Table Of ContentWireless distance estimation with low-power
standard components in wireless sensor nodes
Thorbjörn Jörger∗†, Fabian Höflinger∗, Gerd Ulrich Gamm∗ and Leonhard M. Reindl∗
∗Department of Microsystems Engineering
University of Freiburg - IMTEK, 79106 Freiburg, Germany
{thorbjoern.joerger, fabian.hoeflinger, gerd.ulrich.gamm, reindl}@imtek.de
Abstract—In the context of increasing use of moving signal is available or GPS receivers have too high energy
wireless sensor nodes the interest in localizing these nodes consumption. To provide a cheap and low power localization,
in their application environment is strongly rising. For many
the time of flight measurement (ToF) of a transmitted signal
applications, it is necessary to know the exact position of the
can be used to trilaterate the position of an object in three-
nodes in two- or three-dimensional space. Commonly used
nodes use state-of-the-art transceivers like the CC430 from dimensional space. With the combination of signal strength
6 TexasInstruments with integrated signal strength measurement and runtime measurement, the accuracy and overall reliability
1 for this purpose. This has the disadvantage, that the signal of the system can be further enhanced.
0 strength measurement is strongly dependent on the orientation
Thekeyissueinruntimemeasurementswiththemostwireless
2 of the node through the antennas inhomogeneous radiation
n pattern as well as it has a small accuracy on long ranges. sensor nodes is the relatively slow system clock. It generates
a Also, the nodes overall attenuation and output power has to an uncertainty of one clock cycle which is negligible in ultra
J be calibrated and interference and multipath effects appear in sonic sensing due to the slow speed of sound but becomes
8 closed environments. overwhelmingly large when working with electromagnetic
Another possibility to trilaterate the position of a sensor node
2 waves which are traveling with the speed of light. With a
is the time of flight measurement. This has the advantage, that
26MHzcounterclockoneclockcyclelasts38.4ns.Translated
the position can also be estimated on long ranges, where signal
]
I strength methods give only poor accuracy. In this paper we to distance this clock jitter is equivalent to an error of
N present an investigation of the suitability of the state-of-the-art approximately 11.5m. Additionally the hardware generates a
. transceiver CC430 for a system based on time of flight methods timeoffsetofseveralhundredcyclesoraround6-8µsbetween
s
and give an overview of the optimal settings under various
c physicallyreceivingapacketandlogicallyrisingtherespective
circumstances for the in-field application. For this investigation,
[ RX/TX flag which triggers the integrated counter capturing.
the systematic and statistical errors in the time of flight
2 measurements with the CC430 have been investigated under a Thisoffsetintheanalogdomainofthetransceiverismoreover
v multitude of parameters. Our basic system does not use any dependent on the attenuation, the frequency and the chosen
4 additional components but only the given standard hardware, modulation. We researched influences of the aforementioned
4 which can be found on the TexasInstruments evaluation board parametersonthedelayandtheoverallperformanceinrespect
4 for a CC430. Thus, it can be implemented on already existent
to distance measurement and present settings which promise
7 sensor node networks by a simple software upgrade.
to be the best foundation for further research in this field.
0
. ThepaperstartswithanoverviewofrelatedworkinSectionII.
1
I. INTRODUCTION In Section III the theoretical background of our research is
0
6 There exist many solutions for wireless distance measure- presentedandtheusedequationsaregiven.Theprogramming
1 ofthehardwareisexplainedinSectionIV.SectionVpresents
ment and equipment specifically designed for this purpose.
: the methods used in the experimental part of our work. In
v Our approach is different as we implement precise wireless
i distance measurement in already existing and used standard Section VII the results of the measurements are presented
X
and subsequently discussed. Finally, Section VIII gives a
hardware. A lot of available devices nowadays have an
r conclusion of the research done in the paper and an outlook
a integrated wireless transceiver for communication purposes
for research in the future.
on board. We use these existing wireless transceivers for
localizingthedevices.Thereisahugedemandforinformation
II. RELATEDWORK
on the whereabouts of devices related to their environment. A
For localization of low cost sensor nodes, most of the ex-
possibleapplicationisthenavigationofpedestriansinrailway
isting applications and research papers use the signal strength
stations,airports,tradefairsordepartmentstores.Additionally
indicator [1]. The behavior of radio signals in an indoor
autonomousrobotscanbeguidedinprocessingplantswithout
environment was shown by Hashemi in [2]. Via the received
the need for a human operator. A lot of the localization
signal strength indicator (RSSI) the distance between two
tasks must be realized in indoor environments where no GPS
wireless transceivers can be calculated. In most cases the two
†Correspondingauthor transceivers will consist of an anchor node and a mobile tag.
