Mobile Geo-location Algorithm based on LS-SVM SUN -, GUO (Institute of Communication and Information Engineering, University of Electronic Science and Technology of , Chengdu, 610054, People’s Republic of China) Telephone Number: 86-28-83201410, Email: [email protected]

Abstract: The mobile geo-location is a has been very successfully applied on many requirement driven by the emergency Calls, fields, such as handwriting recognition, face but also by the emergence of new location identification, signal processing and mobile based services and ubiquitous computing. In geo-location [4]. Recently, a new method of order to improve location accuracy, a novel SVMs, Least Squares Support Vector mobile positioning algorithm based on Machines (LS-SVMs) [5], which adopts LS-SVM algorithm is employed to fuse the least squares linear system as loss function, radiolocation TOA measurements of several instead of quadratic program in traditional base stations. Through simulation in the bad SVMs. It has been successfully applied to urban environment, an accuracy of 71m in pattern recognition and nonlinear function 67% of cases and 135m in 95% of cases has estimation problems, which performed well been reached, which satisfies FCC for its simple calculation, fast convergence requirements very well. and high precision. Therefore, this letter Keywords: Mobile geo-location, Least attempts to apply LS-SVMs to Mobile Squares Support vector machines, Data geolocation to satisfy FCC requirements fusion well. Introduction: Location based services in LS-SVMs for mobile ge-olocation: Here, we mobile phone systems have received simply introduce the algorithm of function increased attention now. The Geo-location estimation LS-SVMs: accuracy requirement set by the Phase 2 Dx= {(,y)|k=∈1,2,",N},xRn ,y∈R program of U.S. Federal Communication kk k k Commission (FCC) for emergency services, In the weight (w) space (primal space), For network-based solutions: within 100m optimal problems can be described as for 67%of calls, and within 300m for 95% follows. of calls, is generally difficult for network N 11T 2 based solutions to achieve, due to harsh RF min Jw( ,e) =+22ww γ ek (1) wb,,e ∑ environments and system constraints. For k=1 TOA-base location system, A number of Subject to geo-location algorithms based on yw=+Tϕ(x) b+e k=1,..., N multilateral geometry have been presented kkk in [1]. Another category of geo-location Where, ϕ() : Rn → Rnh is a nonlinear algorithms based on approximate theory such as neural network is investigated in [2]. mapping in kernel space, wR∈ nh , error However, neural networks depend on networks structure and complexity of variable e∈ Rand b is bias. J is loss samples, which cause over fit and low k generalization. function, and γ is an adjustable constant. In 1995, Vapnik presented a new The aim of the mapping function in kernel statistical learning method-Support vector space is picking out features from primal machine (SVM) in [3], which has space and mapping training data into a self-contained basis of statistical learning vector of a high dimensional feature space, theory and excellent learning performance. in order to solve the problem of nonlinear SVM has already become a new research regression. hotspot in the field of machine learning and According to optimal function Eq. (1), we define the Lagrangian function we will focus on RBF kernels which

2 Lw(,b,e;α)= J(w,e) corresponds to Kx( , x) =−exp( xxkl− ) kl 2σ 2 N T （2） −+∑αϕkk{wx()b+ek−yk}The precision and convergence of LS-SVMs k =1 are affected by (,γ σ ). The (,γ σ ) Where α are Lagrange multipliers which k hyper-parameters can be determined by means of 10-fold cross-validation on the are also support vector ( α ∈ R ). The k training data in order to improve the optimality of upper function is as following generalization performance of LS-SVM. In sets of linear equations instead of quadratic our simulation, γ =[1 1.2], σ =[0.87 0.85]. program in traditional SVMs. Simulations: Our geo-location model is applied to classical cellular network with 7  N ∂L Base Stations per cluster, where BS is the  ∂w =→0(wx=∑αϕkk) 0  k=1 service base station with cell radius of  N  ∂L =→0α =0 1000m. The measurement error of TOA,  ∂b ∑ k (3)  k =1 brought by the measurement equipments ∂L  ∂e =→0 αγkk=e could be taken as a Gaussian random  k ∂L =→0(wxTϕ )+b+e−y=0 variable with zero-mean and 0.2 μ s  ∂αk kkk standard variance. Non-light of sight is one For k=1…N. After eliminating variables of the main error sources of TOA, and ( w,e) we get matrix equations (4). NLOS error is assumed to subject to

