144:6·Wan et al. 3.2 Signal Design Low-end commercial acoustic devices have severe clock drifting problems so that the reference time between devices could change by more than 50us per second [341.Such clock drifting leads to errors in ToF measurements that are far larger than the ToF changes due to temperature difference.Traditional acoustic sensing applications require a calibration process for each session,i.e.,whenever the sound play/recording restarts,to reduce the clock drift [33,35,36].In stead of asking user to calibrate the devices for each session,we adopt an OFDM full-duplex signal design to remove the transmitting and receiving delay introduced by low-end commercial devices.When we have two devices,we ask both devices to transmit and receive sound signals at the same time to perform a ToF measurement session.Devices can turn-off between sessions to save energy.Our experiments show that our scheme can output the correct ToF within 0.5 seconds after both devices start sound transmission.Therefore,our system can work with low-duty cycles in stable environments,e.g,turn on for only 0.5 seconds in every minute. We choose the Zadoff Chu(ZC)sequence [37]as our baseband signal,which has an ideal cross-correlation property [38].The baseband ZC sequence with a length of Nzc is: zc[n]exp πun(n+1+2q Nze (2) where 0s n Nzc,g is a constant integer and j is the imaginary unit,i.e.,j2=-1.Nze is the length of sequence, which determines the bandwidth in the final modulated signal.For example,if we set Nze to 653 and the frame length to 4800 sample points,the bandwidth of the modulated signal would be 653/4800x 48=6.53 kHz under 48 kHz sampling rate.The parameter u determines the correlation property and it should be coprime to Nc,i.e., gcd(Nzc,u)=1. We use Orthogonal Frequency-Division Multiple Access(OFDMA)scheme to allow both devices to transmit at the same time and in the same frequency band.Our OFDMA scheme allocates odd subcarriers for one device and even subcarriers for the other to avoid collision.We also choose two different values of u when generating baseband ZC sequence to further reduce the interference between the two devices.Specifically,the frequency domain baseband signals for the two devices are: ZCodaln]=fft_shift FFT exp(-j πodan(n+1+2q) xg[n]. (3) ZCeoen[n]=fft_shift(FFT exp-j- Hevenn(n+1+2q） Nze ×gn+1], (4) where fft_shift()is to switch the order of the sequence's first half and the second half in frequency domain to place the zero-frequency point at the center of the sequence for the following modulation process.We set gIn]=(1-(-1)"+)to pick out odd/even subcarriers.Note that the odd or even subcarriers are relative to the central subcarrier (or the subcarrier corresponding to zero-frequency in baseband)instead of the start of the sequence.Fig.2(a)shows a sample of ZCodd[n]baseband signal with a 2 kHz bandwidth in the frequency domain.As the rectangle window in the frequency domain will cause severe side-lobe(from sinc function)in final time domain Channel Impulse Response(CIR),we add a Hanning window to smooth it (shown in Fig.2(b)). 3.3 Signal Modulation With the baseband signal generated,we move the sequence to carrier frequency fe with OFDM modulation before transmitting.To transform the modulated signal to a real signal,we set the negative frequency of the signal to be the conjugate counterpart of the positive frequency parts.This modulation process is shown in Algorithm 1 and we use ZCbaseband to denote both ZCodd and ZCeoen who share the same modulation process.Since the two Proc.ACM Interact.Mob.Wearable Ubiquitous Technol.,Vol.6,No.3,Article 144.Publication date:September 2022
