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An Effective Localization Algorithm Based on Received Signal Strength

Dr. Rajendra Kumar, Swapnaja Ranade and Balaram Gowda Department of Electrical Engineering

California State University Long Beach, CA 90840

Tel: 562-985-1556

Email: kumar@csulb.edu Abstract—Efficient tracking schemes are becoming very important due to the increasing availability of wireless networks and the importance of location information for applications such as vehicle and object tracking, surveillance, military uses etc. This paper12 presents a simple approach based on the measurements of the received signal strength to determine the position of wireless nodes. An estimation algorithm, using range measurements from multiple, scattered, beacon transmitter stations with known locations, is presented that lowers position location inaccuracies, has relatively low complexity and uses only the local information. Various simulation results are presented that demonstrate the performance of the algorithm.

TABLE OF CONTENTS 1. INTRODUCTION……………………………………1 2. LOCATION TRACKING METHODS…………….. ...2 3. LOCALIZATION ALGORITHM……………………..5 4. PERFORMANCE ANALYSIS…………………… …..7 5. CONCLUSION……………………………….............9 REFERENCES……………………………………………9 BIOGRAPHY……………………………………………10

1. INTRODUCTION Recent advances in wireless communications are opening new ways for wireless mobile users to use their location information for different purposes. This has increased the development of small, inexpensive, low- powered sensor nodes which are able to collect surrounding data, perform small scale computations and communicate among their neighbors. These wireless nodes, when working in a collaborative manner, have great potential in numerous applications. Since sensor nodes are often arbitrarily placed with their position being unknown, node positioning is fundamental and crucial issue for the wireless network operation and management [1]. Ad hoc networks are an example of such network. Ad hoc networks have mostly been studied in the context of high mobility, high power nodes and moderate network sizes. Sensor networks, while typically having low powered nodes, low mobility and large

1 978-1-4244-3888-4/10/$25.00 ©2010 IEEE. 2 IEEEAC paper #1298, Version 3, Updated December 23, 2009

sizes, often classify as ad hoc networks in many cases, when deterministic placement of nodes is not possible. There are several requirements a positioning algorithm needs to satisfy. First, it needs to be distributed over a very large network of low memory and low bandwidth nodes. Second, the algorithm has to minimize the amount of node-to-node communication and computation power so as to maximize the node battery life. This is in view of the fact that the radio and the processor units of the node are the main sources of draining the battery life. Third, the positioning system should work even if the network becomes disconnected - in the context of sensor networks, the data can be later collected by a fly-over base station. Finally, it is desirable to provide absolute positioning, in the global coordinate system used by the GPS (Global Positioning System), as opposed to relative coordinates, since relative positioning might incur a higher signaling cost in the case the network topology changes, and absolute positioning enables a unique name-space, that of GPS coordinates [2]. In an alternative solution to positioning of the nodes with unknown locations, Global Positioning System can be used to find the position of the sensory node. But requiring a GPS receiver on every node is costly in terms of the physical volume of the node which needs to be kept relatively small in many applications of interest, and in terms of the investment needed to build such a network. Also, GPS may not work satisfactorily in indoor environments or in the presence of dense vegetation, foliage and other obstacles that obstruct the line of sight to the GPS satellites. The GPS receiver and antenna also increase the size of the wireless node which is required to be small and not obstructive. Also the power consumption of GPS receiver will reduce the battery life of the nodes thus possibly reducing the lifetime of the entire network. This paper proposes a distributed positioning algorithm without the need for the GPS receivers. Instead, the algorithm uses the Received Signal Strength (RSS) to measure the distance and compute the position of the node iteratively in two dimensions.

