RSSI Based Position Estimation in ZigBee Sensor Networkswseas.us/e-library/conferences/2014/Tenerife/CSST/CSST-07.pdf · many real-life applications need to locate the source of incoming

RSSI Based Position Estimation in ZigBee Sensor Networks

FATIH ILERIBogazici University

Department of Electrical EngineeringBebek, Istanbul

[email protected]

MEHMET AKARBogazici University

Department of Electrical EngineeringBebek, Istanbul

[email protected]

Abstract: Localization in wireless sensor networks has drawn significant research attention in recent years, sincemany real-life applications need to locate the source of incoming measurements as precise as possible. In this paper,two popular localization algorithms based on Trilateration and Weighted Centroid Localization are discussed.Noting that channel propagation and path loss modelling is a key in successful position estimation, we first developan analytical indoor channel model using our experimental setup including ZigBee devices. Subsequently, theperformance of the algorithms are evaluated both experimentally and via simulations with respect to the placementof beacons and channel imperfections.

Key–Words: Position estimation, RSSI, ZigBee

1 Introduction

GPS can be said to be the most popular tool against theoutdoor position estimation problems. But the indoorlocalization problems, where no GPS signals are ableto be received, require wireless sensor networks. Im-provements in the processor technology makes it pos-sible to locate multiple sensors to be used in indoor lo-calization problems. Several distance estimation tech-niques, based on the communication between locatedsensors, are present. RSSI is the most applicable onewith minimum cost [1]. And the position estimationprocess is performed based on the distance data de-rived from the RSSI measurements, as explained inSection 2. The basic problem in such a position esti-mation implementation is the errors in mathematicalmodel of the propagation channel. For instance, re-searchers prove that a WCL based position estimationsystem, distance estimations of which are performedwith Friis’ free space transmission equation [2], yieldshigh error rates [3]. In this paper, differently fromother related researches, an empirical channel modelis developed rather than implementing position es-timation algorithms being dependent on the presentchannel models. In addition, advantages and deficien-cies of the two popular position estimation method-ologies, the WCL and the Trilateration, are introducedby both simulation and implementation.

2 Position Estimation AlgorithmsEstimating coordinates of a node in a 2-D field re-quires communicating with at least three stations si-multaneously. The WCL and the Trilateration algo-rithms, which are developed based on this idea, arebriefly explained in Section 2.2 and Section 2.3, re-spectively. The algorithms in question are based ondistance estimation between transmitter and receiverantennas, and since such a distance estimation re-quires path loss modelling, it is necessary to deal withpath loss modelling before the position estimation al-gorithms in question.

2.1 Path Loss ModellingPath loss is the power density reduction of a radiosignal as it propagates through space, and mathemati-cally, it can be explained as the difference (in dB) be-tween the transmitted signal power and the receivedsignal power, as in (1).

L = 10 · log(PTX/PRX) (1)

where L is the path loss in dB, PTX is the transmis-sion power of the sender in Watts, and PRX is the re-maining power of a wave at the receiver in Watts.

Free space loss, multipath and fading are the lead-ing factors causing path loss. Brief information aboutthe complications in question is presented below.

• Free Space Loss: Radio signals disperse with dis-tance, so when the distance between the receiverand the transmitter antennas increase, less signal

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power is induced at the receiver side. Even if noother impairments are present, the signal attenu-ates over distance since it is spread over a largerarea during transmission.

• Multipath: Multipath problem is the arrival of aradio signal to the destination antenna by two ormore paths. The problem arises from the directand reflected signals that are often opposite inphase. These signals may cancel out each othercausing data loss at the receiver antenna. Mul-tipath problem generally occurs in environmentswhere metallic surfaces are present.

• Fading: Fading is the variability of the power ofa wireless signal depending on the environmentaleffects such as changing atmospheric conditionsfor fixed environments, and changing numbersand locations of the obstacles blocking wirelesstransmission for the mobile media.

