3D fingerprint-based Localization for Wireless

3D fingerprint-based Localization for Wireless Sensor Networks Jorge J. Robles 1, Martin Deicke 2, and Ralf Lehnert1 1

Dresden University of Technology, Dresden, 01069 Germany {robles| lehnert}@ifn.et.tu-dresden.de 2 [email protected] applications and they degrade in accuracy if all or some nodes are mobile. Anchors are nodes, whose positions are known. Several algorithms need the presence of anchors in the networks in order to calculate the position of other nodes. But there are also particular localization algorithms which are able to operate without anchors providing a relative position for the nodes [19].

Abstract—The position information of the nodes in a WSN has become crucial for many advanced features such as routing, clustering, and context-based applications. If the localization algorithm is distributed, the sensor nodes are able to calculate the position on their own without the help of a central computer. In this case the design of localization algorithms is a challenge due to the fact that the nodes are limited in relation to the memory capacity, processing power and energy consumption. In this paper we analyze the suitability of a distributed fingerprint-based localization algorithm, where sensor nodes store relevant information called fingerprints in order to use this knowledge during the position calculation. The localization algorithm has been evaluated in a three dimensional scenario using the framework MIXIM of the simulator tool OMNET++.

Mobility

Mobile/ Static

Index Terms— localization scheme, location fingerprinting, positioning algorithm, radio frequency (RF), wireless sensor networks

Anchor-based/ Anchor-free

Coordinates

Relative/ Absolute

I. INTRODUCTION

W

ireless sensor networks have become a major research field during the last years. They consist of hundreds, sometimes thousands of spatially distributed autonomous devices gathering and exchanging data. The devices are mostly battery powered. Thus, they should be as small, lightweight, cheap and energy-efficient as possible. The information of the localization of a node in a Wireless Sensor Network (WSN) can be used for different aims: in clustering, for example, to assign a node as cluster-head [5]. Several proposals of geographic routing operate based on the node positions [6]. Also in context-based applications the measurements have to be accompanied by the node position to make the gathered information useful. One of the most important considerations in the design of protocols for WSNs is the reduction of the energy consumption of the nodes. Therefore many localization algorithms designed for other technologies, like Wireless LAN, GSM or GPS cannot be implemented directly in a decentralized WSN, where the nodes cannot calculate complex algorithms. The systems for localization in a WSN can be classified under different aspects (see Fig. 1). The localization methods can provide absolute coordinates for all nodes, like GPS, or relative coordinates, where the position is referenced at a known position or thing like a node, or a room in a building. It has to be noted that many algorithms are designed for static 978-1-4244-7157-7/10/$26.00 ©2010 IEEE

Anchors

Calculation

Distributed/ Centralized/ Cluster-based

Scenario

Indoor/ Outdoor

Localization in WSN

Range

Range-free/ Range-based

Fig. 1. Classification of the localization algorithms in WSN

If the calculation of the position of all the nodes is done by just one computer, the localization system is centralized. If the nodes are able to execute the position calculation the localization is distributed. Another option is presented when the network is divided into clusters, and each cluster contains a clusterhead, which calculates the position only for the nodes within its cluster. There is a classification related to the dependency of the result on the inter-node measurements. The range-free algorithms use the connectivity and the proximity information to calculate the position of a node [7]. The range-based algorithms need precise inter-node measurements like the distance or the angle (direction of the propagation) in order to determine the position. There are algorithms which are designed for indoor scenarios, where multipath and shadowing are common 77