144:6 • Wan et al. 3.2 Signal Design Low-end commercial acoustic devices have severe clock drifting problems so that the reference time between devices could change by more than 50𝜇𝑠 per second [34]. Such clock drifting leads to errors in ToF measurements that are far larger than the ToF changes due to temperature difference. Traditional acoustic sensing applications require a calibration process for each session, i.e., whenever the sound play/recording restarts, to reduce the clock drift [33, 35, 36]. In stead of asking user to calibrate the devices for each session, we adopt an OFDM full-duplex signal design to remove the transmitting and receiving delay introduced by low-end commercial devices. When we have two devices, we ask both devices to transmit and receive sound signals at the same time to perform a ToF measurement session. Devices can turn-off between sessions to save energy. Our experiments show that our scheme can output the correct ToF within 0.5 seconds after both devices start sound transmission. Therefore, our system can work with low-duty cycles in stable environments, e.g., turn on for only 0.5 seconds in every minute. We choose the Zadoff Chu (ZC) sequence [37] as our baseband signal, which has an ideal cross-correlation property [38]. The baseband ZC sequence with a length of 𝑁𝑧𝑐 is: 𝑧𝑐[𝑛] = 𝑒𝑥𝑝 −𝑗 𝜋𝑢𝑛(𝑛 + 1 + 2𝑞) 𝑁𝑧𝑐 , (2) where 0 ≤ 𝑛 < 𝑁𝑧𝑐 , 𝑞 is a constant integer and 𝑗 is the imaginary unit, i.e., 𝑗 2 = −1. 𝑁𝑧𝑐 is the length of sequence, which determines the bandwidth in the final modulated signal. For example, if we set 𝑁𝑧𝑐 to 653 and the frame length to 4800 sample points, the bandwidth of the modulated signal would be 653/4800 × 48 = 6.53 𝑘𝐻𝑧 under 48 𝑘𝐻𝑧 sampling rate. The parameter 𝑢 determines the correlation property and it should be coprime to 𝑁𝑧𝑐 , i.e., 𝑔𝑐𝑑 (𝑁𝑧𝑐, 𝑢) = 1. We use Orthogonal Frequency-Division Multiple Access (OFDMA) scheme to allow both devices to transmit at the same time and in the same frequency band. Our OFDMA scheme allocates odd subcarriers for one device and even subcarriers for the other to avoid collision. We also choose two different values of 𝑢 when generating baseband ZC sequence to further reduce the interference between the two devices. Specifically, the frequency domain baseband signals for the two devices are: 𝑍𝐶𝑜𝑑𝑑 [𝑛] = 𝑓 𝑓 𝑡_𝑠ℎ𝑖 𝑓 𝑡 𝐹 𝐹𝑇 𝑒𝑥𝑝 −𝑗 𝜋𝑢𝑜𝑑𝑑𝑛(𝑛 + 1 + 2𝑞) 𝑁𝑧𝑐 × 𝑔[𝑛], (3) 𝑍𝐶𝑒𝑣𝑒𝑛 [𝑛] = 𝑓 𝑓 𝑡_𝑠ℎ𝑖 𝑓 𝑡 𝐹 𝐹𝑇 𝑒𝑥𝑝 −𝑗 𝜋𝑢𝑒𝑣𝑒𝑛𝑛(𝑛 + 1 + 2𝑞) 𝑁𝑧𝑐 × 𝑔[𝑛 + 1], (4) where 𝑓 𝑓 𝑡_𝑠ℎ𝑖 𝑓 𝑡(·) is to switch the order of the sequence’s first half and the second half in frequency domain to place the zero-frequency point at the center of the sequence for the following modulation process. We set 𝑔[𝑛] = 1 2 (1 − (−1) 𝑛+1 ) to pick out odd/even subcarriers. Note that the odd or even subcarriers are relative to the central subcarrier (or the subcarrier corresponding to zero-frequency in baseband) instead of the start of the sequence. Fig. 2(a) shows a sample of 𝑍𝐶𝑜𝑑𝑑 [𝑛] baseband signal with a 2 𝑘𝐻𝑧 bandwidth in the frequency domain. As the rectangle window in the frequency domain will cause severe side-lobe (from 𝑠𝑖𝑛𝑐 function) in final time domain Channel Impulse Response (CIR), we add a Hanning window to smooth it (shown in Fig. 2(b)). 3.3 Signal Modulation With the baseband signal generated, we move the sequence to carrier frequency 𝑓𝑐 with OFDM modulation before transmitting. To transform the modulated signal to a real signal, we set the negative frequency of the signal to be the conjugate counterpart of the positive frequency parts. This modulation process is shown in Algorithm 1 and we use 𝑍𝐶𝑏𝑎𝑠𝑒𝑏𝑎𝑛𝑑 to denote both 𝑍𝐶𝑜𝑑𝑑 and 𝑍𝐶𝑒𝑣𝑒𝑛 who share the same modulation process. Since the two Proc. ACM Interact. Mob. Wearable Ubiquitous Technol., Vol. 6, No. 3, Article 144. Publication date: September 2022
