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Poster Abstract: Bayesian Localization in WirelessNetworks Using Angle of Arrival

Eiman Elnahrawy, John-Austen Francisco, Richard P. Martin{eiman,deymious,rmartin}@cs.rutgers.edu

Department of Computer Science, Rutgers University

110 Frelinghuysen Rd, Piscataway, NJ 08854

ABSTRACT

Using existing wireless communication networks as a localization

infrastructure promises enormous cost and deployment savings over

specific localization infrastructures. In this work we investigate a

Bayesian network approach that uses a combination of radio signal

strength (RSS) to distance estimation along with angle-of-arrival

(AoA) information. We characterize the resulting localization ac-

curacy using data collected outdoors using different radios, indoor

data, and simulated data. We show how the localization perfor-

mance degrades in indoor environments and analyze the different

sources of errors that cause this performance degradation as com-

pared to outdoor settings. We found our network is quite sensitive

to variations in the distance to signal strength, and the additionalangle information had only a small impact on localization accu-

racy.

Categories and Subject Descriptors

C.2.5 [Local and Wide-Area Networks]

General Terms

Algorithms, Measurement, Performance, Design, Experimentation

Keywords

Localization, Angle of Arrival, Wireless Local Area Networks,

Bayesian Statistics

1. INTRODUCTIONRecent years have seen intense research investigating using wire-

less networks as a localization infrastructure. If successful, us-

ing the same infrastructure for both communication and position-

ing would provide a tremendous cost and deployment savings over

a specific localization infrastructure, such as ceiling-based ultra-

sound.

In this research we investigate using a machine learning tech-

nique that uses received signal strength (RSS) in combination with

both Angle of Arrival (AoA) and distance estimation to provide lo-

calization in wireless networks. More specifically, we use a Bayesian

network that incorporates both angle and signal to distance in a sin-

gle network in order to estimate the propagation parameters as well

as estimate a radios position. We build on previous work usingBayesian networks using only RSS for distance estimation [2, 1].

We first constructed a simple base station incorporating a rotat-

ing directional parabolic antenna. The base station can then con-

struct a curve of the measured RSS as a function of the angle of the

This research was supported by NSF grant #CNS-0448062 andNSF grant #CCR 03-14161.

Copyright is held by the author/owner.SenSys05, November 24, 2005, San Diego, California, USA.ACM 159593054X/05/0011.

antenna. This function of RSS to angle, or the, AoA curve, provides

the base radio property of our approach. We use both our own data,

as well as that in [3].

We prove that our Bayesian technique is feasible by first showing

that a simple propagation model fits the observed AoA as a function

of the angle (the AoA curve), in outdoor settings. Figure 1 shows

a sample raw and smoothed sample AoA curve for the Telos Mote

in an outdoor setting. We also found our Bayesian approach has

equivalent accuracy to [3], but uses less base-stations (4 vs. 7).

We also demonstrate that our approach is applicable to a variety

of technologies by showing that the propagation models work well

for both 802.11 as well as 802.15.4 networks. Using our derived

propagation models, we show that our proposed Bayesian network

can give highly accurate results and it is robust to significant errors

in the angle estimation. With minimal errors in the AoA curve, the

network can provide a mean error of less than 1 ft and a maximum

error of 3 ft. Even with random errors of up to 45 degrees, the

maximum error for a building floor is still only 7ft.

Telos Mote AoA Curve at 60 ft

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-100

-95

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-65

180 230 280 330 20 70 120 170

Antenna Angle (deg)

SignalStrength(dBm)

Original Data Smoothed Data Cosine Fit

Figure 1: A sample AoA curve, this is for the Telos Mote (using

802.15.4) at 60ft taken outdoors.

2. THE BAYESIAN NETWORKFigure 2 shows our graphical model for the location estimation.

This model incorporates both the knowledge of AoA and the knowl-edge of RSS from the n different base stations in the localization

system in order to localize an object.

The vertices Xand Yrepresent location. The vertex D1 (respec-

tively D2, . . . , and Dn) represents the Euclidean distance between

the location specified by X and Y and the first (respectively sec-

ond, ..., and nth) base station. We assume the locations of the

access points are known and hence the Dis are deterministic func-

tions of X and Y. The vertex a1 (respectively a2, . . . , and an)

represents the angle-of-arrival (AoA) of the signal received from

the first (respectively second, . . . , and nth) base station.

