Improved Hybrid AML Algorithm without identification of LOS/NLOS nodes

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1 Improved Hybrid AML Algorithm without identification of LOS/NLOS nodes Leïla Gazzah, Leïla Najjar and Hichem Besbes Lab. COSIM, Higher School of Communication of Tunis, Carthage University Tunisia gazzah.leila, leila.najjar, Abstract Novel mobile localization algorithms under non-lineof-sight (NLOS) conditions are here presented, which involve only one base station (BS) and at most three nodes. Using the weighted ranges to the three nodes and the AOA angular beam, the AOA seen at BS may be corrected to some degree, to the BS. We propose a NLOS selective combined scheme for mobile location estimation. These NLOS mitigating scheme is based on the selective hybrid RSS/AOA weighting AML (SHWAML) approach. Performance comparison between the proposed hybrid method and other hybrid location methods are investigated in a NLOS environment. It is found that the proposed method can deal with NLOS range error effectively, and is attractive for location estimation in cellular networks. Index Terms NLOS, weighted range, angular beam, SHWAML. to find all possible weighted ranges that produce special points, defined as potential points which lead to the MS location estimate. The work [3] presents a hybrid AOA/RSSD (RSS difference) combined scheme, where multiple AOA and RSS measurements are used for emitter location, that utilizes non-linear constrained optimization to estimate the mobile terminal s location. The LS and Maximum Likelihood criteria are considered. I. INTRODUCTION In the network-based approaches, location metrics such as Time of Arrival (TOA), Angle of Arrival (AOA) and Received Signal Strength (RSS) are conventionally used in estimating the mobile stations (MS) locations. In this work, we investigate the intra cell localization and will focus on providing some enhancements for accurate MS location estimation. Our approach is selective and uses the three higher RSS measurements obtained at known location points within the cell combined to the unique AOA measure provided by the serving BS in the presence of Non-Line-Of-Sight (NLOS) propagation impairments. Recently, researchers are interested in developing new algorithms that cope with scenario with reduced number of connected BSs. For instance, algorithms that use only one or two BSs only to locate a MS in the case of hearable and excessive network burden problems are desirable. The performance of location technique mentioned previously degrade greatly in NLOS scenarios. Therefore, it is necessary to find methods to mitigate the location bias induced by NLOS propagation. In [1], a selective hybrid RSS/AOA approach is proposed where the best RSS measurements are combined with the serving BS AOA measure in order to locate the MS in the presence of NLOS propagation impairments. In [], a weighting TOA Least Squares (LS) approach is developed, which is among the important NLOS mitigation approaches whereby the system attempts to localize the MS with both Line-Of-Sight (LOS) and NLOS measurements. For different NLOS models (i.e. DOS (Disk of Scatterers), RDOS (Reversed DOS) and Uniform models). The LS algorithm uses only TOA-based circle equations and factors of weighting (a) (c) (b) (d) Fig. 1. Geometric layout of the three circles (respectively weighted circles (dashed circles)) and the line (respectively the angular bounds(dashed lines)) with in (b) intersection forming a potential point and in (c) MS is outside the angular bounds and in (d) intersection of the weighted circles which is not a potential point. In this paper, we propose a weighting HAML schemes to estimate the MS location when the three best nodes, in terms of higher RSS measurements, are involved in the localization process. The scheme is based on the selective hybrid weighting AML (SHWAML) approach. In [1], the position of MS is recovered based on the intersections between the three circles deduced from the RSS measurements and their intersection with the AOA line (the area enclose by ABC) (see figure 1). Contrarily to the work in [1], in this paper, the position