problems and for instance the GPS signal can not be received. In out-door environments there are other challenges, like extreme environmental conditions, which can influence the accuracy of the localization algorithms. The fingerprint technique for localization, also called scene analysis, is usually utilized in indoor-scenarios because it takes the stationary characteristics of the environment (e.g. wall attenuation) into account. Principally this technique consists of two phases: In the first phase, which is called offline phase, the fingerprints are collected and stored in a database. The fingerprints contain information such as the Received Signal Strength Indicator (RSSI) from fixed nodes or sensor measurements, which were taken at known positions. In the online phase, which is the normal network operation, the stored fingerprints and currently measurements are utilized in order to estimate the position. The goal of this technique is to find a selected set of stored fingerprints, which are close to the measurements of the online phase and utilize their respectively associated positions for the position estimation. It is based on the assumption that the characteristics of the environment in the online phase are similar to the offline phase. This assumption is not always valid and if the fingerprints generated in the offline phase are not updated the position accuracy is degraded. RADAR [4] was one of the first works that used the fingerprint technique being a centralized proposal for IEEE 802.11. During its offline phase signal strength measurements are stored at 70 different positions. In the online phase of RADAR the algorithm k-nearest-neighbor is executed. It searches the k fingerprints from the database that are closest in terms of the currently observed signal strengths. Using the geographical positions of the k selected fingerprints a Centroid [1] is calculated. The achieved accuracy is in the range of 2-3 meters (with a 50% confidence). Another famous system, which utilizes signal strength measurements as fingerprints, is MOTETRACK [2]. It is a distributed system which is designed for a wireless sensor network. The accuracy of this system is similar to the obtained with RADAR but it improves the robustness against node failures and signal perturbations. In [3] the authors exploit the environmental properties including in the fingerprints not only readings of the received signal strength indicator (RSSI) but also sensor measurements like temperature, humidity and ambient noise. In some cases this proposal improved the accuracy compared to RADAR. There are several localization systems based on RSSI fingerprints for different technologies such as GSM and WLAN. These systems are usually centralized including a computer with a high amount of memory and processing power, which calculate the position for all the nodes in the network. Thus, complex algorithms based on probabilistic method, neural networks, filter particle, or support vector machine can be executed leading to an improvement in the position accuracy [8]. In most cases the position information is mapped on a two-dimensional coordinate system. We investigate the adaptability of a three-dimensional fingerprint-based distributed localization algorithm to the properties of a WSN. The influence of different parameters on

the position accuracy was analyzed through a simulative study.

II. THE FINGERPRINT TECHNIQUE The fingerprint technique is divided into two phases: A. Offline phase During the offline phase the fingerprints are generated and stored in the database. The usual method is to move a sensor node through the environment for taking measurements at known positions. If the fingerprint contains RSSI measurements fixed anchors are installed in the environment for referencing the RSSI measurements. Naturally the positions of the anchors should not change during the online phase. We represent the database using the set D, which contains the n generated fingerprints. Each element of D is defined as a tuple. The index i identifies the fingerprint in the database.

D = {Fi =1 , Fi = 2 , Fi =3 .....Fi = n } Fi = {Pi , S i }

(1) (2)

The set Pi contains the coordinates of the position. In addition the orientation of the node can be included using for example the azimuth θ and the inclination φ. Si is the measurement dataset collected during the offline phase at the position Pi.

{

Pi = (xi , yi , zi ) | xi , yi , zi ∈R3

S i = {Ri , Ti , H i , Li }

{

}

Ri = ri j =1 , ri j = 2 , ri j = 3 .....ri j = m

}

(3) (4) (5)

The measurement dataset should be able to reference correctly the position Pi. If the fingerprints contain environmental measurements, it is important to investigate their spatial correlations for checking how appropriate the measurements are for this technique. If the anchors are also equipped with environment sensors, it is possible to store not only absolute measurements taken by the mobile node but also relative values to the anchors. To exemplify in (4) we suppose that Si contains RSSI values (Ri) and three environmental measurements such as temperature (Ti), humidity (Hi) and light of the environment (Li).

ri j is the averaged RSSI measurement taken from the

anchor j and m denotes the number of anchors in the system. Additional information related to the measurements, like the standard deviation, could also be included in Si. B. Online phase In the online phase a new measurement set called Son is generated, which will be used for searching the correct 78

T = {X i =1 , X i = 2 , X i =3 ..... X i = p }

fingerprints from the database.