Several groups have researched combinations between round CRC [2] Data [7] Syncword [4] Preamble [4]
trip time (RTT) and RSSI measurements, but for Wi-Fi C C D D D D D D D S S S S P P P P
applications [3], [4], [5] and considerations of Cramér-Rao (a)
bounds [6], [7]. In [8] Will et al. have analyzed a multitude anchor node remote node
t
of error mechanisms and influences on their ToF system, t
0
which also measures the RTT. They use the mean value of 25 C D S P
SYNC_RECEIVED
t
single measurements to find the distance between two nodes. SYNC_SENT 1
Wmeeasturyremtoenotvserwcoitmhemtohree pehxytesnicsaivlelismtaittiasttiiocnasl mofetshiondgsleantidmea d CP DS DS CP tΔlatency tΔRTT
SYNC_RECEIVED t
precise characterization of the underlying error mechanisms. SYNC_SENT 2
P S D C
Also we take into account the different behavior in respect to t
3
attenuation, modulation and data rate.
The wake-up strategies mentioned in the abstract can be used (b)
to lower the overall energy consumption. Wireless sensor
Figure 1. a) Packet structure and size. The numbers in brackets stand
nodes based on the CC430 are capable of utilizing low for the size in bytes corresponding to the number of byte hexagons. b)
power modes, in which they consume only power in the Schematic of the timing parameters of the measurement setup. The time
indices mark the rising flags on which each counter capture is triggered by
range of severalµW compared to about 100mW during radio
anincomingoroutgoingsyncword.Thefiguredepictsoneroundtrip.This
operation [9], [10]. This allows the extension of battery life samemeasurementisrepeatedforseveralhundredtimesinarow.
and operational lifetime by several orders of magnitude [11].
A view on cooperative localization in wireless sensor net-
works and the underlying algorithms can be found in [12]. B. Time of flight
Wendeberg et. al. provide spring-mass based self-localizing Our approach uses the time of flight (ToF) measurement to
evaluation algorithms in [13], which can be fed by the data estimatethedistancebetweentheanchornodeandthemobile
generated by this system. tag and to overcome the above mentioned disadvantages of
RSSI measurements. We use a special form of ToF that is
III. THEORETICALBACKGROUND called round trip time as described in Figure 1. Compared to
the normal ToF measurement the signal of RTT travels the
A. Received signal strength
way back and forth from the anchor node to the mobile tag.
The following Friis equation calculates the maximum pos- Thereforenosynchronizationbetweenanchornodeandmobile
sible power in a receiving node P dependent on the sending tag is needed. The anchor node calculates the time difference.