2. LOCATION TRACKING METHODS

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Location tracking and positioning systems can be classified by the measurement techniques they employ to determine mobile device location (localization). Typically, Real Time Location Systems (RTLS) can be grouped into four basic categories of systems that determine position on the basis of the following: •Cell of origin (nearest cell) •Distance (lateration) •Angle (angulation) •Location patterning (pattern recognition) A combination of some of the above methods is also used in practice. 2.1. Cell of Origin

This technique is one of the easiest to realize and it determines the base station the mobile device is currently connected. This will give an approximate location of the mobile device. Even if the cell size is small, the achievable precision is quite poor. This approach requires an exact knowledge of geographical environment as obstructions like buildings may change the coverage area of the available base station [3]. 2.2 Distance- Based (Lateration) Techniques 2.2.1 Time of Arrival

Time of Arrival (ToA) systems is based on the precise measurement of the propagation delay of the radio signal between a transmitter and one or more receivers. Propagation delay is the amount of time required for the signal to travel from the transmitter to the receiver. The distance between the transmitter and the receiver can be calculated by multiplying the propagation time by the propagation speed, which is approximately the speed of light. Geometrically, this provides a circle, centered at the base station, on which the mobile device must lie. By using at least three base stations, the position of the mobile device is given by the intersection of the circles [4]. To achieve a reasonable precision, the clocks at the base and mobile stations must be highly synchronized. This increases the overall cost of the system as it requires additional infrastructure. 2.2.2 Time Difference of Arrival

Time Difference of Arrival (TDoA) systems uses relative time measurements at each receiving sensor in place of absolute time measurements. Because of this, TDoA does not require the use of a synchronized time source at the point of transmission in order to resolve timestamps and determine location. With TDoA, a transmission with an unknown starting time is received at various receiving sensors, with only the receivers requiring time synchronization. A mathematical concept known as hyperbolic lateration is performed after calculating the

distance between the mobile device and the receiving station to fix the point [5]. ToA and TDoA have several similarities. TDoA requires the clocks of the receivers to be synchronized. The accuracy of the location system is related to the synchronization of the clocks. Also, TDoA systems are affected by multipath propagation, noise and interferences, which result in inaccurate intersections of the hyperbolas. Direct line of sight is preferable such as in open space or large open buildings [6]. 2.2.3 Received Signal Strength

RSS is measured by either the mobile device or the receiving sensor. Knowledge of the transmitter output power, cable losses, and antenna gains as well as the appropriate path loss model allows one to solve for the distance between the two stations [5]. The following is an example of a common path loss model used for indoor propagation: PL = PL1 Meter + 10 log (dn) + s (1) In the model: •PL represents the total path loss experienced between the receiver and sender in dB. This will typically be a value greater than or equal to zero. •PL1Meter represents the reference path loss in dB at the specified frequency when the receiver-to-transmitter distance is 1 meter. This must be specified as a value greater than or equal to zero. •d represents the distance between the transmitter and receiver in meters. •n represents the path loss exponent for the environment. •s represents the standard deviation associated with the degree of shadow fading present in the environment, in dB. This must be specified as a value greater than or equal to zero. Path loss represents the level of signal attenuation present in the environment due to the effects of free space propagation, reflection, diffraction, and scattering. The path loss exponent (n) indicates the rate at which the path loss increases with distance. The value of path loss exponent depends on frequency and environment, and is highly dependent on the degree of obstruction (or “clutter”) present in the environment [7]. Common path loss exponents range from a value of 2 for open free space to values greater than 2 in environments where obstructions are present. A typical path loss exponent for an indoor office environment may be 3.5, a dense commercial or industrial environment may have an exponent in the range of 3.7 to 4.0 while for a dense home environment the exponent might be as high as 4.5. The standard deviation of shadow fading (s) represents a measure of signal strength variability, (sometimes referred to as “noise”) from sources that are not accounted for in the aforementioned path loss equation. This include factors such