Son = {Ron , Ton , H on , Lon }

{

Ron = ronj =1 , ronj =2 , ronj =3 .....ronj =m

{

Wi = wib =1 , wib = 2 , wib = 3 .....wib = e

(6)

}

(7)

}

(10)

b

The weight factors wi are arranged in the subset Wi, where b identifies the different weight factors and e indicates the

Where Ton contains the temperature measurements, Hon corresponds to the humidity measurements and Lon represents the light measurements realized in the online phase. Ron contains the set the averaged RSSI measurements taken from m number of anchors and

(9)

b =1

maximal number of elements of Wi. For example wi

could

be assigned in terms of the similarity of the RSSI measurements between the online phase and the offline phase. There are different distance metrics to identify this similarity. The Euclidean Distance [4] is one of the most used. In (11) this metric is calculated between the elements of Ri and the elements of Ron included in Son.

ronj denotes the averaged RSSI

measurement taken from the anchor j. The environmental measurements can have different spatial correlations for different scenarios. If the correlation is high the measurements do not provide useful information for the position calculation. Keeping the sensors active can be expensive in terms of energy consumption for a mobile node, therefore on-demand activations of the sensors could be an interesting proposal for saving energy.

d Eucl ( Ri , Ron ) =

m

∑ (r

j on

− ri j ) 2

(11)

j =1

MOTETRACK [2] uses the low-complexity Manhattan distance (12). In our example this is: Measurements in the online phase

Fingerprints in the offline phase

m

d Man ( Ri , Ron ) = ∑ (ronj − ri j )

Son

D The Mahalonibis distance [18] needs that the fingerprints contain the information of the variance of the measurements. This metric takes the correlations of the dataset into account and is scale-invariant.

Assignment of weights

T

Another

Filter: Selection on T

wib = 2 could be related to the geographic distance

between the last calculated position by the node and Pi. Thus, this information could be used to filter fingerprints that are not appropriate for the calculation based on the assumption that the actual position of the node is not far from its last registered position. In other cases weight factors could be assigned in relation to the different times of day where the fingerprints were generated. In other words the aim of Wi is to indicate how appropriate the stored Pi for the position calculation are. The Filter Selection on T eliminates unnecessary fingerprints according to the assigned weights, the knowledge of the system and defined criteria. The subset T’ contains the results of this filter. For instance the elements of T could set in

T’ Position calculation Fig 2. Calculating the position in the online phase

The Fig. 2 depicts the general sequence to estimate the position using the fingerprint technique and the k-nearestneighbors method. This method is appropriate for a distributed wireless sensor network due to its low complexity. The goal of the k-nearest-neighbors method is to find the best k stored positions from the database for the position calculation. The fingerprints stored in the database D and the online measurements Son are the main inputs of a process called Assignment of weights. Here the information provided by Son and additional knowledge of the system are used to assign weight factors to the stored positions Pi creating tuples called Xi. The set T is built with the existing Xi having p number of elements.

X i = {Pi ,Wi }

(12)

j =1

b =1

order in a list in relation to the minimal presented wi

. Thus,

the filter eliminates the elements, which are next to the first k positions in the list. This method is used in our implementation. The processes Assignment of weights and Selection on T could be executed many times, where different weights and criteria for filtering are taken into account in each time. During this iterative process the set T and T’ are updated. At the end of this phase the subset T’ contains the k selected elements that will be used for the position calculation. In the last phase called Position calculation the elements of T’ are used by a localization algorithm such as Nearest

(8)

79

Position, Centroid (13) or Weighted Centroid (14)(15)(16) for the position estimation. In case the Nearest Position is executed, T’ is created only with one element: Xi. The estimated position of the node is the position contained in Xi. Otherwise the Centroid takes the k elements of T’ and provides an estimated position Pe averaging the respective Pi of the selected fingerprints:

⎛1 k ⎞ 1 k 1 k Pe (xe , ye , ze ) = ⎜ ∑Pl (xl ), ∑Pl ( yl ), ∑Pl (zl )⎟ k l=1 k l=1 ⎝ k l=1 ⎠

consideration an on-demand implementation can be designed where the receiver takes n RSSI samples in relation to the expected statistical accuracy. Unfortunately the expected standard deviation is normally unknown and is variable with the distance. In this case, t-Student confidence intervals can be considered for providing statistically accuracy. When there is correlation between the RSSI samples the assumption that the measurements are independent cannot be taken. We assume that the link has symmetric properties [10]. This means that in a bidirectional communication between two nodes with the same transmission power the resulting averaged RSSI on both sides will be similar.

