Positioning with moving IEEE 802.15.4 (ZigBee) transponders

M. Pichler1, S. Schwarzer2, A. Stelzer3, and M. Vossiek4

1Linz Center of Mechatronics GmbH, 4040 Linz, Austria2Siemens Corporate Technology, 81739 Munich, Germany

3Johannes Kepler University, Inst. for Communications and Information Engineering, 4040 Linz, Austria4Clausthal University, Inst. of Electrical Information Technology, 38678 Clausthal-Zellerfeld, Germany

Abstract— In an ever-increasing number of wireless communi-cations applications the measurement of positions of transmittersdistributed in space is desired. Demands on low cost and powerconsumption make solutions that allow positioning with existingcommunications hardware during the process of data transmis-sion particularly interesting. In this paper we discuss a methodfor using IEEE 802.15.4 (ZigBee) transmitter nodes with aspecial frequency-hopping scheme for this purpose and show theinsensitivity of this method to transmitter motion mathematicallyas well as by exemplary simulations and measurements.

Index Terms— ZigBee, sensor networks, local positioning, fre-quency hopping.

I. INTRODUCTION

Low-power off-the-shelf communications solutions that si-

multaneously allow the estimation of transmitter positions

provide an additional benefit in applications where low cost

and low maintenance are required. Recently systems and

architectures based on the low-power PHY-layer defined in

IEEE 802.15.4 have been published [1], [2]. Particularly in

indoor environments, however, larger signal bandwidths than

the 5 MHz available in a single IEEE 802.15.4 channel are

required for precise position estimates.

In [3], [4] the authors therefore presented a method for

utilizing the full 80-MHz-bandwidth available in the 2.4-

GHz-ISM-band by employing a particular frequency-hopping

scheme and coherently combining multiple measurements

from different channels to obtain a precise distance estimate.

By this scheme many disturbing effects such as oscillator

errors in both transmitters and receivers are eliminated, and it

is shown how a position estimate for a stationary transponder

T1 can be derived from the slope of the phase of a matched-

filter output as a function of the channel. Due to space

limitations the full signal model cannot be presented in this

context, and the reader is referred to [4].

This paper extends the original model to transmitters T1

that are in motion during the positioning task and shows that

transmitter velocity is, similarly to oscillator errors, to a large

part canceled from the position estimate. Section II will briefly

introduce the system setup and highlight the differences in the

signal model as compared to [4] for moving transmitters. In

Section III simulations and measurements are presented, and

a conclusion is given in Section IV.

Fig. 1. Measurement setup with K receivers R1, . . . , RK , referencetransmitter T2 and transmitter with unknown location T1 moving with

velocity v shaded gray. Superscripts ·[T,R] indicate transmitter T andreceiver R.

II. SETUP AND SIGNALS

The proposed positioning scheme is based on a time-

difference of arrival (TDOA) measurement as it is also de-

scribed e.g. in [5]. As shown in Fig. 1, this scheme employs

a number of receiving base stations R1, . . . , RK distributed

around the region of measurement. For a 1-D measurement

at least two receivers are required, for higher dimensionality

this number increases. A stationary reference transponder T2

and a moving transponder to be located T1 ideally have a

line of sight connection to all base stations. All receiver and

transmitter positions with the exception of that of T1 are

assumed to be known.

Each transmitter consists of a standard IEEE 802.15.4 radio

chip such as the Texas Instruments CC2420 that is clocked

by an external 16-MHz quartz, a microcontroller, and a chip

antenna. Receivers contain an antenna, a downconverter that

mixes the reception in the ISM-band with a 2.4 GHz local

oscillator signal to baseband, a high-speed analog-to-digital

converter, and a signal processing unit. In the current setup

the full ISM bandwidth of 80 MHz is sampled, and channel

separation is performed digitally.

