Accurate and Robust Indoor Localization Systems using Ultra-wideband Signals

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1 Accurate and Robust Indoor Locaization Systems using Utra-wideband Signas Pau Meissner, Erik Leitinger, Markus Fröhe, and Kaus Witrisa Graz University of Technoogy, Austria; E-mai: arxiv:34.798v [cs.et] 3 Apr 3 Abstract Indoor ocaization systems that are accurate and robust with respect to propagation channe conditions are sti a technica chaenge today. In particuar, for systems based on range measurements from radio signas, non-ine-of-sight (NLOS) situations can resut in arge position errors. In this paper, we address these issues using measurements in a representative indoor environment. Resuts show that conventiona tracking schemes using high- and a ow-compexity ranging agorithms are strongy impaired by NLOS conditions uness a very arge signa bandwidth is used. Furthermore, we discuss and evauate the performance of mutipath-assisted indoor navigation and tracking (MINT), that can overcome these impairments by making use of mutipath propagation. Across a wide range of bandwidths, MINT shows superior performance compared to conventiona schemes, and virtuay no degradation in its robustness due to NLOS conditions. I. INTRODUCTION Indoor ocaization systems face many difficuties when they are to be depoyed in practice []. Optica systems might become unusabe in emergency situations due to fire and smoke; signa strength based systems are sensitive to fading effects; fingerprinting systems need dedicated training phases; etc. Range-measurement-based systems using radio signas, which are in the focus of this paper, offer advantages ike the capabiity of being integrated in existing radio devices such as smartphones, the potentia of ow-power impementations and moderate infrastructure requirements. However, they face chaenging performance impairments caused by propagation effects ike strong refections or diffuse scattering. To counter these impairments, a arge signa bandwidth is beneficia for two main reasons: First, the tempora resoution and therefore the attainabe accuracy is increased. Second, the ine-of-sight (LOS) path can be separated from other signa parts easier, which improves the robustness, i.e. the percentage of cases in which the attainabe accuracy can be achieved. For these reasons, systems using utra-wideband (UWB) signas are promising candidates for both accurate and robust indoor ocaization []. In this paper, we examine the performance of a conventiona range-based UWB indoor ocaization and tracking system in a representative indoor environment with severa anchor nodes. Using channe measurements aong a reference trajectory, mimicking the waking path of a pedestrian user, we show the dependence of the robustness and accuracy of the ocaization on changing propagation conditions. The LOS path is estimated using the maximum-ikeihood method as we as using a ow-compexity ranging agorithm. These estimates are provided as inputs to an extended Kaman fiter (EKF), which tracks the user s position. The presence of strong refections in the measurement signa can ead to a arge bias in the estimate of the propagation deay of the direct path between user and anchor. This is especiay true in non-los (NLOS) situations, where the direct path is bocked. Overa, a degradation of the robustness of the system is the resut. Usua countermeasures are to detect such situations based on signa statistics and discard the corresponding measurements [3], [4]. In advanced schemes ike [5], [6], machine earning techniques are used to mitigate the range bias in NLOS situations. However, these approaches discard positionreated information that is inherent in the geometric structure of refected MPCs. The usefuness of this information has been shown in [7] []. We have shown in previous work [9] [] that by using additiona foor pan information, these refected signa paths can be used for ocaization. Extracting these paths from the channe measurements and associating them to the foor pan, signa refections can be seen as direct signas coming from virtua anchor (VA) nodes. In this way, one physicay existing anchor node is turned into a set of virtua anchors, and NLOS situations no onger render this anchor useess for ocaization. This scheme, which we ca mutipath-assisted indoor navigation and tracking (MINT), can thus deiver the desired robustness with respect to the propagation conditions. However, the effect of diffuse scattering is especiay pronounced in indoor environments due to the presence of objects ike, e.g., furniture. This makes the extraction of the refected components from the measurements and the required data association chaenging. To highight these issues in a practica setting, this paper extends our previous work in [] with the use of mutipe base stations, a detaied performance anaysis of the proposed agorithms and a comparison to standard tracking schemes empoyed in indoor ocaization. The key contributions of this work are: We show the performance and the robustness issues of a conventiona, EKF based tracking system with respect to channe conditions. This is done in a representative indoor environment using measured signas. Making expicit use of mutipath, robustness and accuracy can be increased. We discuss an impementation of the proposed MINT approach and examine its performance. Resuts show the exceent robustness of MINT with respect to NLOS situations. The resuts obtained highight genera practica consider-