VECTOR:Velocity Based Temperature-field Monitoring with Distributed Acoustic Devices.144:7 signals occupy separate subcarriers in the frequency domain,they can be transmitted simultaneously.Fig.2(b) shows the modulated signal in the frequency domain. Algorithm 1:Transmitting signal generation Result:The modulated sequence zcr[n]with a length of L and a carrier frequency of fe. 1 Generate frequency domain baseband signal ZCbaseband from Eq.(3)and (4)with a length of Nzc. 2 Multiply ZCbaseband with a Hanning window with length Nic. 3 Generate a all zero sequence ZC[n]with a length of L. 42元[号--：'+Ng-]←ZCbasebandn]. 5ZCL-1:L/2+1]=ZC[1:L/2-1] 6 Perform IFFT on ZC to the time domain zcT[n]. 3.4 Signal Demodulation and ToF Acquisition On both receiving ends,the received signal with P paths can be modeled as: (5) where zcR[n]is received signal,Ai is attenuation coefficient for path i,=-2mife is the phase shift caused by the propagation of path i and ti is the ToF of path i.To get the absolute phase shift for a given path,we first perform FFT on the received signal and extract the ZC baseband sequence directly from the received signal. Then we perform cross-correlation with the conjugate transform of original baseband ZCodd[n]and ZCeven [n] to get the baseband CIR.We use zero-padding on the baseband CIR to expand the length and increase the range resolution brought by sample index,e.g.if we pad the baseband to the length 4x the original frame length,the range difference between each sampling point is 1/48000/45.2 us. To acquire the accurate ToF changes for each path,we combine the index of the cross-correlation peak and the phase of the peak.In the ideal case and without zero-padding.the coarse-grained peak position is expressed as the integer part of rifs,round(rifs),and the fine-grained phase of the peak is expressed as mod(-2mife,2),which is between 0 and 2.We can calculate the absolute phase oi=-2mrife,which considers whole turns of 2 in phase,by combining these two measurements.However,there are inevitable unknown delays for the transmitting and receiving process in low-end commercial devices.Most existing works require user to put devices on a known position to calibrate and calculate the relative distance [33,35].To allow self-calibration without user intervention,we choose to cancel the unknown delays by obtaining reciprocal measurements from both devices. For example,when device A receives signal from device B and the phase shift is oBA =-2(TBA TAR rBT)fc, where TBA is the signal propagation delay that we wish to measure,TAR is the receiving delay for device A and rBT is the transmitting delay for device B.Similarly,we have AA=-2(TAA TAR+rar)fe when device A receive its own signal.Device B can also perform two measurements of AB =-2m(TAB TBR rAr)fe and BB =-2n(TBB TBR TBT)fe.Therefore,we can use AA+BB -AB -OBA =-2(TAA TBB TAB-TBA)fe to cancel the unknown transmitting and receiving delays [39].We can further assume the distances between the speaker and microphone of same device are fixed so that TAA and TBB are known in advance.Therefore,we can measure the ToF by: TAB TBA= TAA+TBB++BB-9AB-9BA (6) 2πfe Proc.ACM Interact.Mob.Wearable Ubiquitous Technol.,Vol.6,No.3,Article 144.Publication date:September 2022