2 of MS is recovered based on the intersection of three RSS weighted circles (dashed circles), and an AOA angular beam (dashed lines) (the area enclose by U V W XY ), where the three weighted circles are deduced from the three best nodes, in terms of higher RSS measurements, and the AOA angular beam is defined around the AOA seen at the BS, in the first step (see figure 1 (a)). In the second step, to effectively locate the MS it should be verified that the three weighted circles intersect at a single point named potential point (see figure 1 (b)) and that the potential point lies within the area enclosed by the AOA angular beam (see figures 1(c) and 1 (d)). The remainder of the paper is organized as follows. In section II, the selective hybrid RSS/AOA weighting AML (SHWAML) approach is detailed in section III. Numerical results are presented in section IV. Finally, section V concludes the paper. II. SYSTEM MODEL Using RSS measurements ( from the MS and received by the ith node), which denoted P i, for localization relies on the path loss model in which the signal strength attenuates at an exponential rate between the node and the MS with a random component modeling shadowing effects. Let Θ = [x y] T the MS coordinates, and Φ i = [x i, y i ] T are the coordinates of the single emitter and the ith node. Then, (x x i ) + (y y i ), i = 1,..., M, is the distance R i = between the MS and the ith node. An empirical prediction model of signal strength can be expressed as RSS i = P L(d 0 ) 10γ log 10 ( Θ Φ i ) + X σrssi,los/nlos, d 0 (1) where RSS i = P T P i is the path loss in dbm at the ith among M nodes (P T is the transmission power), γ is the pathloss exponent, P L(d 0 ) is the power loss in db at a reference distance d 0 (d 0 Θ Φ i ) and X σrssi in db is the shadowing random variable. Contrarily to time varying noise sources, the errors induced by shadowing can not be averaged out by taking multiple measurements and can be modeled in logarithmic scale by a zero mean Gaussian distribution with variance RSS i [4]. The path loss model can be used to compute R i as R i = d 0 10 P L(d0)/10γ 10 ( RSSi+Xσ RSS i,los )/10γ, () From (1), the estimated range between the MS and the ith node can be expressed as l i = R i 10 Xσ /10γ RSS i,los/nlos = R i + N los/nlos,i, (3) ) where N los,i = R i (10 Xσ RSS i,los /10γ 1 N ( 0, σlos,i) under LOS ) environment and Nnlos,i = R i (10 Xσ RSS i,nlos /10γ 1 N ( ε nlos,i, σnlos,i) under NLOS environment [5]. The true ranges can be written in terms of the measured ones as [6] R i = α i l i, (4) where, for NLOS propagation, 0 < α i 1. The values of α i are restricted since the NLOS error is a large positive bias that causes the measured ranges to be greater than the true ranges. Reserving node 1 to the BS, without loss of generality, let the three selected best RSS measurements nodes be indexed by i =, 3 and 4. Given the NLOS corrupted range measurements and node locations, the scale factors, α i, i =, 3, 4, can be derived. Because the NLOS error is always positive, the MS location must lie in the region of overlap of the range circles (region enclosed by U, V, W ) as shown in figure where U, V and W are intersections of circles centered on (x i, y i ) with radius l i (for i =, 3, 4). The details of finding the boundaries of α, α 3, and α 4 are given by [6] α,min 1 CD l α 3,min 1 CD l 3 α 4,min, 1 AB l, 1 EF l 3 1 AB, 1 EF l 4 l 4 (x k x i ) + (y k y i ) is the distance be- where L ik = tween the ith and kth nodes. L3 l 3 L3 l 4 l 4, l l 34 l 4, l 3 l 3 L4 l 34 l 3 (5), l 4 l 4 Fig.. Geometry of RSS-based location showing measured range circles and the region of overlap in which the MS lies The measured distances l i are assumed to be corrupted by independent zero-mean Gaussian noise. These higher RSS nodes lead to measurements such that = [α l, α 3 l 3, α 4 l 4 ] T have covariance Q = diag var, var 3, var 4,where var i = E (α i l i R i ). The AOA measurement at the serving BS, considered as node 1, can be expressed as θ = θ d + φ = tan 1 ( y 1 y ), (6) x 1 x where θ d is the LOS path AOA and φ is the angular deviation caused by NLOS propagation through scatterer, which can be accurately described by a Gaussian random variable in a macrocell or outdoor environment. In the next sections, the serving BS, node 1, is assumed to be at the coordinates origin in a Cartesian system i.e.: x 1 = y 1 = 0 and provides the AOA measure. Besides, only the three higher RSS measurements, among the M nodes of the cell are considered. Note that it may occur that one among nodes, 3 or 4 coincides with the BS (node 1).

