Localization in Wireless Sensor Networks

Transcription

1 Localization in Wireless Sensor Networks Francisco Santos Instituto Superior Técnico Localization is the process of finding a sensor node s position in space. This paper explains the complete procedure for locating nodes in a wireless sensor network, including the techniques for estimating inter-node distances and angles and how nodes compute their positions using trilateration or triangulation. It focuses on the mathematical concepts underlying localization, detailing the computational steps involved in trilateration and triangulation, the steps necessary to compensate for inexact distance or angle estimates, and the derivation of the linear systems for calculating nodal coordinates in D or higher space dimension. Lastly, this work compares three existing localization algorithms: Directionality based Localization Discovery Scheme, TERRAIN, and Hop-TERRAIN, in terms of their major benefits, sources of error, and positioning accuracy. Categories and Subject Descriptors: F.. [Nonnumerical Algorithms and Problems]: Geometrical problems and computations trilateration, triangulation, multilateration; C..4 [Distributed Systems]: Distributed applications localization; C..1 [Network Architectures and Design]: Wireless communication wireless sensor networks; A.1 [INTRODUCTORY AND SURVEY]: General Terms: Algorithms, Performance, Theory Additional Key Words and Phrases: received signal strength, angle-of-arrival, time-of-arrival, distance estimation, angle estimation, position estimation, WSN 1. INTRODUCTION In wireless sensor networks (WSNs), localization is the process of finding a sensor node s position in space. There are two main techniques for computing node positions: trilateration and triangulation [Willig 006]. Both techniques need anchor nodes, which know their accurate positions in space, to locate other sensors. Trilateration uses the distance to three different anchors to compute a node s D position. Conversely, triangulation relies on the angular separation between three different pairs of anchors to locate a node in D space. Depending on the information available at each node, a choice is made between the two techniques. Trilateration can also be used to calculate 3D positions provided a node knows the distance to four anchors, i.e. one more anchor than the number of space dimensions. Similarly, triangulation requires the angular separation between four different pairs of anchors to determine 3D positions. Existing localization algorithms use a combination of trilateration, triangulation, and different techniques for estimating distances and angles to compute nodal coordinates in a WSN. The more successful strategies Author s address: Francisco Santos, fmnsantos@gmail.com; Instituto Superior Técnico, Av. Rovisco Pais, Lisboa, Portugal. Permission to make digital/hard copy of all or part of this material without fee for personal or classroom use provided that the copies are not made or distributed for profit or commercial advantage, the ACM copyright/server notice, the title of the publication, and its date appear, and notice is given that copying is by permission of the ACM, Inc. To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior specific permission and/or a fee. c 008 ACM /008/ $5.00 ACM Journal Name, Vol. V, No. N, November 008, Pages 1 19.

2 Francisco Santos implement methods to reduce the propagation of errors within the network, thus increasing the positioning system s accuracy. Knowing the positions of nodes can improve the way WSNs operate and allows new types of sensing applications to be developed. Large sensor networks may have convoluted topologies, requiring addressing schemes that are topology independent. One such technique uses nodal coordinates to locate groups of nodes deployed near a site of interest [Heidemann et al. 001]. Several routing protocols exploit this idea further and use coordinates to forward data packets inside the network. The Greedy Perimeter Stateless Routing (GPSR) protocol attempts to forward data through the nodes closest to the destination, resulting in near-minimum-length network paths [Karp and Kung 000]. Monitoring systems also benefit greatly from using localization. By linking data samples to positions, sources of data can be tracked on the map. For example, a forest fire surveillance system could use this method to pinpoint the area covered by flames and aid firefighters in planning safe routes to contain the fire [Steingart et al. 005][Fok et al. 005]. Tracking systems rely on sensors attached to moving targets to trace their path on a map. Intelligent inventory systems use this technique to catalog new products entering a warehouse, count them, record where they are stored, and update the inventory database when a product leaves the warehouse [Bonnet et al. 001][Patwari et al. 005]. These examples evidence the clear benefits of integrating positioning systems with sensor networks. Current papers on positioning systems for WSNs typically focus on the isolated parts of the localization process, concentrating on: methods for estimating internode ranges and angles, mathematical techniques for determining the position of a single node, and algorithms for computing the positions of nodes in an entire WSN. This paper aims to dissect the node localization procedure, explaining its individual phases, and to analyze existing positioning systems for sensor networks, describing their major benefits and flaws. The remainder of this article is structured as follows. Section describes some of the existing techniques for estimating inter-node ranges. A mathematical introduction to localization is given in Section 3. Section 4 analyzes real localization algorithms that implement the estimation techniques and mathematical principles described earlier. Lastly, Section 5 concludes.. ESTIMATING DISTANCES The distance estimation phase is the initial step performed when locating a node s position in space. By estimating distances to neighbors with known coordinates, a node can determine its own position using trilateration or triangulation (discussed in Section 3). Once a node determines its position, it becomes an anchor node and can then help other neighbors find their positions. Alternatively, nodes attached to GPS-devices can rely on this instrument for obtaining accurate coordinates, without needing to estimate distances to their neighbors. Depending on the hardware available at each node, different distance estimation methods can be used. The received signal strength (RSS) technique does not require any hardware in addition to the radio transceiver. Knowing the transmitted signal s power and path-loss model, the inter-node separation can be calculated. Although this method is simple to implement and use, it is sometimes disfavored due to