r
power P , the antenna gains G and G , the distance r and The mobile tag is only measuring the processing latency
t r t
the wavelength λ: between incoming signal and outgoing signal. By measuring
in the anchor node the moment of sending the package t and
0
(cid:18) λ (cid:19)2 the moment of receiving back the package t , the complete
P =P ·G ·G · . (1) 3
r t t r 4πr roundtrip time can be calculated with ∆t = t − t
RTT 3 0
including the latency. By measuring in the remote node the
Therefore, if the received power strength is measured in the
moment of receiving the package t and the moment of send-
1
receiving node, the equivalent distance of sender and receiver
ing the package t , the additional signal processing latency
2
can be calculated with:
∆t = t −t in the mobile tag can be calculated. The
latency 2 1
(cid:114) corrected round trip time t is then
λ P RTT,corr
r = · t ·G ·G . (2)
4π P t r
r ∆t =∆t −∆t . (3)
RTT,corr RTT latency
The accuracy depends on the number of anchor nodes and
This round trip time is in our experiments between 6µs and
of the environment, which can lead to dynamic errors. The
1400µs depending primarily on the chosen modulation and
RSSI value is distorted by objects in the direct path, in
data rate. It is therefore assumed, that
the vicinity and by environmental influences, especially air
humidity. Additionally, the RSSI value also depends on the t =∆t −t (4)
signal RTT,corr offset
orientationoftheantenna.Theantennadirectivityisinfluenced
with a, for each setting, constant offset in the analog domain
by the antenna type and the spatial orientation of it compared
and the true signal runtime delay t . The distance d can
to the anchor nodes. Using an RF system for localization, signal
then be calculated according to
people canbe localized withlow accuracy (1.5-3m). Through
combination with other technologies, this accuracy can be d= v·tsignal (5)
improved.Themulti-methodapproachin[14]usesacombina- 2
tion of built-in sensors of mobile devices and the capabilities withv =c·v wherecisthespeedoflightandv thevelocity
p p
of the end-users, which estimates positions with a scanner factor of the medium, which can be either air or the copper
application. of the coaxial cable.
C. Processor cycles
3300 mV DC Power Supply 3300 mV
The first versions of our system used the highest clock Agilent E3631A
rate of the CC430 of 20MHz for the time measurement.
This proved to be extremely error prone due to the fact, COM-Port
RPi PC
that the internal RC oscillator of the CC430 is dependent
on operating voltage with 1.9%/V and ambient temperature
with 0.1%/°C. With a mean round trip time of then about anchor Hardware Hardware remote
30000 cycles and 30mV operating voltage difference, the node Reset GPIO Reset node
distance error increased to unusable 270m. Fortunately, the (EB1) Atten- 50 Ω - Cable (EB2)
CC430 has the ability, to drive the counter with an external CC430 CC430
uator
clock, and with the 26MHz crystal oscillator onboard the
external external
used evaluation boards, such an external clock was already external Oscillator Divider Oscillator
available. The onboard crystal oscillator provides an overall FRAM on XT2 on XT2
accuracy of 80ppm which leads to a clock generated distance 26 MHz 900 mVpp
error of a single measurement of 3.2m. An accurate crystal
Signal Generator
with small temperature and operating voltage dependency is
R&S SMA 100 A
crucial for precise distance measurements.
D. Modulation Figure 2. Block diagram of the system setup. The two evaluation boards
areconnectedwithacoaxialcable.TheRaspberryPi(RPi,seeSectionV-D)
Binary frequency shift keying (2-FSK) is a modulation,
starts the measurement by sending a start command containing the setting
where the information is transferred by shifting the carrier andthenumberofsinglemeasurementstoperformtotheanchornode.The
frequency by a certain amount in one direction or the other. It anchor node (master) is then initiating the communication with the remote
node (slave) and stores all incoming and measured data into the 2MBit
is one of the simplest digital modulations and widely used in
FRAM. After finishing the scheduled amount of measurements, the stored
wireless transceivers. Gaussian shaped frequency shift keying dataaretransferredtotheRPiviaCOMport.
(2-GFSK) differs from standard 2-FSK in the fact that a
Gaussian filter is applied to the output signal which smoothes
law, directly dependent from an integer multiple n of the
the pulse and so reduces the spectral bandwidth of the signal.
wavelength λ
The influence of modulation on the aforementioned time
nλ=2dsinθ, (7)
delay in the analog domain is dominant. The time delay of
2-GFSK modulation is around 40% higher at every data rate a possible method to circumvent such a scenario would be to
than the time delay of the 2-FSK modulation. Apparently, changetheworkingfrequencywheneveranodeisencountered
the processing of the 2-GFSK signal takes up more time with a situation where no connection to the anchor node is
in the analog domain, then the processing of the variant possible.
without the application of a Gaussian filter. Additionally, the For this work, two commonly used frequencies, 868MHz and
standard deviation of the single measurements doubles, when 915MHz, were used. The difference in frequency would be
a Gaussian filter is used. Hence we recommend the use of sufficiently large to change the interference pattern in a way
2-FSK for all distance measurement purposes when feasible. that a connection to the anchor node could be reestablished.