VECTOR: Velocity Based Temperature-field Monitoring with Distributed Acoustic Devices • 144:7 signals occupy separate subcarriers in the frequency domain, they can be transmitted simultaneously. Fig. 2(b) shows the modulated signal in the frequency domain. Algorithm 1: Transmitting signal generation Result: The modulated sequence 𝑧𝑐𝑇 [𝑛] with a length of 𝐿 and a carrier frequency of 𝑓𝑐 . 1 Generate frequency domain baseband signal 𝑍𝐶𝑏𝑎𝑠𝑒𝑏𝑎𝑛𝑑 from Eq. (3) and (4) with a length of 𝑁𝑧𝑐 . 2 Multiply 𝑍𝐶𝑏𝑎𝑠𝑒𝑏𝑎𝑛𝑑 with a Hanning window with length 𝑁𝑧𝑐 . 3 Generate a all zero sequence 𝑍𝐶c [𝑛] with a length of 𝐿. 4 𝑍𝐶c [ 𝑓𝑐𝐿 𝑓𝑠 − (𝑁𝑧𝑐−1) 2 : 𝑓𝑐𝐿 𝑓𝑠 + (𝑁𝑧𝑐−1) 2 ] ⇐ 𝑍𝐶𝑏𝑎𝑠𝑒𝑏𝑎𝑛𝑑 [𝑛]. 5 𝑍𝐶c [𝐿 − 1 : 𝐿/2 + 1] ⇐ 𝑍𝐶c∗ [1 : 𝐿/2 − 1]. 6 Perform IFFT on 𝑍𝐶c to the time domain 𝑧𝑐𝑇 [𝑛]. 3.4 Signal Demodulation and ToF Acquisition On both receiving ends, the received signal with 𝑃 paths can be modeled as: 𝑧𝑐𝑅 [𝑛] = Õ 𝑃 𝑖=1 𝐴𝑖𝑒 𝑗𝜙𝑖𝑧𝑐𝑇 𝑛 − 𝜏𝑖 𝑓𝑠 , (5) where 𝑧𝑐𝑅 [𝑛] is received signal, 𝐴𝑖 is attenuation coefficient for path 𝑖, 𝜙𝑖 = −2𝜋𝜏𝑖𝑓𝑐 is the phase shift caused by the propagation of path 𝑖 and 𝜏𝑖 is the ToF of path 𝑖. To get the absolute phase shift for a given path, we first perform FFT on the received signal and extract the ZC baseband sequence directly from the received signal. Then we perform cross-correlation with the conjugate transform of original baseband 𝑍𝐶𝑜𝑑𝑑 [𝑛] and 𝑍𝐶𝑒𝑣𝑒𝑛 [𝑛] to get the baseband CIR. We use zero-padding on the baseband CIR to expand the length and increase the range resolution brought by sample index, e.g.if we pad the baseband to the length 4× the original frame length, the range difference between each sampling point is 1/48000/4 ≈ 5.2 𝜇𝑠. To acquire the accurate ToF changes for each path, we combine the index of the cross-correlation peak and the phase of the peak. In the ideal case and without zero-padding, the coarse-grained peak position is expressed as the integer part of 𝜏𝑖𝑓𝑠 , 𝑟𝑜𝑢𝑛𝑑 (𝜏𝑖𝑓𝑠), and the fine-grained phase of the peak is expressed as 𝑚𝑜𝑑 (−2𝜋𝜏𝑖𝑓𝑐, 2𝜋), which is between 0 and 2𝜋. We can calculate the absolute phase 𝜙𝑖 = −2𝜋𝜏𝑖𝑓𝑐 , which considers whole turns of 2𝜋 in phase, by combining these two measurements. However, there are inevitable unknown delays for the transmitting and receiving process in low-end commercial devices. Most existing works require user to put devices on a known position to calibrate and calculate the relative distance [33, 35]. To allow self-calibration without user intervention, we choose to cancel the unknown delays by obtaining reciprocal measurements from both devices. For example, when device A receives signal from device B and the phase shift is 𝜙𝐵𝐴 = −2𝜋 (𝜏𝐵𝐴 + 𝜏𝐴𝑅 + 𝜏𝐵𝑇 )𝑓𝑐 , where 𝜏𝐵𝐴 is the signal propagation delay that we wish to measure, 𝜏𝐴𝑅 is the receiving delay for device A and 𝜏𝐵𝑇 is the transmitting delay for device B. Similarly, we have 𝜙𝐴𝐴 = −2𝜋 (𝜏𝐴𝐴 + 𝜏𝐴𝑅 + 𝜏𝐴𝑇 )𝑓𝑐 when device A receive its own signal. Device B can also perform two measurements of 𝜙𝐴𝐵 = −2𝜋 (𝜏𝐴𝐵 + 𝜏𝐵𝑅 + 𝜏𝐴𝑇 )𝑓𝑐 and 𝜙𝐵𝐵 = −2𝜋 (𝜏𝐵𝐵 + 𝜏𝐵𝑅 + 𝜏𝐵𝑇 )𝑓𝑐 . Therefore, we can use 𝜙𝐴𝐴 + 𝜙𝐵𝐵 − 𝜙𝐴𝐵 − 𝜙𝐵𝐴 = −2𝜋 (𝜏𝐴𝐴 + 𝜏𝐵𝐵 − 𝜏𝐴𝐵 − 𝜏𝐵𝐴)𝑓𝑐 to cancel the unknown transmitting and receiving delays [39]. We can further assume the distances between the speaker and microphone of same device are fixed so that 𝜏𝐴𝐴 and 𝜏𝐵𝐵 are known in advance. Therefore, we can measure the ToF by: 𝜏𝐴𝐵 + 𝜏𝐵𝐴 = 𝜏𝐴𝐴 + 𝜏𝐵𝐵 + 𝜙𝐴𝐴 + 𝜙𝐵𝐵 − 𝜙𝐴𝐵 − 𝜙𝐵𝐴 2𝜋 𝑓𝑐 . (6) Proc. ACM Interact. Mob. Wearable Ubiquitous Technol., Vol. 6, No. 3, Article 144. Publication date: September 2022
