Experimental Study on Probabilistic ToA and AoA Joint Localization in Real Indoor Environments
Chunhua Geng, Traian E. Abrudan, Veli-Matti Kolmonen, Howard Huang
EExperimental Study on Probabilistic ToA and AoAJoint Localization in Real Indoor Environments
Chunhua Geng
MediaTek USA Inc.
Irvine, CA, [email protected]
Traian E. Abrudan
Nokia Bell Labs
Espoo, [email protected]
Veli-Matti Kolmonen
Nokia Bell Labs
Espoo, [email protected]
Howard Huang
Nokia Bell Labs
Murray Hill, NJ, [email protected]
Abstract —In this paper, we study probabilistic time-of-arrival(ToA) and angle-of-arrival (AoA) joint localization in real indoorenvironments. To mitigate the effects of multipath propagation,the joint localization algorithm incorporates into the likelihoodfunction Gaussian mixture models (GMM) and the Von Mises-Fisher distribution to model time bias errors and angularuncertainty, respectively. We evaluate the algorithm performanceusing a proprietary prototype deployed in an indoor factoryenvironment with infrastructure receivers in each of the fourcorners at the ceiling of a 10 meter by 20 meter section. Thefield test results show that our joint probabilistic localizationalgorithm significantly outperforms baselines using only ToAor AoA measurements and achieves 2-D sub-meter accuracyat the 90 % -ile. We also numerically demonstrate that the jointlocalization algorithm is more robust to synchronization errorsthan the baseline using ToA measurements only. Index Terms —Indoor positioning, probabilistic localization,time-of-arrival (ToA), angle-of-arrival (AoA), multipath propa-gation, prototype, field tests
I. I
NTRODUCTION
With the proliferation of ubiquitous wireless devices, rang-ing from sensors to cell phones to VR/AR equipment to robots,the capability of determining the device positions in complexindoor environments has becomes integral in modern wirelessnetworks. Indoor localization enables wide-scale applicationsand services, including indoor navigation, warehouse assettracking and management, contextual-aware marketing andcustomer assistant, building surveillance, location based healthservices, among others [1]. For this reason, it has attractedconsiderable research interest from both academia and industryin the past decade.One of the fundamental challenges in wireless indoor lo-calization is multipath propagation. Due to reflections anddiffraction by walls and conductive objects in the indoor en-vironments, multiple replicas of the same transmitted wireless
C. Geng was with Nokia Bell Labs when he finished his contribution tothis work.© 2021 IEEE. Personal use of this material is permitted. Permission fromIEEE must be obtained for all other uses, in any current or future media,including reprinting/republishing this material for advertising or promotionalpurposes, creating new collective works, for resale or redistribution to serversor lists, or reuse of any copyrighted component of this work in other works. signal may arrive at receivers with different delays and com-plex gains, and from multiple angles w.r.t. line-of-sight (LOS).Consequently, the harsh propagation conditions pose seriouschallenges in deconvolving the LOS component, and leadsto significant consequences for localization performance. Forinstance, in the widely-accessible time-of-arrival (ToA) local-ization systems [2]–[4], multipath introduces positive channelbiases, which degrade the localization accuracy significantlyin hostile environments. Similarly, for angular estimation inangle-of-arrivial (AoA) localization, multipath appears as acombination of several coherent signals arriving at the antennaarray at different angles, which makes the angular estimationvery challenging.To effectively mitigate channel bias errors, a Bayesianprobabilistic algorithm has been introduced recently [5] forToA localization, where the channel bias is modeled as arandom variable (RV) following Gaussian mixture models(GMM), and incorporated into a maximum-a-posterior (MAP)estimation to determine the device position in a robust way.This algorithm has been generalized from various perspectives.For instance, in [6], [7] the probabilistic algorithm has beenapplied to hybrid positioning with both cellular networks andglobal