A novel algorithm for graded precision localization in wireless sensor networks

A novel algorithm for graded precision localization in wireless sensor networks S. Sarangi Bharti School of Telecom Technology Management, IIT Delhi, Hauz Khas, New Delhi 110016 INDIA sanat.sarangi@gmail.com S. Kar Bharti School of Telecom Technology Management, IIT Delhi, Hauz Khas, New Delhi 110016 INDIA subrat.kar@gmail.com Abstract A lot of research has been done in finding rangebased methods such as computing RSSI, Time Of Arrival, Angle of Arrival or Time Difference of Arrival range-free methods such as computation, DV-Hop Approximate Position in Triangle, for localization in wireless sensor networks. Range-based methods estimate location more precisely than range-free methods. However, range-free methods are costeffective simpler to implement for resource constrained sensor nodes. In this paper, we propose a novel localization algorithm GRADELOC to allow a mobile node to localize with graded levels of precision using a combination of (a) locally available information from the mobile node itself such as accelerometer, magnetometer gyroscope data (b) information derived from the infrastructure, using both rangefree (centroid computation) range-based (Time difference of arrival TDOA) methods. We present the performance of GRADELOC under different situations suggest suitable configurations, for specific situations, that attempt to minimize the overall cost of the system while maintaining desirable results. Keywords: wireless sensor networks, localization, centroid, TDOA, fixed-grid I. INTRODUCTION We propose an algorithm which can localize a mobile node using information derived from a fixed grid of nodes. The node to be localized is referred to as the. We assume that there are three types of nodes which are mobile need localization: (a) an energy constrained capable of localizing coarsely or coarse-grained (CG-), (b) equipped with TDOA computation hardware or finegrained (FG-) (c) a node equipped with TDOA computation hardware displacement computation setup consisting of accelerometer, magnetometer gyroscope or extra-fine-grained (EFG-). The is assumed to be moving within RF range of the nodes in the fixed grid whose configuration we shall describe shortly. Popular range-based methods for fine-grained localization include computation of RSSI [1], Angle of arrival (AOA) [2] Time-of-arrival (TOA) [1] of signal. However, in any localization using RSSI, location estimates are affected by multi-path reflections other shadowing effects. AOA is affected by multi-path reflections TOA requires temporal synchronization of nodes, which is not realistic. So, we use Time Difference of Arrival (TDOA) [3] in our algorithm as the choice for fine-grained localization since it does not assume the nodes to be temporally synchronized. Though TDOA has some communication overhead, it is only used by the which has the necessary hardware to hle it. Hence, only an with the appropriate hardware (i.e an FG- or EFG-) tries to localize more precisely by requesting the infrastructure for a TDOA based location estimation. A number of Range-free methods have been proposed for coarse-grained localization. Approximate Position in Triangle (APIT) [4] works best with irregular radio pattern rom node placement has a four step localization process. DV-Hop [5] uses multiple passes for localization starting by flooding the network with packets followed by estimating hop-distance between anchor nodes subsequent nodes using hop-count. These methods work best with rom nodeplacement involve multiple passes. We choose the centroid method proposed in [6] as our coarse-grained localization method due to simplicity of implementation the similarity of our fixed-grid infrastructure with the algorithm proposed in [6]. An energy unconstrained reference node set (REFN) at each grid crosspoint consists of at least one node (REFN0) at most two nodes (REFN0, REFN1). s are mobile but are confined to the boundaries of the framework. Moreover, in [7] it has been shown that a combination of accelerometer, gyroscope magnetometer can be used for localization. By computing steps taken, strides heading, an accuracy of upto 95% can be achieved, as shown in [8]. So only an EFG- can precisely