Whistle: Synchronization-Free TDOA for Localization - ResearchGate

st aat bt cFigure 3: An illustration of transmissions of two signalsbFigure 2: A star-like topology of receiversDefinition 1: S is an acoustic source locating at afixed position in a limited 3D space and can generatean omni-directional sound signal that lasts for a specifiedperiod. For convenience, we also use S to denotethe emitted signal.In Whistle, We assume that the signal S canbe mathematically described in advance. Technically,Whistle does not rely on any specific form of acousticsignals and can be accordingly used for general purposes.In the view of hardware, Whistle involves an acousticsource and several receivers. Receivers are deployedat known locations, serving as the basic infrastructureof a TDOA system. Each receiver has a basic setof hardware, including a speaker, a microphone, andwireless connectors, such as Bluetooth or WiFi. Unlessexplicitly pointing out, the words node and receiverare exchangeable henceforth. Fig. 2 shows a star-likenetwork topology of Whistle. Receivers, in recordingmode, capture sound signals and transmit the timerelatedinformation to an access point. The AP relaysthat information to a laptop for further processing.Using a laptop in Whistle is optional. If we use anode to replace the AP and the laptop, the networkmodel described above is changed into a purely starlikemodel.3. The Design of Whistle3.1. Measuring TDOA by TD2SAs TDOA is important, we describe how to accuratelymeasure it in Whistle. Fig. 4 shows a typical timesequence of two Whistle nodes A and B. Let t A1 andt B1 denote the arriving time of S at the microphonesof A and B, respectively. The TDOA measurement isexactly t B1 − t A1 , if nodes are synchronous. But inWhistle, nodes maintain clocks independently. Evenusing a perfect synchronization scheme, however, westill cannot obtain the exact value of TDOA. Due tothe latency of software and hardware, node A detectsS at t A2 instead of t A1 . The same latency occurs atnode B. Many experimental studies demonstrate thatsuch latencies are inevitable and unpredictable [23].Hence, t A2 − t A1 and t B2 − t B1 are not necessarilythe same (basically different from each other), whichprevents using t B2 −t A2 as the estimate of t B1 −t A1 .To eliminate the uncertainties and errors mentionedabove, we introduce a system sound S ′ to avoid timesynchronization.Definition 2: After receiving the source sound signalS, one of the receivers will emit another soundsignal S ′ , which is called the system sound signal. Thenode emitting S ′ is called base node.With the help of the system sound S ′ , we developa method to measure t B1 −t A1 . As shown in Fig. 4,after a specified time interval τ, node A, as the basenode, emits S ′ from its speaker at time t A3 accordingto its own clock.Theorem 1: For all non-base nodes, they alwaysdetect the system sound signal S ′ after the sourcesound signal S.Proof: LetS be the sound source,athe base node,and b a non-base node. Assume that t a and t b are thepropagation time of S from s to a and from s to b,respectively. In addition, the propagation time of S ′from a to b is denoted by t c . Finally, we use t ab as thetime span lasting from emitting S at s and receivingS ′ at b.The locations of s, a and b construct a triangle inFig. 3, or lie in a straight line. In both cases, wehave t b ≤ t a + t c due to triangle inequality. Sincethe base node encounters a delay between receivingS and emitting S ′ , we have t ab > t a +t c . Therefore,t ab > t b can be obtained, meaning that any non-basenode b always firstly senses S, then S ′ .As shown in Fig. 4, S ′ is emitted from A’s speakerat t A3 , and arrives at the microphones of A and B att A4 and t B3 , respectively. A and B’s CPUs detect S ′at t A5 and t B4 , respectively. According to Theorem 1,t B3 is always later than t B1 . We define the TD2Svalue of one node as the elapsed time between thearrival ofS and the arrival ofS ′ at the node. Obviously,