2 y [m] Obstruction 7 Trajectory 4 BS BS 43 Virtua signa path to VA x [m] Fig.. Indoor tracking scenario considered in this paper. The back dotted ine iustrates the user s trajectory in the scenario, seected position indices are given to aow easier interpretation of ater resuts. Bue circed crosses are the base stations, whie back and grey squares with crosses denote some few iustrative VAs for BSs 3 and 4. The area shaded in ight gray denotes the geometric visibiity region of the LOS path of, iustrating the NLOS region caused by the hypothetica obstruction in the center that is used for performance evauations. Additionay, the thin and bod bue ines show two exampe propagation paths that can be modeed by VAs and that are potentiay visibe in the NLOS region. ations for indoor ocaization systems, i.e. the importance of a arge bandwidth and propagation channe conditions is shown. This paper is organized as foows: Section II expains the scenario, the measurement campaign and the geometrica modeing of the environment. A short overview over performance bounds for MINT is given in Section III, whie Section IV discusses channe estimation and ranging agorithms. Tracking is expained in Section V and a detaied discussion of resuts is given in Section VI. II. SCENARIO, MEASUREMENTS, AND GEOMETRIC MODELING Fig. shows the scenario used in this paper. It is the ground foor of a arge three-storey buiding with open ceiings in the corridor areas in a but the uppermost foors. Was are made of reinforced concrete (shown as back outer ines) and doors (shown in grey) are made of meta. The ong grey outer ines on the upper and ower side are arge windows with some meta piars in-between. We paced four base stations (BSs) at known ocations and measured the UWB channe between them and a moving agent. The atter was moved aong a trajectory consisting of points spaced by cm. The obstruction shown near the center of the corridor has not been present in the measurements. It is introduced artificiay in the performance evauations to show the infuence of NLOS scenarios on the ocaization, c.f. Section VI. A. Geometric Modeing of the Environment If a foor pan of the buiding is avaiabe, the BS positions a i, i =,...,4, can be mirrored with respect to refecting surfaces ike was to obtain so-caed first-order virtua anchors (VAs) at positions a i. Using these, the procedure can be repeated to obtain second-order VAs a i, and so on. The visibiity regions of these VAs, i.e. the regions where the corresponding refections are possibe, can be computed by ray tracing as expained in []. If the corresponding MPCs are detectabe at the moving agent, they can be associated to the VAs and used for ocaization. Fig. shows a subset of VAs for BSs 3 and 4 together with two exampe signa paths. In an anaogous manner to [], the overa set of VAs for the i-th BS is denoted as A (i) = {a j : j =,...,N (i) VA }. () Here, the superscript indicating the VA order has been dropped as it is not important in the upcoming discussion. A function f vis (a j,p) determines the visibiity of thej-th VA at a position p, i.e. {, if VA a j is visibe at p f vis (a j,p) = (), ese. The set of expected visibe VAs at a specific position p can then be computed evauating () for a VAs in () A (i) = {a,,...,a (i),k } = {a j : f vis (a j,p ) = }. (3)

3 In the foowing, we omit the BS index i wherever it shoud be cear from the context that the respective quantity exists for a BSs. It can be seen from (3) that a set of anchor nodes significanty arger than the set of BSs can potentiay used for ocaization. We ca this approach mutipath-assisted indoor navigation and tracking (MINT). However, the chaenges are as manifod as the potentia gains: First, the MPCs corresponding to the VAs need to be detected in the signa received at the agent, which depends on infuences such as e.g. materia parameters or refection anges. Second, together with deterministic MPCs, aso some scattered, non-specuar components wi cause a certain eve of cutter in the measurements. Third, the detected MPCs need to be associated to the VAs to make their position-reated information accessibe. Summarizing, a moving agent needs to perform detection of MPCs in the presence of possiby strong diffuse mutipath and noise as we as subsequenty a robust data association procedure to infer its ocation. B. Channe Measurements Measurements were performed in the frequency domain with a vector network anayzer (VNA) over the fu FCC bandwidth from 3. to.6 GHz. These measurements have aso been used in [] []. The discrete frequency representation of the channe s transfer function at position p is denoted as H [k]. Using a frequency spacing of f, it corresponds to a Fourier series (FS) of a time-domain channe impuse response (CIR) h (τ). This CIR is periodic with a period of τ max = / f, which is the maximum resovabe deay. The FS representation