3 Localization in Wireless Sensor Networks 3 its unpredictable nature [Willig 006][Savarese 00]. Alternatively, to calculate distances using the time-of-arrival (ToA) technique, the receiver must know the emitted signal s propagation time and velocity. Depending on the ToA variant used, synchronization between sender and receiver may not always be required. Knowing the distance to three anchors, a node can then compute its D position using trilateration. As opposed to calculating straight-line distances, the angle-of-arrival (AoA) technique computes the angular separation between two nodes. Using special sensor arrangements at each node, the emitted signal s direction is determined and then compared to a reference direction. Using the estimated angular separation between three pairs of anchors, a node can then triangulate its D position. This Section gives an overview of how the RSS, ToA, and AoA methods work. Please see [Patwari et al. 005] for a detailed discussion on the estimation errors of these three techniques, including the calculation of the underlying Cramér-Rao bounds..1 Received Signal Strength By definition, the received signal strength is the voltage measured by the receiver s received signal strength indicator (RSSI) circuit [Patwari et al. 005]. RSSbased localization systems do not require hardware components in addition to the radio transceiver. Moreover, no dedicated packets need to be sent over the network for such systems to function. However, RSS measurements are very unreliable, even when both sender and receiver are stationary [Willig 006]. Ranging errors of ±50% have been observed [Savarese 00], leading to inaccurate distance estimates. Hence, it is important to understand the sources of error before relying on this technique for locating nodes. Multipath and shadowing are two major phenomena affecting the reliability of RSS measurements [Patwari et al. 005]. Different magnitude signals arriving outof-phase at the receiver cause constructive and destructive interference. Spreadspectrum radios effectively mitigate this problem by averaging the received power over multiple frequencies. Shadowing effects are caused by obstructions (e.g. thick vegetation, walls, furniture) that attenuate the signal s strength. Additionally, not all RSSI circuits are factory calibrated, resulting in device-dependent RSS measurements for the same signal strength [Willig 006]. Finally, the actual signal power can be different from the transceiver s intended transmission power, causing further discrepancies in RSS measurements [Willig 006]. Assuming that the transmission power (P tx ), the path-loss model, and the pathloss coefficient (α) are known, it is possible to estimate the distance between a sender and receiver using the power of the received signal (P rx ): P rx d = = c Ptx d α, α c Ptx P rx, (1) where c is a constant dependent on the path-loss model [Willig 006]. In free space, the received power is inversely proportional to the square of the distance between sender and receiver (i.e. α = ). When considering an obstructed channel

4 4 Francisco Santos and assuming multipath effects are mitigated using a spread-spectrum technique, α typically ranges between two and four [Patwari et al. 005].. Time-of-Arrival The time-of-arrival is the instant in time when a signal first arrives at the receiver [Patwari et al. 005]. If the receiver knows when the signal was sent (T 1 ) and the signal s propagation speed in the medium (v p ), the distance to the source can be calculated as follows: d = (T T 1 ) v p, () where T is the ToA. This technique requires the clocks of both the sender and receiver to be synchronized and, depending, on the signal s propagation speed, high resolution clocks may be needed to obtain accurate distance estimates. Further, these distance estimates are hindered by additive noise and multipath effects [Patwari et al. 005]. If sound waves are used, the timing precision requirements are less stringent. However, the propagation speed of sound waves is affected by ambient factors, such as: temperature and pressure, requiring prior calibration of the senders and receivers [Willig 006]. A technique known as two-way time-of-arrival does not require clock synchronization between sender and receiver. In this case, the propagation time is calculated as half the round-trip-time (RTT) between both nodes. The authors in [McCrady et al. 000] modified the request-to-send (RTS) and clear-to-send (CTS) messages, employed in the Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) MAC protocol, to transmit ToA information. Both the sender and receiver undergo an initial calibration phase to estimate internal processing delays. Once this phase is complete, the sender is capable of estimating its distance to the receiver to an accuracy of 1m, even in the presence of multipath interference [McCrady et al. 000]. Another method to compute the inter-nodal range relies on two mediums with very different propagation speeds, for example: radio waves traveling at the speed of light and ultrasound. The faster signal is used to trigger a timer at the receiving node (T 1 ). When the slower signal arrives at the receiver, the timer is stopped (T ). The product of the elapsed time and the propagation speed of the slower signal (v p ) is approximately equal to the inter-node separation (see ()). Like the two-way ToA, this method does not require explicit synchronization between sender and receiver and is significantly more accurate than the RSS approach [Willig 006]. However, one drawback is the need for two types of senders and receivers at each node..3 Angle-of-Arrival The angle-of-arrival 1 is the angle between a signal s propagation direction and some reference direction (e.g. north). There are two main methods for AoA estimation. The most common technique uses a board with several passive sensors (e.g. acoustic, electromagnetic, seismic, etc...), with known positions relative to the sensor board. A model of the sensor board s output signal is then used to estimate 1 Also called direction-of-arrival (DoA).