navigation satellite systems (GNSS); in [8], it hasbeen extended to account for the channel correlations amongdifferent locators; and in [9] a computational efficient approachbased on expectation propagation [10] is proposed to solve thenon-linear and non-convex MAP estimation.In this paper, to improve the indoor localization accuracywe advocate a joint ToA and AoA probabilistic 3-D localiza-tion algorithm, and evaluate its performance with a carefullydesigned prototype system in real indoor environments. Inthe joint localization algorithm, we leverage the probabilisticapproach for ToA positioning in [5], and directional statis-tics [11] to model the uncertainty of the AoA estimates. Theadoption of directional statistics here is motivated by the factthat angles are periodic in their nature, i.e., they are definedon a circle of sphere, rather than Euclidean space. Therefore,the standard Gaussian distribution is not the most appropriate.To the best of our knowledge, directional statistics have been a r X i v : . [ c s . N I] F e b sed for the first time for 2-D AoA positioning in [12], [13] byemploying the von Mises distribution, and for 3-D positioningin [14], [15] by employing the more general von Mises-Fisher distribution. Other 2-D probabilistic AoA positioningapproaches can be found in [16], [17].Notably, in previous studies (e.g., [18], [19]), joint ToAand AoA localization has been mostly analyzed from a theo-retical perspective and evaluated with simulated data in 2-Dlayout. Specifically, for the probability approach, an examplecan be found in a very recent study in [13]. One of themain contributions in our paper is that we experimentallydemonstrate the superiority of probabilistic joint ToA andAoA localization in real world. Towards this end, we set upproprietary ToA and AoA localization systems (both havingmultiple locators) in a real indoor factory environment andassess the joint ToA and AoA localization performance withover-the-air measurements, in order to capture the effectsof real propagation conditions of the complex indoor en-vironments, as well as the hardware imperfections. Real-world measurements have also been used in several previousstudies on indoor localization. For instance, in [20]–[23], thelocalization algorithms using a single locator (i.e., accesspoint in WiFi or base station in LTE) have been evaluatedin indoor environments. Specifically, Chronos in [20] is basedon trilateration to estimate the target position; MonoLoco in[21] is based on triangulation with the help of multipathreflections; SPRING in [22] and the LTE testbed in [23] useangular and ranging measurements to directly compute thetarget location. In [24], a localization system, named SpotFi, isdeveloped based on jointly processing ToA, AoA, and receivedsignal strength indicator (RSSI) from multiple locators, wherethe ranging measurements are specifically utilized to helpidentify the AoA LOS component. It is noteworthy that manyaforementioned algorithms (e.g., in Chronos, MonoLoco andSpotFi) rely on low-level measurements, such as channel stateinformation (CSI) per subcarrier per antenna. In our algorithm,what we need is only high-level ToA and AoA estimations foreach locator, which is an advantage since in many applicationsand services the low-level information like CSI is not disclosedby the vendors. The field test results demonstrate that our jointlocalization algorithm significantly outperforms the baselinesusing either ToA or AoA data only, achieving sub-meterlevel accuracy at 90 % -ile for horizontal localization (giveninter-locator distances no less than 10 meters). In addition,we also numerically illustrate that compared with the ToAbaseline, the joint localization algorithm is much more robustto synchronization errors.II. P ROBLEM F ORMULATION
Consider a joint ToA and AoA localization system with K ToA locators and B AoA locators. We denote the unknownuser device (UD) location by x = [ x, y, z ] . All ToA locators We assume the localization system is an uplink system, where the UDbroadcasts the positioning reference signals, and the locators receive thesignals and estimate the user’s position. The algorithm presented in this papercan be easily adapted for downlink systems.