aows an arbitrariy fine time resoution τ to be achieved. Using an IFFT with size N FFT = ( f τ), the time domain equivaent baseband signa is obtained as r (t) = IFFT NFFT {H [k]s[k]} e jπ(fc f)t. (4) In (4), S[k] is the discrete frequency domain representation of a raised-cosine puse s(t) with puse duration T p and ro-off factor β R [3]. It is used to cut out the desired band of the signa as we as to fiter it to faciitate an MPC estimation agorithm. The frequencies f c and f are the desired center frequency and the ower band edge of the extracted band, respectivey. This procedure is simiar to [4]. Exampes for r (τ) obtained in this way are shown in Fig. for over the trajectory. III. CHANNEL INFLUENCE ON LOCALIZATION The received signa at the -th trajectory position p, corresponding to the processing in (4), is modeed as [9] K r (t) = α k, s(t τ k, )+s(t) ν (t)+w (t). (5) k= It consists of a sum of K deterministic MPCs, scaed and shifted by the compex ampitudesα k, and propagation deays τ k,, respectivey. The signa ν (t) is a stochastic process modeing the diffuse mutipath (DM), i.e. diffuse scattering at rough surfaces and other propagation mechanisms that are not position τ [ns] Fig.. Received signas r (t) in ogarithmic scaing over the trajectory for. The white dashed ines indicate expected deay paths of MPCs modeed by VAs up to order two, computed by geometric ray-tracing. Indices of some of the VAs shown in Fig. are given. captured by the specuar part of the channe. It is observed at the agent as a convoution with the transmit puses(t). Finay, w (t) denotes additive white Gaussian noise (AWGN) with two-sided power spectra density N /. We expect that the deterministic part of r (t) can be modeed by the set of VAs A. In [9], we have derived the Cramér-Rao ower bound (CRLB) on the position error for the MINT scheme, based on the received signar (t). It is given as the inverse of the equivaent Fisher Information matrix (EFIM) [8]. If a K deterministic MPCs are orthogona at p, i.e. there is no path overap in the deay domain, the EFIM can be decomposed as J p = 8π β c K k= SINR k, J r (φ k, ) (6) where β denotes the effective (RMS) bandwidth of s(t) and c is the speed of ight. The decomposition is instructive since it separates the channe s infuence from the geometry of the VAs. The former is given by the signa-to-interference-pusnoise-ratio (SINR) of the deterministic MPCs. For the k-th MPC at position p, it is defined as [9] SINR k, = α k, N +T p S ν, (τ k, ). (7) Here, interference is understood as the contribution of the DM, which is given by the power deay profie (PDP) of the DM, S ν, at the deay τ k, of the respective MPC, scaed with the puse duration. This PDP is defined as the second centra moment of the DM process ν (t). The infuence of the geometry is accounted for by the ranging direction matrix J r (φ k, ) [8], [9], which is defined as [ ] cos J r (φ k, ) = (φ k, ) cos(φ k, )sin(φ k, ) cos(φ k, )sin(φ k, ) sin. (8) (φ k, )

4 This matrix has one eigenvector pointing in the direction φ k,, the ange from the VA at a k to position p. The SINR in (7) is used in the performance evauations to emuate changes of propagation conditions caused by the artificia obstruction that is shown in Fig.. IV. CHANNEL ESTIMATION AND RANGING Conventiona time-of-arriva (ToA) ocaization requires an estimate of the time-of-fight of the signa from the BS to the agent. This process is caed ranging [5]. In this work, we consider two different ranging agorithms, maximum ikeihood (ML) and jump-back search-forward (JBSF). The former is computationay intensive since it requires channe estimation, whie the atter is a popuar ow-compexity agorithm. The MINT approach requires range estimates to a the MPCs that are modeed by VAs, i.e., an estimation of the deterministic part of the UWB channe as for ML ranging. A. Channe Estimation and ML Ranging It has been shown that the MPCs corresponding to the VAs can carry a arge fraction of the energy of the received signa [], hence we extract those ˆK MPCs that resut in the minimum energy of the difference signa {ˆτ k, } = arg min {τ k, } T r (t) ˆK k= ˆα k, s(t ˆτ k, ) dt (9) where T is the observation interva. Of course the parameter ˆK shoud be reated to K in (5). However, without the knowedge of the position, a vaue has to be chosen that aows for the extraction of the geometricay reevant paths over the entire scenario. The choice of this parameter wi be discussed in Section VI-B. For this work, we assume a separabe channe, i.e. there is no overap between deterministic MPCs. In this case, (9) can be performed path-per-path. The ampitudes α k, are nuisance parameters to this estimation and can be obtained by a projection of the unit-energy puse s(t), shifted to the estimated deay ˆτ k,, onto the received signa ˆα k, = r (t)s(t ˆτ k,)dt () T where denotes compex conjugation. With the separabe channe assumption, this procedure is simiar to [6]. For MINT, the set of estimated arriva times in (9), converted to distances, constitutes the measurement input to the tracking agorithms. Additionay, a data association (DA) scheme is necessary, which wi be described in Section V-A. For ML ranging, ony