(13)

The weighted centroid includes the weight factors of the set Wi ∈ T’ to calculate the coordinates, e

k

e

⎞

∑∑w ⎟⎠ b l

MN

(14)

l=1 b=1 k

e

⎞

∑∑w ⎟⎠ b l

(15)

(16)

WCL

l=1 b=1 k

e

⎞

∑∑w ⎟⎠ b l

AN Loc_req

1st STAGE

⎛ Pe (xe ) = ⎜ ∑Pl (xl )∑wlb b=1 ⎝ l=1 k e ⎛ Pe ( ye ) = ⎜ ∑Pl ( yl )∑wlb b=1 ⎝ l=1 k e ⎛ Pe (ze ) = ⎜ ∑Pl (zl )∑wlb b=1 ⎝ l=1 k

l=1 b=1

Loc_resp (RSSI_MN, AN_pos)

2nd STAGE

Avg_rssi (RSSI_AN1,RSSI_AN2,etc)

III. CONSIDERATIONS AND ASSUMPTIONS A. RSSI and radio model In the implemented algorithm the fingerprints contain RSSI measurements. Therefore the most relevant points related to this indicator are described in this section. The RSSI is provided by many wireless devices of different technologies and denotes the strength of the signal observed by the receptor. In free space the behavior of received signal strength Pr(d) in relation to the distance can be described by the Friis equation (20) [9].

Pt Gt Gr λ (4π ) 2 d 2

Fingerprint technique

Loc_resp2 (MN_pos)

Fig. 3. Communication protocol between the mobile node and the anchors

IV. PROTOCOL DESCRIPTION In the proposed scenario there are fixed anchors which know their positions. They maintain a database with the RSSI fingerprints, which were generated during the offline phase. In the online phase the proposed protocol is divided into two stages that can be run separately or in conjunction, (Fig. 3). In the first stage a mobile node (MN), which needs to know its position, broadcasts n localization requests (Loc_req). When the anchors receive the requests they send a packet (Loc_resp) with the averaged RSSI and its position back to the MN. The MN also measures the RSSI and exploiting the symmetric property of the link obtains a unique averaged RSSI from each Anchor (AN). Thus, the MN is able to execute the low-complexity Weighted Centroid Localization (WCL) algorithm [1], providing a coarse position. The achieved accuracy of WCL can be enough for many applications. If more accuracy is needed the second stage is executed. Here the MN sends the averaged RSSI values (Avg_rssi) to

2

Pr (d ) =

Loc_req2

(20)

Gt and Gr are the antenna gains in the transmitter and receiver respectively, d is the distance between transmitter and receiver, Pt is the transmitting power and¸ λ is the wavelength of the transmitter signal in meters. The RSSI is not a stable value. It is affected by reflection, diffraction, noise and fading. The RSSI dispersion can be considered by adding a zero mean gaussian distributed random variable to the attenuation model (expressed in dBm) [14]. By averaging multiple RSSI measurements the influence of the dispersion can be reduced improving the distance estimation. If the expected standard deviation of the gaussian dispersion is known and the RSSI samples are statistically independent confidence intervals can be calculated. Under this

80

the AN from which it received the strongest RSSI. With this information and using its database the selected AN calculates the position for the MN, executing a scheme based on the fingerprint technique and the k-nearest-neighbors method. During this operation the MN goes into sleep mode. If it is required, the MN wakes up for asking for its position (Loc_req2). Then the selected anchor sends the result calculated by the fingerprint technique (Loc_resp2). The second stage can improve the position accuracy at expense of extra signaling. A second proposal for the first stage is that the MN just broadcasts one localization request and then receives n packets from the anchors. A similar protocol is used by [2]. If this second proposal is implemented in an IEEE 802.15.4 [17] beaconless network the MN has to be active for a long time to receive enough packets from the anchors. This is due to the time that is required by the MAC layer (CSMA/CA) for a successful transmission. The MN is listening during the time between successful transmissions of the ANs (because it does not know when the next packet arrives) consuming a high amount of energy. By synchronizing the responses of the ANs the idle listening can be reduced. One advantage of the second proposal over the first one is that the MN transmits fewer packets decreasing the collision probability when there are other MNs in the same region. The second proposal was not implemented due to the high energy consumption in the MN, when it needs to take several RSSI measurements from each anchor for achieving a higher accuracy.