5 Localization in Wireless Sensor Networks 5 the emitted signal s AoA [Stoica and Moses 1997]. Assuming that the emitters and the sensor board are on the same plane, the propagation medium is non-dispersive, the emitted waves are narrowband, have a known carrier frequency, and are approximately planar at a reference point close to the sensors, then our quest to find the source s AoA becomes less taxing. Consider the sensor board arrangement shown in Figure 1. The m sensors in the array are uniformly distributed along a line, with a constant inter-sensor spacing of d meters. Let x(t) denote the value of the source signal measured at a reference point close to the array, at time t: x(t) = α(t) cos (ω c t + φ(t)), (3) where α(t) is the amplitude, φ(t) denotes the phase shift, and ω c is the carrier frequency. Further, let τ k denote the time for the source signal to reach sensor k (k = 1,..., m) from the reference point. Under the narrowband assumption, the signal s amplitude and phase vary slowly relative to the propagation time for the wave to cross the array [Ottersten et al. 1993]. Hence, the value of the emitted signal when it reaches sensor k is given by: x(t τ k ) = α(t τ k ) cos (ω c (t τ k ) + φ(t τ k )) α(t) cos (ω c t ω c τ k + φ(t)). (4) In other words, the propagation delay τ k can be modeled as a phase shift of the carrier frequency: ω c τ k. Lastly, under the planar wave assumption and taking sensor 1 as the reference point, the propagation delay τ k can be expressed in terms of the source s AoA θ: d sin (θ) τ k = (k 1) for θ [ π/, π/], (5) v p where v p is the signal s propagation velocity. Since the sensor arrangement shown in Figure 1 cannot distinguish between two sources symmetric about the array s line axis, θ values must lie within the [ π/, π/] angle range. Another technique for measuring the source signal s AoA, relies on rotating, directional antennas, with known coordinates. Knowing the period and phase differences of the revolving antennas, the receiver calculates the time delay between two consecutive, received signals, and determines the angular distance between the two emitters. Upon receiving a signal from a third antenna, it can then compute its D position [Nasipuri and Li 00]. 3. LOCATING THE NODES Two main techniques exist for determining a node s position in space: trilateration and triangulation. By knowing the distance to three anchors, a node can find its D position using trilateration. The main problem with this technique is that it relies on exact measurements to determine a position. If a node estimates the distance to more than three anchors, it can use multilateration to compute a least-squares fitting of the data, producing better results than trilateration in the presence of erroneous measurements. Both methods can be extended to compute Recall that anchors are nodes that have already determined their coordinates.

6 6 Francisco Santos source d sin m d Fig. 1. The uniform linear array scenario [Stoica and Moses 1997]. nodal positions in 3D or greater space dimension, provided the node knows the distance to at least one more anchor than the number of space dimensions. Triangulation relies on the angular separation between three different pairs of anchors to compute the node s D position. Triangulation and trilateration are very similar in nature. Due to the similarities between both strategies, triangulation problems can be translated as trilateration scenarios. One immediate benefit of this conversion is the possibility of using multilateration to perform a least-squares fitting of the angle measurements. The remaining subsections introduce the mathematical concepts underlying trilateration, multilateration, and triangulation. 3.1 Trilateration Trilateration is the process of finding the position of a node in space based on its distance to three anchors [Fang 1986][Karl and Willig 005] (see Figure ). Let the positions of the three fixed anchors be defined by vectors: n 0, n 1, and n R. Further, let p R be the position vector to be determined. Consider three circles, centered at each anchor, having radii of d i meters, equal to the distances between p and each anchor n i. These geometric constraints can be expressed by the following system of equations: p n 0 = d 0, (6) p n 1 = d 1, (7) p n = d. (8) Since p n i = ( p n i ) ( p n i ) = p n i p + n i, the equations (6) (8) can be rewritten as follows: p n 0 p + n 0 = d 0, (9) p n 1 p + n 1 = d 1, (10) p n p + n = d. (11)

7 Localization in Wireless Sensor Networks 7 n r p d s d 0 d 1 n 0 q n 1 Fig.. Trilateration. Subtracting the second and third equations from the first, results in the following two equations: ( n 1 n 0 ) p = d 0 d 1 n 0 + n 1, (1) ( n n 0 ) p = d 0 d n 0 + n. (13) By solving the following linear system, p (expressed as a column vector) can be determined: ( ) n1 n A = 0, n n 0 b = ( d 0 d 1 n 0 + n 1 d 0 d n 0 + n ), A p = b. (14) More generally, to determine p R N, N + 1 fixed anchors are required: n 0,..., n N R N. Additionally, the distances between p and the N + 1 fixed anchors need to be known. These geometric constraints may be expressed by the following set of equations: p n i = d i, for 0 i N. Using a similar reasoning as before, subtracting equations,..., N + 1 from the first, results in the following system of N linear equations: A = b = n 1 n 0., n N n 0 N N d 0 d 1 n 0 + n 1. d 0 d N n 0 + n N, A p = b. (15) Assuming that the distances between the fixed anchors are known, but the anchors absolute positions are unknown, it is possible to construct a generic coordi-