3 III. THE SHWAML APPROACH In [1], we consider the intersections between the circles deduced from the RSS measurements and their intersection with the AOA line (see figure 1 (a) (the area enclose by ABC)). Here, we study the enhancement obtained by combining a weighting procedure, which aims to mitigate the NLOS range bias (dashed circles), to the incorporation of an uncertainty about the AOA through considering an angular beam, (θ max θ min ) (see paragraph IV. B), around the measured AOA to the BS (see figure 1 (a) (the area enclose by UV W XY )). A. Coarse estimate Let the vector of the three LOS ranges between the MS and nodes, 3 and 4 and the LOS AOA measurement at the serving BS be R H (Θ) = [R, R 3, R 4, θ d ] T, R i = s + k i xx i yy i, s = x + y, (7) and k i = x i + y i. (8) The vector of estimated parameters becomes H = [α l, α 3 l 3, α 4 l 4, θ] T. The covariance matrix becomes Q H = diag var, var 3, var 4, var AOA, var AOA = var(φ). Then, the probability density function (pdf) [7] of H given Θ is expressed as ( f( H Θ) = (π) det (Q H ) 1/ exp J ) H,(9) 4 (α i l i R i ) J H = + (θ θ d). (10) var i var AOA The WML estimation principle seeks to minimize the quantity in J H. Then, setting the gradient of J H with respect to Θ to zero J H Θ = R H (Θ) Θ = ( ) T RH (Θ) Q 1 H Θ ( H R H (Θ)) = 0. x x y y R R x x 3 y y 3 R 3 R 3 x x 4 y y 4 R 4 R 4 y y1 x x 1 R1 R1. gives two nonlinear WML equations : 4 (x x i ) (R i α i l i ) + (y y 1) (θ θ d ) R i var i R1 var AOA 4 (y y i ) (R i α i l i ) (x x 1) (θ θ d ) R i var i R1 var AOA = 0, = 0.(11) which is equivalent to 4 ( p i s + ki αi li ) 4 = p i (x i x + y i y) w(y y 1 ), 4 ( q i s + ki αi li ) 4 = q i (x i x + y i y) + w(x x 1 ), where p i = (x x i )/ ((α i l i + R i )R i var i ), (1) q i = (y y i )/ ((α i l i + R i )R i var i ), (13) w = 1/ (θ θ d ) /R 1var AOA. (14) Reordering (1) yields in a matrix notation where A = b 1 = and b = AΘ = b 1 s + b, (15) p ix i p ] iy i w q ix i + w q, iy i ] p i q i p i(k i αi l i ) wy 1 q i(k i αi l i ) + wx 1 (16) ]. (17) Then the estimated Θ is obtained in terms of the variable s as follows Θ = 1 ( A T A ) 1 A T (b 1 s + b ), (18) Combining (18) and (7) yields a quadratic in s. Solving this quadratic yields three possible cases upon which the RSR selects the adequate solution [1]. After choose the correct value of s among the roots solutions of the resulted quadratic, we calculate Θ through (18) and update the values of the coefficients p i, q i and w. Repeating this procedure n (n = 5) times gives n values of Θ, then the WHAML selects the one that gives the minimum JH as the final location estimate. The initial solution Θ 0 can be determined using the selective hybrid Least Squares (SHLS) approach [1]. B. Fine estimator The LOS path AOA must be in an interval with a certain high confidence level. It is assumed that θ min and θ max are corresponding lower and upper bounds [8] θ min θ d θ max. (19) For example, if the angle deviation φ seen at the serving BS is modeled by a Gaussian distribution N(0, σ ), θ d lies in the interval [θ σ, θ + σ] with probability 95%. By constraining the MS position to lie within a small enclosed region overlapped by the three disks intersection and the angular beam around the measured AOA, the area enclose by UV W XY, (see figure 1 (a) ), the estimated MS position

4 must satisfy the following restrictions R i = α i l i, i =, 3, 4, θ min θ d θ max, (0) where R i and θ d are respectively the estimates of LOS range between the ith node and the MS and the LOS AOA between the BS and the MS. In the following, steps that summarize the estimation of the MS location using the proposed SHWAML are listed. Steps 1. For all allowable combinations of the weighting factors, α, α 3, and α 4,define the weighted circles equations (4) and SHWAML application is applied. 