E. Frequency F. Time delay in the analog domain
Fresnel described the implications of objects being in the One of the most interesting effects encountered, is the
socalledFresnelzoneF .Theradiusofthen-thFresnelzone time delay in the analog domain. It is not documented in
n
at the point P is derived with the wavelength λ, the distance the datasheets and manuals from Texas Instruments. It is
betweenantennasdandthedistancesd andd oftheantennas speculated,thatthedelaydependsontheinternalprogramming
1 2
to the respective point P according to of the state machine, the rise times of the preamplifiers and
(cid:114) the data processing of the sync word. The delay seems to
nλd d
F = 1 2. (6) stay constant over time and is in the same range between
n d
different evaluation boards, but preliminary results show, it is
ObstaclesintheunevenFresnelzonesreflecttheincidentwave temperature and supply voltage dependent to some degree. It
in a way, that destructive interference occurs and the attenua- changes strongly between frequencies, data rates and modula-
tion rises. To get a small attenuation in radio communication tions.Furtherinvestigationofthiseffectisnecessarytocancel
the first Fresnel zone F has to be clear of obstacles, which out its effects in the final application.
1
mostlycannotbeensuredinindoorenvironments.Interference
IV. PROGRAMMING
patternsinclosedenvironmentsarisebymultipathwaveprop-
A. State machine
agation and can lead to situations where no communication is
possiblebecausereflectedwavescanceleachothercompletely For the time measurement, a finite state machine has been
out. Because the interference pattern is, according to Bragg’s implemented in both evaluation boards. The programming is
oscillator already available on the evaluation board to use the
highest allowed and available frequency. The corresponding
period is 38.4ns and as such the smallest resolvable time unit
in this system, further referred to as cycle.
Thelargestroundtriptimeresolvableis216 cyclesorapprox-
imately2.5ms,whichwasnotenoughforourpurpose.Hence
thecounterwasenlargedwithanadditional16-bitregisterand
TX-Flag Slave RX-Flag Slave an overflow interrupt service routine to provide 232 cycles or
approximately 165s capacity.
The counter is triggered by the rising internal sync word
received/sent flag. The counter value is stored in the corre-
RX/TX-Flag Master
spondingregisterandthensavedbyaninterruptserviceroutine
for calculating the time difference between the occurrences
of the triggered events. This measurement is repeated for at
least several hundred times. Due to this many samples, a very
precise measurement value can be obtained.
To ensure the reliability of the measured events, the val-
Figure 3. Time difference between rising of the sending flag (TX) on one
node and rising of the receiving flag (RX) of the same packet on the other ues were compared to measurements taken with a Tektronix
node is much larger than it is supposed to be by the runtime effect only. TDS3034B oscilloscope. Figure 3 shows the oscilloscope
The runtime is superimposed by the time delay in the analog domain. The analysis of the micro controller flags utilized for the time
oscilloscope was connected to the GDO1s of the CC430s with pin setting:
IOCFG1=0x06.Thecablelengthbetweenbothevaluationboardswas2m. measurement. This was used to confirm the validity of the
time measurements with the integrated counter of the CC430.
All values were inside the measurement resolution of the
mostly identical. The only differences exist in the state ma- oscilloscope and therefore this is an apt method of time
chine,wherethemasterisallowedtoinitiatethemeasurement measurement for our application.
procedurewhiletheslaveisnot,aswellastheinterruptservice
V. MATERIALANDMETHOD
routine,wherethemastercountsthetimebetweensendingand
receiving while the slave counts the time between receiving For the sake of reproducibility and conformability, all mea-
and sending a packet. To start the measurement procedure, surements were performed with hardware freely and commer-
a data package has to be received via the COM port. It cially available. The system setup used for all measurements
containsthenecessaryinformationaboutthenumberofsingle is depicted in Figure 2. In this section, you will find a listing
measurements that should be taken and the RF settings that ofallnecessaryhardwareandthemeasurementmethodsused.
