Locating Multiple Ultrasound Targets in Chorus
LLocating Multiple Ultrasound Targets in Chorus
Lei Song
Institute for Interdisciplinary Information Sciences,Tsinghua University, Beijing, P.R.ChinaEmail:[email protected]
Yongcai Wang
Institute for Interdisciplinary Information Sciences,Tsinghua University, Beijing, P.R.ChinaEmail: [email protected]
Abstract —Ranging by Time of Arrival (TOA) of Narrow-band ultrasound (NBU) has been widely used by many locatingsystems for its characteristics of low cost and high accuracy.However, because it is hard to support code division multipleaccess in narrowband signal, to track multiple targets, existingNBU-based locating systems generally need to assign exclusivetime slot to each target to avoid the signal conflicts. Becausethe propagation speed of ultrasound is slow in air, dividingexclusive time slots on a single channel causes the locationupdating rate for each target rather low, leading to unsatisfiedtracking performances as the number of targets increases. Inthis paper, we investigated a new multiple target locating methodusing NBU, called
UltraChorus , which is to locate multiple targetswhile allowing them sending NBU signals simultaneously, i.e., inchorus mode. It can dramatically increase the location updatingrate. In particular, we investigated by both experiments andtheoretical analysis on the necessary and sufficient conditions forresolving the conflicts of multiple NBU signals on a single channel,which is referred as the conditions for chorus ranging and choruslocating . To tackle the difficulty caused by the anonymity ofthe measured distances, we further developed consistent positiongeneration algorithm and probabilistic particle filter algorithm tolabel the distances by sources, to generate reasonable locationestimations, and to disambiguate the motion trajectories of themultiple concurrent targets based on the anonymous distancemeasurements. Extensive evaluations by both simulation andtestbed were carried out, which verified the effectiveness of ourproposed theories and algorithms.
I. I
NTRODUCTION
Locating by Time-of-Arrival (ToA) of Narrow band ultra-sound provides good positioning accuracy by using very lowcost hardware and simple system architecture, which is widelyused in many locating system. e.g. ActiveBat[9], Cricket[6].However, when multiple targets are transmitting the same bandultrasound to a common set of receivers, inevitable conflictswill happen at the receivers if the multiple targets are notappropriately coordinated. Further, because it is hard to codetarget ID into NBU, even if the NBU signals from multipletargets can be separated at a receiver, the receiver can hardlydetermine the source (transmitter) of the NBUs, resulting atlocating ambiguity. To tackle these multiple target locatingproblems, existing NBU based locating systems generally relyon the exclusive working mode of the multiple targets, inwhich each target is assigned an exclusive time slot by TDMAor CSMA scheme to guarantee the NBU signal transmittedfrom one target is not conflicted to the others.However, because the propagation speed of the ultrasound israther slow in the air (e.g., 100 ms are needed for ultrasound propagating 34 meters), the time slot for each target’s eachtransmission has to be long enough to avoid the transmittedNBU being conflicted with the same frequency NBUs fromthe other targets. Therefore, in exclusive mode[10][6][9], atany time, only NBU from one target is in propagation, whichresults at low locating updating rate for individual target whenthe number of target is large. This on one hand limits thelocating capacity (number of simultaneously located targets),on the other hand affects the tracking fidelity, especially whenthe targets are moving quickly.To deal with these problems, in this paper, we investigatedthe problem of locating multiple NBU targets in chorus mode,which is to locate a set of targets concurrently by allowingthem to transmit NBU signals in the same time slot. In thisstudy, we conducted not only theoretical analysis, but alsoextensive simulations and hardware experiments. In particular,we addressed the difficulties of chorus ranging (measuringTOAs from multiple concurrent targets) and chorus locating (calculating locations for the multiple targets) from followingfive aspects:1) We investigated via experiments on the conditions for areceiver to reliably separate the multiple NBUs from multipleconcurrent targets. 2) It leads to the geometric conditions onthe relationship among the targets to guarantee non-conflictmultiple TOA measurements. 3) Since the measured TOAslack source identity, we present consistent position generationalgorithm, which exploits the historical consistence (in termsof the deviation to the historical position of the targets) tolabel the potential sources (transmitters) for the anonymousdistances, and then to generate and to filter the potentialpositions via evaluating their self-consistence (in terms of theresidue of location calculation). 4) By using the generatedconsistent positions as input, we proposed probabilistic particlefilter algorithm to further disambiguate the trajectories ofthe multiple targets by using the consistence of the movingspeeds and accelerations of targets as the evaluation metrics.5) At last, location based transmission scheduling algorithmwas proposed, which schedules the concurrent transmitters forreliable, online multi-target locating in chorus mode.The rest of this paper is organized as follows. Related workand background are introduced in Section II. We introducedthe feasibility of chorus ranging in Section III. The conditionsfor successful multi-target chorus locating are presented in sec-tion IV. Techniques for identifying potential sources of TOAand the particle filter algorithms for trajectory disambiguat- a r X i v : . [ c s . I T ] D ec ReceiverEmitter (a) one target, one receiver (b) two targets have different distances tothe receiver
ReceiverEmitter (c) two targets have the same distance tothe receiverFig. 1. Experiments to test how the separation of NBU peaks are affected by the distances between the transmitters ing are presented in Section V. We proposed location-basedtransmitter scheduling scheme in Section VI. Simulations andexperimental results are presented in Section VII. The paperis concluded with remarks in Section VIII.II. R