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as attenuation due to the number of obstructions present, orientation differences between location receiver antennas and the antennas of the mobile devices, reflections due to multipath, and so on. The generally accepted method to calculate receiver signal strength given the transmit power, the path loss, the antenna gain, and the cable losses is as follows: RXPWR = TXPWR – LossTX + GainTX – PL + GainRX – LossRX (2) Substituting for the path loss PL in equation (2) from equation (1), and solving the resulting equation for the distance d, one obtains

pwr TX TX 1Meter pwr

RX RX

log(d) [TX Loss Gain PL RX

s Gain Loss ] /10n

= − + − −

− + − (3) where • RXPWR represents the detected receive signal strength in dBW. • TXPWR represents the transmitter output power in dBW. • LossTX represents the sum of all transmit-side cable and connector losses in dB. • GainTX represents the transmit-side antenna gain in dBi. • LossRX represents the sum of all receive-side cable and connector losses in dB. • GainRX represents the receive-side antenna gain in dBi. Solving for distance between the receiver and mobile device allows RSS tri-lateration or RSS multi-lateration to be performed to locate the position. The signal strength information used to determine position can be obtained from one of two sources: •The network infrastructure reporting the received signal strength at which it receives mobile device transmissions (“network-side”) •The mobile device reporting the signal strength at which it receives transmissions from the network (“client-side”) Implementations using RSS lateration have enjoyed a cost advantage by not requiring specialized hardware at the mobile device or network infrastructure locations. This makes signal strength-based lateration techniques very attractive from a cost-performance standpoint [8]. 2.3 Angle- Based (Angulation ) Techniques The Angle of Arrival (AoA) method is based on the calculation of the angle of arriving signal by at least two cell towers. The towers that receive the signals measure the direction of the signal and send this information to the AOA equipment, which determines the user location by triangulation using basic trigonometric formulas. The accuracy of AOA is rather high but may be affected by signal interference and multipath, especially in urban areas.

Combining AOA with TOA will give much better results [9].

3. LOCALIZATION ALGORITHM This section provides an overview of the proposed localization algorithm. A node consists of a transmitter and a receiver. The network consists of nodes belonging to two categories, beacons and unknowns. Beacons have a priori knowledge of their position, which can be either configured before deployment or discovered with a GPS receiver. Unknown nodes estimate their position with the help of beacons. [10] Beacons send beacon packets, which are packets meant to assist unknown nodes in estimating their position. The thing that distinguishes beacon packets from normal communication packets is they are formatted to include an X, Y, Z location (either in a local reference frame or in latitude, longitude, altitude), and a parameter for the power level and antenna gain of the beacon. Distance or range measurements can be achieved in several different ways as discussed earlier. The proposed algorithm is based on RSS measurements. The distance and the direction cosines between the beacons and the initial guess position of the unknown are used to move towards the actual position of the unknown in an iterative manner. We used the IEEE 802.11 Wireless LAN model with the ad hoc network configuration for simulating the simple localization algorithm. The signal strength method uses the relationship of RF signal attenuation as a function of distance. From this relationship a mathematical propagation model can be derived. A simplified model for the purpose of localization is given by

n0RSS P / d= (4)

In (4) P0 includes the known factors such as the transmit power and transmit antenna gain as in equation (2), d is the pseudo range from the beacon to the mobile, and n represents the path loss exponent. Note that d is termed pseudo range as it may differ from the true range due to various errors in the model (4) as discussed below. The propagation characteristics of radio signals can vary with changes in the surrounding environment. Another source of inconsistency is the variation of RSS associated with the altitude of the radio antenna. These factors will introduce some error when the model (4) is applied to evaluate the range from the measured RSS and are accounted for in the algorithm in the form of a random error in the evaluation of the range. Also the antenna gain of the mobile is taken equal to 1 assuming that the mobile antenna is omni directional.

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In the simulations P0 is taken equal to 1000 with the exponent n equal to 3.63. These are considered to be typical values for a WiFi beacon transmitting on maximum power and antenna gain in a typical building environment. Both of these values may vary widely in practice, due to differences in selected beacon equipment and differences in building construction. However, such differences do not impact the performance of the algorithm analyzed in the paper. RSS is selected for range measurements as against other possible measurements because of the following reasons: • The short transmit ranges of 1 to 10 m require an

unacceptably high synchronization accuracy to achieve a reasonable positioning accuracy. An error of 3 cm in range corresponds to only a 100 psec of error in the synchronization time.

• The AOA approach requires costly antenna arrays on each node.