World frame User
Locator frame
Fig. 1: Illustration of the 3-D angular positioning. are time-synchronized with each other, but not with the UD.Denote the ToA of the positioning reference signal at k -th ToAlocator by t k = || p k − x || + τ + γ k + n k , ∀ k ∈ { , , . . . , K } (1)where p k = [ x k , y k , z k ] is the position of the k -th ToA locator(in the World frame), τ is the unknown transmit time of thereference signal with respect to the clock at locators, γ k rep-resents the channel bias introduced by unresolvable multipathand NLOS reflections, and n k ∼ N (0 , σ ) accounts for boththe locator synchronization errors and the ToA measurementerror due to thermal noise. Following [5], we assume that thechannel bias γ k is a RV following GMM with L k components,i.e., p ( γ k ) = L k (cid:88) i =1 w ik ˜ σ ik √ π exp (cid:20) − σ ik ( γ k − µ ik ) (cid:21) (2)where w ik , ˜ σ ik , and µ ik represent the weight, variance, andmean value of the i -th Gaussian component for the k -thlocator.The model for angular positioning is illustrated in Fig. 1. Weconsider B AoA locators whose 3-D positions are representedin the World frame by a × vectors l b , and whose 3-Dorientations are represented by a × orthogonal matrices Ω b . Both the positions and orientations of all B AoA locators( b ∈ { , , . . . , B } ) are assumed to be known with reasonableaccuracy. The AoA locators are equipped with phased antennaarrays that are able to estimate the directions of the incomingsignals. These directions are defined w.r.t the local frame ofcoordinates of each of the locators. Let us denote the user’sposition vector in the locator’s frame by r b . The user’s positionvector expressed in the World frame can be written as x = l b + Ω b r b (3)Since there is no range information available at the AoAlocator, the length of r b is unknown, i.e., only its direction u b = r b / (cid:107) r b (cid:107) can be estimated. From Eq. (3), we can express For notation brevity, we convert time to distance by multiplying with thespeed of light implicitly. he true direction of the user as a function of user’s trueposition x , as follows u b ( x ) = Ω T b x − l b (cid:107) x − l b (cid:107) . (4)Throughout this paper, we adopt the unit-vector model intro-duced in [14] to represent the direction of arrival, as well asthe corresponding 3-D directional statistics approach. Errors inestimating the directions of arrival are modeled by using thevon Mises-Fisher distribution, which is the correspondent ofthe 2-D normal distribution to the two-dimensional unit sphere S ⊂ R . For a × unit vector u ∈ S , the von Mises-Fisherdistribution is given by VMF( u | µ , κ ) = c exp (cid:0) κ µ T u (cid:1) . (5)where µ is the mean direction, κ is the concentration param-eter, and c = κ/ (4 π sinh κ ) is the normalization constant.As mentioned earlier, the reason for adopting a directionalstatistics approach is that the natural parameter space ofangles is not an Euclidean space, but a sphere. Angles areperiodic in their nature, and therefore, the natural support ofthe corresponding probability density functions should be theunit sphere.III. P ROBABILISTIC T O A AND A O A P
OSITIONING
A. Probabilistic ToA posiitoning