should be used. The master then sends this information to
A. Statistical evaluation
the slave, which adjusts its configuration accordingly. After
For statistical evaluations of measurements, the standard
reestablishing the communication with the new configuration,
deviation estimation correction factor
the scheduled number of measurements is taken. During this
time, the master is not communicating with the Raspberry Pi (cid:114)N −1 Γ(cid:0)N−1(cid:1)
c = · 2 , (8)
(RPi,seeSectionV-D)noracceptinganyinputfromitinorder σ 2 Γ(cid:0)N(cid:1)
to take a clean and undisturbed measurement. Therefore the 2
is used to calculate the influence of small numbers of mea-
data transfer to the RPi is initiated by the master.
surements to a populations standard deviation. It is for the
B. Data transfer smallest amount of measurements taken for this paper of 10k
measurements around 25ppm. This means that the number of
The measurement data is recorded by the evaluation boards
samples is sufficient to estimate the standard deviation with
designated as master. It measures its own time span and
an error smaller than 25ppm.
received signal strength and receives the time span and the
For a given population mean value with a certain population
RSSI from the remotely installed second evaluation board
standard deviation σ , the resulting standard deviations of the
designatedasslave.Thedatafromtheremoteevaluationboard 1
meansσ overabatchofN measurementsiscalculatedwith
is simply piggy-backed onto the packages sent and received N
anyway. All information is then sent to the RPi via a standard (cid:114) 1
COM port. The RPi administrates the data reorganization and σN =σ1· N. (9)
storage as well as all calculations.
To get the number of measurements it takes to get a mean
C. Time measurement value of the batch near the population mean with a desired
uncertainty σ , Equation 9 could be written as
In order to achieve a precise time measurement without x
additional hardware, the internal 16-bit counter of the CC430 σ2
N = 1. (10)
was used. It was fed by the external 26-MHz crystal RF σ2
x
CRC [2] Data [7] Syncword [4] Preamble [4] boards of 3300mV was supplied by an Agilent E3631A DC
C C D D D D D D D S S S S P P P P power supply.
D D D D D D D
Δt [4] RSSI [1] Address [2] D. Raspberry Pi
latency
In consideration of the long uptimes and high reliability,
Figure4. Packetstructureandsizeaswellaspacketcontent.Thenumbers
inbracketsstandforthesizeinbytes.TheCRCiscalculatedforeachpacket versatilityandexpandabilityrequirementsofthemeasurement
automaticallybytheCC430.Thesyncwordisconstantandhastobeidentical setup, a Raspberry Pi was chosen to serve as a base. It
onmasterandslave.Thepreambleisgeneratedbythetransceiversandused
runs Raspbian Wheezy, a debian linux derivative. The RPi
forPLLlock-in.
communicates with one of the evaluation boards, the anchor
node, over a native COM port. It controls every action of the
Withthosetwoequationsonlyagoodpopulationmeanvalue measurement setup, the communication and the data storage
with a known population standard deviation is necessary to and evaluation.
calculate the number of measurements needed.
E. RF settings
B. Packet structure and size
Differentsetsofsettingswereusedtodeterminetheoptimal
Thepacketsizefortheexperimentsconductedinthispaper
parameters, such as frequency, data rate and modulation, for
is 17 byte. The packet consists of a 4 byte long preamble, a
wireless distance measurement with CC430 based systems.
4 byte long sync word, 7 data bytes and a 2 byte CRC check
Table I contains an overview over the evaluated parameters.
sum,asdepictedinFigure4.Thedatabytescontainthe4byte
They span the whole range of possible settings of the CC430,
timervalue∆t ,the1bytelongRSSIvalueanda2byte
latency with data rates between the highest possible setting 250kb/s
long address for node identification. Because the accuracy of
and the lowest possible setting 1.2kb/s.
the system depends on a high number of measurements, it is
desirable to use very short packages and high data rates, so
that more measurements can be conducted in a given time F. Cable connection
frame. On the other hand, high data rates require a small
Forthedistancevariationmeasurements,elspec LL335low
overallattenuation,whichisdifficulttoachievewhendistances
loss high frequency cables of certain lengths and an attenua-
increase and the output power is limited.