ELATED W ORK AND B ACKGROUND
Ranging by TOA of NBU is a very attractive techniquefor fine-grained indoor locating due to its high accuracy,low cost, safe-to-user and user-imperceptibility. It can providepositioning accuracy in centimeter level even in 3D space,which makes it very fascinating in may indoor applications.Popular ultrasound TOA-based indoor locating system includeBat[9], Cricket [6], AUITS[10], LOSNUS[7], etc. Popularapplication scenario include location-based access control [8],location based advertising delivery[4], healthcare etc.Multiple target locating problem has been investigated inexisting systems. When using NBU for TOA-based rang-ing, there is no room for coding the ID of target. Exist-ing approaches let the target send a ultrasound-radio fre-quency (RF) pair. The RF signal is for synchronization andidentification[9][6][10]. Since there are several Media AccessControl(MAC) protocol for RF signal, they can be adopted tocoordinating target by just extending the length of the time-slot.Another approach is to explore the broadband ultrasound.Compared to the narrowband version, broadband ultrasoundrequires the transducer [3] to have better frequency responseperformance. The broadband ultrasound wave can accommo-date identity of target to support multiple targets. Furthermore,if the wave is encoded with orthogonal code[1], two wavescan be decoded respectively even overlapped. But broadbandlocating needs high cost transducers, and the signal is moresensitive to the Doppler effects. To the best of our knowledge,very few results have been reported for locating in chorusmode, because the collision problem of NBUs are generallyhard to tackle. In this paper, we investigate conditions andalgorithms to resolve this challenge.III. F
EASIBILITY OF C HORUS R ANGING
At first, we introduce exclusive mode and chorus mode and presents experiments to investigate the conditions fora receiver to successfully detect NBUs from concurrentlytransmitting targets.
A. Exclusive Mode
In conventional approach, when there are multiple targets,to avoid conflicting of NBUs, RF+US signals from differenttargets are scheduled into different time slots (called exclusivemode ). In each slot one target broadcasts RF+US signalssimultaneously, where the RF signal is used to synchronizetimers among the target and the receivers. Then the synchro-nized receivers measure the TOAs of the successive ultrasoundwave from the target to estimate their distances to the targetand to calculate the target’s location via by least squareestimation or trilateration[5]. The exclusive slot assignmentcan be realized by utilizing the media access control(MAC)protocols of the RF signal, e.g., CSMA, TDMA[6][9][10].But, because the propagation speed of ultrasound is quiteslow in the air (340 m per second), the time-slot for eachexclusive target has to be long enough to avoid NBU conflict-ing to the successively arrived NBU from other targets. Foran example, Cricket[6] assigns each target nearly ms byCSMA protocol. Because n targets need n exclusive slots, thelocation updating rate of each individual target is only O ( n ) ,which may become unsatisfactory when there are large numberof targets. B. Chorus Mode
In contrast to the exclusive mode, in chorus mode, we allowmultiple targets to broadcast NBUs in the same time slot.A general way is to use a
RF commander to broad RF tosynchronize the timers of the targets and the receivers, andlet the targets to broadcast NBU signals simultaneously andconcurrently with the RF. Each receiver detects the mixed ul-trasound signals from the multiple targets in its communicationrange and tries to separate the NBU signals to estimate theTOAs from the targets, and then to determine the locations ofthe multiple targets.
C. Experiments on Multiple NBU signal Detection
Detecting TOAs from concurrently transmitted NBU wavesat the receiver is the critically first step for chorus ranging,which determines the feasibility of chorus ranging and lo-cating. We conducted experiments using MTS450CA Cricketnodes [6] to investigate the conditions for successfully multipleTOA detection at a receiver.Before carrying out the experiments, we made some mod-ification to the firmware of Cricket node. Firstly, the policy to detect only the first arising edge was canceled, which isoriginally designed in Cricket to filter out the NLOS (non-line-of-sight) and the echo signals, because the NLOS andecho waves arrive later than the direct path NBU. In the newversion, the received wave power is continuously comparedto a threshold. When a rising edge (or wavefront) is detected,a TOA event is reported and the comparator state is set to“high”. When the wave power decreases to be lower than thethreshold, the comparator state returns to “low” to be ready fordetecting the next wavefront. Secondly, we disable the CSMAprotocol in target, so that the targets can send ultrasoundsimultaneously.
1) Aftershock:
The first experiment used one receiver andone target. The screen-shot on oscilloscope is shown in Fig.1(a). The target send µs ultrasound wave. After about ms, this NBU wave arrives at the receiver, which cause a ms shock on the receiver’s sensor. Because the ultrasound ismechanical wave, the shock on the receiver is much longerthan the length of the wave sent by the target. This phe-nomenon is called aftershock . When the sensor in the receiveris experiencing an aftershock, the comparator in the sensoris kept in high state , which will block the detection of thenewly arrived NBU wavefront. In other word, aftershock willcause loss of TOA measurements at the receiver. Intuitively,the longer is the aftershock, the more frequent is the loss. Fromthe oscilloscope output, we can also see some secondary peakscaused by the echoes. These secondary peaks can be filteredout because their powers are lower than the threshold. Afterthe energy of the aftershock fades below the threshold, thecomparator switches to low state , which is ready for detectingthe next NBU wave.