RSSI is the information related to the receivedpower on the antenna during the related data packetreception. RSSI can be expressed in dB using a ref-erence signal strength PRef value (usually taken as1mW ), as in (2):

RSSI = 10 · log (PRX/PRef ) (2)

where PRX is the remaining power of a wave at thereceiver in Watts.

The RSSI value related to any received datapacket is available at the physical layer in the IEEE802.15.4 network. Signal power at the receiver an-tenna can be obtained by using the RSSI data capturedfrom any ZigBee receiver in (2). Once the receivedsignal power is obtained, then estimating the distancebetween the receiver and the transmitter antennas ispossible by using a path loss model. Two of the com-monly used path loss models are briefly explained be-low.

• Log-Distance Path Loss Model: The Log-Distance Path Loss Model is an indoor radiopropagation model which estimates the attenua-tion of a radio signal that occurs while the signaltravels in a closed area. The model is formallyexpressed in (3) [4].

L(d) = L(d0) + 10 · η · log(d/d0) +Xg (3)

where L(d) is the total path loss measured in dBat distance d, L(d0) is the path loss at the ref-erence distance d0 which is generally taken as1m, η is the path loss exponent, and Xg is a zeromean Gaussian random variable, modelling theshadowing effect on the received signal power.

• ITU Model For Indoor Attenuation: The ITUIndoor Propagation Model, also known as ITUModel for Indoor Attenuation, is a radio propa-gation model that is used to estimate the path lossinside a closed area delimited by walls. As beinga suitable indoor channel model, the ITU IndoorPropagation Model approximates the total pathloss that an indoor link may experience. Whilethe model is applicable only to the indoor envi-ronments, generally it uses the lower microwavebands around 2.4 GHz. However, the model issuitable to be applied to a much wider range.Mathematical formulation of this model is givenby [5]

L(d) = 20·log(f)+N ·log(d)+Pf (n)−28 (4)

where L(d) is the total path loss in dB, f isthe data transmission frequency in megahertz(MHz), d is the distance between the receiverand the transmitter antennas in meters (m), N isthe distance power loss coefficient, n is the num-ber of floors or walls to be penetrated betweenthe transmitter and the receiver, and Pf (n) is thefloor loss penetration factor. The distance powerloss coefficient, N , is the empirically determinedquantity which expresses the loss of signal powerwith distance. Some commonly encountered val-ues for the distance power loss coefficient aregiven in Table 1 [5].

Table 1: Some commonly encountered values of thedistance power loss coefficient.

Frequency Residential Office Commercial900MHz N/A 33 201.2GHz N/A 32 221.3GHz N/A 32 221.8GHz 28 30 224GHz N/A 28 22

5.2GHz N/A 31 N/A

2.2 Weighted Centroid Localization (WCL)

The Centroid Localization (CL) algorithm estimatesthe unknown node coordinates simply by taking theaverage of the coordinates received from the transmit-ter antennas each of which broadcast their own posi-tion data [6]. The mathematical representation of the


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algorithm is given by [6]

P(CL)i (x, y) = (1/n)

n∑j=1

Bj(x, y) (5)

where P (CL)i (x, y) is the estimated coordinates of the

ith node, Bj(x, y) is the exact coordinates of the jthbeacon where the beacons are the transmitter antennaseach of which continuously broadcasts its own coor-dinates, and n is the number of beacons, coordinatesof which are received by the ith node.

The WCL, proposed by [3], is an extension of theCL algorithm. In WCL, every position data receivedby a node is added to the sum after being multipliedby a weight coefficient between the node and the bea-con. The same procedure is implemented for each ofthe beacons covering the subject node. Once the sumis obtained, then it is divided by the sum of all theweight coefficients between the subject node and thecommunicated beacons. The mathematical expressionof the method is given by

P(WCL)i (x, y) =

∑nj=1(ωij ·Bj(x, y))∑n

j=1 ωij(6)

where P (WCL)i (x, y) is the estimated coordinates of

the ith node, Bj(x, y) is the exact coordinates of thejth beacon, and ωij is the weight coefficient betweenthe ith node and the jth beacon.

