Muliple arge racking by a disribued UWB sensor nework based on he PHD filer Snezhana Jovanoska and Reiner Thomä Deparmen of Elecrical Engineering and Informaion Technology Technical Universiy of Ilmenau, Ilmenau, Germany Email: snezhana.jovanoska@u-ilmenau.de Absrac In his paper we describe a mehod for deecion, localizaion and racking of muliple non-cooperaive moving arges by muliple saic ulra-wideband (UWB) radar sensors. The arges are deeced using elecromagneic waves backscaered by he arge owards he receivers. The sensors consis of wo receiving and one ransmiing anenna conneced o a single UWB module, making he sensors capable of auonomous arge localizaion. Gaussian mixure implemenaion of he probabiliy hypohesis densiy (PHD) filer is used for esimaing he ranges of he deeced arges and fusion of he locaion esimaes provided by each sensor, resuling in refined arge racks. The proposed mehod is verified in a realisic scenario wih hree moving persons. The resuls show ha UWB sensors can be used as complimenary echnology for muliple moving arge racking. Index Terms UWB, racking, PHD filer, muli-arge racking. I. INTRODUCTION In he pas decades here was a growing need for noninrusive monioring sysems for civilian and miliary applicaions. Localizaion and racking of non-cooperaive arges (arges ha do no carry an acive ag or device o help heir deecion) is needed for boh securiy and rescue applicaions. Opical or visual sensors have limied performance in poor visibiliy condiions, infrared sensors are emperaure dependen and LADAR performance decreases in dusy and foggy environmens. The ulra-wideband (UWB) radar echnology has advanages for deecion and localizaion of moving objecs in poor visibiliy, hrough-wall or in mulipah condiions. This makes i suiable as a complimenary echnology for human or oher moving objec deecion. Due o he mulipah immuniy [], i is well suied for indoor applicaions. I is also useful for deecion of small movemens such as hearbea or respiraion of a saionary person due o he high spaial precision [2]. I is suiable in search and rescue applicaions for deecion and localizaion of humans rapped under rubble, snow and oher non-meallic objecs. UWB sensors suffer inerference from coexising sysems, shadowing in he presence of muliple arges and limied area coverage. By using muliple disribued UWB sensors he arges invisible o one sensor can be deeced by anoher sensor of he nework. The posiions of he deeced arges can be refined by fusing arge locaion informaion from he The work presened in his paper was suppored by Fraunhofer FKIE, Wachberg, Germany muliple sensors [3], [4]. In his paper, when referring o UWB sensor we consider an independen UWB module wih wo receiving and one ransmiing anenna conneced o a local processing uni. Targe racking has raised a lo of ineres as a mehod for improving arge locaion esimaes. Single arge racking mehods such as Kalman filer are widely used since he 96s. Muliple arge racking (MTT) mehods are radiionally based on observaion-arge daa associaion followed by a single arge racking approach [] [7]. A mehod mos commonly used for muliple arge racking is he muliple hypohesis racking (MHT) [8], [9]. Based on hreshold heurisics, each observaion is eiher associaed o an exising arge, or i is considered o be a deecion of a new arge or false alarm. I is a solid approach wih compuaional and combinaorial load increasing exponenially wih he number of arges due o he observaion-arge daa associaion sep and he propagaion of muliple hypohesis. Following he work of Mahler [], here has been increasing ineres in applying finie se saisics (FISST) o Bayesian MTT. I allows for racking unknown, ime-varian number of arges in he presence of false alarms, miss-deecions and cluer. Approximaion of he Bayesian MTT represened as a random finie se (RFS) by is firs order momen leads o he probabiliy hypohesis densiy (PHD) filer []. Two possible implemenaions of he PHD filer are found in lieraure, he Gaussian mixure approach (GM-PHD) [] and he Sequenial Mone-Carlo approach (SMC-PHD) [2]. The firs implemenaion is a closed-form