2) Multiple TOA Detections:
Two targets and one receiverare used in the second experiment, in which the two targetsare placed at different distances from the receiver. When thetwo targets broadcast ultrasound signal simultaneously, the de-tected waves at the receiver are shown in Fig. 1(b). In this case,the receiver detects two NBU wavefronts successfully (i.e., twoTOAs of ultrasound), which is because the separation betweenthe wavefronts is greater than the length of the aftershock, butnote that the detected TOAs are anonymous, i.e., the receiverdon’t know their targets. In the third experiments, the twotargets have the same distance to the receiver, their generatedwaves at the receiver are overlapped, as shown in Fig. 1(c). Inthis case, only one TOA is measured at the first arising edge,which is also anonymous.
D. Condition on Detecting Multiple TOAs
The above experiments showed clearly that whether twosuccessive NBU waves arrived at a receiver can be successfullydetected is determined by the time separation between thetwo waves. If the time separation is longer than the lengthof the aftershock generated by the first wave, the wavefrontof the second wave can be detected, otherwise, the secondwavefront will be lost because the comparator is already inhigh state. Since the length of the aftershock is affected bythe received energy of the NBU signal detected at the receiver and by the inertia of the ultrasound transducer of the receiver,it will be better to choose ultrasound transducer with weakinertia to get shorter aftershock to improve the capability ofdetecting the successive ultrasound pulses. To formulate theimpact of the aftershock, let’s denote L max as the longestpossible aftershock generated by the strongest signal at thereceivers. Let v u be the speed of the ultrasound, then Definition 1 (confident separation distance):
We define ω = L max v u as the confident separation distance betweenthe successively arrived waves for the receiver to successfullydetect their TOAs.From triangle inequality, it is easy to verify that if the TOAsfrom two concurrent targets can be successfully detected by areceiver, the distance between the two targets must be largerthan ω . Let’s further take the audible region of the ultrasoundinto consideration. We assume all the targets have the samebroadcasting power, then: Definition 2 (audible range of ultrasound):
We define r asthe audible range of the ultrasound, which is the propagationdistance of the ultrasound from a target before the wave poweris lower than the detectable threshold of the receivers.By combining the separation distance and the audible range,we can arrive at the condition for a receiver to successfullydetect TOAs from two concurrent targets. Theorem 1: We consider two targets a and b are at location x a and x b respectively, who send NBU waves in the same timeslot, a receiver at location x x can detect the TOAs of the twowaves if: (cid:26) | d a,x − d b,x | > ωd a,x (cid:54) r, d b,x (cid:54) r (1)where d i,j calculates the distance between x i and x j . Fig. 2. The blind region of a caused by b For the case of multiple targets, to check whether a receivercan detect TOAs from their concurrent transmissions, we cansimply sort their distances to the receiver in an ascendingorder. When the difference between any two adjacent sorteddistances are larger than ω , and when the receiver is in theircommon audible region, the receiver can successfully detectthe TOAs of their concurrent ultrasound waves. E. “Blind Region” Impacted by a Concurrent Target
Based on Theorem1, let’s now consider in which region willa receiver lose the TOA from a target a when another target b is transmitting concurrently. Definition 3 (Blind region):
Blind region of a caused by b is referred to the region in which the receivers cannot captureTOA from a , if a and b send wave at the same time. The areaof blind region of a caused by b is denoted by S Ba ← b . -10 -5 0 5 10 15 20-10-551015 a b (a) d a,b > r -10 -5 0 5 10 15 20-10-551015 a b (b) r − ω ≤ d a,b ≤ r -10 -5 0 5 10 15 20-10-551015 a b (c) ω In Fig.2 the blind region of a caused by b is shown by thegray region, which is characterized by inequality functions: < d a,x − d b,x ≤ ω and d ax ≤ r . When the receivers arelocating in this region, the NBU wave from a will be hidden inthe aftershock of the wave from b , so that the receiver cannotdetect TOA from a . Depending on the distance between a and b , i.e., d a,b , S Ba ← b changes from 0 to πr . Figure 3 showshow S Ba ← b changes with d a,b , which indicates that S Ba ← b isa function of d a,b . Moreover the area of blind-region can beexpressed in close form. S Ba ← b ( d a,b )= d a,b > rr ( θ − sin θ cos θ ) 2 r − ω ≤ d a,b ≤ rr ( θ − sin θ cos θ ) − S e ω < d a,b < r − ωr ( θ − sin θ cos θ ) 0 < d a,b ≤ ω (2)For clarity of expression, the detailed expansion of S Ba ← b ( d a,b ) can be referred in Appendix. We can just note that it is amonotone decreasing function of d a,b .IV. C ONDITIONS FOR C HORUS L OCATING Now let’s consider the conditions for localizing multipletargets in the chorus mode. It is widely known that in rangingbased locating algorithms such as trilateration, three distancemeasurements from non-collinear beacons are necessarily re-quired for uniquely determining the position of a target. Wetherefore investigated the condition for obtaining at least threeTOA measurements for a target in the chorus mode. Notethat for randomly deployed receivers, the probability of threechosen receivers are collinear are small, therefore, the non-colinear constraint is not considered at this stage. A. How Many TOA Detectable Regions Are Left? We define the TOA detectable region (TDR) of a target asits audible region minus its blind region. Fig.5 shows the blindregion caused by one concurrent target. The white region in theaudible circle is the TDR region. When multiple concurrenttargets are presenting, the left TDR will be further reduced. Wedenote the TDR of a target a caused by a concurrent target set T as S Da ← T . The area of S Da ← T will affect the possible numberof receivers in it for whatever distributions of the receivers,which determines the number of TOAs that can be obtainedfor a target. 