144:8·Wan et al. If the environment is homogeneous in temperature,using the sum of rAB and TBA increases the temperature sensitivity of the system,because the same temperature changes will cause larger ToF changes in longer distance If the environment is not homogeneous in temperature,paths passing along different temperature regions can help us to reconstruct the temperature distribution discussed in Section 5. Since we only use half of the baseband frequency bins for each transmitter,the final CIR will have two repeated peaks,as shown in Fig.2(c).For the device using the even subcarriers,the DC component is not zero and the two peaks are completely the same in both phase and amplitude so that we can use either part for position and phase measurement.For the device using odd subcarriers,the DC component is zero,so the phase for the first peak and the second peak has a phase difference of To find the right peak,the device using odd subcarriers first transmits several OFDM frames with full bandwidth to estimate the right delay which,according to our observation,only incurs hundreds of millisecond delay before returning the right temperature result.And the detailed demodulation process is shown in Algorithm 2 and the essential steps of whole signal process is shown in Fig.2. Algorithm 2:Received signal demodulation Result:The interpolated time-domain cir[n]. 1 Perform FFT on zcR[n]to get ZCR[n]. 2 CIRoasebend(n ZCNx ZCbasebanaln]. 3 Generate an all-zero sequence CIR[n]with length Nx L. 4CIR[Y-Ns二：y+Ng]=CIRpaseband[m. s CIR[n]fft_shift (CIR[n]) 6 Perform IFFT on CIR[n]to the time domain cir[n] 3.5 Engineering Details and Discussions For implementation in real acoustic devices,there are some details and discussions need mentioning: Streaming mode.We use the streaming control mode for audio playback and recording.The data is periodically put into/get from the playing/recording buffers,which means the recording and playback delays stay the same after the stream starts.Switching from full sequence to odd sequence will not change these delays during one measurement session.For each temperature measurement session,we restart the playback/recording,which introduces unknown delays.However,such delays can be canceled using Eq.(6) so that our ToF results are consistent across different sessions. Influence of multipath.Due to the limited bandwidth of commercial acoustic devices,the correlation peaks corresponding to paths with close ToF(less than 30 cm in distance)will merge together to form a new peak.In this condition,we cannot distinguish neither peaks'index and phase.Wider bandwidth and longer frame length can reach a higher path resolution and further mitigate this impact.There are also solutions to separate the merged paths with deep learning methods,e.g,using Neural Network to get the right peak location and distance measurement [40,41].However,both attempts still cannot separate all the echoes.As we utilize multiple paths to perform measurement,we choose to ignore paths that are interfered by nearby multipath and only use those clean paths to reduce the complexity of our system. Clock drifts.Different devices with separate clocks will experience clock drifts between each others.The offset will be added in the unknown transmitting and receiving delays which can be canceled along with the delays.Our experiment in Section 6.2 shows that our system can stably measure ToF with drifts less than 0.5 us for 8 hours. Proc.ACM Interact.Mob.Wearable Ubiquitous Technol.,Vol.6,No.3,Article 144.Publication date:September 2022