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Error in Feet

Probability

Error CDF:AoA and SS vs SS Only 4 Basestations

AoA and SSM1SS Only

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Error in Feet

Probability

Error CDF:Effect of Random Angle Ahift, Lobes Noise and Attenuation on AngleModel

lobes0,shift0,atten0lobes0,shift0,atten5lobes0,shift45,atten5lobes0.8,shift0,atten5lobes0.8,shift45,atten5lobes0.8,shift45,atten15

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Error in Feet

Probability

Error CDF:Effect of Different Corrections on Indoor Data

A=0, S=0, W=1, L=120A=0, S=0, W=181, L=0A=0, S=0, W=241, L=0A=0, S=100, W=1, L=0

A=100, S=0, W=1, L=0A=100, S=100, W=61, L=60A=100, S=100, W=181, L=120A=100, S=100, W=241, L=60A=100, S=100, W=61, L=0A=100, S=100, W=241, L=0

(a) (b) (c)

Figure 3: The figures show CDFs of localization accuracy. Figure (a) compares our Bayesian network to one that does not incorporate

angle information, while (b) presents error CDFs of the synthetic data with varying degrees of distortion, and (c) presents accuracy

results for real indoor data with varying amounts of correction applied.

D1

D2

Dn

S1

S2

Sn

a1

a2

an

X Y

t1

b10

b11

b12

b13

t2

b20

b21

b22

b23

tn

bn0

bn1

bn2

bn3

Figure 2: A Bayesian network for location estimation that com-

bines both AoA and signal to distance in one graphical model.

The vertex Si represents the combined function of both the sig-

nal strength measured at (X, Y) with respect to the ith base station,i = 1, . . . , n and the angle information at this base station. Themodel assumes that X and Y are marginally independent and are

independent of the angle measurement. Note that we must quantize

the AoA curve for Si in 10o increments and fit it to a cosine curve

in order to make the model tractable. Figure 1 shows a fitted cosine

curve.

3. LOCALIZATION PERFORMANCEUsing primarily 802.11, we found that indoor environments have

a high degree of error in both the AoA measurement as well as the

distance measurement results in performance that is only marginally

better than not using angle information at all, as is shown in Fig-

ure 3(a).

In order to understand the differences between the indoor and

outdoor environments, we first characterize the resulting AoA curves.

We found that the curves are quite noisy, with angle estimation er-

rors of up to 60 degrees not uncommon. We also found that there

are significant deviations from the outdoor models in terms of dis-

tance estimation. Finally, we found that the shapes of indoor AoA

curves are quite distorted, with many peaks in the data that are close

to the true peak.In order to explore the impact of these effects on the AoA curve

on our localization approach we both perturbed a set of synthetic

data as well as correct a set of real data. We systematically altered

the (1) angle of the peak (shift), (2) mean RSS as a function of

distance (attenuation), and (3) sizes of the side lobes, as percentage

of the main lobe.

Our work shows that accuracy degrades as a function of all these

error types. Figure 3(b) shows the results of applying increasing

distortions to a set of synthetic data. The results show that although

our model is robust to a single type of error, the combination of

errors in both the angle and the distance to signal measurements

make indoor localization very challenging.

Figure 3(c) shows the results of fixing the 3 error types in mea-

sured data in indoor environments. The figure shows significant im-

provements in localization accuracy as we adjust the AOA curvestowards those predicted by outdoor measurements. Our results

show that the resulting AoA curves are quite distorted in terms of

distance, shift and lobe errors.

Both of these results also show that our network is quite sensitive

to RSS to distance distortions, and we found that these are the most

common and severe ones observed. Also, comparing the distorted

synthetic and correct real data shows that the performance of our

network is consistent with the classes and magnitudes of these er-

rors on the AoA curves. A key open question is thus how to resolve

the better performance of many other algorithms as compared to

our network, despite our addition of angle information.

4. REFERENCES

[1] EIMAN ELNAHRAWY, X IAOYAN LI, AN D RICHARD P.MARTIN The limits of Localization Using Signal Strength: A

Comparative Study. In IEEE SECON (October 2004).

[2] DAVID MADIGAN , EIMAN ELNAHRAWY, R ICHARD P.

MARTIN, WEN -H UA JU, P. KRISHNAN, AN D A.S.

KRISHNAKUMAR . Bayesian Indoor Positioning Systems.

IEEE Infocom (March 2005).

[3] DRAGOS NICULESCU AND BADRI NATH. VOR Base

Stations for Indoor 802.11 Positioning. ACM MobiCom

(September 2004).