soluion for linear Gaussian arge dynamics, and is easier for implemenaion in MTT conex since he arge saes are simply represened by he Gaussian mixure componens. The second approach requires exracion of he arge saes from he poserior arge densiy represened by a number of paricles. Typically clusering echniques are applied [3], [4]. Targe localizaion and racking based on UWB radar echnology has been invesigaed before for single arges and by using a single UWB radar [] [8]. In [9] muliple arge localizaion and racking by using measuremen-arge daa associaion and a Kalman filer bank is presened. Similarly, muliple sensor muliple arge localizaion based on a simplificaion assumpion of single arge deecion per sensor and sensor daa fusion based on imaging is presened in [2]. 9
We use a sensor nework as in [2] wihou he limiaion of a single arge deecion per sensor. Targes are localized by each sensor using a ime-of-fligh (ToF) informaion i.e. he ime needed for a ransmied elecromagneic signal o reflec of a arge and is backscaered echo o be received by he sensors receivers. Since persons are used as arges, we have he case of exended arge deecion which means ha each arge is deeced by muliple ToF values. Noise, cluer, miss-deecions and false alarms influence he ToF values. By applying GM-PHD filer before sensor informaion fusion mos cluer and false alarms are removed, however his also resuls in loss of some arge informaion. The informaion loss is insignifican compared o he benefis of false informaion reducion for furher processing. The esimaed ToF arge informaion from boh receivers of each sensor is used o esimae arge locaions wih respec o ha sensor. These locaions are hen fused ogeher o resul in a wo dimensional arge locaion esimaion. The ToF informaion of all sensors can also be fused ogeher direcly by using a likelihood funcion. Alhough his mehod is more prune o arge informaion loss, i can lead o ghos racks due o he muliple possible combinaions. In his paper we concenrae on he firs mehod, which is more immune o he ghos racks. The res of he paper is srucured as follows. Secion II gives a descripion of he sensor nework and scenario considered. A shor overview of he GM-PHD filer implemenaion is given in Secion III. The proposed MTT mehod is explained in Secion IV. In Secion V he verificaion measuremen scenario and resuls are presened and finally conclusions are derivedinsecionvi. II. DISTRIBUTED UWB SENSOR NETWORK Since UWB needs o share is specrum wih oher exising communicaion sysems which ransmi a higher power levels, i may suffer from some inerference. In addiion, for he applicaion of muliple arge localizaion, an UWB radar sensor capabiliies may be hindered by he presence of a arge very close o he sensor which causes shadowing over he oher arges in he scenario. This arge aenuaes he propagaed elecromagneic wave, prevening he sensor from deecing arge echoes by any oher arge. By using a nework of disribued UWB sensors, he muliple arge deecion and localizaion is improved by fusing he arge informaion available by all sensors. Targes are observed from differen angles, resuling in more arge informaion available for localizaion. Depending on he applicaion, a disribued UWB sensor nework can be defined in differen ways. A muli-saic srucure uses muliple widely disribued and synchronized cooperaing sensor nodes. Each node s posiion can be esimaed (and racked in case of moving nodes) wih regard o anchor nodes placed in sraegic posiions around he area of ineres. Anoher sensor srucure is definedbyusingsandalone bisaic ba-ype UWB radar sensors [4]. This means ha each sensor consiss of wo receivers placed in a linear array wih a ransmiing anenna placed in he middle of hem. The anennas are conneced o an UWB radar module which in urn is conneced o a local processing uni. The sensor nodes are saionary and able o auonomously localize he deeced arges. There is no direc synchronizaion beween he sensors since each module is conrolled by an independen RF clock. For he scope of his paper we assume ha he sensor locaions are known. The fusion node is responsible