tion of 14dB/100m were used to eliminate the influence of
multipath effects, reflections and antenna orientation. Several
C. TI evaluation board cables of 10m and 20m length were available. To counteract
The Texas Instruments EM-CC430F6137-900 evaluation the cable attenuation which varies with its length and to vary
board is a ready-made platform for the single-chip RF-MCU the overall attenuation, an array of one hp8494B attenuator
CC430.Itcandirectlybeusedforthemeasurementspresented and one hp8496B attenuator was used. The connection from
in this publication. The MCU supports a frequency range and to the attenuator and to the elspec cables was realized
from 433 - 915MHz with four different modulations of with standard RG223 cable of 1m length available in the lab.
which 2-GFSK and 2-FSK were used in this work while on-
off keying (OOK) and minimum shift keying (MSK) were VI. MEASUREMENTS
disregarded, because of their rare use in wireless sensor node
networks. Also it provides several low-power modes and an To generate an accurate model, both main influences
overall low power consumption which makes it popular and on the time measurement signal had to be investigated,
widely used for low-power energy self-sufficient systems and namely distance and attenuation. For each point in the
wireless sensor nodes. measurements presented 25 rounds with 1000 measurements
The used boards underwent only minor hardware changes, each were taken. The results were then cleaned of spikes.
namely soldering connectors on several port pin drill holes Every result for which the runtime was negative or greater
and ground taps, bridging the reset button with a NMOS for than 42000cycles was viewed as flawed and removed. For
external reset and replacing the onboard RF crystal oscillator the RSSI measurements, the first 60 measurements of each
with a tap to feed the MCU with a clock reference from a 1000-measurement round were discarded, as well as every
signal generator. No other modifications were necessary in measurement which deviated more than ±3dB or about at
order to measure the distance. least 4σ from the mean value. This was necessary since the
The removed 26MHz quarz on the evaluation boards was RSSI register in the CC430 did not provide any plausible
replaced with a 26MHz 900mV feed from a Rohde & values for the first 60 measurements taken and sometimes
pp
Schwarz SMA100A signal generator in order to provide during the measurement gave single values that were up to
temperature independent frequency stability and reproducible ±20dB off compared to the mean value. For the remaining
measurement results as well as a synchronous clock on both values the means and standard deviations were calculated.
evaluation boards. The operating voltage for the evaluation
2 5 0 k b /s - G F S K - 8 6 8 M H z
5 2 0 ,4
1 0 2 5 0 k b /s - G F S K - 9 1 5 M H z O ffs e t - 2 m - 2 5 0 k b /s - 2 -F S K - 8 6 8 M H z
2 5 0 k b /s - F S K - 8 6 8 M H z 5 2 0 ,2 E x p o n e n tia l D e c a y F it
8 2 5 0 k b /s - F S K - 9 1 5 M H z 5 2 0 ,0
Id e a l - 0 .2 2 c y c le s /m e te r
5 1 9 ,8
t [cycles]signal 46 et [cycles]555 111 999 ,,,246 Ayy0 = == y 150,+14 8,A ,t7e =5(x , 7- xx,08)0 / =t w -8ith0 ,4 5
D ffs5 1 9 ,0
2 O
5 1 8 ,8
0 5 1 8 ,6
5 1 8 ,4
2 1 3 2 3 3 3 4 3
-8 0 -7 0 -6 0 -5 0 -4 0 -3 0
D is ta n c e [m e te r]
A tte n u a tio n [d B m ]
Figure 5. Results of reference measurement. The ideal line has a slope of Figure6. Resultsofattenuationmeasurementwithadatarateof250kb/s,
0.22cycles/mwhichcorrespondstoavelocityfactorinthecableof0.8.The FSK modulation and with a frequency of 868MHz in climate chamber at
points standard deviation of the means is smaller than the symbol size and 20°C.Theexponentialdecay’sfitfunctionisgiveninthegraph.
wasthereforeneglectedforthisgraph.