the propagation deay of the first arriving path, the LOS path, is interesting and can be obtained from (9) as ˆτ (ML) LOS, = min{ˆτ k,}. () r (t), normaized r (t), normaized r (t) r, ML (t) τ LOS,, ML τ LOS,, JBSF τ k,, ML τ [ns] Fig. 3. Exempary ranging resuts for and position = (c.f. Fig. ), using T p =.5 ns. The ower pot is a cose-up. The back ine denotes the received signa, whie the red signa iustrates the reconstruction using the ML channe estimator. The atter aso provides estimates for the MPC arriva times τ k, (grey dashed ines), where the ML range estimate (in red) is the minimum of these. Here, JBSF (ight grey) outperforms ML due to path overap. The simpified impementation of the ML channe estimator assumes a separabe channe and ony detects the arger second component. B. Jump-back Search-forward (JBSF) Ranging If rea-time ocaization is desired, a channe estimation ike (9) might not be feasibe. JBSF is a threshod-based ranging agorithm that aso works for ow-compexity receiver structures ike energy detectors [5]. Backwards from the maximum of the received signa at deay τ max, a search-back window of ength τ sb is defined. The JBSF range estimate is the minimum deay within this window that exceeds a certain threshod ˆτ (JBSF) LOS, = min{ˆτ : τ max τ sb ˆτ τ max, r (ˆτ) A ξ }. () The choice of the threshod A ξ is usuay based on the noise eve. An iustrative exampe for the channe estimation and ranging agorithms is given in Fig. 3. In this case, the LOS path is not separabe from the rest of the channe. Since the ampitude of the second arriving MPC is arger, it is detected in an earier iteration of the ML estimator. Due to the separabe channe assumption, the ML estimator is constrained not to estimate any MPCs within one T p of aready detected ones, hence the LOS path is not detected. However, the LOS component is above the threshod of JBSF and within its search-back window, so JBSF can outperform the ML estimator in this case. V. TRACKING AND DATA ASSOCIATION The conventiona tracking schemes based on ranging and the MINT approach are both impemented in this work using extended Kaman fiters (EKFs) [7], [8] empoying inearized observation equations for the estimated path deays. As in [], we use a simpe constant-veocity state-space mode of the

5 moving agent node. Stacking the position p = [p x,p y ] T and veocity v = [v x,v y ] T in the state vector x = [p T,v T ] T the mode reads x + =Fx +Gn a, (3) T T = T x T + T n a,. T Here, T is the update interva and n a, denotes the driving process noise, which aows for motion at non-constant veocity. The measurement inputs for the conventiona tracking scheme using EKFs are either the ML or JBSF ranging estimates. Using () or (), ranging is performed to each of the four BSs. The entries of the vector of distance estimates are obtained as z (i) = cˆτ (ML,i) LOS, or z (i) = cˆτ (JBSF,i) LOS,, where i is the BS index. A. MINT Using EKF with Data Association (DA) For the MINT scheme impemented using an EKF, the MPC estimation in (9) ony resuts in an unordered set of distance estimates, i.e. Z (i) = c {ˆτ (i) k, }, where the cardinaity of the set is Z (i) (i) = ˆK. To obtain a suitabe input for the observation equations of the EKF, a DA scheme is necessary. As the association to the BS is known, we ony consider the DA for one BS and drop the index i. After the DA, a associated distance estimates are stacked into one measurement vector. The empoyed DA approach is the same as used in [] and is just shorty re-sketched here. We introduce a set C of correspondence variabes [9], whose n-th entry c,n represents the association of then-th entry ofz and is defined as { j, if z,n corresponds to VA a j (j =,...,N VA ) c,n =, if z,n corresponds to cutter. (4) Using the predicted position of the EKF, p, the set of expected visibe VAs A can be computed using () and (3). From this, the set of expected path engths, denoted as D, can be obtained by cacuating the Eucidean distances d(a j,p ) between a VAs a j A and the position p. The task of the DA is now to match the two sets Z and D in an optimum way. The approach used is optima sub-pattern assignment []. Noting that the cardinaity of D is K (c.f. (3)) and assuming that ˆK K, which can aways be ensured by fiing up Z with dummy cutter, we search the sub-pattern of Z that fits best to the set D. Using a distance function d (dc) ( ), that simpy saturates at the cut-off distance d c, this is expressed as π opt = arg min π Π ˆK K i= d (dc) (d,i,z,πi ). (5) Here, Π ˆK is the set of permutations of positive integers up to ˆK and the vector π opt hods the permutation with the minimum cumuative distance in the sense of the cutoff K LOS [db] BS BS position Fig. 4. Instantaneous K-factor with respect to the LOS component K LOS for a BSs over the trajectory using a puse duration T p =.5 ns. distance function d (dc) ( ). Hence, the first K entries of π opt contain the indices of those entries of Z that have been optimay assigned to D. As a ast step in the DA process, we reject those measurements for which d (dc) (d,i,z,πopt,i ) = d c, i.e. those that have been assigned at a distance greater or equa than the cutoff distance. This is done to