For ToA localization, the least square (LS) optimizationtechnique is widely used [25]. For instance, the well-knownnonlinear LS method solves the optimization below to deter-mine the UD position x (and the unknown transmit time τ asa byproduct) (ˆ x , ˆ τ ) = arg min x ,τ K (cid:88) k =1 ( || p k − x || + τ − t k ) (6)The main disadvantage of the LS-based approach is that itdoes not take into account the channel bias errors γ k and thusdegrades the localization accuracy in positioning-challengeenvironments such as urban canyon and indoors.To overcome the above drawback, in the Bayesian prob-abilistic ToA localization algorithm [5], the channel biasis incorporated into a MAP estimator as a RV to robustlydetermine the UD location. Denote the ToA measurementvector for all locators by t = [ t t ... t K ] T . The UD positionand the unknown signal transmit time can be estimated asfollows (with a non-informative prior p ( x , τ ) ), ˆ x , ˆ τ = arg max x ,τ ln p ( t | x , τ ) (7)Assuming that the ToA measurements from different locatorsare independent, the joint log-likelihood is given by ln p ( t | x , τ ) = K (cid:88) k =1 ln p ( t k | x , τ )= K (cid:88) k =1 ln (cid:90) p ( t k | x , τ, γ k ) p ( γ k ) dγ k (8) where p ( t k | x , τ, γ k ) is a Gaussian distribution with mean || x k − x || + τ + γ k and variance σ . Given Eq. (2), the estimator(7) can be rewritten as ˆ x , ˆ τ = arg max x ,τ K (cid:88) k =1 ln p ( t k | x , τ )= arg max x ,τ K (cid:88) k =1 ln (cid:26) L k (cid:88) i =1 w ik σ ik √ π exp (cid:20) − ( t k − || p k − x || − τ − µ ik ) σ ik (cid:21) (cid:27) (9)where σ ik = ˜ σ ik + σ . B. Probabilistic AoA positioning
Using the model outlined in Section II, the noisy directionalestimates at the b -th AoA locator are assumed to have a vonmises-Fisher distribution with the mean direction µ b = ˆ u b ,and a concentration parameter κ b whose value reflects thereliability of the estimate. Given B locators whose directionalestimates are ˆ u b , and assuming that they are affected by inde-pendent errors, the joint log-likelihood of the user’s positionmay be expressed using Eqs. (4), and (5): L ∠ ( x ) = B (cid:88) b =1 ln VMF( u b ( x ); ˆ u b , κ b ) , = B ln c + B (cid:88) b =1 κ b ˆ u T b Ω T b x − l b (cid:107) x − l b (cid:107) (10)The user’s position can be estimated by maximizing the abovejoint likelihood, i.e., ˆ x = arg max x L ∠ ( x ) (11) C. Probabilistic joint positioning
For the problem of joint ToA and AoA positioning, weassume that the measurements from ToA and AoA locatorsare all independent. As a result, we could solve the followingestimation problem to estimate the user position, ˆ x , ˆ τ = arg max x ,τ (cid:34) K (cid:88) k =1 ln p ( t k | x , τ )+ B (cid:88) b =1 ln VMF( u b | ˆ u b ( x ) , κ b ) (cid:35) (12)Solving the non-convex optimization problem (12) requires atrade-off between convergence speed and computation com-plexity. Possible solutions include, e.g., gradient ascent [14],expectation propagation [10], and Monte Carlo methods [13].IV. P ROTOTYPE S ETUP
To evaluate the performance of the probabilistic ToA andAoA joint localization in real indoor environments, we builda prototype based on proprietary ToA and AoA localizationsystems in the ARENA2036 research building, which aimsto offer a realistic indoor factory environment for developingand testing concepts of future transport [26]. The entireARENA2036 building is 130m long and 46m wide, with ig. 2: The experiment area in an indoor factory environment. The area of interest is 20 meters ×
10 meters, as shown in the red rectanglein the left figure. At each corner of the area, there is a pair of co-located ToA and AoA locators, as depicted by the yellow cuboids in theright figure. The heights of the locators are around 7.3 meters.Fig. 3: The top-down view of the experiment area. The green trianglesand dots indicate the positions of the locators and TPs, respectively. a sawtooth roof and folded aluminum fac¸ade (as shown inFig. 2). In our experiment, we focus on a smaller area insidewith a size of 20m × XPERIMENT R ESULTS
In this section, we use over-the-air measurements from theproprietary joint ToA and AoA localization system in theARENA2036 experiment area (described in Section IV) to