1) Consider Pairwise Separation Among Targets: When thenumber of the concurrent targets is more than 2, the blindregion of the target a is the union area of the blind-regions caused by all other targets in set T . S Ba ← T = ∪ s ∈ T S Ba ← s (3)As indicated in (2), S Ba ← b is a monotone decreasing functionof d a,b , therefore, an intuition is that the less are the pair-wise distances among the targets, the larger is the blind regioncased by each target. Therefore, we consider S Ba ← T when thepair-wise distances among all concurrent targets are the same,denoted by d . Via such a way, we characterize how the interdistances among the targets and their distributions affect theblind region of a particular target. 2) Lower Bound of S Da ← T in Multiple Target Case: Whenall targets have the same pair-wise distance d , because theisotropous feature of the audible circle of a , the blind regioncaused by each individual target has the same shape and thesame size. By inclusion-exclusion principle, the union area ofthese blind regions is the largest when the intersection areaof the blind regions is the smallest. This case appears whenthe other targets are geometrically symmetrically distributedaround a . Fig.4(e) shows the largest union area of the blindregions of a when | T | = 2 , , , , respectively. The corre-sponding TDR area is the lower bound of S Da ← T for pairwiseseparation distance ≥ d and when the number of concurrenttargets in the audible region is known. We omit the expressionsof these lower bounds for space limitation.More generally, when there are unknown number of targetsare presenting, we can also derive a lower bound of S Da ← T for given d . It is the area of the inscribed circle centered at a with radius d/ in the TDR as shown in Fig. 5. Therefore,the lower bound of S Da ← T for given pairwise separation d is: S Da ← T ≥ π (cid:18) d (cid:19) (4)It is a monotone increasing function of d , which means thatthe larger is the pair-wise separation among the targets, thelarger is the area of TDR for each target. mid-‐perpendicular Emitters d d Fig. 5. Lower bound of blind-region B. Probability of Having At Least Three Receivers in TDR Based on the lower bound of S Da ← T , for any given distribu-tion of the receivers, we can evaluate the probability and theexpectation of at least three receivers in the TDR region of a . Note that different formulas can be utilized to estimate thelower bound of S Da ← T if we know the number of concurrenttargets in the audible region and the minimum separationdistance d . (a) Blind Region by 2 targets (b) by 3 targets (c) by 4 targets (d) by 5 targets (e) by 6 targetsFig. 4. Blind-region of target a caused by different number of other targets Let’s consider a general case when the receivers are inPoisson distribution, i.e. P ( n r = k ) = λ k e − λ k ! , where λ isthe expected number of receivers in a unit area (e.g. 1 m ).By substituting the lower bound of S Da ← T ≥ π (cid:0) d (cid:1) , theprobability of at least three receivers are in S Da ← T can becalculated as: − (cid:88) i =0 p ( n r = i ) ≥ − e − λπd (cid:20) λπd λ π d (cid:21) (5) Theorem 2: When receivers are in Poisson distribution with λ expected receivers in a unit area, when the pair-wiseseparation among targets are larger than d , the probability ofat least three receivers are presenting in the TDR of a targetis lower bounded by − e − λπd (cid:20) λπd λ π d (cid:21) . (6)Fig.6 plots the lower bound of P ( n r ≥ as a function of d and λ . We can see that for given λ , the lower bound of atleast three receivers presenting in the TDR of a target increasesexponentially with d . Note that the figure plots only the lowerbound. Because the real TDR area can be much larger thanthe lower bound area of TDR, in real case, the probability ofthree receivers are in the TDR of a target can be much closerto 1. The results in Fig.6 show the strong feasibility of chorus Seperation Distance Among Emitters: d (m) P ( n r >= ) lambda=0.2lambda=0.5lambda=1 Fig. 6. The lower bound of the probability of at least three receivers are inthe TDR of a target as a function of d and λ locating. It only needs the targets are well separated and thereceivers have enough density for receivers to obtain at leastthree TOA-based distances for each concurrent target. V. L OCATE M ULTIPLE T ARGETS BY A NONYMOUS D ISTANCES Above analysis shows the feasibility of detecting multipleanonymous TOAs at a receiver in chorus mode. But thereceiver don’t know the source (target) of each TOA. To utilizethese TOAs to locate the multiple targets, we developed meth-ods to effectively utilize the anonymous distances to locatethe multiple targets and to disambiguate their trajectories. Weintroduce the proposed algorithms in this Section. A. Overview The overview of the proposed techniques are shown inFig.7, which contain mainly two parts: 1) consistent positiongeneration and 2) probabilistic particle filter for trajectorydisaggregation. In the first part, the inputs are the set ofanonymous distances measured by the receivers, denoted by [ D , · · · , D m ] , and the coordinates of these receivers, denotedby [ x , · · · , x m ] , where m is the number of receivers. Thenumber of distances measured by the i th receiver is | D i | = k i . 