Note that equating ωij = 1 for all i, j; we getthe simple CL algorithm in (5). Considering a con-centric wave expansion with a linear characteristic ofthe receiver and a uniform density of the beacons, re-searchers form the weight coefficients as [3]:

ωij =1

(dij)g(7)

where ωij is the weight coefficient between the ithnode and the jth beacon, dij is the distance betweenthe ith node and the jth beacon, and g is the weightingdegree.

Considering (6) and (7) one can easily concludethat increasing the weighting degree decreases the ef-fect of the far away beacons marginally, but exces-sively high weighting degree will make a node to esti-mate its coordinates nearly the same with the nearestbeacon, thus increasing the error. Hence the weight-ing degree has to be optimized.

2.3 Trilateration

Consider a nodeN with an unknown location (nx, ny)and three beacons A, B and C, known as the posi-tions (ax, ay), (bx, by) and (cx, cy), respectively. The

trilateration problem is to compute the coordinates ofnode N , given distances da, db and dc, from the nodeto beacons A, B and C, respectively. Using the esti-mated distances from the node to the three beacons,the problem can be defined as in the following systemof equations:

(nx − ax)2 + (ny − ay)

2 − d2a = 0 (8)

(nx − bx)2 + (ny − by)

2 − d2b = 0 (9)

(nx − cx)2 + (ny − cy)

2 − d2c = 0 (10)

In most cases, due to the errors in path loss measure-ments causing distance estimation errors, right handsides of (8) - (10) are nonzero, thus the system doesnot have a solution. If this is the case, Circle Inter-sections With Clustering method can be used in esti-mating position of the node in question [7]. Considerthe circles of radii da, db and dc around points A, Band C, respectively. Since the circles’ centers andradii, derived from path loss measurements togetherwith the considered channel model, are obtained withmeasurement errors, the circles will not intersect at asingle point and probably overlap in a small region,where the unknown node N is located inside. If themeasurement errors are not extremely high, then eachpair of circles yields two intersection points. Three ofthese points are clustered closely together, while theothers are located far from this group. The node N islocated in the middle of this cluster as shown in Fig.1 [7].

Fig. 1: Clustered regions among the three trilaterationcircles.

3 Simulation Based Study of Local-ization Techniques

As a preliminary work of indoor position estimationsystem design, we tested the most common two po-


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Fig. 2: Mean estimation error vs number of MonteCarlo iterations in Trilateration simulations under ran-dom noise with arbitrarily located nodes and 3 bea-cons.

sition estimation methodologies: WCL and Trilater-ation. There are two important parameters for bothmethods to perform successful estimations, which arethe number and the position of the beacons. Besides,there is an additional crucial parameter for the WCLmethodology which is the weighting degree. We de-veloped a software program to simulate the WCLmethod, and a Matlab tool to simulate the Trilatera-tion. We tested both of the methods with various bea-con placements, with the aim of optimizing the posi-tion estimation setup. We implemented the algorithmsfor all the possible node locations on a 2-D fieldmodel of 400 units width and 600 units length, set-ting the weighting degree for WCL to 2.78, which isthe derived path loss exponent in the empirical chan-nel model development (see Section 4.1). We run bothmethods by applying the same random noise vector onthe distance values to model the unreliability of RSSIdata.

We used the circle intersections with clusteringmethod in the Trilateration implementations. Werun the Trilateration algorithm by performing MonteCarlo simulations with 400 iterations, which can besaid to be a reasonable number considering the simu-lation results displayed in Fig.2.