1) Starting from an initial solution Θ 0. ) Then, calculate p i, q i and w, 3) Perform Eq. (18) to obtain Θ. 4) Then, update p i, q i and w, 5) Repeat steps 3) and 4) for a given number of n iterations, 6) For each iteration the quantity J H to be minimized is calculated. The algorithm selects the estimate Θ that gives the minimum value of J H. Step. If the intersection point lies on the weighted circles (i.e. satisfies circles equations (4)) intersection and satisfies the inequality (0)), that point is a potential point as shown in figure 1 (b). If not, as shown in figures 1 (c) and 1 (d), discard these weighting factors and repeat step 1 after updating the weighting factors. Step 3. The optimal MS location is the mean value of the computed potential points. IV. SIMULATIONS AND DISCUSSION OF RESULTS In this section, the performance of the proposed SWAML and SHWAML schemes and all other methods will be examined which use the 3 best RSSs measurements at known positions nodes and the AOA measure in the serving BS. Namely, as benchmarks, we will consider SWAML which is the version of SWHAML not accounting for the AOA. We consider a macro cell with a serving BS and six nodes with locations (0, 0), (866, 1500), (173, 0), (866, 750), (866, 0), (433, 750) and (199, 750). The MS location is chosen randomly according to a uniform distribution within the area covered by the triangle formed by the points (0, 0), (866, 1500) and (173, 0). All units are in meters. By selective RSS we refer to the choice of the 3 higher RSS among the 7 nodes measurements. The path loss exponent is fixed to γ =. The results are averaged over 1000 Monte-Carlo trials. The number of AOA measurements (if not specified otherwise) is fixed to 100 and the angular bounds are as (19) which are selected with a confidence level of 95%. RSS and AOA measurements are assumed to be corrupted by independent Gaussian noise with variances σ RSS and var AOA = 10 if not mentioned otherwise, respectively. A scenario where the standard deviation of the RSS nodes depends on the distance between the emitter and the receiver was simulated, where for d [0, 144m[, σ RSS = 1dB and an increase of 1dB per additional distance of 144m is adopted. All methods are here envisaged in a selective framework, where a subset of RSS measurements are available and where only the three best RSS measurements are considered. The performances of several methods are compared with the selective aspect, including the proposed methods, Weighting Least Squares techniques in [] denoted by SWLS (Selective WLS), the hybrid AOA/RSS AML (SHAML with no weighting) ), the AML (SAML with no weighting) algorithms in [1], and the weighting hybrid ML AOA/RSSD (RSS Difference) in [3] denoted by SWHML (the simulation results is shown for the cost function with weight factor λ = 0.4). The improvement in location accuracy provided by these methods can be seen in the Cumulative Distribution Function (CDF) curves of the location error as shown in figure 3. It can be seen that the proposed SHWAML algorithm two versions, with and without considering the angular beam around the measured AOA, outperforms all the envisaged methods. Thus, it is clear that adding angular beam aspect to the weighting aspect leads to an enhanced performance compared to schemes using selective weighting aspect with deviated NLOS AOA line as the angular beam allows to compensate to a certain degree the AOA deviation caused by NLOS propagation. Also, as could be predicted, for SHWAML incorporating the angular beam, the location error decreases when the number of the available AOA measurements (indicated in parentheses) increases. Fig. 3. CDF plots of the average radiolocation error for the different selective methods. Table 1 was performed to study how the average radiolocation error is affected by the number of NLOS nodes among the three selected ones when the proposed approaches are employed and compared to the SWHML, SHAML, SAML and SWLS algorithms. As expected, it is observed from table 1 that the performance of the proposed selective hybrid weighting AML schemes, with angular beam and AOA line respectively, outperform all the envisaged benchmarks. For all considered weighting algorithms, the average radiolocation error decreases slightly when all nodes are NLOS as compared to the case when two nodes are NLOS, which is not the case with the versions not including range weighting SHAML and