8 8 Francisco Santos nate system for locating p. Consider three fixed anchors: n 0, n 1, n R, such that only the distances between each pair of anchors are known. One possible way to define these vectors is described next: ( ) ( ) ( ) 0 q nx n 0 =, n 0 1 =, n 0 =. n y By expanding n n 1, the following is obtained: n n 1 = ( n n 1 ) ( n n 1 ), = n n 1 n + n 1. (16) Rearranging (16) in terms of n 1 n, yields the following: n 1 n = 1 ( n 1 + n n n 1 ), = 1 ( q + r s ). (17) The components of vector n can now be determined as follows: ( ) ( ) q nx 0 n y = 1 ( q + r s ), q n x = 1 ( q + r s ), n x = 1 ( q + r s ), q n x + n y = r, n y = ± r n x. Assuming that n y 0, then n is given by: ( 1 ( q q + r s ) ) n = r n x. (18) Provided vectors n 1 and n are not collinear, i.e. n 1x 0 and n y 0, they form a basis for this two-dimensional vector space, and p can be determined by substituting n 1 and n into linear system 3 (14). The previous reasoning can be extended to consider a three-dimensional vector space. In this case, four position vectors: n 0,..., n 3 R 3 are necessary. Intuitively, n 0, n 1, n form the base of a tetrahedron, and the fourth anchor n 3 is the tetrahedron s apex (see Figure 3). Assuming the tetrahedron s base lies on the z = 0 plane, the base position vectors can be easily defined using the previous results: ( 1 0 q q q + r s ) n 0 = 0, n 1 = 0, n = r n x Since in this case n 0 = 0, it can be omitted from the linear system.

9 Localization in Wireless Sensor Networks 9 n r v s t n 3 u n 0 = (0,0,0) q n 1 Fig. 3. Tetrahedron formed by position vectors: n 0, n 1, n, and n 3 (the apex). The apex of the tetrahedron n 3 = ( ) n 3x, n 3y, n 3z can be determined by solving the following three equations: n 1 n 3 = 1 ( q + t u ), (19) n n 3 = 1 ( r + t v ), (0) n 3 = t. (1) Equations (19) and (0) can be expressed as a linear system, which can be used to solve for the unknown x and y components of n 3 : ( ) n1 n n 3 = 1 ( ) q + t u r + t v, () n 3x = 1 ( q + t u ), (3) q n 3y = q ( r + t v ) n x ( q + t u ) q n y. (4) Lastly, the z component of n 3 is found by rearranging (1). Assuming n 3z 0: n 3z = t ( n 3x + n ) 3y (5) Provided vectors n 1, n, and n 3 are linearly independent, i.e. n 1x 0, n y 0, and n 3z 0, they form a basis for this three-dimensional vector space, and p can be determined by substituting n 1, n, and n 3 into linear system 4 (15). 3. Multilateration Trilateration assumes perfect range measurements between p, the position to be determined, and three fixed anchors. However, if these measurements contain errors, solving linear system (14) will yield an incorrect position p. In multilateration this problem is mitigated by considering the distance estimates to three or more 4 Since n 0 = 0, it can be omitted from the linear system.

10 10 Francisco Santos fixed anchors. When more than three anchors are used, an overdetermined system of equations results. By solving this linear system, the measurements mean square error is minimized, thus producing better results than trilateration in the presence of inaccurate distance estimates. More generally, to determine p R N, M + 1 fixed anchors are required: n 0,..., n M R N, where M N. The distance estimates between p and each of the M + 1 fixed anchors are defined by: d0,..., dm. The distance constraints between p and the fixed anchors may be expressed by the following set of equations: p n i = d i, for 0 i M. By subtracting equations,..., M + 1 from the first, results in the following system of M linear equations: n 1 n 0 A =., n M n 0 M N b = d 0 d1 n0 + n 1. d 0 dm n0 + n M, A p = b, (6) where for M > N an overdetermined system results, and M = N is the required minimum number of equations to uniquely determine p. One way to solve an overdetermined linear system is to use QR-decomposition. Provided the columns of matrix A in (6) are linearly independent, A may be decomposed into two matrices Q and R, such that A = QR, where Q is a matrix with orthonormal columns (Q T Q = I), obtained from the Gram-Schmidt process, and R is an upper-triangular matrix with a positive diagonal [Magalhães 1989]. Matrix A may be written as: ) A = ( a 1... a N, M N where a 1,..., a N R M are its column vectors. The set of orthonormal vectors e 1,..., e N can be obtained from the columns of A using the Gram-Schmidt process, as described next: u 1 = a 1, e 1 = u 1 u 1 N 1 u N = a N proj ei a N, e N = u N u N i=1 Matrices Q and R are then given by: ) Q = ( e 1... e N. M N, (7) R = Q T A. (8)

11 Localization in Wireless Sensor Networks 11 Substituting Q and R into (6) yields the following: A p = b, QR p = b, R p = Q T b. (9) The solution to linear system (9) is our best estimate for the unknown point p since it minimizes: A p b. 3.3 Triangulation The last two sections described a simple method for computing a node s position based on its distance to the anchor nodes. Triangulation, unlike trilateration, computes the position of a node in space based on the angular distance between three different pairs of anchors, measured from the node. Consider the example depicted in Figure, where p is the node s position and n 0,..., n are the anchor nodes. If we know the angles between the line segments connecting p and the anchors, but not the segment lengths (i.e. d 0,..., d ), then the unknown coordinates must be found using triangulation instead of trilateration. Fortunately, both techniques are very similar and we can adapt the trilateration method to find p in this case. Let A 0,..., A denote the angles between the line segments connecting p to the anchors, as illustrated in Figure 4. Further, let p be the intersection point of the three (imaginary) circles centered at c 0,..., c. Knowing the angular distance between the anchor nodes, the centers of the circles can be obtained. Consider the circle centered at c 0. The major arc ( n 1, n ) subtends a central angle of A 0 rad. Hence, the minor arc ( n 1, n ) subtends a central angle of π A 0 = (π A 0 ) rad. By applying the law of sines to triangle ( n 1, p, n ), the radius of the circumscribed circle, centered at c 0, can be found: The midpoint of line segment ( n 1, n ) is given by: r c0 = 1 n 1 n. (30) sin A 0 m 1 = n + 1 ( n 1 n ). (31) Position vector c 0 can be determined by solving the following equation: ( n 1 n ) n 1 n R(π/) = ( c 0 m 1 ) c 0 m 1 for R(π/) = [ ] (3) where matrix R(π/) describes a counterclockwise rotation of π/ rad. Knowing that c 0 m 1 = r c0 cos(π A 0 ), (3) can be rewritten with respect to c 0 : c 0 = m 1 + r c0 cos(π A 0 ) ( n 1 n ) R(π/) (33) n 1 n