Fig. 4: The CDF of horizontal localization errors for different local-ization algorithms in the field test. Note that the curves correspondto unfiltered (raw) measurements. evaluate the positioning performance in real indoor environ-ments. As shown in Fig. 3, there are totally 28 test points (TPs)in that area. We took both ToA and AoA measurements at eachTP. To avoid sophisticated training of the probabilistic models,in this study we heuristically choose the following parametersfor the probabilistic localization algorithms: L k = 1 , µ k = 0 , ˜ σ k = 1 , σ = 10 − , and κ = 10 , where k ∈ { , , , } . We compare the localization performance of the joint posi-tioning algorithm with the baseline approaches using eitherToA or AoA data only. Specifically, for the baseline withAoA measurements only, we use the probabilistic algorithmpresented in Section III-B. For the baseline with ToA mea-surements only, we note that in our filed test since the ToAprobabilistic model only includes a single Gaussian compo-nent, the nonlinear LS approach achieves similar or slightlybetter performance compared with the probabilistic algorithmin Section III-A with parameters mentioned before in thissection. As a result, we adopt the nonlinear LS algorithm asthe ToA baseline here. Fig. 4 depicts the empirical cumulativedistribution functions (CDF) of horizontal localization error It is possible to improve the localization performance by learning andfine-tuning the parameters in the probabilistic models, which, however, is outthe scope of this paper. For instance, see [5], [8] for training GMM in ToAlocalization. ig. 5: Mean and standard deviation (STD) of horizontal localization errors at each TP for different positioning algorithms: TOA only – toprow, AoA only – middle row, joint ToA+AoA – bottom row. Colorbar encodes the mean and the standard deviation values in meters. for all three algorithms in the field test. It shows that the jointpositioning algorithms significantly outperforms the baselines.A detailed comparison is given in Table I. As shown, in termsof mean, RMS, -ile and -ile localization errors, thejoint positioning algorithm outperforms the ToA baseline by . , . , . , and . , respectively, and the AoAbaseline by . , . , . , and . , respectively.The overall localization performance depends on key factorssuch as: the density and geometry of the deployed locators,antenna array, time synchronization, and propagation environ-ment. TABLE I: Horizontal Localization Error
Joint ToA-only AoA-onlyMean 0.763m 1.079m 1.357mRMS 1.528m 1.803m 2.276m50% CDF 0.522m 0.714m 0.853m90% CDF 0.981m 1.753m 2.282mFig. 5 further depicts the mean and standard deviation (STD)of horizontal localization errors for all three positioning algo-rithms at each TP. One can find that for the joint positioningalgorithm, in almost all TPs, the mean and STD of localizationerrors are both in the sub-meter level (not the case for ToA-only and AoA-only baselines). The long tail of the jointpositioning error in Fig. 4 mainly comes from A06 and A23,which is due to the severe NLOS and multipath errors which
Fig. 6: The impact of synchronization errors on joint ToA+AoApositioning and the ToA baseline, where η is the standard deviationof the zero-mean Gaussian synchronization error, with the unit meter(i.e., converted from time by multiplying with the speed of light). are not well-captured in the probabilisitic model. It is well known that synchronization among locators isessential for ToA localization. In practice, it is challenging tomaintain accurate synchronization, unless some sophisticatedsynchronization protocols (e.g., WR in our prototype) areapplied. One may wonder how larger synchronization errorsaffect the performance of joint ToA and AoA localization.To model additional synchronization