3.1 Evaluation of 3 Beacons Case

In this section we evaluate the performance of thetwo algorithms for the following 5 configurations asshown in Fig.3. Fig.3(a) - Fig.3(e) represent thebeacon placements in each configuration. For in-stance, let (x, y) be any location on the 2-D simulationfield, then beacons are located at (2, 2), (2, 398) and(598, 398) on the 2-D simulation field of 400 unitswidth and 600 units length in the beacon placementcase 1 as displayed in Fig. 3(a). With these beaconplacement configurations we aim to examine the per-formances of the Trilateration and WCL covering all

the significant beacon placement variations possiblewith 3 beacons on a rectangular 2-D field. We simu-late the algorithms for all possible node locations onthe simulation field. Simulation results are shown inFig.4 - Fig.9.

(a) Beacon placementcase 1.

(b) Beacon placementcase 2.

(c) Beacon placementcase 3.

(d) Beacon placementcase 4.

(e) Beacon placementcase 5.

Fig. 3: Placements of the beacons in three beaconscase simulations.

In the simulation results shown in Fig.4 - Fig.8it is seen that estimation error of WCL increases ex-cessively as the unknown node position gets out ofthe borders set by the beacons. Besides, mean er-rors of WCL estimations in cases 1 through 5 arefound as 25.7%, 17.3%, 19.1%, 25.2%, and 22.3%,respectively. Thus, beacon placements in case 2 (seeFig.3(b)) can be said to be the optimal beacon deploy-ment formation for a WCL based position estimationsystem with three beacons.

On the other hand, it is seen that the performanceof Trilateration stays constant in all the five deploy-ment formations in question. The estimation errorsof Trilateration for the three beacons cases displayedin Fig.9 is only due to the random noise matrix ap-plied to the distance data between the node and thebeacons, duplicate of which is also applied in WCLestimations.


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Fig. 4: WCL performance for case 1 displayed inFig.3(a).

Fig. 5: WCL performance for case 2 displayed inFig.3(b).

Fig. 6: WCL performance for case 3 displayed inFig.3(c).

Fig. 7: WCL performance for case 4 displayed inFig.3(d).

Fig. 8: WCL performance for case 5 displayed inFig.3(e).

Fig. 9: Trilateration performance for all the cases dis-played in Fig.3.


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3.2 Evaluation of 4 Beacons Case

In this section, we evaluate the performance of the Tri-lateration and WCL algorithms for 2 different beaconplacement configurations with four beacons as shownin Fig.10. Beacon placement case 6 and beacon place-ment case 7 are displayed in Fig.10(a) and Fig.10(b),respectively.

The Trilateration algorithm is modified such thatthe algorithm takes the average of the results obtainedfrom the four different combinations built by differentthree beacons sets. This modification is set active forall the Trilateration simulations for the cases wherethe number of beacons is greater than 3. Results ofthe four beacons case simulations are shown in Fig.11- Fig.13.



Fig. 10: Placements of the beacons in four beaconscase simulations.

Fig. 11: WCL performance for case 6 displayed inFig.10(a).

Simulation results displayed in Fig.11 show thatperformance of WCL decreases as the node getscloser to the centroid of two beacons located on acommon edge of the field. On the other hand, con-sidering the error distribution displayed in Fig.12 it isagain seen that estimation error increases as the nodegets out of the borders set by the beacons. Moreovermean errors of WCL in beacon placement cases 6 and

Fig. 12: WCL performance for case 7 displayed inFig.10(b)

Fig. 13: Trilateration performance for the cases dis-played in Fig.10.


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7 are found as 16.6% and 14%. Thus, beacon deploy-ment formation displayed in Fig.10(b) can be said tobe the appropriate one for a WCL based position es-timation system with four beacons. Besides, Trilater-ation performance again stays constant independentlyfrom the beacon placements. But it is worth to notethat estimation error of Trilateration decreased from2% to 1.5% although the random noise matrix is keptconstant, since the modified Trilateration algorithmtakes the average of the results obtained from the fourdifferent combinations built by different three beaconssets.