12 1 Francisco Santos c 1 n rc 0 1 n r r 1 n = sina 0 A 1 p A 0 m 1 A 0 c 0 n 0 A n 1 c Fig. 4. Triangulation. Similarly, the remaining vectors c 1 and c are defined as: c 1 = m 0 + r c1 cos(π A 1 ) ( n 0 n ) R(π/), n 0 n (34) c = m 01 + r c cos(π A ) ( n 0 n 1 ) R(π/). n 0 n 1 (35) Recall that p is the intersection point of the circles centered at c 0,..., c. geometric constraint can be modeled as follows: This p c i = r c i for i = 0,..., (36) Lastly, we can use linear system (14) to find p, substituting n i with c i and d i with r ci, for i = 0,...,. 4. LOCALIZATION ALGORITHMS This Section presents existing algorithms for determining the positions of nodes, based on adaptations of the different distance estimation and localization techniques presented earlier. The Directionality based Localization Discovery Scheme (DLDS) [Nasipuri and Li 00] combines signal AoA with triangulation to locate nodes. Wireless stations, equipped with directional antennae, emit continuous RF signals that must be within range of all sensor nodes. Nodes then compute the angular distance between consecutive stations and use triangulation to find their positions.

13 Localization in Wireless Sensor Networks 13 (0,M) ϕ ω (L,M) BN- γ BN-1 ω CONTROL UNIT M Y α X ω β (Xp,Yp) ω SN ϕ Z δ 3ϕ BN-3 (0,0) L BN-4 (L,0) example of a sensor network that inway nodes. Fig. 5. The model of rotating directional beacon signals from 4 beacon nodes: BN-1, BN-, BN-3, and BN-4 [Nasipuri and Li 00]. Figure : The model of rotating directional beacon k Model signals from 4 beacon nodes: BN-1, BN-, BN-3, sensor network model as depictedinin TERRAIN Figtwork and and BN-4, Hop-TERRAIN located on the[savarese corners of 00], the sensor anchors net- may be scattered consists of a large numberthroughout of sensor thework sensor area. fieldthe and figure do notshows need to a test be within sensorrange nodeof SNevery sensor node. hich are located in random but Both fixed locantral processing and control unit. The sen- beacon nodes. rely on RSS with distance its angular estimates bearings and trilateration with respecttoto locate the four nodes. According to the authors [Savarese 00], TERRAIN allows erroneous distance estimates to propagate contami- throughout the network and is too inaccurate to be useful. Hop-TERRAIN ic observations to detect the existence of a its vicinity (such as temperature, ysical movements, etc.), and transmit takes aextra loinformation to the control unit (CU) making when it more care to ensure that only reliable measurements permeate the network, ure. The transmissions from different beacon nodes must be accurate distinguishable, than TERRAIN. which may be The achieved aforementioned by using unique algorithms will be h SN has a processor, memory, analyzed and hard-ilimited signal processing, data compression, therf following carrier frequencies subsections. for each beacon. It may also be implemented by using different signature sequences or codes tworking operations. The SNs have limited nge. Hence, they rely on store-and-forward 4.1 Directionality the based samelocation carrier frequency. DiscoveryThere is a constant angular separation of φ degrees between the directional beams from t transmission for communication. The All nodes Directionality the four based beacon Location nodes BN-1, Discovery BN-, BN-3, Scheme and[nasipuri BN-4, (see and Li 00] is op routes to one of several gateway nodes in an AoA-based Figure algorithm ) where forφperforming can be any value. nodesince localization. all beacons This nodes location discovery scheme of requires are wired at and least controlled three fixed by thewireless central controller, transmission it possi- stations or beacon hich have wired links to the CU. The CU is taking the final decision on the existence and determining the its locationnodes, based on equipped blewith to achieve directional phase synchronization antennae. Sensor and maintain nodes use identical the directional signals angular speeds in all of them, which is a requirement for the s sent by the sensors and other geographical emitted by these functioning stationsof tothe determine proposed the localization angularprinciple. separation A rotating Fordirectional this purpose, beamitmay is assumed be implemented that each by abeacon directional signal consists of a between consecutive achieve scalability, the sensor network beaconmay nodes. h that the SNs cooperate and combine their antenna that is mechanically rotated as done in a radar system, or it could be generated by an electronically steerable ally before sending any message through continuous the RF carrier signal, detectable by all nodes within the WSN deployment CU. It must be noted that the actual area, funcetworking operations is not a direct gular concern speed of: ω rad s 1. There is a constant angular separation of φ rad between transmitted in a narrow directional beam, and that rotates with a constant an- smart antenna [6]. We assume that the transmission range is sufficient for the beacon signals to be received by all sensor e describe the network model forconsecutive the reader beacon nodesnodes: in the network. BN-1, BN-, Consequently, BN-3, each and sensor BN-4 node (see will Figure 5). Using a application scenario where the localization central controller, receive it periodic is possible bursts to of achieve the four phase beacon synchronization signals, all with and maintain a lied. constant angular thespeed same period for the of 360/ω beaconseconds. signals. However, periodic bursts signal generation By knowing from the arrival different time beacons of the will be different staggered beacon in time signals, by amounts node SN is capable he presence of at least three fixed wireless that depend on the location of the sensor node. of determining angles: α, β, and δ. Let T 1 and T be defined as the times at which ations or beacon nodes in the network. SN receives These the signals from beacons BN-1 and BN-, respectively. At time T, SN ped with special transmission capabilities for s beacon signals throughout the has sensor received neton signals are designed to enablerad any to sensor reach SN. 4. Rotating LOCALIZATION BN-1 s signalprinciple by φ rad counter-clockwise would make it BN- s signal but BN-1 s signal must still rotate another (T 1 T ) ω ine its angular bearings with respect parallel to the to that of The beacon localization BN-. principle Hence, is angle based on α aissensor givennode by: noting or this purpose, we assume that each beacon of a continuous RF carrier signal on a narbeam that rotates with a constant angular the times when it receives the different beacon signals, and evaluating its angular α = bearings (T 1 T and ) ω location + φ. with respect to the beacon nodes by triangulation. Denote the times at (37) ees/s. The locations of the beacon nodes can or illustration, we assume a rectangular netfour beacon nodes denoted by BN-1, BN-, 4 placed in the four corners of the network with the gateway nodes, as shown in Figwhich an SN receives the beacons ACMsignals Journal from Name, BN-1, Vol. BN-, V, No. N, November 008. BN-3, and BN-4 by t 1,t,t 3,andt 4, respectively. Since the sensor nodes have no time synchronization with the beacon nodes, the absolute values of these times bear no useful information. However, the time difference of arrivals can be 107