errors (besides the errors We expect that a more sophisticated well-trained model could furtherimprove the localization performance. lready induced by the WR protocol in real measurements), weadd each ToA measurement together with an i.i.d Gaussian RVof mean 0 and variance η . Fig. 6 shows the CDF of horizontallocalization error for the joint localization algorithm and theToA baseline, with respect to different η values. One can findthat by leveraging additional AoA data, the former is muchmore robust to synchronization errors than the latter.VI. C ONCLUSION
In this work, we advocate a joint probabilistic ToA andAoA 3-D localization algorithm and evaluate its performancein an indoor factory environment with proprietary localizationsystems. The prototype is with 4 pairs of co-located ToA andAoA locators, each of which is at a corner at the ceiling ofa 10 meter by 20 meter section, where the WR protocol isemployed to achieve high accuracy synchronization amongToA locators. In the joint localization algorithm, only ToA andAoA measurements are needed, and the low-level informationlike CSI is not required. To mitigate multipath, the ToAchannel bias error and angular uncertainty (due to multipathand NLOS reflections) are modeled as RVs following GMMand von Mises-Fisher distributions, respectively. In the fieldtest, the joint localization algorithm is able to achieve sub-meter level accuracy at -ile for horizontal localization,which significantly outperforms the baselines using either ToAor AoA data individually. In addition, we numerically assesshow different synchronization errors affect the performance ofthe joint localization algorithm. It turns out that, comparedwith the baseline using only ToA measurements, the jointlocalization algorithm is much more robust to synchroniza-tion errors by leveraging additional AoA data. Future workincludes evaluating the algorithm comprehensively in moreindoor scenarios, and generalizing the algorithm to rejectoutlying measurements and track mobile users.R
EFERENCES[1] F. Zafari, A. Gkelias, and K. K. Leung, “A survey of indoor localizationsystems and technologies,”
IEEE Communications Surveys Tutorials ,vol. 21, no. 3, pp. 2568–2599, 2019.[2] P. Misra and P. Enge,
Global Positioning System: Signals, Measurements,and Performance , 2nd ed. Ganga-Jamuna Press, Lincoln MA, 2006.[3] J. A. del Peral-Rosado, R. Raulefs, J. A. L´opez-Salcedo, and G. Seco-Granados, “Survey of cellular mobile radio localization methods: From1G to 5G,”
IEEE Communications Surveys Tutorials , vol. 20, no. 2, pp.1124–1148, 2018.[4] D. Dardari, A. Conti, U. Ferner, A. Giorgetti, and M. Z. Win, “Rangingwith ultrawide bandwidth signals in multipath environments,”
Proceed-ings of the IEEE , vol. 97, no. 2, pp. 404–426, Feb. 2009.[5] F. Perez-Cruz, C. Lin, and H. Huang, “BLADE: A universal, blindlearning algorithm for ToA localization in NLOS channels,” in
IEEEGlobecom Workshops (GC Workshops) , Dec. 2016, pp. 1–7.[6] C. Geng and H. Huang, “A Bayesian probabilistic approach to hybridlocalization with GNSS and LTE-OTDOA in multipath channels,” in
IEEE International Conference on Communications Workshops (ICCWorkshops) , May 2018, pp. 1–6.[7] C. Geng, R. Saxon, and H. Huang, “H-BLADE: A Bayesian prob-abilistic GNSS/LTE-OTDOA hybrid localization algorithm for harshenvironments,” in , Oct. 2018, pp. 559–563.[8] C. Geng, X. Yuan, and H. Huang, “Exploiting channel correlations forNLOS ToA localization with multivariate Gaussian mixture models,”
IEEE Wireless Communications Letters , vol. 9, no. 1, pp. 70–73, Jan.2020. [9] F. P´erez-Cruz, P. M. Olmos, M. M. Zhang, and H. Huang, “Probabilistictime of arrival localization,”