have a mechanism to tune the DA to the uncertainty in the MPC deay estimates. As UWB signas are used, if an MPC is detectabe at a, its deay wi have a reativey sma uncertainty that depends on the used puse duration T p and the inaccuracies of the foor pan. Hence, the correspondence variabes in (4) are obtained as { j, if π j = n and d (dc) (d,j,z,πopt,n ) < d c c,n = (6), ese. The optima sub-pattern assignment can be efficienty impemented using the Munkres agorithm []. B. Genie-aided Data Association (GADA) for Evauation The DA discussed above depends cruciay on the EKF s predicted position p. To enabe an evauation of the ocaization performance where the errors due to fase DA are mosty eiminated, we use a so-caed genie-aided version of the DA (GADA). The GADA reies on the true position p for performing the DA, i.e. in the cacuation of the set D. This can be used to benchmark the usefuness of the MPC deay estimates for ocaization using MINT. VI. RESULTS This section iustrates the accuracy and robustness of the proposed indoor tracking agorithms for the scenario in Fig.. A first rough evauation of the propagation conditions can be obtained by evauating the K-factor with respect to the LOS component, i.e. the ratio of its energy to the energy of the rest of the CIR. It is estimated using (9) and (), where ony the LOS component is subtracted from r (t), i.e. ˆα LOS, ˆK LOS, = T r (t) ˆα LOS, s(t ˆτ LOS, ) dt where we note that the puse s(t) is energy-normaized. (7)

6 TABLE I PARAMETERS AND RESULTS FOR THE PERFORMANCE EVALUATION. FOR THE PERFORMANCE MEASURES, A PAIR OF VALUES IS GIVEN WHERE THE FIRST ONE INDICATES THE SCENARIO WITHOUT THE OBSTRUCTION AND THE SECOND ONE WITH THE OBSTRUCTION. T p =. ns T p =.5 ns T p = ns T p = ns T p = 4 ns Process noise variance σa [m /s 4 ] σa = ( vx,max 3 T ), covariance matrix Q = σagg T, with v x,max =.5 m/s EKF measurement noise variance σz [m ] DA cutoff distance d c (MINT) [m] JBSF SB-window [ns] JBSF threshod ξ [] Mean number of assoc. MPCs (EKF-GADA) [] 8. / / / / /. Mean number of assoc. MPCs (EKF-DA) [] 8. / / / / 4..8 /. RMS position error MINT (EKF-GADA) [m].3 /.3.39 /.4.6 / /.83.7 /.36 RMS position error MINT (EKF-DA) [m].73 / /.65.8 /.97. /.49.7 /.34 RMS position error EKF, ML ranging [m].5 /.5.58 / /.3.9 / /.396 RMS position error EKF, JBSF ranging [m].3 /.5.35 / / / /.74 average HDOP MINT (EKF-GADA) [].4 /.39.4 / / / /.5 average HDOP MINT (EKF-DA) [].67 / / / /.6.68 /.76 average HDOP EKF, ML ranging [].9 /..3 /..35 /.3.9 /.96.4 /.8 average HDOP EKF, JBSF ranging [].3 /.8.7 /.5.56 /.49.8 /.4.3 /.4 Fig. 4 shows ˆK LOS, for a BSs over the trajectory, estimated using the origina measurements (without the obstruction) with T p =.5 ns. Some geometric infuences, ike the drop in K LOS in the NLOS regions of BSs 3 and 4 or the genera distance dependence can be easiy observed. Other causes of arge variations are not immediatey intuitive and require more carefu inspection of the oca propagation conditions. For exampe, the drop of K LOS for BS around position 9 is due to strong scattered components from meta piars within the ower windows, c.f. Fig.. A. Evauation Setup The obstruction introduced in Fig. is meant to mode a change in the propagation environment, e.g. a group of peope. As it causes NLOS regions for a BSs, its infuence on the tracking performance is interesting. MINT is not aware of this obstruction in its foor pan knowedge. The origina channe measurements where performed without this obstruction, hence they need to be modified. For this, we cacuate the positions which are now in NLOS due to the changed conditions. At these positions, we reduce K LOS by a factor of db, which is done by subtracting the LOS component and adding it again with a suitabe ampitude and its origina phase. To enabe a fair comparison with MINT, we aso change the ampitudes of a the MPCs affected by the change in visibiity conditions. We do so by reducing their SINR (7) aso by db. Note that this factor eaves the LOS component sti detectabe in most cases, whie for the ater arriving MPCs it causes an effective oss of the respective component B. Choice of Parameters a) Measurement parameters: We perform the performance evauation for severa exempary signa bandwidths, i.e. the puse duration of the raised cosine puse is chosen as T p {. ns,.5 ns,ns,ns,4ns}. The corresponding 3 db bandwidths are {5 GHz,GHz,GHz,.5 GHz,.5 GHz}. Using a ro-off factor of β R =.5, the center frequency is aways f c = 7 GHz, except for T p =. ns which corresponds to the fu measurement bandwidth, hence the overa center frequency f c = 6.85 GHz has to be used. Tabe I contains an overview of a reevant parameters for these setups. b) EKF parameters: The EKF s measurement noise covariance matrix is R = σzi, where I is the identity matrix. For the variance σz, we choose vaues based on the expected ranging uncertainty, i.e. it is sighty increased with the puse duration T p. The same consideration appies for the DA cutoff distance d c used in (5) and (6). Tabe I ists the vaues used in the different measurement parameter setups. The choice of the process noise variance σa depends on the maximum veocity in e.g. the x-direction, denoted