1) Overview of Consistent Position Generation: Since eachthree distances from non-collinear receivers can generate aposition estimation, enumerating the combinations of theseanonymous distances will generate a large amount of possiblepositions, in which most of the positions are wrong. To avoidthe pain of finding needless from the sea of large amountof potential positions, we proposed to firstly find the feasibledistance groups by historical-consistency, i.e., by utilizing theconsistency of distance measurements with the latest locationestimations of the targets (which are provided by the particlefilter). After this step, the distance groups are utilized togenerate a set of potential positions. To further narrow downthe potential position set, we proposed self-consistency toevaluate the residue of location calculation of each potentialposition. Only the top N c potential locations with good self-consistency will retained to be used as input to the particlefilter at time t . 2) Overview of Probabilistic Particle Filter: The particlefilter maintains the positions of n targets at time t − , denotedby { x i ( t − } ; maintains l most possible tracks for each targetup to time t − , denoted by { T i (1 : t − ∈ R l ∗ ( t − } ; theprobability distribution function (pdf) of each target’s velocity,denoted by p v ( x ) ; and the probability distribution function ofeach target’s acceleration, denoted by p a ( x ) . Then at time t ,for each target i , by connecting its l tracks at time t − to Distance
grouping
by
historical-‐
consistency { D , D ,…, D m , } { x , x ,…, x m , } Anonymous
distance
set
measured
by
receivers Coordinates
of
receivers Input: Generate
Potential
Positions Potential
Position
Filtering
by
Self-‐Consistency Retain N c Potential
Positions
with
good
historical
and
Self-‐Consistency States
kept
in
Particle
Filter { x i ( t -‐1)}:
Position
of ith targes
at t -‐1,
i=1… n { T i (1:t-‐1)}: l tracks
of
target i up
to
time t -‐1 p v ( x ):
pdf
of i th
target’s
velocity p a ( x ):
pdf
of i th
target’s
acceleration Generate l * N c particles
for
each
target Calculate
v j (t),
a j (t)
for
the j th
particle Evaluate p v (v j (t)) p a (a j (t)),
for
all
particles
Select
the
top l particles
who
have
the
best p v (v j (t)) p a (a j (t)) Update
locations
and
tracks
to
time t ;
update
statistics
of
velocities
and
accelerations
of
all
targets Output
location
at t Consistent
position
generation Probabilistic
Particle
Rilter Executed
for
each
target Receiver j v e x i ( t-‐1 ) D k d j , i ( t − b)
Labeling
distances
to
common
sources a)
The
triangle
relationship Fig. 7. The diagram of consistent location generation and probabilistic particle filter algorithms to utilize the anonymous distances measured by receivers tolocate and disambiguate the tracks of multiple targets N c potential positions at time t , lN c particles are generated.The velocity ( v j ( t ) , j = 1 , · · · , l ∗ N c ) and acceleration( a j ( t ) , j = 1 , · · · , l ∗ N c ) of each particle are calculated,based on which, the likelihood of the particle j is evaluatedby p v ( v j ( t )) p a ( a j ( t )) . Then by ranking the likelihoods ofthe particles, l top particles will be retained for target i attime t , which are used to update the location estimation oftarget i at time t , the historical tracks and the pdfs of velocityand acceleration. We introduce key points of the algorithm infollowing subsections. B. Consistent Potential Position Generation1) Historical Consistency: To avoid generating a largeamount of misleading potential positions by blind combina-tions of the anonymous distances, we proposed to measure the historical consistency of the distances to label the distances toreasonable sources . The input of this step is the historicalpositions of the n targets provided by particle filter and thedistance set from the receivers. For a target, since the velocityof the target is upper-bounded in the real scenarios, which isdenoted by v e , its position at time t will be bounded inside adisk centered at its position at t − , with radius v e , i.e., || x i ( t ) − x i ( t − || ≤ v e (7)For a receiver j , let d j,i ( t − represent the distance from it to x i ( t − . From triangular inequality, for every distance D k measured by receiver j at time t , D k ’s potential source islabeled to target i if: | D k − d j,i ( t − | ≤ v e (8)Then, only the distances with the same source (target) labelwill be selected to generate potential positions for the targetsusing trilateration. This step on one hand reduces the com-putation cost of generating massive possible positions, on theother hand avoids generating the obviously wrong positions. 