For positioning, each of the two transmitters sends out data

packets in different channels that are received in all base

stations after a time of travel τ [T,R] = r[T,R]

c0proportional

by the speed of light c0 to the distance r between sender Tand receiver R. To utilize the full available bandwidth, the

positioning result is obtained from a sequence of consecutive

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Fig. 2. Possible frequency-hopping sequence of channels c[T ]p used

for transmission of packet p by two transmitters T1 and T2.

measurements, for each of which the receptions are correlated

with an ideal data signal that is synthetically generated in the

receivers. By using a particular hopping sequence, a possibility

for which is depicted in Fig. 2, it is ensured that most

perturbing factors such as oscillator frequency error and—as

we will show—transmitter motion can be eliminated during

the computation. The hopping sequence is distinguished by

its symmetry and by a constant packet spacing, both of which

are necessary for the positioning method to work properly.

We assume a model of constant transmitter velocity v during

the short time span of the measurement sequence. In the

absence of noise, the received signal sR is a replica of the

transmitted signal sT that is delayed by the time-of-flight delay

τ[T,R]0 =

r[T,R]0

c0at the beginning of the transmission of the

first data packet, and stretched by the Doppler shift caused by

τ̇0[T,R] =

v[T,R]0

c0, the temporal derivative of τ0 proportional to

the relative radial velocity v0 of the transmitter as seen from

the receiver, i.e.

s[T,R]R (t) = s

[T ]T

(

t −(

τ[T,R]0 + τ̇

[T,R]0 t

))

. (1)

After analog downconversion, sampling, channel separation,

digital conversion to baseband, and decimation, a signal of

the form

s[T,R]F,p [m] = s0,d[T ]

p

(

T[T,R]F

(

m − n[T,R]F,p

)

)

ei(

k[T,R]F,p

m 2π

M+ϕ

[T,R]F,p

)

(2)

with parameters

T[T,R]F = 2π

ωSI

(

1 − τ̇[T,R]0

)

NM

(3)

n[T,R]F,p = ωSI

2π

1

1−τ̇[T,R]0

MN

(

τ[T,R]0 −

ϕ[T ]C0−2πn

[T ]D,p

ωCI− ϕD0

ωDI

)

+ MN

ϕ[R]S0

2π− pM

(4)

k[T,R]F,p = −

ωRI,c[T ]p

ωSINτ̇

[T,R]0 (5)

ϕ[T,R]F,p = ωRI,c[T ]

p

(

− τ[T,R]0 +

ϕ[T ]C0−2πn

[T ]R,p

ωCI−

(

1−τ̇[T,R]0

)

ϕ[R]S0

ωSI

)

+ ϕR0,c

[T ]p

− ϕ[R]L0 + ωLI

ϕ[R]S0

ωSI− ωRI,c[T ]

p

2πτ̇[T,R]0

ωSIpN

(6)

is obtained [4]. In (2)-(6), p denotes the index of the data

packet, s0,dpthe signal transmitted for data packet dp, N

is the number of samples per packet before, M after digital

decimation, ωCI , ωRI,cp, ωLI , and ωSI are the angular trans-

mitter clock frequency, RF center frequency in channel cp,

receiver local oscillator frequency, and sampling frequency,

respectively, ϕC0 is the transmitter main clock phase relative

to time zero, ϕD0 the data signal phase relative to the main

transmitter clock edge number nD,p, ϕL0 and ϕS0 are the

initial phases of the local oscillator and the receiver sampling

clock, respectively, and ϕR0,cpis the transmitter RF signal

phase in channel cp relative to the main transmitter clock

edge number nR,p. The parameters (3)-(6) are computed from

every measurement with respect to an ideal synthetic signal

by correlation.