as v x,max. The process noise, assumed to be Gaussian, shoud aow movement at this veocity. Hence, we seect the 3σ point of the veocity noise as v x,max and obtain for the corresponding process noise variance in the acceeration domain ( σa vx,max ). = (8) 3 T In this paper, we choose to mode pedestrian motion and set v x,max =.5 m/s. The update interva is T =. s, resuting in a magnitude of the veocity in x- or y-direction of m/s aong straight segments of the trajectory. The conventiona tracking schemes and MINT aways use the same σz and σa for every puse duration considered. c) Initiaization: A EKFs are initiaized with the correct position and zero veocity. We note that this is a more chaenging probem for MINT than for the conventiona schemes, since the DA depends on the estimated position. However, we have addressed this probem for a different impementation

7 CDF, BS CDF, BS CDF, CDF,.5 JBSF, obstructed ranging error [m] ML ML, obstructed JBSF Fig. 5. CDFs of the ranging error for ML (red) and JBSF (back) with and without the obstruction for a BSs and T p = ns. of MINT in [] using a Gaussian-sum fiter [3]. In this approach, a bank of parae weighted Kaman fiters (KFs) is used to represent mutipe initia position hypotheses. After convergence, the KFs with sma weights can be discarded. This can aso be appied for the MINT impementation in this paper. d) Channe estimation and ranging: The choice of ˆK in (9), i.e. the number of extracted components, is based on the average number of expected visibe VAs in the ocaization environment. For the performance evauations, we take into account VAs up to order two and fix ˆK = ˆK =. However, we define a threshod between the noise foor and the maximum ampitude of the received signa, beow which no further MPCs are extracted. The noise signa ŵ (t) is estimated from the pre-los part of r (t). Denoting the time average of a signa with, the threshod is obtained as [] A γ, = γ (max{ r (t) } ŵ (t) )+ ŵ (t). (9) In this paper, γ =. is used. The JBSF ranging threshod A ξ in () is aso chosen using a reative threshod ξ, in the same manner as γ in (9). For every puse duration used, we seected a threshod at which ranging works we in the unobstructed scenario, c.f. Tabe I. The ength of the search-back window τ sb is chosen for each BS as the maximum distance between the BS and any firstorder VA, expressed in ns. This corresponds to the maximum deay difference of the LOS component and any first-order refection. The reasoning behind this is the assumption that if the LOS component is not the maximum itsef, then the maximum wi be among the first-order MPCs. A vaue of ns is seected for the geometry in Fig.. It approximatey corresponds to the excess deay of the refection path on the far right end of the corridor. C. Ranging Performance Resuts A comparison of the performance of ML and JBSF ranging agorithms in terms of the ranging error CDF is shown in Fig. 5 with and without the obstruction. A puse duration of T p = ns has been used for this. The most striking resut is that JBSF cosey approaches ML ranging for a cases, at a much ower computationa compexity. One reason for the good performance of JBSF is the rather ow noise eve in the VNA measurements. However, when ooking at the instantaneous ranging errors over the trajectory (not shown), some isoated outiers of JBSF can be observed. The impications for the ocaization performance wi be discussed in the next subsection. D. Locaization and Tracking Performance Resuts Tabe I contains detaied performance resuts in terms of RMS position error, the mean number of associated MPCs for MINT and the average horizonta diution of precision (HDOP). The atter vaue is cacuated as the average of the instantaneous HDOP vaues over the trajectory. These are the ratio of instantaneous position error and RMS ranging error [5], hence they provide snap-shots of the quaity of the ocaization geometry. For MINT, the RMS ranging error is computed from those range estimates that have been associated to VAs by the DA procedure. Looking at the RMS position error in Tabe I obtained using both ranging methods reveas that the EKF using ML ranging sti ceary outperforms the one using JBSF. This behavior woud not be suspected by ooking at the ranging CDFs aone. The few isoated outiers of JBSF mentioned above cause the gap in ocaization performance. As this subsection shows, MINT does not show such robustness issues with respect to ranging outages. Fig. 6 contains the position error CDFs for a considered puse durations. MINT using EKF-GADA aways shows the best performance of a tracking agorithms. Athough this is just an upper bound for this impementation of MINT, it shows the potentia gain of expoiting mutipath propagation. This is not ony true for the achieved accuracy, but aso for the robustness with respect to difficut propagation conditions, since MINT using EKF-GADA shows amost no performance oss for the obstructed scenario. Aso with reaistic DA, MINT is abe to overcome impairments caused by the obstruction better than the conventiona approaches. The conventiona approaches show significant performance impairments, especiay when the puse duration is increased.