for sensor node discovery and conrol, as well as for he final fusion of he arge locaions. Since he arges of ineres are non-cooperaive, he ToF informaion by each sensor receiver is used for localizaion. Having wo receivers, and direcional anennas direced oward he area of ineres, he arge locaions can be calculaed analyically. Once arges are deeced by a sensor, he deecions are locally processed o resul in arge range esimaes, which are hen fused ogeher by he fusion node o resul in final arge locaions. A similar sensor arrangemen is used in [2]. III. TARGET TRACKING VIA GM-PHD The arge racking problem can be summarized as an esimaion of he number of arges and heir saes (locaions) a each poin in ime using a se of noisy measuremens and he informaion of he previous arge saes. In FISST erminology, a a given ime, he RFS of arges saes is X = {x (i) } Nx, i= and he RFS of measuremens is Z = {z (i) } Nz, i=, where N x, is he esimaed number of arges a ime and N z, is he number of available measuremens a ime. Each z (i) is eiher a noisy measuremen of one of he arges or a false alarm. There can be muliple measuremens belonging o a single arge. Each arge sae is represened by x (i). A. The PHD filer The probabiliy hypohesis densiy is he firs momen of he muli-arge poserior disribuion. I is a muli-modal disribuion over he arge space, where each mode, or peak, means here is a high probabiliy of a arge being presen here. Since a a given ime he arge saes are considered o be a se-valued sae, i operaes on single arge sae space and avoids he complexiies arising from daa associaion. I is no a densiy funcion and does no inegrae o uniy. Is inegraion over a finie subse of he space gives an esimaed number of he arges in his subse. In his work we use he Gaussian mixure implemenaion of he PHD filer similar o he one in []. Linear Gaussian arge sae dynamics is assumed for modeling he arges and he measuremens f (x ξ) =N (x; F ξ,q ) g (z x) =N (z; H x, R ) () where N ( ;m, P) denoes a Gaussian densiy funcion wih mean m and covariance P, O is he process noise covariance, R is he measuremen noise covariance, F is he sae evoluion marix, and H is he observaion marix. The PHD is approximaed by weighed Gaussian mixures which are projeced o he nex ime sep by predicion 96
equaions. Le he poserior inensiy a ime be known as N x, v (x) = N (x; m(i),p(i) ) (2) i= where m and P are he mean and covariance of he Gaussian componens represening he RFS of arge saes a ime. The prediced inensiy a ime is hen where N x, v S, (x) =p s v (x) =v S, (x)+γ (x) (3) i= N (x; m(i) S,,P(i) S, ) (4) m (i) S, = F m (i) () P (i) S, = F P (i) F T + Q (6) (7) is he inensiy of he arges ha survive from ime wih sae independen survival probabiliy p s and N γ, γ (x) = i= γ, N (x; m (i) γ,,p (i) γ, (8) is he arge birh RFS inensiy defined as a weighed Gaussian mixure wih N γ, componens wih weigh γ,, mean m(i) γ, and covariance P γ,. (i) Targe spawning is no considered, however random arge birh a each ime sep is considered. When measuremens or observaions of he arges are obained, he weighs of he Gaussian mixure componens are updaed based on he likelihood funcion g (z x). Le he prediced inensiy v (x) be a Gaussian mixure of he form v (x) = N x, i= N (x; m(i),p(i) ) (9) wih N x, = N x, + N γ,. The poserior inensiy a ime is v (x) =( p D ) v (x)+ v D, (x; z) () z Z where p D is he sae independen arge deecion probabiliy and v D, (x; z) = N x, i= (z) N (x; m (i) (z),p (i) ) () is he inensiy of he deeced arges. The parameer of he Gaussian componens describing he deeced arges are given as (z) = p D q(i) (z) λc(z)+p D Nx, l= w (l) q(l) (z) (2) m (i) (z) =m (i) + K(i) (z H m i ) (3) P (i) =[I K (i) H ]P (i) (4) where S (i) = H P (i) HT + R () K (i) = P (i) HT S(i) (6) q (i) (z) =N (z; H m i,s(i) ) (7) and λc(z) is he cluer inensiy. The componens wih a weigh below a predefined runcaion hreshold τ runc are eliminaed and he componens wihin a small disance of each oher are merged ogeher. The Gaussian mixure componens wih weigh above a confirmaion hreshold τ c (ypically.) are considered for arge sae esimaion, and