3.3 Evaluation of 8 and 16 Beacons Cases

In order to examine the performances of the two meth-ods for higher number of beacons, we run simula-tions for eight beacons and 16 beacons cases. Beaconplacements are shown in Fig.14. Results are shown inFig.15 - 18.



Fig. 14: Placements of the beacons in eight and 16beacons cases.

Fig. 15: WCL performance for case 8 displayed inFig.14(a)

Also simulation results displayed in Fig.15 andFig.16 show that WCL performance decreases as thenode gets closer to the centroid of two consecutivebeacons located on a common edge of the simulation

Fig. 16: WCL performance for case 9 displayed inFig.14(b)

Fig. 17: Trilateration performance for case 8 dis-played in Fig.14(a)

Fig. 18: Trilateration performance for case 9 dis-played in Fig.14(b)


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field, as seen in the previous cases. The mean erroralso decreases as the number of beacons is increased,such that mean error for the eight beacons case (place-ment case 8 displayed in Fig.14(a)) is found as 11%while the mean error for the 16 beacons case (place-ment case 9 displayed in Fig.14(b)) is found as 4.3%.The mean estimation error of the Trilateration also de-creased from 1.4% for the eight beacons case to 1.2%for the 16 beacons case.

3.4 Evaluation of the Trilateration and WCLwith Erroneous Channel Model

All the simulations up to now are performed assum-ing that the estimated distances between the node andthe beacons are only exposed to random noise, whichcould be lowered by increasing the number of MonteCarlo iterations. In order to get a better knowledgeabout performance of both two position estimationmethodologies, we modified our simulation softwarein order to calculate the distances as if they are derivedfrom the ITU Model (see Section 2.1). We assignedthe floor loss penetration factor parameter (Pf (n)) ofthe ITU Model with varying error rates, and observedthe performances of WCL and Trilateration methods.Simulations are run for the beacon placement case 6(see Fig.10(a)). Results are shown in Fig.19 - Fig.22.

Fig. 19: WCL performance with the ITU Model,Pf (n) parameter of which is provided with 20% er-ror.

3.5 Comparison of WCL and TrilaterationBased on the Implemented Simulations

To make a reasonable comparison between the WCLand the Trilateration methods, we simulated them onthe same test setup with the same noise vector. Sce-narios with 3, 4, 8 and 16 beacons with various place-ments are implemented. We also simulated the case

Fig. 20: Trilateration performance with the ITUModel, Pf (n) parameter of which is provided with20% error.

Fig. 21: WCL performance with the ITU Model,Pf (n) parameter of which is provided with 100% er-ror.

Fig. 22: Trilateration performance with the ITUModel, Pf (n) parameter of which is provided with100% error.


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where one of the channel model parameters is pro-vided with error.

Considering the simulation results displayed inFig.4 - Fig.8, one can easily conclude that WCL failswith high error rates with three beacons. It is also seenthat WCL performs worse when the node position tobe estimated is located outside of the boundaries setby the beacons. It is also seen that the region on the 2-D simulation field where the estimation error of WCLis less than 2%, expands as the number of beaconsincreases. Furthermore, maximum estimation error ofWCL encountered decreases as the number of beaconsincreases. For instance the maximum error is 52% forthe beacon placement case 6 (see Fig.11), while it is23% for the beacon placement case 9 (see Fig.14(b)).On the other hand, it is seen in Fig.9, Fig.13, Fig.17and Fig.18 that the Trilateration is quite robust againstthe number and placements of the beacons, such thatthe estimation error does not exceed 5% for any of thecases in question.

Simulation results displayed in Fig.11, Fig.12, 15and 16 show that the position estimation performanceof the WCL algorithm decreases as the node getscloser to the edges of the 2-D simulation field, espe-cially as the node location gets closer to the centroidof two consecutive beacons. Besides, considering thesimulation results displayed in Fig.19 - Fig.22, onecan easily conclude that WCL method is much morerobust against errors in the path loss model used indistance estimations, when compared to the Trilater-ation method, since the estimation error of the WCLalgorithm stays nearly constant even if the parame-ter Pf (n) is assigned with error rates up to 100%,while the Trilateration performance decreases exces-sively when erroneous Pf (n) is provided.

