan-nels with good phase offset measurements is higher than athreshold. Currently this limit is set to 10.

After these three filtering stages, the ratio of the measure-ments with less then one quarter wavelength error can beimproved by approximately 50% as illustrated on Figure 9.

0

500

1000

1500

2000

2500

3000

3500

-2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

error (m)

nu

mb

er o

f ra

ng

e m

easu

rem

ents

Figure 8: Error distribution of all the ranges.

0

100

200

300

400

500

600

700

-2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

error (m)

nu

mb

er o

f ra

ng

e m

easu

rem

ents

Figure 9: Error distribution of the filtered ranges.

Figure 10 shows the central portion of the error distribu-tion after filtering. The accuracy of these over 2000 measure-ments clearly demonstrates the potentially extreme high-

0

100

200

300

400

500

600

700

-0.20

-0.16

-0.12

-0.08

-0.04

0.00

0.04

0.08

0.12

0.16

0.20

error (m)

nu

mb

er o

f ra

ng

e m

easu

rem

ents

Figure 10: Central portion of the error distributionof the filtered ranges.

precision of overall localization using RIPS if one can elimi-nate the “side lobes” of the distribution. We can either de-velop more advanced filtering methods to discard measure-ments with full wavelength errors, increase the accuracy ofthe phase measurements, or increase the frequency band be-yond the [400, 460] MHz range. Even a small improvementin phase estimation accuracy could potentially dramaticallyincrease the ratio of good to bad measurements. Intuitivelythere is a threshold in the phase measurement error whereit is not large enough to cause the range estimator to missby a full wavelength. An analytical evaluation is needed toquantify this relationship.

7.5 Localization accuracyWe ran a localization experiment using the setup described

above utilizing the filtered ranging data shown in Figure 9.The genetic optimization procedure ran for 2 minutes. Theerror distribution of the resulting localization is shown inFigure 11. The average accuracy was 3 cm, while the largesterror was approximately 6 cm. The results are shown in Fig-ure 12 with the three anchor nodes depicted by large circles.At this resolution and localization accuracy the small circlesshowing the actual and estimated positions overlap.

0

1

2

3

4

5

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

error (m)

num

ber

of

no

des

0.1

Figure 11: Error distribution of localization.

To test the scalability of the approach we reran the lo-calization utilizing only 20% of the raw ranging data. Weselected 48 transmitter pairs out of the possible

�162

�= 240

randomly. After filtering, approximately 1000 measurementsremained with 28% of them shifted by integer multiples of

10

the wavelengths. This ratio is about the same as for thewhole data set. The localization algorithm achieved 5 cm av-erage accuracy, while the worst error remained under 10 cm.

Figure 12: Localization results.

Note that the estimated accuracy of the ground truthand the accuracy of the localization results are compara-ble. Therefore, these numbers are not exact; they are justindications of the very high precision RIPS can achieve.

7.6 LatencyThere are

�162

��142

�different configurations of transmit-

ter/receiver pairs in the 16-node experiment described above.We use three different amplitude combinations for any givenfour-node setup. Therefore, there are altogether approxi-mately 32,000 measurements carried out. Note that not allof these measurements are independent but we wanted togather as much ranging data as possible. There is quite abit of concurrency, as for any particular transmitter pair,all receivers perform their measurements in parallel. On theother hand, each transmitter pair needs to do multiple mea-surements for frequency tuning and then multiple frequencychannels are used for the actual measurements. The tuningalgorithm, range calculations and localization are carriedout on the base station, so there is a large amount of datathat is shipped to the root of the network.

Currently, the entire process takes about 80 minutes. Thiscan be sped up significantly. Localization does not needthis amount of data; potentially an order of magnitude lesswould work well enough. If we use only one fifth of the pos-sible transmitter pairs—to be conservative—that would im-mediately decrease the time to below twenty minutes. Fur-thermore, the tuning algorithm can be implemented on themotes. It needs to run on one of the receivers of an interfer-ence signal. The results then need to be communicated backto the transmitters. This would help scalability in larger se-tups since the base station need not be involved in tuningat all and hence, message routes would be much shorter. Asmentioned earlier, data filtering based on the interferencesignal amplitude can be done locally on the mote. Addi-tional filtering requires communication between the differentreceivers of the same interference signal. In a small setup,it would not provide any speedup. For a large deployment,however, this would significantly increase the scalability.

Additional optimization could involve decreasing the num-ber of frequency tuning steps to the minimum necessary.

The number of channels used for the actual phase measure-ments could also be decreased somewhat if the phase esti-mation accuracy can be improved. Finally, the mote imple-mentation code is not fully optimized in this first version ofRIPS. We estimate that the entire localization process couldbe carried out in under 5 minutes for smaller scale setups.Large setups would require more time, but the process scaleswell because the network can be automatically divided intosets of non-overlapping regions determined by the radio in-terferometric range where the procedure can be carried outconcurrently. The design of an efficient scheduling algorithmis an area of further research.

8. CONCLUSIONS AND FUTURE WORKThe Radio Interferometric Position System (RIPS) repre-

sents a significant advance in node localization in WSNs. Itachieves high accuracy and long range simultaneously, sup-ports 3D localization and does not require extra hardwareor calibration. The key enabling ideas behind this perfor-mance are the application of two transmitters to create aninterference signal, the measurements of the relative phaseoffset at two receivers cancelling out many sources of error,and the fact that we measure the phase of a low-frequencysignal, yet it relates to the wavelength of the high-frequencycarrier signal.