heir mean componen is considered as he arge sae esimae. The number of arges is esimaed by he sum of he weighs of he Gaussian mixure componens used for arge sae esimaion. B. Sae and measuremen models In our applicaion we apply he PHD filer wice: firs for pre-filering range esimaes and hen for fusing he locaion esimaes ogeher. In he firs case he arge sae consiss of a arge range and velociy wih respec o he sensor i.e. x =[r ṙ] T (8) The classical consan velociy model is used ( ) d F = wih d being he ime inerval beween wo measuremens and is differen for each sensor depending on he measuremen rae used. The observaions consis of he ToF values represened as arge range measuremens H = ( ) In he second case he arge sae consiss of he Caresian posiion and velociy vecor of he arge: x =[x ẋyẏ] T (9) and he observaions are he arge Caresian coordinaes calculaed analyically by each sensor node as described in Secion IV-C ( ) H = Again he classical consan velociy model is used d F = d wih d being he ime inerval beween wo measuremens for he slowes sensor node. 97
IV. THE UWB MULTI-SENSOR MULTI-TARGET TRACKING METHOD The mehod described in his secion consiss of muliple algorihms. The daa received by each receiver of each sensor goes hrough he arge deecion and range esimaion sage. The esimaed ranges wih he informaion of he ideniy of he respecive receiver are hen sen o he fusion node, where arge locaions are calculaed and fused ogeher o resul in final arge locaions and racks. In Fig., we show he processing done on a measured impulse response saring from raw measuremen unil he arge ranges are esimaed. The impulse response in he figure is from a measuremen aken by one of he receivers of an UWB sensor in he presence of wo moving arges. The ToF of he wo arges is approximaely 2 ns and 6 ns, respecively... Normalized measured impulse response Normalized magniude afer background subracion Targe range esimaes 2 4 6 8 Time of fligh [ns] Fig.. Targe echo deecion - measured impulse response (blue), normalized signal magniude afer background subracion (green), CFAR es saisic (red), CFAR adapive hreshold (cyan), indexes of deeced arges by CFAR (magena) and Gaussian mixures represening he esimaed arge ranges (black) are shown The received impulse response is shown in dark blue. As can be seen, he arges echoes are no deecable. Afer we apply a background subracion algorihm as described in Secion IV-A, he resuling signal emphasizes he arge echoes (shown in green in Fig. ). For esimaing he ranges of he arges we firs use a consan false alarm rae (CFAR) algorihm as explained in Secion IV-B. In Fig. he adapive hreshold is shown in cyan and he muliple range esimaes per arge are shown in magena. As can be seen in he figure, here is one false arge deecion around 77 ns. Afer applying he GM-PHD algorihm and he subsequen Gaussian componen merging and pruning as explained in Secion III, only wo Gaussian componens remain o represen he saes of he deeced arges, as shown in Fig. in black. A. Deecion of arges Each sensor of he nework performs a arge deecion sage using he backscaered elecromagneic wave. The arge echoes are very weak compared o he srong mulipah signals such as he direc Tx-Rx feed and he reflecions of dominan or meallic objecs. However, hese signals are usually imeinvarian, and since he sensors are saic hey can be esimaed using a sequence of impulse responses. The esimaed background can hen be subraced from he received impulse response o resul in a signal where he weak arge echoes can be more easily deeced. Differen approaches for background subracion have been suggesed in he lieraure [2], [22]. We use a mehod based on exponenial averaging as in []. The background esimae as seen by receiver i of sensor s a ime, b s,i, is compued using he previous background esimae b s,i and he newly received impulse response m s,i b s,i = κb s,i +( κ)ms,i (2) wih κ being a consan scalar weighing (or forgeing) facor beween and. This facor deermines wheher recen or long-erm evens are emphasized. The signal of ineres is hen s s,i = m s,i b s,i (2) B. Range esimaion of