14 14 Francisco Santos By applying a similar reasoning, the remaining angles can be found: β = (T T 3 ) ω + φ, (38) δ = (T 3 T 4 ) ω + φ, (39) where T 3 and T 4 are the arrival times of BN-3 and BN-4 s signals at node SN. Using triangulation, the D coordinates of node SN can be calculated (see Section 3.3). Since each node finds its position individually, the performance of this method is unaffected by the WSN s density. Additionally, since it depends on angle estimates, its performance does not depend on the network s size. However, there are several causes of error for this particular localization scheme. Each signal beacon has a non-zero width, which makes it difficult for nodes to record the precise arrival time of the signal. According to simulation results, for beam widths of π/1 rad or less and for a square WSN deployment with a side-length of 75m, the node position estimates are within ±m of the real positions [Nasipuri and Li 00]. Reflections from surrounding objects are an additional source of error, causing beacon signals to be received at the sensor nodes even when they are not directed toward them. In this case, simulation results suggest positioning errors greater than ±50m are possible [Nasipuri and Li 00], making DLDS an inviable option in the presence of multipath interference. Other drawbacks of this algorithm include: the requirement of expensive directional antennae for the beacon nodes, a centralized infra-structure to control beam synchronization, and the limitation on network size imposed by the finite range of the beacon signals. 4. TERRAIN The Triangulation via Extended Range and Redundant Association of Intermediate Nodes (TERRAIN) [Savarese 00] is an algorithm for performing node localization. The anchors, which have access to precise positioning information, need not be directly connected to the other nodes for TERRAIN to operate. For locating a node in three-dimensional space, at least four anchors are required (see Section 3.1), although they may be randomly placed within the network deployment area. TERRAIN is initiated at the anchor nodes. Each anchor waits for three regular nodes to connect. Knowing the distances between the anchor and each of the regular nodes, and the pairwise distances of the three nodes, it is possible to construct a local coordinate system, as was explained at the end of Section 3.1. A fourth node may determine its position in this coordinate system by performing trilateration, using the relative positions of the three initial nodes. Since the anchor is located at the origin, the norm of the fourth node s position vector will equal the distance to that anchor. Nodes which have determined their positions relative to a particular anchor, broadcast this information to the rest of the network. Through multilateration (see Section 3.), other nodes determine their positions relative to each of the existing anchor nodes. By calculating the norm of these position vectors, the distance to each anchor is thus found. Knowing the anchors global positions, and the distance to each anchor, a node is able to find its global position through multilateration. This algorithm relies on the RSS technique for estimating distances between nodes. However, RSS-based distance estimates are unreliable. As nodes perform