Our prototype implementation was enabled by the highlyconfigurable Chipcon CC1000 radio. Hence, it is availableon the MICA2 and XSM platforms, but not on MICAZ-sor Telos-es. In the future we foresee the implementationof the ranging technique in hardware: the radio frequencyshould be tunable and the radio chip needs to support fre-quency and phase measurements natively. This would sim-plify the localization service, speed up the operation andprovide higher accuracy.

Our current work involves the evaluation of the techniqueindoors. We are researching how RF multipath effects dis-tort the measurements. Efficient scheduling of the individ-ual measurements in order to minimize localization time ina large scale WSN deployment is another area of study. Fi-nally, we plan to verify the performance of RIPS in a largescale 3D field experiment in the near future.

9. ACKNOWLEDGMENTThe authors would like to thank Janos Sallai, Manish

Kushwaha, Martin Haenggi, Vijay Raghavan, Janos Szti-panovits and Lambert Meertens for their valuable contribu-tion to this work. We also thank our shepherd, AndreasSavvides for his guidance and the anonymous reviewers fortheir constructive criticism.

The DARPA/IXO NEST program (F33615-01-C-1903) hassupported the research described in this paper.

10. REFERENCES[1] Gy. Simon, M. Maroti, A. Ledeczi et al., Sensor

network-based countersniper system, in Proc. of ACM2nd Conference on Embedded Networked SensorSystems (SenSys), November 2004, 1–12.

[2] T. He, S. Krishnamurthy, J. Stankovic, et al. AnEnergy-Efficient Surveillance System Using WirelessSensor Networks, in Proc. of MobiSys’04, June 2004.

11

[3] H. Wang, J. Elson, L. Girod, D. Estrin, K. Yao, Targetclassification and localization in a habitat monitoringapplication, In Proc. of the IEEE ICASSP, April 2003.

[4] Y. Kwon, K. Mechitov, S. Sundresh, W. Kim andG. Agha, Resilient localization for sensor networks inoutdoor environments, Technical ReportUIUCDCS-R-2004-2449, Department of ComputerScience, University of Illinois at Urbana Champaign,2004.

[5] K. Whitehouse and D. Culler, Calibration asparameter estimation in sensor networks, In Proc. ofthe ACM international workshop on wireless sensornetworks and applications, Atlanta, GA, 2002.

[6] J. Sallai, Gy. Balogh, M. Maroti, A. Ledeczi andB. Kusy, Acoustic ranging in resource-constrainedsensor networks, in Proc. of International Conferenceon Wireless and Mobile Computing (ICWN), June2004.

[7] N.B. Priyantha, A. Chakraborty and H. Balakrishnan,The Cricket Location-Support System, In Proc. ofMobiCom 2000: The Sixth Annual InternationalConference on Mobile Computing and Networking,Boston, MA, August 2000.

[8] K. Whitehouse, C. Karlof, A. Woo, F. Jiang andD. Culler, The Effects of Ranging Noise on MultihopLocalization: An Empirical Study, in Proc. of IPSN,Los Angeles, CA, April, 2005.

[9] J. Hightower, R. Want and G. Borriello, SpotON: AnIndoor 3D Location Sensing Technology Based on RFSignal Strength, University of Washingtion, Tech. Rep.UW CSE 2000-02-02, Feb 2000.

[10] K. Yedavalli, B. Krishnamachari, S. Ravula andB. Srinivasan: Ecolocation: A Technique for RF BasedLocalization in Wireless Sensor Networks, in Proc. ofIPSN, Los Angeles, CA, April, 2005.

[11] D. Niculescu and B. Nath, Ad Hoc Positioning System(APS), in Proc. of IEEE GLOBECOM 2001, SanAntonio, Nov 2001.

[12] L. Meertens, The Dimension of the Vector SpaceSpanned by Sets of Radio-InterferometricMeasurements, Technical Report KES.U.05.02, KestrelInstitute, July 2005.

[13] D. Rife, R. Boorstyn, Single tone parameterestimation from discrete-time observations, IEEETransactions on Information Theory, Volume 20, Issue5, pp. 591–598, September 1974.

[14] S.A. Tretter, Estimating the Frequency of a NoisySinusoid by Linear Regression, IEEE Transactions onInformation Theory, Volume 31, Issue 6, pp. 832–835,November 1985.

[15] M. Maroti, B. Kusy, Gy. Simon and A. Ledeczi, Theflooding time synchronization protocol, in Proc. ofACM 2nd Conference on Embedded Networked SensorSystems (SenSys), November 2004, 39–49.

[16] J. Hill, R. Szewczyk, A. Woo, S. Hollar, D. Culler, andK. Pister, System architecture directions for networkedsensors, in Proc. of ASPLOS 2000, Cambridge, MA,November 2000.

[17] J. Polastre, R. Szewczyk, C. Sharp, D. Culler, TheMote Revolution: Low Power Wireless Sensor NetworkDevices, in Proc. of Hot Chips 16, August 2004.

[18] Chipcon Inc., Chipcon CC1000 Data Sheet, ver. 2.2,http://www.chipcon.com/.

12