model proposed in [16]. The consumption of the different modes (sleep, transition, active) was obtained from the corresponding datasheets. 7) The accuracy is represented using an averaged error distance (Euclidean distance) between the real position and the estimated position of the node. Confidence intervals of 95% were considered in the simulation results.

Mobile node Anchor

50m

Fig 4. Reference scenario for the simulation.

B. Localization algorithms In the offline phase the MN sends packets at different positions inside the cube. The fingerprints Fi are built with the RSSI that were measured by the ANs. The RSSI values are calculated considering the attenuation model given in (20). For an AN1 the set Ri ∈ Fi contains the RSSI values registered by it and its direct neighboring anchors. We consider that the direct neighbors of AN1 are not all the anchors in the scenario. In contrast, they are the anchors whose positions are inside of sphere with center in AN1 and radius m. This radius is 3 times the minimal separation between the anchors in the scenario. In the online phase the MN takes random positions inside the cube, where the described protocol is executed. For the WCL the MN estimates its position Pe using (22),

V. IMPLEMENTATION A. Scenario We analyze the performance of the proposed algorithm using the simulator OMNeT++ and the framework MiXiM. The main characteristics and parameters of the reference scenario are: 1) There are 27 ANs regularly distributed in a cube (50m*50m*50m). The MN, which requires knowing its position, is placed inside the cube. See Fig. 4. 2) CSMA is selected for the MAC layer. 3) The MN broadcasts 5 requests in the first stage. Then, it listens during 80ms for receiving the answer of the ANs. In the second stage when the MN receives its position it goes into sleep mode waiting for the next period. The duration of the localization period is one second. 4) The RSSI values are registered in dBm. The RSSI dispersion is characterized by a gaussian distributed random variable with standard deviation set to 3 dBm. 5) There is a separation of 5 meters between fingerprints in each direction. Thus, a 3D grid is built with 1331 fingerprints. 6) The reference node contains the transceiver AT86RF212 [11] and the microcontroller ATMega1281 [12]. It is assumed that the node operates at 3 Volts. The energy consumption was analytically calculated using the energy

q q ⎛ q ⎞ ⎜ ∑ Al ( xl ) * ronl ∑ Al ( yl ) * ronl ∑ Al ( zl ) * ronl ⎟ ⎟ (22) , l =1 q , l =1 q Pe ( xe , ye , ze ) = ⎜ l =1 q ⎜ ⎟ ronl ronl ronl ⎜ ⎟ ∑ ∑ ∑ l =1 l =1 l =1 ⎝ ⎠

where q represents the number of anchors that participate in the calculation. Al(xl), Al(yl) and Al(zl) indicate the coordinates l

of the respective anchors and ron is the averaged RSSI obtained of the anchor Al . In the utilized fingerprint technique Wi is assigned in relation to the Manhattan distance between the online measurements and the stored fingerprints (12). Using the k closest fingerprints (in terms of RSSI) and the weighted centroid (14) (15) (16) the position of the MN is estimated. 81

The value k is set to 8.

the correct fingerprints set difficult.

C. Number of Anchors The Fig. 5 shows that the accuracy achieved by both algorithms is improved incrementing the available anchors. If p is the number of anchors per direction, the number of anchors in the scenario is p3. For WCL the anchors around the MN define a region where the MN can be found. If p is higher the anchors are closer to each other reducing this region. When the number of anchors increases the position of fingerprints can be better referenced including stronger RSSI from more anchors. It allows a better differentiation between the stored fingerprints during the position calculation.