For proper operation we must demand that the relative offset

between the data clock and the RF signal phase must be

constant for every channel, that is, the offset may be described

by a number of offset clock cycles ∆nR,cponly dependent

on the channel. Furthermore, we have already stated that the

packet spacing in time must be constant after an initial number

of clock cycles nD,0. Hence,

n[T ]R,p = n

[T ]D,p + ∆nR,c[T ]

pn

[T ]D,p = n

[T ]D,0 +

ωCI

ωSI

Np (7)

The employed symmetric frequency-hopping scheme may be

formulated as

c[T ]p = c

[T ]P−1−p c = c[T1]

p1= c[T2]

p2(p1 6= p2), (8)

that is, each transmitter sends a packet in the same channel at

an equal spacing before and after the center of the measure-

ment sequence that is indicated by a dash-dot line in Fig. 2,

and both transmitters occupy each channel exactly twice in

different time slots.

For the following we assume a setup with two receivers R1

and R2 with which a one-dimensional position estimate can

be computed. The measurement can be extended to higher

dimensions e.g. by using all possible receiver pairs for 1D-

estimation and deriving the higher dimension estimate from

multiple 1D results.

From the 8 phase estimates ϕF,p according to (6) that are

obtained in every channel c at packet positions p we can

compute a phase measure ϕF,c that is a function of channel

index c as

ϕF,c =(

ϕ[T1,R1]F,p1

+ ϕ[T1,R1]F,P−1−p1

)

−(

ϕ[T1,R2]F,p1

+ ϕ[T1,R2]F,P−1−p1

)

−(

ϕ[T2,R1]F,p2

+ ϕ[T2,R1]F,P−1−p2

)

+(

ϕ[T2,R2]F,p2

+ ϕ[T2,R2]F,P−1−p2

)

.

(9)

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After insertion of (6) into (9) we obtain ϕF,c as

ϕF,c ≅ 2ωRI,c

(

− τ̃ [T1,R1] + τ̃ [T2,R1] + τ̃ [T1,R2] − τ̃ [T2,R2]

+

(

τ̇[T1,R1]0 − τ̇

[T2,R1]0

)

ϕ[R1]S0 −

(

τ̇[T1,R2]0 + τ̇

[T2,R2]0

)

ϕ[R2]S0

ωSI

)

(10)

where

τ̃ [T,R] = τ[T,R]0 + τ̇

[T,R]0

2π

ωSI

(P − 1)N

2. (11)

With an expression for a phase ϕF,c as a function of channel

index c we have now obtained the quantity of interest. As

ϕF,c depends on the channel center frequency ωRI,c, it is

a linear function with a slope ideally proportional to the

desired TDOA −τ̃ [T1,R1] + τ̃ [T2,R1] + τ̃ [T1,R2] − τ̃ [T2,R2].

For a stationary reference transponder T2, τ̇[T2,Rk]0 = 0 and

τ̃ [T2,Rk] = τ[T2,Rk]0 ∀k, which further simplifies the result.

The remaining terms can be split in two parts. The first line

in (10) describes the TDOA corresponding to the position of

the transmitter at the center of the frequency-hopping sequence

that is indicated by a dash-dot line in Fig. 2. From the phase

terms ϕF,c it can be estimated e.g. as the slope of a linear

least squares fit or by a Fourier-analysis [3], [4]. The second

line contains the error terms remaining even after application

of the frequency-hopping scheme. These are dependent on

the initial phase of the receiver sampling clocks, that is,

on the synchronization mismatch between the receivers. For

equal starting points of the sampling process in the receivers

all ϕ[Rk]S0 are identical and this error vanishes. Otherwise, a

small error in the phase slope remains, but it is shown to

be negligible for realistic system parameters in the following

section. All other unknown perturbing terms such as initial

oscillator phases and, most importantly, terms depending on

transponder velocity have been eliminated in (10).

III. SIMULATION AND MEASUREMENT

For verification of the claimed insensitivity to transmitter

motion simulations in 1D- and 2D-scenarios and measure-

ments in a 2D-scenario have been carried out.