2) Self-Consistency: We further evaluate the self-consistency of the generated potential positions to furtherfilter out the unreasonable position candidates. Consideringa potential position x calculated by trilateration using m distances [ D , · · · , D m ] from receivers at location x r , · · · , x r m , the self-consistency of this location ismeasured by the residue of the location calculation: S x = 1 m m (cid:88) i =1 ( D i − d x,r i ) (9)where d x,r i is the distance from x to receiver x r i . Thenonly top N c potential positions with the best self-consistencyperformances will be retained as the input for particle filter tobe further processed by particle filter at time t . C. Probabilistic Particle Filter The particle filter maintains 1) the locations of n targets at t − ; 2) l most possible tracks for each target up to time t − ,and 3) the probability density functions (pdfs) of each target’svelocity and acceleration. The pdfs of each target’s velocityand acceleration are calculated based on historically velocityand acceleration up to t − . They are utilized to evaluate thelikelihood of the generated particles. 1) Generate and Evaluate Particles: For each target, say i ,by connecting its l ending locations at t − (in its l tracks)to the N c potential positions at time t , l ∗ N c particles aregenerated, each particle represents a potential track. Then weevaluate the likelihood of each particle k, k = 1 , · · · , l ∗ N c by the following likelihood function: c k = p v ( v k ( t )) p a ( a k ( t )) (10)where v k ( t ) and a k ( t ) are calculated on the particle k by: v k ( t ) = | x k ( t ) − x k ( t − | , a k ( t ) = v k ( t ) − v k ( t − (11)Then the top l particles with best likelihood will be retainedfor the target for the next step, and x ( t ) in the most possibleparticle will be output as the position estimation at time t . The x ( t − x ( t ) x ( t − x ( t − x ( t − x l ( t − x ( t − x ( t − x ( t − x ( t − x l ( t − x ( t ) x ( t ) x ( t ) x l ( t ) v j ( t ), a j ( t ) ( ) Particle j c j = p v v j ( t ) ( ) p a a j ( t ) ( ) Pdf
of v Pdf
of a Fig. 8. Evaluate the cost of each generated particle pdfs of velocity and acceleration are updated accordingly. Sucha progress will be applied to all the targets, and the algorithmof the probabilistic particle filter is listed in Algorithm 1.Complexity of Algorithm1 can be easily verified. Lemma 1: Complexity of algorithm 1 is O ( nN c l log( N c l )) Proof: For each target, the most expensive step is to sortthe l ∗ N c elements, which takes O ( N c l log( N c l ))) , so the over-all complexity for locating the n targets is O ( nN c l log( N c l ))) .The probabilistic particle filter provides good flexibility. 1)It supports the trade off between the locating accuracy andthe executing time by changing the number of the preservedparticles. 2) The likelihood of each Particle is calculated byconsidering both the velocity and the acceleration, which isonline continuously updated, so that it can be suitable evenwhen the targets have variated motion characters.A potential drawback of this particle filter approach is that atarget may be lost when it is too close to other targets. Whenthe location candidates of two targets are almost the same,all particles may follow one target and none particle followsthe other. Although such kind of target lost happens only in Algorithm 1 Probability Particle Filter for a Target i Require: T i (1 : t − , possible location { x , x , . . . , x n c } .PDF of velocity p v ( · ) and PDF of acceleration p a ( · ) . Ensure: Updated T i (1 : t ) , p v ( · ) and p a ( · ) , x i ( t ) . { p , . . . , p l × n c } ← T i (1 : t − ×{ x , . . . , x n c } // Generateparticles by posible locations of tracks at t − { c , . . . , c l × n c } ← for i = 1 : l × n c do v k ( t ) = | x k ( t ) − x k ( t − | a k ( t ) = v k ( t ) − v k ( t − c k = p v ( v k ( t )) · p a ( a k ( t )) end for { ˆ p , . . . , ˆ p l × n c } ← sorting { p , . . . , p l × n c } by { c , . . . , c l × n c } in ascending order T i (1 : t ) ← { ˆ p , . . . , ˆ p l } // preserve the first l sortedparticle p a ( · ) ← U pdateP DF ( p a ( · ) , { v ( t ) , . . . , v l ( t ) } ) p v ( · ) ← U pdateP DF ( p v ( · ) , { a ( t ) , . . . , a l ( t ) } ) x i ( t ) = ˆ p chance, it affects the tracking performance occasionally. Weshow this problem can be well solved by location based time-slot scheduling, which is discussed in the next section.VI. L OCATION BASED T IME - SLOT S CHEDULING Locating in chorus mode requires concurrent targets haveenough pair-wise separation distances, otherwise the receiverscannot detect TOAs from their concurrent waves. Keeping con-current targets to be spatially well separated is also importantfor the particle filter to confidentially disambiguate their tracks.In addition, the initial condition of the particle filter needs theinitial location estimations to be as accurate as possible toavoid cascading errors.With consideration of these requirements, we designedlocation based time-slot assignment (LBTA) to appropriatelyschedule the concurrent transmissions of the targets. In gen-eral, LBTA assigns targets which are close to others orwith unknown locations to work in exclusive time-slots toavoid conflict. Targets satisfying the separation distance arescheduled to transmit concurrently.At first in LBTA, a confident separation distance d s iscalculated by the lower bound of TDR region (6) based ongiven density of the receivers, i.e., λ to guarantee P ( n r ≥ approaching 1. Then the targets with known locations willbe separated into a set of d s -separated groups . Each groupconsists of several targets with the pair-wise distance amongtargets in the group is at least d s . Then an exclusive timeslot is assigned to the targets in the same d s -separated group .Exclusive slots are also assigned to the targets with unknownlocations. Locations of targets 1-5 are known ! Location of target 6 is unknown ! Divide
-‐separated
groups
Target
with
unknown
location ! ! ! Time