Fig. 6. Position error in terms of the number of anchors when the RSSI discretization is not considered

E. RSSI dispersion Fig. 7 shows that the position accuracy is degraded by incrementing the RSSI dispersion. In most cases the WCL presents less position accuracy but it is more robust than the fingerprint-based proposal. For a high dispersion such as 7dBm (standard deviation) the fingerprint technique can not find the adequate set of fingerprints for the calculation. Thus, in this case WCL provides better results in the reference scenario. With low dispersion errors of 2 meters can be obtained using the fingerprint technique.

Fig 5. Achieved accuracy in terms of the number of anchors

Adjacent fingerprints can be better differentiated when they are near to the anchor. Analyzing the relationship between the distance and the RSSI provided by the attenuation model, when the MN is near to an AN, the RSSI value is strong and changes significantly when the MN moves. On the other side if the MN is far from the anchor the RSSI is lower and changes slightly if the MN moves. The MN always listens during 80ms in the first stage of the protocol limiting the number of anchors that are considered for the online measurements and the position calculation. Due to this factor when p is higher than 4 a significant rise of the accuracy is not registered. D. RSSI discretization For each analysis the transceiver AT86RF212 of Atmel was used as reference providing 28 different RSSI values in steps of 3dbm. A RSSI value of 0 represents an input power less than or equal to the sensitivity of the transceiver (-100dbm). If the signal strength is equal to or larger than -13dbm the RSSI value is 28. Fig. 6 shows the impact of the number of anchors when the RSSI discretization is not considered. We do not find significantly variations in case the WCL algorithm is executed. The fingerprint technique is influenced due to fact that the RSSI discretization makes the searching of

Fig. 7. Impact of the RSSI dispersion on the localization error

F. Number of transmitted requests The MN can transmit more requests in the first stage of the proposed protocol in order to obtain a more accurate averaged RSSI in spite of the dispersion. The accuracy of the fingerprint technique is influenced for this factor in a stronger way than the WCL (Fig. 8).

82

power. The inclusion of a power control scheme becomes an interesting option when the MN is in the same place during long time. The MN can efficiently adjust its transmission power reducing the collisions with other nodes and saving energy. When the MN moves quickly and if the RSSI dispersion is very high the MN can temporally lose the connectivity with some ANs. This can degrade the position accuracy and generate additional signaling for a new power adjustment. Besides in the reality the relationship between the RSSI values and the transmission power levels is not exactly linear leading to an additional error. G. On-Demand Localization System An adaptive localization system can be implemented, which executes different localization schemes regarding the expected position accuracy and energy consumption. So the MN´s lifetime can be extended, because only the necessary amount of energy is consumed. For instance, if it is needed to know if a person is in a building or not, exact localization algorithms (with high energy consumption) should not be used. The same application can have different demands at different times or for different users, therefore an adaptive system could improve the energetic performance. Table. I shows the MN´s energy consumption in one localization period for achieving a certain accuracy level in the reference scenario. Thus, in relation to the demand it is possible to strategically change the number of localization requests (Loc_req) and the used localization algorithm. It has to be noted that these values are very environment dependent. The collisions between MN´s transmissions and high RSSI dispersions can increment the error and the energy consumption of the MN.

Fig. 8. Influence of the number of transmitted requests on the accuracy and energy consumption

The reason is that the fingerprints were obtained averaging several RSSI values (more than 30) in the offline phase. Considering that the MN is at the same position, the more request are transmitted in the online phase the more similar the averaged RSSI and the stored fingerprints are. Thus it is more probable to find the correct set of fingerprints from the database for the position calculation. For instance in case of only two requests the registered localization error is about 5.1 meters, when the node transmits five requests the error drops to 3.7 meters. Naturally there is a trade-off between the achieved accuracy and the energy consumption. The Fig. 8 presents the energy consumed by the MN [11] in one localization period when both stages of the proposed protocol are executed. The transceiver can be configured to transmit at different transmission powers. In general there is a non-linear relationship between the different transmission power levels and the energy consumption. For the selected transceiver the first eight levels approximately consume the same energy. From this level on, the energy consumption significantly increases depending on the transceiver’s efficiency and other configurations [11]. The Fig. 8 plots the consumed energy of the MN for two boundary cases: when the node transmits at maximal and minimal power. Thus, if a control power scheme is implemented the maximal energy to be saved is 0.282 mJ in case of only one request while this value is 0.531mJ for six requests. The MN´s lifetime is about 33 days in the worst case considering six requests at maximal transmission power, the capacity of the battery (3V - 1200 mAh) and one estimation per second. At minimal transmission power the MN´s lifetime is 37 days. Previous research works [13] assume a linear relationship between the measured RSSI and the different transmission power levels considering the same separation between the nodes. Thus, the stored RSSI fingerprints, which were generated at maximal transmission power, could be used inclusive when the RSSI of the online measurements are referenced to other transmission power. The anchor, that estimates the position for the MN, has to convert the measured RSSI to a RSSI value referenced to the maximal transmission