144:8 • Wan et al. If the environment is homogeneous in temperature, using the sum of 𝜏𝐴𝐵 and 𝜏𝐵𝐴 increases the temperature sensitivity of the system, because the same temperature changes will cause larger ToF changes in longer distance. If the environment is not homogeneous in temperature, paths passing along different temperature regions can help us to reconstruct the temperature distribution discussed in Section 5. Since we only use half of the baseband frequency bins for each transmitter, the final CIR will have two repeated peaks, as shown in Fig. 2(c). For the device using the even subcarriers, the DC component is not zero and the two peaks are completely the same in both phase and amplitude so that we can use either part for position and phase measurement. For the device using odd subcarriers, the DC component is zero, so the phase for the first peak and the second peak has a phase difference of 𝜋. To find the right peak, the device using odd subcarriers first transmits several OFDM frames with full bandwidth to estimate the right delay which, according to our observation, only incurs hundreds of millisecond delay before returning the right temperature result. And the detailed demodulation process is shown in Algorithm 2 and the essential steps of whole signal process is shown in Fig. 2. Algorithm 2: Received signal demodulation Result: The interpolated time-domain 𝑐𝑖𝑟[𝑛]. 1 Perform FFT on 𝑧𝑐𝑅 [𝑛] to get 𝑍𝐶𝑅 [𝑛]. 2 𝐶𝐼𝑅𝑏𝑎𝑠𝑒𝑏𝑎𝑛𝑑 [𝑛] ⇐ 𝑍𝐶𝑅 [ 𝑓𝑐𝐿 𝑓𝑠 − (𝑁𝑧𝑐−1) 2 : 𝑓𝑐𝐿 𝑓𝑠 + (𝑁𝑧𝑐−1) 2 ] × 𝑍𝐶∗ 𝑏𝑎𝑠𝑒𝑏𝑎𝑛𝑑 [𝑛]. 3 Generate an all-zero sequence 𝐶𝐼𝑅[𝑛] with length 𝑁 × 𝐿. 4 𝐶𝐼𝑅[ 𝑁 𝐿 2 − 𝑁𝑧𝑐−1 2 : 𝑁 𝐿 2 + 𝑁𝑧𝑐−1 2 ] ⇐ 𝐶𝐼𝑅𝑏𝑎𝑠𝑒𝑏𝑎𝑛𝑑 [𝑛]. 5 𝐶𝐼𝑅[𝑛] ⇐ 𝑓 𝑓 𝑡_𝑠ℎ𝑖 𝑓 𝑡 (𝐶𝐼𝑅[𝑛]) 6 Perform IFFT on 𝐶𝐼𝑅[𝑛] to the time domain 𝑐𝑖𝑟[𝑛]. 3.5 Engineering Details and Discussions For implementation in real acoustic devices, there are some details and discussions need mentioning: • Streaming mode. We use the streaming control mode for audio playback and recording. The data is periodically put into/get from the playing/recording buffers, which means the recording and playback delays stay the same after the stream starts. Switching from full sequence to odd sequence will not change these delays during one measurement session. For each temperature measurement session, we restart the playback/recording, which introduces unknown delays. However, such delays can be canceled using Eq. (6) so that our ToF results are consistent across different sessions. • Influence of multipath. Due to the limited bandwidth of commercial acoustic devices, the correlation peaks corresponding to paths with close ToF (less than 30 𝑐𝑚 in distance) will merge together to form a new peak. In this condition, we cannot distinguish neither peaks’ index and phase. Wider bandwidth and longer frame length can reach a higher path resolution and further mitigate this impact. There are also solutions to separate the merged paths with deep learning methods, e.g., using Neural Network to get the right peak location and distance measurement [40, 41]. However, both attempts still cannot separate all the echoes. As we utilize multiple paths to perform measurement, we choose to ignore paths that are interfered by nearby multipath and only use those clean paths to reduce the complexity of our system. • Clock drifts. Different devices with separate clocks will experience clock drifts between each others. The offset will be added in the unknown transmitting and receiving delays which can be canceled along with the delays. Our experiment in Section 6.2 shows that our system can stably measure ToF with drifts less than 0.5 𝜇𝑠 for 8 hours. Proc. ACM Interact. Mob. Wearable Ubiquitous Technol., Vol. 6, No. 3, Article 144. Publication date: September 2022