Thus, it can be concluded that Trilateration ismore robust against varying number and locations ofthe beacons, while WCL is more dependent on thebeacon numbers and placements. On the other hand,WCL is much more robust against errors in channelmodelling when compared to the Trilateration.

4 Experimental Evaluation of theLocalization Methods

Here we introduce our position estimation system, in-cluding the design procedures and performance com-parison with the ITU Indoor Channel Model. Initiallywe designed a ZigBee based path loss measurementsystem composed of a transmitter (see Fig.23) and areceiver (see Fig.24) connected to the PC, where thedeveloped position estimation software is run. Subse-quently we collected path loss data in an indoor area.

Fig. 23: RSSI transmitter.

Fig. 24: ZigBee receiver module.

Based on the collected path loss data we derived anindoor path loss model and performed position esti-mations with both WCL and Trilateration methods.

After completing the hardware design and soft-ware update procedures, RSSI measurements are im-plemented in a 20 meters x 50 meters closed industrialarea as a requirement for our empirical indoor chan-nel model design. The ZigBee receiver together with aPC are placed to a corner of the stated closed area, andthen we moved RSSI transmitter along the diagonal ofthe area (54 meters) sending 200 RSSI samples per 1meter. Once an RSSI byte is received by the software,it is than converted to path loss in dB as follows: TheRSSI data output from the XBee module is in [dBm],hence the received power can be derived from (2) byassigning PRef = 1mW . Once the received poweris derived, than the corresponding path loss value isgenerated by (1). The measurements are displayed inFig.25.

We also tested the correlation of the ITU Modelwith our measurements. The corresponding ITU


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Fig. 25: Path loss vs distance (The blue dots and thered bars represent the average path loss and the varia-tion of the path loss measurements at the related dis-tances, respectively).

Fig. 26: ITU Model path loss estimations vs our mea-surements (The red curve and the blue plot representthe theoretical path loss estimations of the ITU Modeland the measured path loss values, respectively).

Model for the same floor case is as [5]

PL(d) = 39.6 + 30 · log(d) (11)

where PL(d) is the path loss in dB, and d is the dis-tance in meters.

ITU Model estimations and the measurements aredisplayed together in Fig.26. It can easily be con-cluded from Fig.26 that the ITU Model performanceis not satisfactory in the industrial area, where we col-lected our measurement data.

4.1 Empirical Channel Model Design

We have derived an empirical log distance path lossmodel based on our measurements and the generic logdistance model, which is expressed as

L(d) = L(1) + η · log(d) (12)

By rewriting (12) as

L(d)− L(1) = η · log(d) (13)

and considering the distances varying between 1 me-ter and 54 meters (d1 through d54 = 1m through 54m),we can represent (13) in matrix form: log(2)

...log(54)

· η =

L(2)...

L(54)

−

L(1)...

L(1)

By letting

A =

log(2)...

log(54)

, b = L(2)− L(1)

...L(54)− L(1)

we obtain the system of

A · η = b (14)

The least squares solution of the above system is givenby

η = (ATA)−1 ·AT b =

∑54i=2 log(i) · [L(i)− L(1)]∑54

i=2 log2(i)

(15)The numerical value of (15) for the data yields

η = 27.7753 (16)

Noting that the path loss at reference distance 1m ismeasured as L(1) = 46.3118, our path loss model isthus finalized as:

L(d) = 46.3118 + 27.7753 · log(d) (17)

Fig.27 displays the performance of our path lossmodel when compared with the real path loss mea-surements.