estimate its location by computing relative displacement from a previous position. II. TOPOLOGY Our simulation test-bed is an open square field with dimensions 400m 400m with an overlay of 25 (5 5) grids as shown in Fig. 1, with successive REFNs separated by 100m. The energy unconstrained reference node for periodic beaconing (REFN0) the optional energy unconstrained reference node for participating in TDOA based localization (REFN1) comprising the REFN, have transmission ranges of 89.4m 100 2m (=141.4m) respectively. All REFN0s keep sending beacons with their grid location (x,y), on a common channel A, at regular intervals. All REFN1s simply keep listening to Fine-grained Localization(FGL) Initiation beacon

REFN-1 (REFN0-1, REFN1-1) REFN-5 (100,100) (100,500) REFN-6 REFN-10 89.4m REFN0-1 REFN0-2 (100,100) (100,200) R3 REFN-11 REFN-15 R1 R2 R4 REFN-16 REFN-20 (200,100) REFN0-6 (200,200) REFN0-7 REFN-21 REFN-25 (500,100) (500,500) Fig. 1. 5x5 REFNs arranged in a grid Fig. 2. Four REFN0s on the top left side of the grid of 5 5 REFNs requests from s on a common channel B. We assume an ideal circular radio range for all purposes also that REFN0s REFN1s have the intelligence to arbitrate usage of channels A B respectively, with a common mode of communication like TDM, FDM or CDM. Each REFN is placed in a grid from (100,100) to (500,500), similar to the setup proposed in [6]. The distance between successive REFNs is 100m. It is to be noted that the figures of 89.4m 100m are within realistic range limits of high-range sensor nodes are obtained solely by scaling the transmission range distance between reference nodes respectively in [6], ten times, for comparison. Each of the four regions, R1, R2, R3 R4 in Fig. 2 is covered by a different set of REFN0s. Movement to a new region triggers a TDOA-based location computation for an FG- or EFG-. For clarity we analyze the behaviour of a single in different modes i.e. CG-, FG- EFG-, desiring graded localization with a mobility model discussed later. A. Flow Diagram III. THE GRADELOC ALGORITHM Fig. 4 gives the flow diagram of GRADELOC in its default configuration. B. Node classification for GRADELOC The three variants running GRADELOC- CG-, FG- EFG-, have their parameter set (coarsegrained, finegrained, selflocalize) initialized as per Tab. I. C. Explanation GRADELOC is invoked once for every beacon received from a REFN0. T is the period between successive beacon transmissions by a REFN0. MAXBEACONS is the maximum number of beacons expected to have been transmitted by each REFN0 before the computes the centroid of received Fig. 3. REFN1-1 (100,100) (100,200) REFN1-2 REFN1-6 (200,100) 141.4m ~ 30m (200,200) REFN1-7 Four REFN1 nodes involved in Fine-grained Localization by TDOA beacons. For a CG-, coarsegrainedthreshold is 0.9 as proposed by [6] for FG- or EFG- we use the simulation results to decide a value for finegrainedthreshold to get a good tradeoff between accuracy of FGL communication overhead. TABLE I NODE CLASSIFICATION coarsegrained finegrained selflocalize None false false false CG- true false false FG- true/false true false EFG- true/false true true 2

coarsegrained, finegrained, selflocalize, finegrainedthreshold (coarsegrained == true) (finegrained == false) iteration = 1 Previous = (0,0) = (0,0) (0,0) Time = SystemTime coarsegrainedthreshold = 0.9 MAXBEACONS = 10, T = 1 Threshold = coarsegrainedthreshold Start (coarsegrained == false) == false) finegrained == true Threshold = finegrainedthreshold Stop TABLE II GLOBAL PARAMETERS Parameter Value T 1s MAXBEACONS 10 TABLE III MOBILITY MODEL Activity Probability speed (m/s) stationary 0.5 0 moving 0.5 D False wait for beacon from a REFN0-x Increment BeaconCount(REFN0-x) (SystemTime - Time) >= MAXBEACONS*T*Iteration seconds compute from location info of beacons received from REFN0-xs where, for each REFN0-x BeaconCount(REFN0-x)/MAXBEACONS >= Threshold Clear BeaconCount(REFN0-x) for all REFN0s Iteration = Iteration + 1 True REFN1 have overlapped ranges to about 30m beyond the sides of the square grid giving sufficient elbow-room to localize a node that is about to leave its grid. E. GetACCELLoc() We may calculate displacement accurately as in [7] [8]. However, the displacement cannot be used for localization if the initial position error is not removed. Hence, for the results of GetACCELLoc() to be meaningful, it is required that an EFG- has both finegrained selflocalize enabled as shown in Tab. I. IV. SIMULATION (!