Given a known transmission power and a good model of the wireless channel, the distance between transmitter and receiver can be estimated based on the received signal power. Unfortunately, the accuracy of these RSS range measurements is highly sensitive to multi-path, fading, non-line of sight scenarios, and other sources of interference, which may result in large errors. Fortunately, sensor networks possess two properties that may help to overcome these concerns: (i) dense interconnectivity leading to redundancy in the range measurements; (ii) limited mobility which allows for long observation times and the removal of some of the fast-fading effects through integration [11]. In the wireless network model considered here, the position of nodes and the number of nodes can be arbitrarily chosen. Since the position estimation algorithm does not pose any limitation on the number of beacons used by each unknown node to estimate its position, the number of beacons is arbitrarily selected in the simulations of the algorithm. In the network model, the beacons have a transmitter with 1 Watt or less of transmit RF power, with a transmit frequency in the range of 2.4 and 2.483 GHz, and QPSK or GMSK modulation. The unknown node has a receiver of high sensitivity (-70 dBm for WiFi signal reception) and high dynamic range (up to 60 dB) in order to accurately measure RSS over a wide range of distances and with signal attenuation in a building environment. These are typical parameters for a WiFi network. The nodes are assumed to be placed on a single floor, thus only a two dimensional positioning is considered in the paper. The first step in the localization algorithm is to determine the distance or range between the mobile with unknown position and the beacons with known positions, This range is determined using the RSS formula (4). The possible error introduced in the measurement of RSS introduced due to various uncertainties such as the receive antenna altitude, variations in the propagation environment causing variations in attenuation, multipath propagation etc.,

is modeled as a random additive error in the range with a relatively high value. Using the pseudo ranges to various beacons, the receiver then determines its own position using the following iterative algorithm. The Localization Algorithm 1. Extract beacon’s X and Y coordinates from the data

transmitted from the beacons. Let the co-ordinates of the beacons (nodes whose locations are known) be (X1,Y1), (X2, Y2),…,(XN, YN) where N denotes the number of beacons. Let (Xu, Yu) denote the co-ordinates of the node whose position needs to be determined.

2 From the data transmitted from the beacons determine

the constant P0 in (4). In general this constant may differ among different beacons due to transmit power and antenna gain differences among the beacons. With the knowledge of the constant Poi ,the value of P0 for beacon i, and RSSi, the received signal strength from the beacon i, evaluate the pseudo range di between the beacon and the node with the unknown position, using the RSS formula (4) for i = 1,2,…,N. Thus

1/n

i 0,i id (P / RSS )= ; i=1, 2,…, N (5)

In actual applications, the pseudo range di computed form (5) will differ from the true range. In the simulations, there is no modeling error in (4) and thus the range Ri = di. The difference between the actual range and the measured range is modeled by is modeled by a random error e.

3. The range Ri = di computed from (5) is distorted by a random error ei yielding the distorted range Di used in the algorithm.

i i iD R (1 e )= + (6)

The error ei is random and uniformly distributed over the interval (-0.25, 0.25)Ri. Effectively multiplicative error occurs in view of the RSS formula (4) where in the RSS is first measured in dBW units with error in dB units and then converted to the Watt units for use of (4).

4 The initial estimate of the unknown location is taken as

the centroid (Xc, Yc) of the N beacons. The centroid of the beacons is obtained by taking the average of X and Y coordinates of all the beacons.

5 Find the geometric distance Gi and direction cosines

between the ith beacon and the estimated position of the unknown node. The geometric distance Gi and the direction cosines Dx,i and Dy,i for the ith beacon, for i = 1, 2,…, N, at the first iteration are given by

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2 2i c i c iG [(X X ) (Y Y ) ]= − + − (7)

x,i c i iD (X X ) / G= − (8)

y,i c i iD (Y Y ) / G= − (9)

6 Find the difference vectors defined as the difference between the geometric distance Gi and the measured pseudo range Di for all the beacons. The adjustment in the position estimate of the mobile is then obtained in terms of the differences Δβx,i and Δβy,i for i =1, 2, …, N, defined as

x,i x,i i iD (D G )Δβ = α − (10)

y,i y,i i iD (D G )Δβ = α − (11)

In (10) and (11), the parameter α denotes the step size selected equal to 0.27 in the simulations. The step size is selected based on the considerations of stability and the convergence speed.