15 Localization in Wireless Sensor Networks ' 5 anchor node 3 4 regular node Fig. 6. Example of a D hard-topology: node 4 does not have a uniquely determined position [Savarese 00]. multilateration based on incorrect position vectors, the errors may accumulate and affect future calculations. According to the authors [Savarese 00], the final position estimates are too far from the true positions to be useful. 4.3 Hop-TERRAIN Unlike TERRAIN, the Hop-TERRAIN [Savarese 00] algorithm does not use the RSS values directly to estimate distances to the anchor nodes (see Section 4.). In this algorithm, nodes determine the minimum hop-count to the anchors and then multiply this by the average distance per hop measure. This value may be pre-configured, or calculated at runtime by the anchor nodes and then broadcast to the remainder of the network. Hop-TERRAIN operates in two phases: start-up and refinement. A crude initial position estimate is calculated during the start-up phase, which is later improved during refinement. In the start-up phase, the anchor nodes flood the network with positioning packets, containing their locations and a hop-count field initially set to zero. Upon receiving a positioning packet, a node records the anchor s position, increments and stores the hop-count value, computes the distance to the anchor node, and, finally, re-broadcasts the packet. To avoid unnecessary broadcasts, a node only accepts a new positioning packet if it refers to a new anchor, or the hop-count to an existing anchor is lower than the previously recorded value. Knowing the positions and distances to at least four different anchors, a node is able to find its position in three-dimensional space using multilateration. After making the initial position estimate, the node may enter the refinement phase. Refinement is an iterative algorithm for improving the nodes initial position estimates. At the beginning of each step, a node broadcasts its position and listens for the positioning packets of its direct neighbors. Using the estimated distances to its one-hop neighbors and their respective locations, the node re-calculates its own position using multilateration, and broadcasts the result. Nodes end the refinement phase when their updated positions are sufficiently close to their previous estimates, or when a pre-configured maximum number of iterations is reached. The study of the refinement algorithm revealed two main problems [Basagni et al. 004][Savarese 00]: (i) error propagation through the network due to unreliable position estimates, and (ii) failure when applied to hard topologies, where parts of a network can be mirrored while preserving inter-node ranges (see Figure 6). To minimize the effects of an erroneous position estimate on the remaining calcu-

16 16 Francisco Santos anchor node regular node Fig. 7. Example of a D hard-topology where the heuristic, defined in [Savarese 00], fails. lations, weights reflecting the confidence of each estimate are used [Savarese 00]. Confidence levels range between 0 and 1. Anchors are assigned a value of 1, and nodes that enter the refinement phase are assigned a confidence of 0.1. Each time a node successfully performs multilateration, it updates its confidence level to the average confidence levels of its neighbors. If multilateration fails due to insufficient constraints or because other consistency criteria where not met, confidence is set to 0 to avoid propagating inaccurate data. A node is excluded from refinement if it persistently fails to provide consistent results. The simulation results note that although the use of confidence levels yields an improvement on the average error in computed results, it cannot be used as an indicator of the estimated accuracy [Basagni et al. 004]. A network with a hard-topology can be partially reflected while maintaining the distances between nodes. For example, node 4 in Figure 6 has two possible positions that are consistent with the distance measurements. In such a case, only those nodes that have edge-disjoint paths to at least four anchors (or three for two dimensional scenarios) are capable of determining their positions [Willig 006]. Such nodes are called sound. The authors propose a heuristic that can filter-out most non-sound nodes [Savarese 00]. During the start-up phase, nodes record the ID of the next-hop neighbor along the shortest path to a given anchor. When the number of unique neighbor IDs recorded reaches four (or three for two dimensional scenarios), the node declares itself sound, and enters the refinement phase. The neighbors then record the sound node s ID, and the process continues around the network. The hard-topology heuristic described in [Savarese 00] can sometimes fail. All nodes in Figure 7 can reach the three anchors, and, hence, proceed to refinement. The information stored in each node at the end of the start-up phase is presented in Table I (the anchor positions are not shown for brevity). Nodes 6 and 7 are correctly marked not-sound by Hop-TERRAIN, since both nodes can have two valid positions while still obeying inter-node ranges. Node 8 can have only one position. Either of the two possible physical locations for 6 and 7 can be used in node 8 s trilateration, together with node 3 s position. Hop-TERRAIN will only mark node 8 sound if the next-hop neighbor along the path to anchor 1 is different than that of anchor, which is the only case when the size of the neighbor ID set is equal to three. Node 5 can compute its location by trilaterating node 4 s position

17 Localization in Wireless Sensor Networks 17 Table I. Hop-TERRAIN start-up tables for the example in Figure 7. Node 4 Anchor Next-hop Hop-count Neighbor IDs: {1,, 5} Node 5 Anchor Next-hop Hop-count or 7 a 4 Neighbor IDs: {4, 6} or {4, 7} Node 6 Anchor Next-hop Hop-count Neighbor IDs: {5, 8} Node 7 Anchor Next-hop Hop-count Neighbor IDs: {5, 8} Node 8 Anchor Next-hop Hop-count 1 6 or or Neighbor IDs: {3, 6} or {3, 7} or {3, 6, 7} b (a) Depends on the route taken by anchor s positioning packet. (b) Route taken by a positioning packet can affect the soundness of a node. and the real or reflected positions for node s 6 and 7. However, Hop-TERRAIN mistakenly considers 5 a non-sound node since its neighbor set does not contain three unique IDs. Finally, node 4 is correctly marked sound, as it can find its position by trilaterating the positions of nodes 1,, and 5. According to the simulation results, the Hop-TERRAIN algorithm achieves, on average, position errors of less than 33% of a node s radio range in the presence of a 5% range measurement error, when at least 5% of the nodes are anchors [Basagni et al. 004]. 5. CONCLUSION Current papers on positioning systems for WSNs typically focus on the isolated parts of the localization process, concentrating on: methods for estimating internode ranges and angles, mathematical techniques for determining the position of a single node, and algorithms for computing the positions of nodes in an entire WSN. This paper aims to dissect the node localization procedure, explaining its individual phases, and to analyze existing positioning systems for sensor networks, describing their major benefits and flaws. The localization task for WSNs is divided into three main phases. A node starts by finding the ranges or angular separation between nodes with pre-calculated coordinates, known as anchors. Knowing the ranges to three distinct anchors, a node performs trilateration to find its D position. Alternatively, it can triangulate its D position using the angular distance between three different pairs of anchors.