= == false ) (coarsegrained == true) Remaining Conditions ( == (finegrained==true) (selflocalize==true) The proposed algorithm is simulated using a discrete-event simulator with the global parameters set according to Tab. II. The behaviour of an is analyzed by configuring it as a CG-, FG- EFG- by setting the parameters according to Tab. I. (!= == true) Fig. 4. GetTDOALoc() Previous = Previous = Print ComputedLocation ComputedLocation + GetACCELLoc() Flow Diagram of GRADELOC algorithm D. Architecture for implementation of GetTDOALoc() An FG- or EFG- invokes GetTDOALoc() for a FGL of itself. To start FGL, the broadcasts a beacon giving the current location of the which alerts at least one of the REFN1 listening on channel B that an FGL is being demed. The REFN1 uses the location information of the to alert at least three surrounding non-collinear REFN1s to participate in localizing the. The maximum transmission range for an FG- or EFG- to reach a REFN is 50 2m i.e. when the FG- or EFG- is at the center of a grid. From Fig. 3, it can be observed that even when an is about to leave its grid, at least 3 non-collinear A. Mobility Model of We assume a simple mobility model for an for demonstrating the performance of GRADELOC. The node is stationary or mobile with a probability of 0.5. It displaces itself by D in x or in y or in both x y, all with equal probabilities, as shown in Tab. III. For simulation we position the at (100,100) allow it to move across the test-bed according to the proposed mobility model with a displacement of D (1m right or 1m down or 1.414m diagonally), as shown in Fig. 5. B. GetTDOALoc() Approximation [3] discusses performance of many TDOA algorithms under LOS NLOS conditions. We use their simulation results to assume that the location (x,y) computed by GetTDOALoc() has a deviation of (xerror, yerror), both values being outcomes of two independent uniform pdfs with ± 4 as limits, so that the minimum maximum errors in location are 0 ( (4 2 + 4 2 ) = 5.656) respectively. We focus on the problem of setting the value of finegrainedthreshold that achieves an optimum tradeoff between precision of localization number of TDOA invocations, to conserve energy. 3

Fig. 5. Movement direction diplacement(d) of an TABLE IV NOTATION Abbreviation Exped Form CL Computed Location AL Actual Location N number of centroid computations MAE mean absolute error in CL RMSE root mean squared error in CL NTDOA no. of invocations of GetTDOALoc() PTDOA NTDOA/N 100 Fig. 6. PTDOA Vs FineGrainedThreshold for FG- EFG- C. GetACCELLoc() Approximation We assume accuracy of the displacement computation returned by GetACCELLoc() to be 95% of the actual displacement, as per the results obtained in [8]. A. Notation V. RESULTS We use the notation in Tab. IV for our results: B. Performance comparison of s The performance of s is tabulated in Tab. V. We give the maximum minimum values of FG- EFG- obtained from different finegrainedthreshold (FGT) configurations. C. Choosing a value for finegrainedthreshold Fig. 6 Fig. 7 show PTDOA Vs finegrainedthreshold RMSE Vs finegrainedthreshold respectively, for FG- EFG-, obtained by varying finegrainedthreshold from 0.1 to 0.9 with successive values separated by an interval TABLE V PERFORMANCE COMPARISON OF S MAE(m) RMSE(m) CG- 16.3465 19.5105 FG-(min) 11.7320(FGT=0.7) 14.6692(FGT=0.7) FG-(max) 13.8842(FGT=0.3) 17.6133(FGT=0.3) EFG-(min) 0.7380(FGT=0.3) 1.3455(FGT=0.3) EFG-(max) 0.8857(FGT=0.5) 1.5716(FGT=0.5) Fig. 7. RMSE Vs FineGrainedThreshold for FG- EFG- of 0.2. We observe that PTDOA is about 20% for both the s, for the entire range of finegrainedthreshold, indicating that overheads associated with GetTDOALoc() ( hence communication costs) are low. This also shows that the choice of finegrainedthreshold does not affect the value of PTDOA significantly. So, we take finegrainedthreshold as 0.9 for FG- s EFG-s in order to compare them with CG- s which have a fixed coarsegrainedthreshold of 0.9, for obtaining the Error Distribution which is given by Fig. 8. Tab. V shows that the minimum maximum difference in MAE RMSE for an FG- is 2.1522m 2.9441m respectively, for an EFG-, it is 0.1478m 0.2261m respectively. D. Error Distribution of Location Estimation for s Fig. 8 uses error index from Tab. VI to show the error distribution for a CG-, FG- an EFG-. EFG- s estimate location most accurately with over 87% of the Computed Locations (CLs) falling within 2m (e=1) of the Actual Locations (ALs). FG-s have 30% of the CLs 4