Slots d s {6} {1,2,5} {3,4} Fig. 9. An example of LBTA to assign time slots An example of LBTA is shown in Fig. 9, in which, sixtargets are presenting. We assume the locations of target { , . . . , } are known and the locations of targets is stillunknown. In this case, the targets with known locations areseparated into two d s -seperated groups . An exclusive time-slot is assigned to every d s -seperated group and the targetwith unknown location. LBTA can help to solve both initialization problem and therisk of missing target in particle filter. At initial state, locationof all n targets are unknown. So n time slots are required tolocate the n targets. From then on, all n targets share one timeslot unless pairwise distances between some targets are lessthan d s . In this case, partition method on the n target is used toseparate the targets into d s -separated groups. Although finding Algorithm 2 DivideClosestTargets Require: { x , . . . , x n } and d s Ensure: d s -seperated group partition, G , . . . , G n d n d ← , tempg ← { x , . . . , x n } , tempg = ∅ while ∪ n d − i =1 G i (cid:54) = { x , . . . , x n } do while (MinPairWiseDis(temp G ) < d s ) do [ i, j ] = select the closest pair in tempg temp G = temp G \ i , temp G = temp G + i end while G n d = temp G , n d = n d + 1 temp G = temp G , temp G = ∅ end while the minimum number of d s -seperated group is NP-hard[2], thisproblem can be effectively addressed by a greedy approach inpractice when the number of targets are limited. We proposeda greedy DivideClosestTargets algorithm to address it. Thealgorithm always selects the closest pair in the current tempgroup, and put one of them into a new temp group, until alltargets in current temp group have pairwise distance largerthan d s . This temp group will form a d s -separated group. Thenthe algorithm process the new temp group, until all targets areassigned into d s -separated groups.VII. E VALUATION Both simulations and experiments were conducted to eval-uate the performances of multiple target locating in chorusmode. More specifically, the locating accuracy, efficiency ofscheduling and, robustness of chorus locating against noisewere evaluated and reported in this section. A. Simulation 12 3 45 678 910 12 3 45 678 910 ReceiverReal objEst obj Fig. 10. Settings of simulation for chorus locating. 1) Settings of Simulation: We conducted simulation bydeveloping a multi-agent simulator in MATLAB environment.The setting of our simulation scenario is shown in figure 10.The black diamonds stand for receivers, which are deployed ingrid of size m × m . The blue stars stand for targets. Motionsof targets are identically independent random walk, that eachtarget walks along a line and turns a random angle every 5seconds. The velocities of the targets are normally distributed,with µ = 1 and σ = 0 . . This motion character is close toreal action of human in open space. In simulation, we set the number of targets to 10, whose actions are constrained in abox of size m × m . The length of a time slot, i.e., locatingupdating interval is set to ms . The audible radius, i.e., r of target is set to be m . ω , which the length of the aftershockis set to . m . The values of r , δ and ω in above setting areobtained from real values of Cricket [6] locating system. 2) Locating accuracy without ranging noise: We firstlyevaluate the multiple target locating and trajectory disaggre-gation performances when no ranging noise is incurred, i.e.,ranging error is zero. The accuracy for concurrently multipletarget tracking is shown in figure 11(a) and 11(b). Fig.11(a)plots the real trajectories and estimated trajectories, whichshows that the estimated trajectories coincide well with thereal trajectories even trajectories overlap. The correspondingCDF of the locating error is shown in figure 11(b), whichshows that more than of the locating error is less than cm . We found that greater than cm location error appearedwhen ranges was lost due to aftershock at a receiver resultingat < TOAs which leads to incorrect location estimation. 3) Accuracy vs. ω vs. time-slots: Location accuracy underdifferent ω is shown in figure 11(c). The CDFs of rangingerrors when ω equals to cm, cm, cm are presented,which are the corresponding cases when the length of theaftershock are ms, ms, ms respectively. Although theaccuracy gets worse with growing of ω , of the locatingerrors in the 3 cases are still very small. We investigatedand found that the good locating performances against thevariation of ω were contributed by LBTA. With the growth ofthe aftershock, LBTA started to assign more time slots to thetargets. The slot assignment results are also shown in Figure11(d), where the average number of concurrent targets locatedper times-slot are highly dependent on ω . With growing of ω ,the number of concurrently located targets per slot drops from8 to 1.7. In other word, the chorus mode degenerated to theexclusive mode when ω is large, i.e., when the aftershock islong. 4) Accuracy vs. ranging noises: Ranging noises are in-evitable in ultrasound based locating systems, therefore noiseresistance ability of chorus locating was also evaluated. Tosimulate the effect of ranging noise, positive offset is randomlyadded to every distance measurement. Offset is distributedfrom 0 to l o uniformly. The CDFs of locating errors withdifferent l o ( cm ) is presented in Fig. 11(e), with l o being cm , cm and cm respectively. The corresponding -error is cm , cm and cm . Although there are no explicate anti-noise modules, it is shown that chorus locating can work underthe impacts of the ranging noises. B. Testbed experiment We also conduct hardware experiments by using Cricketnodes. 