IEEE Signal Processing Letters , vol. 26,no. 11, pp. 1683–1687, Nov. 2019.[10] T. P. Minka, “Expectation propagation for approximate Bayesian infer-ence,” in
Proceedings of the Seventeenth Conference on Uncertainty inArtificial Intelligence , 2001, pp. 362–369.[11] K. Mardia and P. Jupp,
Directional Statistics , ser. Wiley Series inProbability and Statistics. Wiley, 2009.[12] S. Wang, B. R. Jackson, and R. Inkol, “Performance characterizationof AOA geolocation systems using the von mises distribution,” in , Sept 2012, pp. 1–5.[13] H. Naseri and V. Koivunen, “A Bayesian algorithm for distributed net-work localization using distance and direction data,”
IEEE Transactionson Signal and Information Processing over Networks , vol. 5, no. 2, pp.290–304, June 2019.[14] T. E. Abrudan, Z. Xiao, A. Markham, and N. Trigoni, “Underground,incrementally deployed magneto-inductive 3-D positioning network,”
IEEE Transactions on Geoscience and Remote Sensing , vol. 54, no. 8,pp. 4376–4391, Aug. 2016.[15] H. Nurminen, L. Suomalainen, S. Ali-L¨oytty, and R. Pich´e, “3D angle-of-arrival positioning using von Mises-Fisher distribution,” arXiv, Sep2017, [Online]: https://arxiv.org/abs/1709.02437.[16] J. Xiong and K. Jamieson, “ArrayTrack: A fine-grained indoor locationsystem,” in , Lombard, IL, 2013, pp. 71–84.[17] N. BniLam, G. Ergeerts, D. Subotic, J. Steckel, and M. Weyn, “Adaptiveprobabilistic model using angle of arrival estimation for IoT indoorlocalization,” in , Sept 2017, pp. 1–7.[18] L. Cong and W. Zhuang, “Hybrid TDOA/AOA mobile user locationfor wideband CDMA cellular systems,”
IEEE Transactions on WirelessCommunications , vol. 1, no. 3, pp. 439–447, July 2002.[19] T. Eren, “Cooperative localization in wireless ad hoc and sensor net-works using hybrid distance and bearing (angle of arrival) measure-ments,”
EURASIP Journal on Wireless Communications and Network-ing , vol. 2011, no. 1, p. 72, 2011.[20] D. Vasisht, S. Kumar, and D. Katabi, “Decimeter-level localization witha single WiFi access point,” in , Santa Clara, CA, Mar.2016, pp. 165–178.[21] E. Soltanaghaei, A. Kalyanaraman, and K. Whitehouse, “Multipathtriangulation: Decimeter-level WiFi localization and orientation with asingle unaided receiver,” in
Proceedings of the 16th Annual InternationalConference on Mobile Systems, Applications, and Services , New York,NY, USA, 2018, pp. 376–388.[22] M. Rea, T. Abrudan, D. Giustiniano, H. Claussen, and V.-M. Kolmonen,“Smartphone positioning with radio measurements from a single WiFiaccess point,” in
Proceedings of the 15th International Conference onEmerging Networking Experiments And Technologies , Orlando, Florida,Dec 2019, pp. 200–206.[23] A. Blanco, N. Ludant, P. J. Mateo, Z. Shi, Y. Wang, and J. Widmer,“Performance evaluation of single base station ToA-AoA localizationin an LTE testbed,” in
IEEE 30th Annual International Symposium onPersonal, Indoor and Mobile Radio Communications (PIMRC) , Sep.2019, pp. 1–6.[24] M. Kotaru, K. Joshi, D. Bharadia, and S. Katti, “SpotFi: Decimeter levellocalization using WiFi,”
SIGCOMM Comput. Commun. Rev. , vol. 45,no. 4, p. 269–282, Aug. 2015.[25] I. Guvenc and C. Chong, “A survey on TOA based wireless localiza-tion and NLOS mitigation techniques,”
IEEE Communications SurveysTutorials , vol. 11, no. 3, pp. 107–124, 2009.[26] “Arena2036,” https://europa.eu/investeu/projects/arena-2036-%E2%80%93-active-research-environment-next-generation-automobiles en, [Ac-cessed: 21-January-2020].[27] Z. Latinovi´c, C. Geng, and H. Huang, “Channel measurements andperformance of indoor time-of-arrival localization at 5GHz,” in
IEEEWireless Communications and Networking Conference (WCNC) , Apr.2018, pp. 1–6.[28] M. Lipi´nski, T. Włostowski, J. Serrano, and P. Alvarez, “White rab-bit: a PTP application for robust sub-nanosecond synchronization,” in