T exponential distribution in COST 259 01v b 0 = (4) Channel Model in Bad Urban environments 1 Ω+ 1 I α y v γ   [6]. Mobile Station is placed in uniform random locations in a cell, so that we can Where yy= [," y], 1[= 1,",1], 1 N v obtain 5000 mobile station positions. The training phase use 4000 mobile positions α = [α,," α] and Ω=ϕ()x T ϕ(x ), 1 N kl k l and 1000 mobile station positions are used in the test phase to estimate the position kl,1= "N.According to Mercer’s error. Here, we defined the RMS position condition, there is mapping ϕ and kernel error shown as: function 2 2 err= (u− xMS) +(v− yMS) T Kx(,klx)= ϕ(xk)ϕ(xl) Where, (xMS, yMS) is the real position Which cause such coordinates of MS, (u, v) is the estimated

N position coordinates of MS.. yx()=+∑αkK(x,xk) b (5) In figure 2, it is obvious to see the k=1 succeeding probability between the real distance and estimated distance using Where α,b are obtained by solving Eq. (4). LS-SVM. Diagonal denote that LS-SVM Kernel function has different types, such as algorithm succeeds to location mobile poly-nominal, MLP, Splines, RBF and so on. stations without position error. In figure 3, it In our multiple outputs regression model, could be seen that the performance of cumulative position error distribution. It will Switzerland, 1998 be seen from point A, the LS-SVM Figure captions: algorithm could location the mobile station TOA1 with a location error lower than 71m in 67% Kernel1 TOA2 of cases. Point B denotes SVR algorithm x Kernel2 can location the mobile station with a TOA3 location error low 135m in 95% of the cases, TOA4 which is obviously higher than phase 2nd y location requirement of FCC E-911 TOA5 (Emergency call ‘911’), published in 1999. TOA6 KernelN Conclusions: In wireless cellular networks, our data fusion algorithm based on LS-SVM Figure 1 Data fusion model based on can locate the position of mobile stations LS-SVM for Mobile geo-location with a location error lower than 71m in 67% of the time, with a higher performance than the requirement of FCC for E-911 emergency callers, whose complexity is lower than the classical SVM algorithm. Compared to Multilateral geometry positioning algorithm, LS-SVM has far more adaptable, robust and intelligent. References [1] J. Caffery, G.L. Stuber, "Overview of Figure 2 Performance of the LS-SVR Radiolocation in CDMA Cellular Systems", Algorithm for IEEE Communications Magazine, Vol. 36, Positioning No. 4, April 1998, pp. 38-45 [2] Merigeault, S., Batariere, M., Patillon, J.N., “Data fusion based on neural network for the mobile subscriber location”, IEEE Vehicular Technology Conference 2000, Volume 2, Sept. 2000, pp. 536–541 [3] V. Vapnik. “The Nature of Statistical Learning Theory”, John Wiley & Sons, New York, 1998 [4] Guolin Sun, Wei Guo, "SVR-based Data Figure 3 Cumulative Distribution of fusion algorithm for wireless location", The Positioning RMS Error Chinese Communication Journal, Supplementary Issue, Dec. 2002 [5] Suykens J.A.K., Van Gestel T., De Brabanter J., De Moor B., Vandewalle J., Least Squares Support Vector Machines, World Scientific, , 2002 [6] H. Asplund et. al., A Channel Model for Positioning, COST 259TD20, Bern,