8 CDF CDF CDF CDF CDF MINT, EKF GADA MINT, EKF DA EKF, ML ranging EKF, JBSF ranging (a) T p =. ns (b) T p =.5 ns (c) T p = ns (d) T p = ns (e) T p = 4 ns Fig. 6. CDFs of the position error over the trajectory for a considered puse durations T p. The eft coumn shows runs without the obstruction (c.f. Fig. ), in the right coumn, signas have been modified according to the obstruction. Ony for puse durations of T p =. ns and T p = ns, MINT with DA can not provide a performance gain. In the first case, the channe estimation can resove very cosey spaced MPCs that are chaenging for the DA due to their custered structure. In the second case, interference by puse overap situations causes the detection of severa MPCs to fai. Since neither the channe estimation (9) nor the DA as proposed here can dea with path overap situations, this is identified as an important topic for future research. An unexpected resut is obtained for T p = 4 ns, which, corresponding to a 3 db bandwidth of 5 MHz, is no onger UWB by definition [4]. Athough MINT generay benefits from a arge bandwidth, it can yied the argest performance and robustness gain here. The conventiona tracking schemes show outiers due to very arge ranging biases, whie MINT sti expoits information from some MPCs, athough their number decreases significanty (c.f. Tabe I). The mentioned arge ranging biases are aso the reason for the ower HDOP in the obstructed scenario in these parameter setups. Furthermore, it shoud be noted that in terms of the RMS position error, MINT using the EKF-DA aways outperforms the conventiona EKF approach using JBSF ranging. An iustrative exampe for T p =.5 ns and the NLOS scenario is shown in Figs. 7 and 8. The estimated trajectories of the agent node are dispayed in Fig. 7. Whie MINT and the EKF using ML range estimates can both foow the trajectory we, the EKF empoying JBSF ranging is severey impaired by the NLOS regions of BSs and 4 (at the start of the trajectory), (around position, c.f. Fig. ) and and (near the end of the trajectory). As Fig. 8 confirms, in the first two of these NLOS regions, rather arge vaues of the instantaneous HDOP occur. This highights the bad geometry for conventiona schemes when there are ranging outages. For MINT, most of the HDOP vaues aong the trajectory are beow one, indicating exceent geometry for ocaization. This is due to the arge set of virtua BSs spanned by the VAs (c.f. (6) and (8)). VII. CONCLUSION AND FUTURE WORK We have presented a comparison of conventiona indoor UWB ranging and tracking schemes and an impementation of the proposed MINT approach using data from a measurement campaign in a representative indoor environment. The infuence of NLOS situations on the accuracy and robustness of these systems has been investigated. Resuts confirm the potentias of MINT: Using foor pan information, mutipath propagation can be efficienty used to obtain position-reevant information in situations where conventiona approaches fai. Even at comparaby ow bandwidths, MINT shows a cear gain in ocaization performance. Ongoing and future work incudes the modeing of foor pan uncertainties and the combination of ocaization and channe estimation. The atter can be used to reduce the amount of cutter in the extracted path deay estimates. Aso, other impementations of MINT, e.g. using soft cassification in the data association, are within the scope of our work. ACKNOWLEDGMENT The authors thank Danie Arnitz and Thomas Gig for their invauabe hep in the channe measurement campaign. This work was party supported by the Austrian Science Fund (FWF) within the Nationa Research Network SISE project