18 18 Francisco Santos Lastly, a node must forward its position so that other nodes can calculate their coordinates. The more successful localization algorithms take additional steps to achieve positioning accuracy by preventing the propagation of calculation errors. Depending on the hardware available at each node, different distance and angle estimation strategies can be used. The RSS strategy uses the voltage of the radio transceiver s RSSI circuit as an indicator of distance, requiring no dedicated network packets to operate. Unfortunately, the RSS ranging technique is error prone and is disfavored when accuracy is a priority. One alternative method computes the inter-node range by measuring the time-of-flight of a signal with a known propagation velocity. This method requires high-precision clocks and tight synchronization between sender and receiver to yield accurate results. As opposed to measuring inter-node distances, nodes may opt to estimate the angular separation between pairs of anchors, at the cost of extra hardware. To illustrate the more theoretical concepts introduced in this article, three existing localization algorithms were analyzed. The Directionality based Localization Discovery Scheme combines signal AoA with triangulation to locate nodes. Since each node performs triangulation independently, the performance of DLDS is unaffected by the WSN s density. One major drawback of this algorithm is its intolerance to multipath interference, yielding positioning errors of ±50m for a square WSN with a side length of 75m. Unlike DLDS, the TERRAIN and Hop-TERRAIN algorithms do not require anchors to be within range of the regular nodes. Both algorithms use RSS-based distance estimates and triangulation to find nodal positions. While TERRAIN is too inaccurate to be useful, Hop-TERRAIN takes serious measures to contain calculation errors. According to simulation results, Hop-TERRAIN achieves, on average, position errors of less than 33% of a node s radio range in the presence of a 5% range measurement error, when at least 5% of the nodes are anchors. ACKNOWLEDGMENTS The author wishes to thank Prof. José Luís Fachada for his insightful help in presenting the mathematical concepts underlying localization and to all contributors whose suggestions and feedback have improved this work. REFERENCES Basagni, S., Conti, M., Giordano, S., and Stojmenovic, I Mobile Ad-hoc Networking. John Wiley & Sons. Bonnet, P., Gehrke, J., and Seshadri, P Towards Sensor Database Systems. In MDM 001: Proceedings of the Second International Conference on Mobile Data Management. Springer-Verlag, London, UK, Fang, B Trilateration and Extension to Global Positioning System Navigation. Journal of Guidance, Control, and Dynamics 9, Fok, C.-L., Roman, G.-C., and Lu, C Mobile agent middleware for sensor networks: an application case study. In IPSN 005: Proceedings of the 4th international symposium on Information processing in sensor networks. IEEE Press, Piscataway, NJ, USA, Heidemann, J., Silva, F., Intanagonwiwat, C., Govindan, R., Estrin, D., and Ganesan, D Building efficient wireless sensor networks with low-level naming. In SOSP 001: Proceedings of the eighteenth ACM symposium on Operating systems principles. ACM, New York, NY, USA,

19 Localization in Wireless Sensor Networks 19 Karl, H. and Willig, A Protocols and Architectures for Wireless Sensor Networks. John Wiley and Sons, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England. Karp, B. and Kung, H. T GPSR: Greedy Perimeter Stateless Routing for Wireless Networks. In MobiCom 000: Proceedings of the 6th Annual International Conference on Mobile Computing and Networking. ACM Press, New York, NY, USA, Magalhães, L Álgebra Linear como Introdução à Matemática Aplicada. Texto Editora. McCrady, D., Doyle, L., Forstrom, H., Dempsey, T., and Martorana, M Mobile ranging using low-accuracy clocks. IEEE Transactions on Microwave Theory and Techniques 48, 6 (June), Nasipuri, A. and Li, K. 00. A Directionality Based Location Discovery Scheme for Wireless Sensor Networks. In WSNA 00: Proceedings of the 1st ACM International Workshop on Wireless Sensor Networks and Applications. ACM Press, New York, NY, USA, Ottersten, B., Viberg, M., Stoica, P., and Nehorai, A Exact and large sample ML techniques for parameter estimation and detection in array processing. In Radar Array Processing Chapter 4. Springer-Verlag New York, Inc., Secaucus, NJ, USA, Patwari, N., Ash, J., Kyperountas, S., III, A. H., Moses, R., and Correal, N. July 005. Locating the nodes: cooperative localization in wireless sensor networks. Signal Processing Magazine, IEEE, 4, Savarese, C. 00. Robust Positioning Algorithms for Distributed Ad-hoc Wireless Sensor Networks. M.S. thesis, Department of Electrical Engineering and Computer Sciences, University of California. Steingart, D., Wilson, J., Redfern, A., Wright, P., Romero, R., and Lim, L Augmented Cognition for Fire Emergency Response: An Iterative User Study. In Proceedings of the 1st International Conference on Augmented Cognition. Las Vegas, NV. Stoica, P. and Moses, R Introduction to Spectral Analysis, 1st ed. Prentice Hall, Inc., Upper Saddle River, NJ 07458, USA. Willig, A Wireless Sensor Networks: Concept, Challenges and Approaches. In e & i Elektrotechnik und Informationstechnik. Vol. 13. Springer Wien, Received Month Year; revised Month Year; accepted Month Year