5 SAML. Number of NLOS nodes 1 3 SHWAML with angular beam SHWAML without angular beam SWHML SWAML SHAML SAML SWLS Table 1: Average location error for different selective methods versus the number of NLOS nodes. The performance of these methods against the AOA standard deviation was also investigated. As shown in figure 4, the accuracy of the MS location estimate calculated with the SHWAML, the SWHML, and the SHAML algorithms is enhanced when more accurate AOA measurements are used. It shows a better robustness of the selective weighting algorithms in the case of severe AOA standard deviation. As expected, no effect is introduced on the position estimate calculated with the SWLS and the SAML since it does not use the AOA information. It is worth noting that the performance of the proposed SHWAML algorithm are still better than all others methods using any AOA standard deviation. Fig. 5. Average location error versus the standard deviation of the RSS nodes for the different methods. and the AOA angular beam (for the hybrid scheme) around that seen at the BS. This combination which is expected to correct to some degree the AOA deviation due to NLOS has shown its capacity to reduce location errors. Simulation results showed that the proposed SHWAML offers a considerable accuracy enhancement compared to the SWAML (not hybrid), the SWLS and their un-weighted counterparts. The SHWAML algorithm outperforms all the envisaged benchmarks even under highly severe NLOS conditions. REFERENCES Fig. 4. Average location error versus the standard deviation of the AOA BS for the different methods. Figure 5 studies the performance of these methods against the RSS standard deviation. Twelve scenarios, which differ in the standard deviation σ RSS of the RSS nodes, were simulated. The standard deviation σ RSS of the RSS nodes ranged from 1dB to 1dB in increments of 1dB. For all scenarios, the standard deviation of the AOA sensors was fixed at 10. The simulation results are shown in figure 5. It is expected that the performance of any location algorithm deteriorates when the standard deviation σ RSS of the RSS nodes increases. [1] L.Gazzah, L.Najjar, and H.Besbes, Selective Hybrid RSS/AOA Approximate Maximum Likelihood Mobile intra cell Localization, European Wireless, Guildford, April 013. [] Refat A. Al-Nimnim, Ali H. Muqaibel and Mohamed A. Landolsi, Improved Weighting Algorithm for NLOS Radiolocation, IEEE 9th Malaysia International Conference on Communications, December 009. [3] Sichun Wang, Brad R.Jackson, Robert Inkol, Hybrid RSS/AOA emitter location estimation based on least squares and maximum likelihood criteria, In Proc. IEEE Communications (QBSC), Kingston, pp.4-9, June 01. [4] A. LaMarca, June. Hightower, I. Smith, and S. Consolvo, Self-mapping in location systems, In Proc. 7th International Conference on Ubiquitous Computing (Ubicomp05), pp , Tokyo, Japan, September 005. [5] S. Slijepcevic, S. Megerian, and M. Potkonjak, Characterization of location error in wireless sensor networks: analysis and applications, in Proceedings of the nd International Workshop on Information Processing in Sensor Networks, pp , Palo Alto, Calif, USA, 003. [6] S. Venkatraman, James Caffery, and Heung-Ryeol, A Novel TOA Location Using LOS Range Estimation for NLOS Environments, IEEE Transactions on Vehicular Technology, September 004. [7] Steven M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, PrenticeHall PTR Upper Saddle River, NJ 07458, [8] H. Tang, Y. Park, and T. Qiu, A TOA-AOA-Based NLOS Error Mitigation Method for Location Estimation, Hindawi Publishing Corporation, EURASIP Journal on Advances in Signal Processing, 008, Article ID 6858, 14 pages, doi: /008/6858. V. CONCLUSION In this paper, we presented a selective hybrid RSS/AOA weighting AML algorithm. The main contribution of our combining scheme is based on using the weighted ranges to the three best nodes, in terms of higher RSS measurements,