VECTOR:Velocity Based Temperature-field Monitoring with Distributed Acoustic Devices.144:9 Influence of noise and audibility.Normal noise from indoor environments occupies different frequency band with our system,so the noise will barely affect our system's performance.And our signal is working on 17~21 kHz which is insensitive for most of people and will not affect the daily activities. Blocked LOS path.The LOS path could be blocked in certain extreme cases.We can use paths other than LOS path if the other paths are stable enough,e.g.reflection from a nearby wall.The length of the non-LOS path can be estimated with one extra input of temperature and it's an one-time calibration,see details in Section 5. 3.6 Sound-based Temperature Sensing We use a basic two-device setup to illustrate the fundamentals of sound-based temperature sensing.In this scenario,we separate two devices by a fixed known distance and measure the ToF,ie.,TAB+rBa in Eq.(6),to derive the temperature.The number of full wave cycles can be determined by the coarse-grained cross-correlation and the decimal part of the cycles can be determined by the fine-grained phase measurement.The wavelength Ae can be derived by dividing the known distance by the number of wave cycles.We can then calculate the speed of sound by c =feAc and use Eq.(1)to get the temperature.Note that the distance between devices can either be measured in advance,or determined after deployment by calibrating the ToF under a known temperature. Sound-based temperature sensing is more sensitive than traditional temperature sensors such as thermistors or thermocouples.Acoustic sensing directly measures the temperature of the air,while traditional sensors measure the temperature of the probe that needs to be heated or cooled by surrounding air when the air temperature changes.To evaluate the key features of sound-based temperature sensing,we perform an experiment in a room with controlled temperature changes.Fig.3 shows the measurements of VECTOR and a traditional Bosch BME280 temperature sensor [42]within a period of two hours.We turned on the air conditioner to heat the room at t =500 seconds,turned it off and opened the window at 2760 seconds,and closed the window at 4270 seconds.Note that we carefully avoided direct air flows towards the sound path in these experiments so that these temperature fluctuations are not caused by air flows.We have three key observations on the result shown in Fig.3. For stable environments,the difference between the two temperature measurements is smaller than 0.5C.For example,before we start the air conditioner and after we close the window,the sound-based temperature measurement is stable and very close to the readings of BME280 sensor.Therefore,our system can provide accurate temperature readings that are comparable to commercial sensors. We observe that VECTOR responses to temperature changes much faster than traditional sensors.This can be seen from the differences in the two temperature curves when we turn on/off the heating.For example, when we stopped heating,the measurement of VECTOR drops by 0.5C within 5 seconds,while BME280 takes 30 seconds to detect the same