Firstly, a simulation of the effect of the phase slope error

caused by transmitter velocity and unsynchronized receivers

was performed. Basis of the simulation is a 1-dimensional

setup with receivers R1 at 0 m and R2 at 10 m, respectively,

the reference transmitter T2 at 5 m, and the transmitter T1 to be

located at 2.5 m. For demonstration the moving transmitter was

assumed to have a positive velocity of τ̇[T1,R1]0 c0 = 50 m/s,

which is high for all relevant applications. According to (10)

the influence of the receiver synchronization mismatch on the

position estimate is equal to the negative transmitter velocity,

that is,d δr

d(ϕ

[R2]

S0

ωSI

)

= −50m/s. (12)

ϕ[R2]

S0

ωSI(µs)

δr(µ

m)

−5 −4 −3 −2 −1 0 1 2 3 4 5−300

−200

−100

0

100

200

300

Fig. 3. Simulation of the range estimation error δr for a transmittermoving at 50 m/s and a receiver synchronization error between −5

and 5 µs.

Fig. 3 shows the simulation result that is aside from numerical

error in the correlation in accordance with the theoretical value

(12), so the line exhibits a slope of −50 µm/µs. Note that even

for a high velocity and receiver synchronization imperfection

of 5 µs the distance error of only 250 µm is negligible.

Secondly, two-dimensional simulations and measurements

were performed. The setups can be seen in Fig. 4 and 5. They

consisted of four receivers R1, . . . , R4 set up in a rough square

around the region of interest. The reference transponder T2

was placed in the center and the measurement transponder T1

was moving diagonally across the field of measurement and on

a circle around the center in the two scenarios. The estimate of

the 2-dimensional transponder position was obtained from the

measurements of each of 6 possible pairs of receivers using an

optimization criterion over the xy-plane from which estimates

in x- and y-directions were derived.

In the simulation the velocity of the transponder was set to

a high value of 50 m/s for the motion on the diagonal, and

the angular velocity was set to 19.6 rad/s for the motion on a

circle with 2.5 m radius, which corresponds to a translational

velocity of 49 m/s. In Fig. 4 the estimation results for the

position of T1 are shown, where gray dots mark transmitter

positions at the beginning of the measurement, gray lines

the position estimate projection to the temporal center of

the frequency hopping sequence due to transmitter velocity,

and small black dots the actual position estimates that should

ideally be at the tip of the position projection vectors. In both

scenarios there is obviously little error between the theoretical

value and the estimate.

Measurements with a setup similar to that of the simulation

were carried out, with a person carrying the moving transpon-

der T1 on a diagonal and a circular path in two scenarios, as

it can be seen in Fig. 5. While only a qualitative conclusion

can be drawn from this measurement result, it demonstrates

that the proposed IEEE 802.15.4 positioning method works

not only for stationary, but also for moving transponders.

IEEE MTT-S International Microwave Workshop on Wireless Sensing, Local Positioning, and RFID (IMWS 2009 - Croatia)

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Fig. 4. Simulation results for 2-dimensional setup consisting of four receivers R1, . . . , R4, stationary reference transmitter T2 andmoving transmitter T1 with position projection vectors. Black dots indicate position estimates.

Fig. 5. Measurement results for 2-dimensional setup consisting of four receivers R1, . . . , R4, stationary reference transmitter T2 andmoving transmitter T1. Black dots indicate position estimates.

IV. CONCLUSION

In this paper an extension of a proposed localization

method using IEEE 802.15.4 (ZigBee) off-the-shelf transmitter

chips and data signals for positioning to the case of moving

transponders was presented. It was shown that most error

terms due to the Doppler shift that are present in received

signals are canceled by a proposed symmetric frequency-

hopping sequence. Via a simulation it was verified that the

remaining position estimation error that depends on receiver

synchronization imperfection will be negligible for reasonable

parameters. The method has been shown to work also for fast-

moving transponders in 1- and 2-dimensional scenarios.

ACKNOWLEDGEMENT

This work was sponsored by the “Austrian Center of

Competence in Mechatronics (ACCM)” within the COMET

Program of the Austrian federal government, the Province of

Upper Austria, and the Scientific Partners of ACCM.

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IEEE MTT-S International Microwave Workshop on Wireless Sensing, Local Positioning, and RFID (IMWS 2009 - Croatia)

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