7 The estimate of the mobile position at iteration k

denoted by k ku u(X Y )+ at time k is then obtained by

adjusting the estimate at the iteration (k-1) by the sum of the differences Δβx,i and Δβy,i evaluated in step 6. Thus

Nk k 1

u u x,ii 1

X X −

== + Δβ (12a)

Nk k 1u u y,i

i 1Y Y −

== + Δβ (12b)

8 The steps 5 to 7 are repeated till the adjustment vector is close to 0.

4. PERFORMANCE ANALYSIS

This section presents the performance of the localization algorithm in terms of accuracy, rate of convergence and other performance measures obtained by simulations. Figure1 plots the X and Y coordinates of the beacons, and the true location of the mobile node which needs to be estimated by the algorithm. The figure also depicts the estimated position of the mobile at various iterations of the algorithm starting with the initial estimate at the centroid of the beacons. As may be inferred from the figure, the estimate after 12 iterations is very close to the true position of the unknown node.

Figure1. Trace of the position estimates of the node moving towards the true location of the mobile.

Figure 2 plots the position error in meters as a function of the iteration number for the example considered in Figure 1. The distance measurements using received signal strength is not very effective in situations where a good path loss model is not available. Figure 3 shows the variations in the distance as computed from the RSS formula (4) for different values of the exponent n. As is obvious, for any given RSS value, the estimated distance can vary over a wide range depending upon the value of n. Thus in the simulations runs wherein the values of n used in the algorithm were significantly different from their true values, the position estimates were not reliable. These results are not presented in the paper. Figure 4 shows the application of the algorithm for trajectory following. The figure shows the position of the mobile at certain time intervals. At each point in time, the initial estimate is made equal to the estimate at the previous time instance. The algorithm is then applied to the RSS measurements obtained at the present time instance to obtain the position of the mobile at the present time. The figure also depicts the estimated positions of the mobile at various time instances showing a good trajectory following.

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Figure 2. Position error versus the iteration number

Figure 3. Variation in distance measurement using RSS formula for different values of the path loss exponents

Figure 4. Trajectory trace of the unknown node

As is intuitively obvious, for good positioning and tracking performance, an adequate number of beacons are required. As the number of beacons increases, the location error correspondingly decreases. For example, when only two beacons are used the position error is around 60 meters. The error approaches zero as the number of beacons is increased. Figure 5 plots the average error in the trajectory following of figure 4 with different number of beacons showing that the average error is reduced to about 1 meter with the use of 30 beacons. In addition to the number of beacons, proper placement of beacons is also very important for achieving good positioning accuracy.

Figure 5. Average tracking error versus the number of beacons.

5. CONCLUSION

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A simple algorithm for determining the position estimates in a wireless sensor network is proposed. This algorithm has fewer computations and uses RSS measurements there by reducing the cost for any additional hardware. The algorithm has been implemented in MATLAB for evaluating its performance. The beacons have been arranged in a somewhat random fashion. The beacons send signals in intervals. The unknown node collects these signals and applies the estimation algorithm to find its location. The algorithm first finds the RSS distance between the beacons and the estimated position of the unknown node and then uses iterative computations to find the geometric distance between the estimated position and the beacons. The estimate of the node position is then updated on the basis of the difference between the RSS distance and the geometric distance as described in the paper. In various simulation examples, good positioning accuracy has been obtained by the algorithm. The performance of the algorithm is impacted by the placement of the beacons and the number of beacons used by the node, as expected. The algorithm works very well when the propagation exponent n is known for all the beacons. With small deviations between the true and estimates of n result in relatively small distance errors wherein the algorithm provides Also a propagation model with equal n for all beacons was used which is not true in a real world. Despite the small distance measurement error, the algorithm provides sufficient location information and accuracy to support the network.