4 nodes were tuned as receivers, which were deployedin an umbrella-type topology. Three nodes were programmedas targets, which were controlled by a sync-node. Morespecially, every target sends a NBU pulse once it hears thesynchronizing signal from the sync-node. The time slot wasset to ms . We modified the firmware of cricket, so that x(m) y ( m ) Real trackEstiamted track (a) Real and estimated trace r a t i o (b) CDF of locating CD F ω =33cml o =165cml o =330cm (c) CDF vs. ω a v e r age nu m be r o f l o c a t ed t a r ge t (d) Efficiency vs. ω CD F l o =1cml o =5cml o =10cm (e) CDF vs. NoiseFig. 11. Performance evaluation obtained by simulation each receiver reports all detectable range measurements to aPC via rs232 cable. Chorus locating algorithm was run at thePC end to calculate the locations for the multiple targets. Thesetting of the test-bed is shown in Fig.12. (a) Receivers (b) TargetsFig. 12. Setting of test-bed Fig.13(a) shows the locating accuracy when a target A wasattached to a toy train, which ran along a trail at m/s , whiletwo concurrent targets b and c were placed on the ground. Thelocations of these concurrent targets were tracked by the fourreceivers. The obtained trajectories of the target on the trainare presented in figure 13(a). Since it is difficult to obtainthe ground-truth of mobile target. CDF of static targets ispresented in Fig. 13(b). It is shown that more than ofthe locating errors is less than cm .Therefore these simulation and experiment results verifiedthe efficiency of locating multiple targets in chorus mode andthe effectiveness of the proposed algorithms. They show thatsatisfactory accuracy can generally be obtained by locating inchorus mode. y ( m ) Mobiel TargetStatic Obj (a) Trace of two target CD F (b) Locating CDF of static targetFig. 13. Performance evaluation obtained by testbed experiment VIII. C ONCLUSION We have investigated to locate multiple narrowband ultra-sound targets in chorus mode, which is to allow the targets broadcast ultrasound concurrently to improve position updat-ing rate, while disambiguating their locations by algorithmsat the receiver end. We investigated the geometric conditionsamong the targets for confidently separating the NBU wavesat the receivers, and the geometrical conditions for obtain-ing at least three distances for each concurrent target. Todeal with the anonymous distance measurements, we presentconsistent position generation and probabilistic particle filteralgorithms to label potential sources for anonymous distancesand to disambiguate the trajectories of the multiple concur-rent targets. To avoid conflicts of the close by targets andfor reliable initialization, we have also developed a locationbased concurrent transmission scheduling algorithm. Furtherwork includes more flexible wavefront detection technique toimprove threshold based detection which is to further shortenthe aftershock and to make the detection be more robust toechoes and noises. R EFERENCES[1] M. Alloulah and M. Hazas. An efficient cdma core for indoor acousticposition sensing. In Indoor Positioning and Indoor Navigation (IPIN),2010 International Conference on , pages 1–5, 2010.[2] A. V. Fishkin. Disk Graphs: A Short Survey. pages 1–5, Jan. 2004.[3] M. Hazas and A. Hopper. Broadband ultrasonic location systems forimproved indoor positioning. IEEE Transactions on Mobile Computing ,5(5):536–547, 2006.[4] Z. Junhui and W. Yongcai. Pospush: A highly accurate location-basedinformation delivery system. UBICOMM ’09, pages 52–58, 2009.[5] H. Liu, H. Darabi, P. Banerjee, and J. Liu. Survey of wireless indoorpositioning techniques and systems. Systems, Man, and Cybernetics,IEEE Transactions on , 37(6):1067 –1080, nov. 2007.[6] N. B. Priyantha, A. Chakraborty, and H. Balakrishnan. The Cricketlocation-support system. In MobiCom ’00: Proceedings of the 6th annualinternational conference on Mobile computing and networking . ACMRequest Permissions, Aug. 2000.[7] H. Schweinzer and M. Syafrudin. Losnus: An ultrasonic system enablinghigh accuracy and secure tdoa locating of numerous devices. In IPIN2010 , pages 1 –8, 2010.[8] Y. Wang, J. Zhao, and T. Fukushima. Lock: A highly accurate, easy-to-use location-based access control system. In LoCA , volume 5561 of Lecture Notes in Computer Science , pages 254–270. Springer, 2009.[9] A. Ward, A. Jones, and A. Hopper. A new location technique for theactive office. Personal Communications, IEEE , 4(5):42–47, 1997.[10] J. Zhao and Y. Wang. Autonomous ultrasonic indoor tracking system.In ISPA ’08 , pages 532 –539, 2008. IX. A PENDIX Parameters in (2) can be expanded as: θ = arccos d a,b r (12) and S e = (cid:90) y β (cid:32) (cid:112) r − y − ωv u (cid:115) y d a,b − ω v u (cid:33) dy (13)where y β = b h c h (cid:113) r − b h − a h r (14)refers to the y coordination of intersection point of hyperbolaand circle. a h = v u ω , b h = d a,b , c hh Parameters in (2) can be expanded as: θ = arccos d a,b r (12) and S e = (cid:90) y β (cid:32) (cid:112) r − y − ωv u (cid:115) y d a,b − ω v u (cid:33) dy (13)where y β = b h c h (cid:113) r − b h − a h r (14)refers to the y coordination of intersection point of hyperbolaand circle. a h = v u ω , b h = d a,b , c hh = (cid:113) a hh Parameters in (2) can be expanded as: θ = arccos d a,b r (12) and S e = (cid:90) y β (cid:32) (cid:112) r − y − ωv u (cid:115) y d a,b − ω v u (cid:33) dy (13)where y β = b h c h (cid:113) r − b h − a h r (14)refers to the y coordination of intersection point of hyperbolaand circle. a h = v u ω , b h = d a,b , c hh = (cid:113) a hh + b hh