A. Distance variation
1 5 1 0 k
S ta n d a rd d e v ia tio n o f m e a n s - 2 5 0 k b /s - G F S K - 8 6 8 M H z
The distance was varied by varying the length of the cables S ta n d a rd d e v ia tio n o f m e a n s - 2 5 0 k b /s - F S K - 8 6 8 M H z
1 3 1 k
connecting the nodes. The length of the cables was set to 2m W ith E q u a tio n 9 c a lc u la te d s ta n d a rd d e v ia tio n o f m e a n s
M e a s u re m e n t d u ra tio n
and13-43min10msteps.Themeasurementswereperformed 1 1 1 0 0 [s]
ocovnertroallpeedriaomdboifenstevteemrapledraaytusrea.ndThienaatnteennuvaitrioonnmweanstfiwxiethdoutot ns [m] 9 1 0 uration
-60dBm. The offset value for 2m was subtracted from the f mea 7 1 ent d
results of all other distances to normalize the results. rror o 5 1 0 0 m surem
E a
e
3 1 0 m M
B. Attenuation variation 1 1 m
The second main influence is the attenuation. The eval-
1 2 5 1 0 2 0 5 0 1 0 0 2 0 0 5 0 0 1 k 2 k 5 k 1 0 k 2 0 k
uation boards were working between -36dBm to -81dBm
S iz e o f m e a s u re m e n t b a tc h
attenuation. The attenuation was varied in this range in 1dB
(a)
steps. The measurements were performed inside a climate 8 0 1 0 k
S ta n d a rd d e v ia tio n o f m e a n s - 3 8 ,4 k b /s - G F S K - 8 6 8 M H z
chamber to exclude thermal influence. The temperature inside
7 0 S ta n d a rd d e v ia tio n o f m e a n s - 3 8 ,4 k b /s - F S K - 8 6 8 M H z 1 k
the chamber was set to 20°C. W ith E q u a tio n 9 c a lc u la te d s ta n d a rd d e v ia tio n o f m e a n s
M e a s u re m e n t d u ra tio n
6 0 1 0 0 ]
[s
] n
C. Batch size variation ns [m5 0 1 0 uratio
ea4 0 1 t d
For the determination of the necessary batch size, a combi- f m en
nation of the aforementioned measurements, namely -60dBm rror o3 0 1 0 0 m surem
attenuation and 18m cable length, was used. For the fast data E2 0 1 0 m ea
M
rates of 250kb/s and 38.4kb/s 300k single measurements and
1 0 1 m
50ksinglemeasurementsfortheslowdatarateof1.2kb/swere
performed to achieve a stable population mean and standard 1 1 0 0 µ
deviation. These single measurements were then grouped to 1 2 5 1 0 2 0 5 0 1 0 0 2 0 0 5 0 0 1 k 2 k 5 k 1 0 k 2 0 k
batchesoflogarithmicsizesfrom1to5000samplesperbatch. S iz e o f m e a s u re m e n t b a tc h
Thestandarddeviationofthemeansofthesinglebatcheswas (b)
subsequently calculated and the resulting values translated to Figure 7. Influence of the batch size to the standard deviation of means
as presented in Table I for a) 250kb/s and b) 38.4kb/s at a frequency of
distancewiththesignalvelocityv of9.2244m/cyclederived
s 868MHz with respect to modulation and the measurement duration. The
fromEquation5withthevelocityfactorofthecablevp =0.8. measuredvaluesmatchthelinescalculatedwithEquation9fromthestandard
deviationofthepopulation.
TableI
STANDARDDEVIATIONSOFMEANSOFTHEMEASUREMENTSWITH-60±1DBATTENUATIONAND18MCABLELENGTH.