arges Once he background has been subraced from he received impulse response, he range informaion of he deeced arges should be exraced. For his purpose we use a Gaussian adapive hreshold CFAR mehod as in [23]. A Neyman- Pearson deecor is used o discriminae beween noise and arge echo, and he adapive hreshold is deermined using exponenial weighed moving average (EWMA) filer. Firs a es saisic X is defined using an EWMA over he unbiased, normalized signal magniude. The background Y is esimaed using a slower moving EWMA over he signal magniude and he signal variance σ 2 is defined by using he same slowmoving EWMA filer over he signal energy. The adapive hreshold is hen compued using where α saisfies P FA = θ = ασ + Y (22) α 2π e 2 x2 dx (23) for a given false alarm rae P FA. The calculaed hreshold θ is hen used o define he oupu of he CFAR deecor as { if X > θ H(X) = if X θ The resuling binary sequence is used o define he ime indexes of he signal when a arge has been deeced (he indexes of he s). This in urn gives us he ime of fligh (ToF) informaion. The range of arge k a ime deeced by sensor s using receiver i is defined as he disance from he s ransmier o he arge, d Txk, s,i arge o receiver i, d Rx k, plus he disance from he s,i. I is calculaed using he ToF, τk, r s,i k, = d Tx s k, + d Rx s,i k, = τ s,i k, c (24) where c is he speed of ligh. 98
The performance of he deecor depends on he false alarm rae and he choice of parameers for he EWMA filers. Alhough hese parameers can be adjused, depending on he posiion, qualiy and direcion of he sensors, some cluer poins will sill be classified as arges. These false posiives hinder he arge localizaion and should be removed o improve i. In addiion o he false-posiives, due o he exended naure of he arges, here are muliple deecions available for each arge. One possibiliy o deal wih he muliple deecions is o model or define he exen of he arges of ineres. In our case his raises some difficulies since arges furher from he sensors (especially he hird or furher deeced arge a a given ime) are represened by much less observaions compared o he arges closer (or deeced firs) by he sensor. To improve he arge range esimaes and remove cluer, agm-phdfiler as explained in Secion III is applied on he CFAR range deecions. The arge saes are defined by he arge s range and velociy wih respec o he sensor, x = [r ṙ] T, whereas he observaions used for sae updae are he CFAR range deecions. C. Targe localizaion Typically, a arge is deeced by boh receivers of a respecive sensor. This means ha for each arge deeced by he sensor, range informaion wih respec o boh receivers is available. By choosing he righ range esimaes available from boh receivers corresponding o he same arge, i s locaion can be calculaed analyically. A arge range esimae defines an ellipse whose focal poins are deermined by he locaions of he ransmiing and he respecive receiving anenna. This ellipse represens all possible locaions a arge can have around he sensor for he given range. Having he range esimae of he same arge wih respec o he oher receiver of he sensor, anoher similar ellipse is defined. This reduces he possible arge locaion only o he ellipse inersecion poins. Since he ellipses share one foci and all foci lie on he same line, he number of possible ellipse inersecions is maximum wo. In addiion, he sensor direcion is also known, which helps in choosing he ellipse inersecion ha lies in he correc half-plane as he arge locaion. When here is only one arge, in heory here is only one range esimae per receiver, leading o only one possible ellipse inersecion for he arge locaion. However, when muliple arges are deeced, here are muliple possible combinaions of range esimaes. Ellipse inersecion calculaion is compuaionally expensive and ime consuming, hus we associae he range esimaes from boh receivers ha correspond o he same arge before calculaing all possible ellipse inersecions. For each sensor we define an inersecion hreshold. I is defined as he maximum possible difference beween range esimaes of he same arge bu wih respec o he differen receivers, such