9 MINT, EKF DA.5 MINT, EKF GADA and EKF DA EKF GADA EKF DA y [m] 4 BS BS HDOP EKF with ML ranging 5 5 x [m] EKF with ML ranging HDOP y [m] y [m] 4 4 BS BS 5 5 x [m] EKF with JBSF ranging BS BS 5 5 x [m] Fig. 7. Tracking resuts for the NLOS scenario and T p =.5 ns. The three pots show the estimated trajectories using MINT with the EKF and data association, and EKFs using ML and JBSF ranging, respectivey. S6, and by the Austria Research Promotion Agency (FFG) within KIRAS PL3, grant no LOBSTER. REFERENCES [] R. Mautz, Overview of Current Indoor Positioning Systems, Geodesy and Cartography, vo. 35, pp. 8, 9. [] S. Gezici and H. Poor, Position estimation via utra-wide-band signas, Proceedings of the IEEE, vo. 97, no., pp , feb. 9. [3] J. Borras, P. Hatrack, and N. B. Mandayam, Decision theoretic framework for NLOS identification, in IEEE Vehicuar Technoogy Conference (VTC), 998, 998. [4] S. Gezici, H. Kobayashi, and V. Poor, Non-Parametric Non-Line-of- Sight Identification, in IEEE Vehicuar Technoogy Conference (VTC) 3, 3. [5] H. Wymeersch, S. Marano, W. Gifford, and M. Win, A Machine Learning Approach to Ranging Error Mitigation for UWB Locaization, IEEE Transactions on Communications, vo. 6, pp ,. [6] S. Marano and, W. Gifford, H. Wymeersch, and M. Win, NLOS identification and mitigation for ocaization based on UWB experimenta data, IEEE Journa on Seected Areas in Communications, vo. 8, no. 7, pp. 6 35,. [7] Y. Shen and M. Win, On the Use of Mutipath Geometry for Wideband Cooperative Locaization, in Goba Teecommunications Conference, 9. GLOBECOM 9. IEEE, 9. [8], Fundamenta Limits of Wideband Locaization - Part I: A Genera Framework, IEEE Transactions on Information Theory, pp , Oct.. HDOP EKF with JBSF ranging position Fig. 8. Tracking resuts for the NLOS scenario and T p =.5 ns. The pots iustrate the HDOP for the tracking agorithms used. [9] K. Witrisa and P. Meissner, Performance Bounds for Mutipath-aided Indoor Navigation and Tracking (MINT), in Internationa Conference on Communications (ICC), Ottawa, Canada,. [] P. Meissner and K. Witrisa, Anaysis of Position-Reated Information in Measured UWB Indoor Channes, in 6th European Conference on Antennas and Propagation (EuCAP), Prague, Czech Repupic,. [], Mutipath-Assisted Singe-Anchor Indoor Locaization in an Office Environment, in 9th Internationa Conference on Systems, Signas and Image Processing (IWSSIP), Vienna, Austria,. [] P. Meissner, D. Arnitz, T. Gig, and K. Witrisa, Anaysis of an Indoor UWB Channe for Mutipath-Aided Locaization, in IEEE Internationa Conference on Utra-Wideband (ICUWB), Boogna, Itay,. [3] J. G. Proakis and M. Saehi, Digita Communications, 5th ed. McGraw- Hi, 8. [4] T. Santos, J. Kareda, P. Amers, F. Tufvesson, and A. Moisch, Modeing the utra-wideband outdoor channe: Measurements and parameter extraction method, IEEE Transactions on Wireess Communications, vo. 9, no., pp. 8 9, Jan.. [5] Z. Sahinogu, S. Gezici, and I. Guvenc, Position Estimation in Utrawideband Wireess Systems. Cambridge University Press, 8. [6] M. Win and R. Schotz, Characterization of utra-wide bandwidth wireess indoor channes: A communication-theoretic view, IEEE Journa on Seected Areas in Communications, vo., no. 9, pp , Dec.. [7] D. Simon, Optima State Estimation, st ed. Wiey, 6. [8] Y. Bar-Shaom and T. Fortmann, Tracking and Data Association. Academic Press, 988. [9] S. Thrun, W. Burgard, and D. Fox, Probabiistic Robotics. MIT, 6. [] D. Schuhmacher, B.-T. Vo, and B.-N. Vo, A Consistent Metric for Performance Evauation of Muti-Object Fiters, IEEE Transactions on Signa Processing, vo. 56, no. 8, pp , 8. [] J. Munkres, Agorithms for the Assignment and Transportation Probems, Journa of the Society for Industria and Appied Mathematics, vo. 5, no., pp. pp. 3 38, 957. [] P. Meissner, T. Gig, and K. Witrisa, UWB Sequentia Monte Caro Positioning using Virtua Anchors, in Proc. Internationa Conference on Indoor Positioning and Indoor Navigation, IPIN, Zurich,. [3] D. Aspach and H. Sorenson, Noninear Bayesian estimation using Gaussian sum approximations, IEEE Transactions on Automatic Contro, vo. 7, no. 4, pp , Aug. 97. [4] A. F. Moisch, Utra-Wide-Band Propagation Channes, Proc. IEEE, vo. 97, no., pp , Feb. 9.