Sizeofmeasurementbatch 1 20 50 100 200 500 1000 2000 5000
K 868MHz 12.80 2.85 1.80 1.26 0.88 0.58 0.41 0.29 0.19
S
Standard b/sGF 915MHz 12.83 2.87 1.82 1.28 0.91 0.55 0.37 0.24 0.15
deviationsof k
0
means[m] 25K 868MHz 6.09 1.37 0.86 0.61 0.44 0.27 0.19 0.13 0.08
S
F 915MHz 6.26 1.40 0.88 0.62 0.44 0.28 0.21 0.14 0.09
Measurementduration1 [ms] 1.4 28 70 140 280 700 1400 2800 7000
K 868MHz 78.93 17.73 11.19 7.87 5.59 3.57 2.59 1.71 1.12
S
Standard b/sGF 915MHz 78.36 17.56 11.12 7.88 5.62 3.63 2.42 1.69 1.04
deviationsof k
4
means[m] 38.K 868MHz 30.10 7.11 4.50 3.17 2.27 1.45 1.02 0.77 0.43
S
F 915MHz 29.85 7.04 4.55 3.20 2.25 1.41 1.03 0.77 0.49
Measurementduration[ms] 4.3 86 215 430 860 2150 4300 8600 21500
Sdmeteavaninadtsaior[dnms]of 1.2kb/sGFSK 896185MMHHzz 11774415..3132 339945..1248 225503.5.21 117797..7868 112263..2426 8861..4419 6545..9220 5383..4382 2294..1561
Measurementduration[ms] 110 2200 5500 11000 22000 55000 110000 220000 550000
Errorcoloring: 2m<σ 2m≤σ<1m 1m≤σ<0.5m σ<0.5m
1Allvalueswerecalculatedfromthemeasuredtimeofsinglemeasurement.
VII. RESULTSANDDISCUSSION VIII. CONCLUSIONANDOUTLOOK
In the paper, wireless distance estimation with the CC430
The results of the distance measurements as depicted in was evaluated in respect to accuracy and the influence of
Figure 5 show the dependence of the round trip time from attenuation. The achievable accuracy for the round trip mea-
the distance between the nodes as described by Equation 5. surement, when the offset value is measured precisely, is in
The deviations from the ideal line are most probably caused the decimeter range. The accuracy and speed of the distance
by temperature changes of the environment, because they are measurement with the CC430 are very promising. The mea-
close together for all setting. This makes a systematical error surementscanbeconductedveryfast.Atrilaterationfromfour
more probable. The offset value t at 2m distance was fixed nodes with an accuracy under 0.5m could be performed
offset
used to normalize the measurements. After the removal of the inonesecond,whilewithanaccuracyrequirementof1monly
offset,onlythecontributionoftheruntimetothewholesignal 300ms suffice.
is left. The second prime target of this experiment was to single
The results of the attenuation measurement is given in Fig- out reliable settings for the CC430 to conduct distance mea-
ure 6. The offset increases exponentially with increasing surements. The result clearly show, that 2-FSK modulation is
attenuationandthereforewithincreasingdistance.Thismeans, superiorto2-GFSKmodulationbyafactorof2.Weconclude,
that the measured value overestimates the factual distance thatfurtherresearchinthisfieldshouldconcentrateon2-FSK
when using a linear equation like Equation 5. This effect has modulation, as we will do in the future. With respect to
to be taken into account for future measurements. We suspect data rate, the result is not as obvious, but instead a trade-off
the offsets behaviour to be as well temperature dependent so between range, speed and accuracy requirements. We discard
a precise investigation of the offsets behavior is necessary. thesettingswith1.2kb/sdatarate,becausetheyareobviously
The results of the variation of the batch size are presented unusable for our objective. We suggest either a system which
in Table I as well as in Figure 7. It shows the as well the uses one high and one low data rate and changes between
influence of data rate and modulation. The Gaussian filtering them when the nodes gets out of range, or a system which
of the signal approximately doubles the standard deviation of uses a compromise such as a data rate of 125kb/s.
the measurements. A slow data rate increases the offset and The transmission frequency has no practically relevant influ-
the ratio between offset and desired signal. ence and can be chosen according to regulations or compati-
The time measurement itself is sufficiently precise when the bility to existing systems.
RFsettingsandthenumberofsamplesarechosenaccordingly. Preliminarymeasurementsshowedtheoffsettobetemperature
Thisscalabilityallowsatrade-offbetweenspeed,accuracyand and supply voltage dependent. Further research has to be
energyrequirements.Thenumberofmeasurementscanaswell done with respect to the behavior of the offset in the analog
be calculated with Equation 10. domain. If it cannot be calibrated by precise measurements
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Research Foundation (DFG) within the Research Training Guimarães,Portugal,21-23September2011.
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