ha he arge lies in he inspeced area A (see (2)). The size of he inspeced area is known (a leas approximaely due o he sensor locaions) leading o calculaion of he inersecion hreshold T s once before he sar of he procedure T s =max k A rs, k r s,2 k (2) For each range esimae available from he firs receiver, r s, k,, we choose he range esimae from he second receiver, r s,2 k,, which saisfies r s, k, rs,2 k, T s (26) as a range esimae ha belongs o he same arge. When muliple range esimaes ha saisfy (26) are available, he esimae, wih which he absolue difference is he smalles, is chosen. The arge locaion is hen esimaed by calculaing he inersecion of he ellipses defined by he range esimaes found o correspond o he same arge. The above associaion does no only reduce he compuaional load, bu i also helps in reducing ghos locaion esimaes. Ghos locaion esimaes may resul due o inersecion of ellipses defined by ranges belonging o differen arges, or by choosing muliple inersecions of one ellipse wih he oher ellipses. D. Sensor daa fusion The esimaed arge locaions by each sensor are finally fused ogeher resuling in a single arge locaion per arge. The esimaed arge locaions using he analyical mehod conain significan amoun of noise due o he small errors in he range esimaion procedure. These locaion esimaes are used as noisy observaions of he arges in he scenario, and asimplified GM-PHD filer is applied for fusing hese noisy observaions from all sensors and resul in final arge locaion esimaes for all arges in he scenario. The arge sae is defined by he wo dimensional Caresian arge coordinaes and velociy vecor, x =[xẋyẏ] T. V. MEASUREMENT RESULTS A. Measuremen seup A sensor nework consellaion as shown in Fig. 2 is used for verificaion of he proposed mehod. Six similar UWB sensors are used, five of which are placed inside he room wih he arges and one is placed behind one of he walls. Each module has one ransmier and wo receivers perfecly synchronized on he plaform driven by a digial resonance oscillaor. The sensors are driven by differen clocks and have a differen measuremen rae. Four sensors (,3, and 6 in Fig. 2) have a 7 GHz clock and measuremen rae of abou 2 impulse responses per second, one (Sensor 2) has a 9 GHz clock and measuremen rae of abou 6.2 impulse responses per second, and he las one (Sensor 4) has a 4. GHz clock and measuremen rae of abou 2. impulse responses per second. The anennas used on he sensors are direcional horn anennas wih differen size and qualiy resuling in varying sensor performance wih respec o daa qualiy. The UWB module of he sensors is conneced o a local PC where he measured impulse responses are sored. There is no synchronizaion or cooperaion beween he sensors. The processing is laer done 99
off-line using MATLAB. The measuremens were aken in our universiy foyer wih mos of is furniure removed. The sensor locaions are measured in advance. A scenario wih hree 3 2 7 Sensor 6 3 Windows Sensor 6 Sensor 2 Ranges [m] 2 Y [m] 4 3 Sensor 2 Coridoor Coridoor Sensor 4 Sensor Saircases 7 6 4 3 2 2 3 4 6 7 8 X [m] 2 2 3 3 4 4 Measuremen ime [s] Fig. 3. Moving arge signal echoes as seen by Sensor Fig. 2. The verificaion scenario arges moving in a sraigh line owards a wall and back is used. One arge moves from he viciniy of sensor oward he opposie wall and back o is original posiion. The oher wo arges move parallel wih respec o each oher, one from viciniy of Sensor 3 and he oher from he viciniy of Sensor 4, oward he opposie wall and back. The saring posiion of he arges and he direcion of he iniial movemen is shown in Fig. 2 by he gray circles and arrows for iniial movemen direcion. The same scenario was used in [2]. B. Mehod verificaion In his secion we presen he resuls obained from processing he measured daa using he proposed mehod. The normalized impulse responses afer background subracion are shown in Fig. 3. The horizonal axis of he figure represens he measuremen ime and he verical axis is he sensor range. The color is relaed o he normalized magniude of he impulse response. I can be seen ha when a arge is very close