REFERENCES

[1] Frankie K. W. Chan, H. C. So and W.-K Ma, “A Novel Subspace Approach for Wireless Sensor Network Positioning with Range Measurements,” IEEE ICASSP ‘07, Vol. 2, Page(s) II-1037-II-1040, April 2007

[2] Dragos Niculescu and Badri Nath, "Ad Hoc Positioning

System (APS)," GLOBECOM 2001, San Antonio, Nov 2001

[3] Patrick Loschmidt, Georg Gardener, Hilo Saunter

“Location based Services for IEEE 802.11a/b/g Nodes” in proc. of the 6th Intl WORKSHOP On Real Time Networks (RTN 07), Pisa, Italy, S. 64-70, July 2007.

[4] J.Caffery, Jr. and G. Stüber, "Overview of Radiolocation

in CDMA Cellular Systems," IEEE Commun. Mag., Vol. 36, No. 4, pp. 38-45, 1998.

[5] Wi-Fi Location-Based Services 4.1 Design Guide©

2008 Cisco Systems, Inc, pp 2-1 to 2-14.

[6] Real Time Location Systems (RTLS). A White Paper from Nanotron Technologies GmbH. http://www.nanotron.com/EN/pdf/WP_RTLS.pdf

[7] Nima Alam, Asghar Tabatabaie Balaie, Andrew G.

Dempster “Dynamic Path Loss Exponent Estimation in a Vehicular Network using Doppler Effect and Received Signal Strength.” http://www.gmat.unsw.edu.au/snap/publications/alam_etal2010a.pdf

[8] Xinrong Li, "Performance study of RSS-based location

estimation techniques for wireless sensor networks," IEEE Military Communications Conference (MILCOM), Atlantic City, NJ, October 2005.

[9] Hassan A. Karimi, Amin Hammad, “Telegeoinformatics:

Location-Based Computing and Services,” Boca Raton, Florida , CRC Press LLC, 2004, pp. 90-94.

[10] Vaidyanathan Ramadurai, Mihail L. Sichitiu,

“Simulation-based Analysis of a Localization Algorithm for Wireless Ad-Hoc Sensor Networks” in Proc. of OPNETWORK 2003, (Washington, DC), Oct. 2003.

[11] Chris Savarese, Jan M. Rabaey and Jan Beutel,

“Location in distributed ad-hoc wireless sensor networks,” IEEE ICASSP ‘01, Vol. 4, Page(s):2037 – 2040, 2001

BIOGRAPHY

Dr. Rajendra Kumar is Professor of Electrical Engineering at California State University, Long Beach. He is also a Senior Engineering Specialist at The Aerospace Corporation. He has published more than 100 papers on communication systems, GPS, adaptive signal processing, and adaptive control. He has received nine patents in the area of communication and GPS systems and has 5 patents pending. He has about 30 years of experience in these areas. He is the recipient of twelve NASA Tech. Brief and Patent Disclosure awards from the National Aeronautics and Space Administration, Washington D.C. He is also recipient of several Patent Disclosure and Spot Achievement Awards at the Aerospace Corporation. He received the Best Paper award at the International Telemetering Conference and the Distinguished Faculty award at California State University, Long Beach. He is a Senior Member of IEEE and a member

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of AIAA and ION. He received his B.Tech. and M.Tech. in electrical engineering from the Indian Institute of Technology, Kanpur, Ph.D. in electrical engineering from the University of Newcastle in Australia and did post doctoral research at Brown University, Rhode Island, U.S.A. His biography is listed in Who is Who in the World, Who is Who in America, Who is Who in Science and Engineering, and seven other biographical reference works.

Balaram Gowda was born in India in 1984. He obtained his Bachelor of Engineering degree in Electronics and Communication from Visvesvaraya Technological University, India. Presently he is working towards his M.S degree in Electrical Engineering at California State University, Long Beach. He is also working as an Electrical Engineer with Terralliance Technologies, Inc