Expected MN´s energy consumption 3.188 mJ 3.328 mJ 3.468 mJ 4.021 mJ 4.161 mJ 4.301 mJ 4.441 mJ 4.581 mJ

TABLE I LOCALIZATION SCHEMES Number of transmitted Localization localization Algorithm requests WCL 1 WCL 2 WCL 3 Fingerprint technique 2 Fingerprint technique 3 Fingerprint technique 4 Fingerprint technique 5 Fingerprint technique 6

Expected mean error 7.7 m 7.1 m 6.3 m 5.1 m 4.3 m 4m 3.7 m 3.6 m

H. Separation between fingerprints in the offline phase The localization error is influenced by varying the separation between the positions of the fingerprints. Fig. 9 shows the case where the RSSI discretization is not considered. Large separations increase the position error. In the last step of the calculation the k selected fingerprints (in T’) limit a geographic region where the MN can be found. The larger the separation between the fingerprints the bigger the 83

defined region. In our scenario the accuracy does not improve significantly for a shorter separation than 5 meters. This is due to the low complexity of the used algorithm that cannot find the appropriate fingerprints in presence of the RSSI dispersion and when adjacent fingerprints are similar. The accuracy could be improved if other methods for the fingerprints set selection are included. An additional error of about 0.6 meters was registered when the discretization of the RSSI was taken into account.

required accuracy and expected energy consumption. The more RSSI samples the lower the influence of the RSSI dispersion in the accuracy. The RSSI discretization realized by the transceiver can degrade the position accuracy. For the investigated transceiver an additional error of about 0.8 meters was registered for the fingerprint technique in the worst case. The latency for searching the correct set of fingerprints in the database of the anchors has to be taken into consideration in such 3D scenarios, where a high amount of fingerprints could be generated. In general, the WCL algorithm provides a lower accuracy than the fingerprint technique, but it is more robust against the variability of the investigated parameters. Our future work will consist of the inclusion of obstacles in the scenario, a detailed analysis of the influence of the collisions and the implementation as well as the optimization of other fingerprint-based algorithms in the proposed scenario.

REFERENCES [1]

[2]

Fig. 9. Influence of the different separations between fingerprints on the accuracy and the number of generated fingerprints inside the reference scenario.

[3]

[4]

Naturally the number of generated fingerprints increases when the separation between fingerprints is shorter. For a separation of 2 meters there are 17576 fingerprints distributed inside the scenario. In contrast only 1331 fingerprints are generated if there is a separation of 5 meters. The size of one fingerprint is variable and depends on how many anchor are referencing the position. In the implementation the maximum fingerprint size is 216 Bytes. Thus, an available memory of about 280KB is required by the anchors for storing the database of the reference scenario. The delay introduced by reading the database can be high when it contains several fingerprints. For instance, in the best case, assuming that three clocks cycles are necessary for reading one byte from the database, a delay of about 49 ms should be considered for reading 128Kb with the ATMega1281 [12] at 8MHz. During this time the transceiver should sleep in order to save energy.

[5] [6] [7]

[8] [9] [10]

[11] [12] [13]

VI. CONCLUSIONS We presented a simulative study of a distributed fingerprintbased localization algorithm for WSNs. The influence of various parameters such as the number of anchors, RSSI dispersion, and the separation between fingerprints were investigated in order to identify the main trade-offs in the algorithm. An on-demand localization algorithm is proposed, which adjusts the number of RSSI samples depending on the

[14] [15]

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