o a sensor, i compleely shadows he oher arges from he scenario. This is explained by he fac ha a arge in close viciniy of he ransmiing anenna aenuaes he elecromagneic signal. When he arge closes o a given sensor is furher from i, he elecromagneic wave is propagaed around in he inspeced area, and par of i reaches he oher moving arges. However, a arge posiioned behind anoher arge wih respec o he sensor is shadowed since only a very small aenuaed signal reaches i. For reducing he shadowing influence of arges close o a sensor, he sensor anennas can be placed on an elevaed surface wih a skewed viewing angle oward he scenario. Nex he CFAR range deecion algorihm is applied on he impulse responses processed by he background subracion. Fig. 4 shows he ranges esimaed for Sensor and 6. Due o he naure of he daa, he range of he closes arge is bes deeced, whereas he oher wo arges are mosly invisible. This is due o he fac ha he sensors were posiioned wih around meer elevaion from he ground, and when a arge was close o he sensor, he oher arges were mainly invisible. Range [m] Range [m] 3 2 2 Range deecions by Rx of Sensor 2 2 3 3 4 4 Measuremen ime [s] 3 2 2 (a) Range deecions by Rx of Sensor 6 2 2 3 3 4 4 Measuremen ime [s] (b) Fig. 4. Ranges deeced by GM-PHD for a) Sensor and b) Sensor 6 The deeced ranges in he case of Sensor conain very lile cluer and false alarms. However, in he case of Sensor 6, furher processing for cluer removal is necessary.
3 Ranges esimaed by Rx of Sensor 2 7 Sensor 6 3 Sensor 6 Sensor 2 2 Range [m] Y [m] 4 3 2 Sensor 2 2 3 3 4 4 Measuremen ime [s] Sensor 4 Sensor 6 4 2 2 4 6 8 X [m] (a) (a) 3 Ranges esimaed by Rx of Sensor 6 2 Range [m] 2 2 2 3 3 4 4 Measuremen ime [s] (b) Fig.. Ranges deeced by GM-PHD for a) Sensor and b) Sensor 6 Y [m] 7 Sensor 6 3 Sensor 6 Sensor 2 4 3 Sensor 2 Sensor 4 Sensor 6 4 2 2 4 6 8 X [m] By applying he PHD filer, we remove mos of he cluer poins and he muliple deecions per arge are reduced o one (Fig ). The esimaed ranges relaed o he wo receivers of each sensor are used o calculae he locaion esimaes. Each locaion esimae is a probable locaion of one of he arges he sensor could deec. Fig. 6a shows he locaion esimaes for each sensor for half of he measuremen ime. The differen colors represen he locaions esimaed by he differen sensors. I can be noiced ha for each sensor, he closes arge has he leas noisy locaion esimae. This is due o he geomerical diluion of precision. The esimaed locaions by each of he sensors are fused ogeher o complimen each oher and arrive a a more precise locaion esimaes for he arge in he room. As can be seen in Fig. 6b, he arge racks are much more clear afer he locaion informaion fusion. VI. CONCLUSION AND FUTURE WORK Targe localizaion for surveillance, securiy and rescue applicaions can be complimened by UWB echnology due o i s immuniy o visual, emperaure, humidiy and oher inerferences. In his paper we described a mehod for localizaion and racking of muliple moving arges by using muliple UWB radar sensors. Each sensor has a ransmier and wo (b) Fig. 6. a) Localizaion of arges by each sensor and b) Fusion of locaion esimaes ino arge racks receivers and is hus capable of auonomous arge localizaion in 2D. The mehod is applicable for inruder deecion and localizaion since i does no require cooperaion of he arges wih he sensor nework. I is implemened and opimized for on-line real-ime applicaion. For verificaion, daa measured by six independen M-sequence UWB radar sensors in he presence of hree moving persons is used. The daa analysis show ha he deeced arges can be accuraely localized. The proposed mehod can be improved by using he sensor informaion of he arge locaion which has been discarded in he arge localizaion sage. Direc fusion of he arge range esimaes using belief funcions is considered. However, since his mehod suffers from ghos rack deecions, soluions for ghos rack eliminaion should be firs invesigaed. The mehod performance can be improved by using Cardinalized PHD filer and ieraive muliple movemen models.
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