TABLE VI MAPPING OF ERROR INDEX TO RANGE Error Index e (Absolute Error in m) 1 0 e 2 2 0 e 5 3 0 e 10 4 0 e 20 5 0 e 30 6 0 e 50 added precision in location estimation comes from the energy spent on the accelerometer, magnetometer gyroscope setup attached to them which does not require any communication in addition to that required by FG-. What deserves a mention here is that all s use the same GRADELOC algorithm simply with the parameter set (coarsegrained, finegrained, selflocalize) if required coarsegrainedthreshold fine- GrainedThreshold, initialized suitably. VII. CONCLUSION In this paper we have proposed a novel method to unify different localization principles into a system that takes advantage of each principle to achieve varied levels of localization for different sensor nodes where the localization precision is a function of the capabilities of the node deming such a precision. Future work involves analyzing the performance of GRADELOC under various mobility models adjusting its parameters for obtaining an optimum configuration. REFERENCES Fig. 8. Error Distribution for CG-, FG- EFG- falling within 5m (e=2) of the ALs when compared to 8% for CG-s. Again, FG-s have 48% (e=3) 98% (e=5) of the CLs within 10m 30m whereas for CG-s the values are 35% 83% respectively. E. Inferences From the results we infer that EFG-s are best for the highest level of precision. FG-s are able to estimate their position with a maximum error of 5m for about 30% of the total number estimations, with a small TDOA computation overhead CG-s are best for estimating the region in which they lie. PTDOA values indicate a low usage of REFN1s to achieve the given results thereby minimizing communication overheads. [1] A. Savvides, C. chieh Han, M. B. Srivastava, Dynamic fine-grained localization in ad-hoc networks of sensors, in Proc. of 7th Annual ACM/IEEE Intl Conf. on Mobile Computing Networking (Mobicom 2001), Rome, Italy, July 2001, pp. 166 179. [2] D. Niculescu B. Nath, Ad hoc positioning system (aps) using aoa, in Proc. of IEEE INFOCOM, San Francisco, 2003, pp. 1734 1743. [3] D. Ping, Yongjun, X., L. Xiaowei, A robust location algorithm with biased extended kalman filtering of tdoa data for wireless sensor networks, in Proc. of Intl Conf. on Wireless Comm., Networking & Mobile Computing (WCNM 05), vol. 2, Wuhan, China, 2005, pp. 883 886. [4] T. He, C. Huang, B. M. Blum, J. A. Stankovic, T. Abdelzaher, Range-free localization schemes for large scale sensor networks, in Proc. of 9th Ann. Intl Conf on Mobile Computing Networking, 2003, pp. 81 95. [5] D. Niculescu B. Nath, Dv based positioning in ad hoc networks, Telecommunication Systems, vol. 22, no. 1-4, pp. 267 280, 2003. [6] N. Bulusu, J. Heidemann, D. Estrin, Gps-less low cost outdoor localization for very small devices, IEEE Personal Commun. Mag., vol. 7, pp. 28 34, 2000. [7] L. Klingbeil T. Wark, A wireless sensor network for real-time indoor localization motion monitoring, in Proc. of 7th Intl Conf. on Inf. Proc. in sensor networks, 2008, pp. 39 50. [8] J. W. Kim, H. J. Jang, D. Hwang, C. Park, A step, stride heading determination for the pedestrian navigation system, Journal of Global Positioning Systems, vol. 3, no. 1-2, pp. 273 279, 2004. VI. ENERGY CONSIDERATIONS With our architecture, we help save energy through design modularity. The system is completely backward compatible with the algorithm proposed in [6]. With a setup having just CG- nodes running GRADELOC, REFN1s can be completely removed to turn the system into pure coarsegrained localization system. With FG-s EFG-s, REFN1s come into picture but they do not have any role except to field FGL requests from FG-s EFG-s participate in FGL using TDOA, thus minimizing the communication overhead. Again, EFG-s behave exactly like FG- s from the perspective of cost of communication. Their 5