4.2 Position Estimation ImplementationsBased on the Designed Model

After completing the design procedures, we tested ourpath loss model in position estimations by using pathloss values corresponding to distances of all the pos-sible positions to where the ZigBee receiver is placed.Since we could not obtain enough number of ZigBeemodules, we tested our model on the simulator soft-ware we had developed. We made the simulations us-ing both WCL and Trilateration methods for the bea-con placement case 6, by setting the simulation fielddimensions to 20 x 50.


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Fig. 27: Predictions of our path loss model vs mea-sured path loss values (The red curve and the blue plotrepresent the theoretical path loss estimations of ourmodel and the real path loss measurements, respec-tively).

At each step of the simulations, once the distancebetween the node and a beacon is calculated, then thecorresponding path loss value obtained from our mea-surements to the calculated distance, is input to ourmodel. Then the distances output from our model areused in position estimations, as explained in previoussections.

Fig. 28: Position estimations performed by our pathloss model with the WCL method.

Considering the results shown in Fig.28 andFig.29 we see that the overall performance of WCLhas a minor difference when compared to running thealgorithm with ideal distance values. But the case isworse for the Trilateration simulations, such that theerror is about 16%, supporting our assertion that theTrilateration method is much more dependent on theerrors in the channel model parameters.

Fig. 29: Position estimations performed by our pathloss model with the Trilateration method.

5 Conclusion

In this paper, a 2-D indoor position estimation sys-tem is designed and implemented following the designof a log-distance based empirical indoor channel pathloss model for ZigBee sensor networks using the pathloss data measured in an industrial area. The designedmodel is realized by applying curve fitting on the pathloss measurements using the Least Squares Solutionmethod. The performance of the designed model iscompared with the ITU model for indoor attenuation.Based on the collected path loss data, our model givesobviously more successful distance estimates. Wealso compared the position estimation methods whichare the WCL and the Trilateration, with simulationsbased on both the exact distances exposed to Gaus-sian noise, and the distance estimation results of ourmodel. It is concluded that; under the same noisecharacteristics, Trilateration method gives more pre-cise position estimates compared to the WCL, if thechannel model perfectly matches with the real chan-nel characteristics. In contrast, WCL is much morerobust against errors in the channel model parameters,when compared to the Trilateration. Hence, WCL willbe a better choice unless the path loss based distanceestimating channel model perfectly represents the realchannel characteristics of the indoor area in question.Future work will concentrate on designing a 3-D po-sition estimation system for multi-floored buildings.

6 Acknowledgement

This work was sponsored by SANTEZ project grantnumber 01109.STZ.2011-2.


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References:

[1] R. Mardeni, S.N. Othman, Node Positioningin ZigBee Network Using Trilateration MethodBased on the Received Signal Strength Indica-tor (RSSI), European Journal of Scientific Re-search, 2010, pp. 48–61.

[2] T.S. Rappaport, Wireless Communications:Principles and Practice, Prentice-Hall Inc.,1996.

[3] J. Blumenthal, R. Grossmann, F. Golatowski andD. Timmermann, Weighted Centroid Localiza-tion in ZigBee-based Sensor Networks, IEEEInternational Symposium on Intelligent SignalProcessing, 2007, pp. 1–6.

[4] A. Goldsmith, Wireless Communications, Cam-bridge University Press, 2005.

[5] S.M. Hameed, Indoor Propagation Modeling forWireless Local Area Network (WLAN), Inter-national Journal of Computers, Communica-tions and Control (IJCCC), 2011.

[6] N. Bulusu, J. Heidemann and D. Estrin, GPS-less Low Cost Outdoor Localization For VerySmall Devices, IEEE Personal Communications,2000, pp. 28–34.

[7] A. Kaminsky, Trilateration, Lecture note,Rochester Institute of Technology, 2007.


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RSSI Based Position Estimation in ZigBee Sensor Networkswseas.us/e-library/conferences/2014/Tenerife/CSST/CSST-07.pdf · many real-life applications need to locate the source of incoming