temperature change.The output of sound-based sensing agrees with human perceptions,since human beings could notice temperature change caused by such events within seconds.The low latency feedback provided by VECTOR could potentially improve the performance of control algorithms in HVAC systems.We further study this phenomenon with detailed experiments in Section 6.6. When the temperature is unstable,VECTOR observes larger short-term variance in the measurements.For example,when the air conditioner is on or the window is opening,the sound-based measurements have higher fluctuation than the BME280 sensor's readings as shown in Fig.3.This phenomenon is consistent with our daily experience.When the air conditioner is on,human can perceive the fluctuation of temperatures due to the cool/warm air from the air-conditioner,which is quite different to natural stable environments However,traditional sensors only perceive smooth temperature changes as shown by Fig.3.We can leverage Proc.ACM Interact.Mob.Wearable Ubiquitous Technol.,Vol.6,No.3,Article 144.Publication date:September 2022
VECTOR: Velocity Based Temperature-field Monitoring with Distributed Acoustic Devices • 144:9 • Influence of noise and audibility. Normal noise from indoor environments occupies different frequency band with our system, so the noise will barely affect our system’s performance. And our signal is working on 17 ∼ 21 𝑘𝐻𝑧 which is insensitive for most of people and will not affect the daily activities. • Blocked LOS path. The LOS path could be blocked in certain extreme cases. We can use paths other than LOS path if the other paths are stable enough, e.g.reflection from a nearby wall. The length of the non-LOS path can be estimated with one extra input of temperature and it’s an one-time calibration, see details in Section 5. 3.6 Sound-based Temperature Sensing We use a basic two-device setup to illustrate the fundamentals of sound-based temperature sensing. In this scenario, we separate two devices by a fixed known distance and measure the ToF, i.e., 𝜏𝐴𝐵 + 𝜏𝐵𝐴 in Eq. (6), to derive the temperature. The number of full wave cycles can be determined by the coarse-grained cross-correlation and the decimal part of the cycles can be determined by the fine-grained phase measurement. The wavelength 𝜆𝑐 can be derived by dividing the known distance by the number of wave cycles. We can then calculate the speed of sound by 𝑐 = 𝑓𝑐𝜆𝑐 and use Eq. (1) to get the temperature. Note that the distance between devices can either be measured in advance, or determined after deployment by calibrating the ToF under a known temperature. Sound-based temperature sensing is more sensitive than traditional temperature sensors such as thermistors or thermocouples. Acoustic sensing directly measures the temperature of the air, while traditional sensors measure the temperature of the probe that needs to be heated or cooled by surrounding air when the air temperature changes. To evaluate the key features of sound-based temperature sensing, we perform an experiment in a room with controlled temperature changes. Fig. 3 shows the measurements of VECTOR and a traditional Bosch BME280 temperature sensor [42] within a period of two hours. We turned on the air conditioner to heat the room at 𝑡 = 500 seconds, turned it off and opened the window at 2760 seconds, and closed the window at 4270 seconds. Note that we carefully avoided direct air flows towards the sound path in these experiments so that these temperature fluctuations are not caused by air flows. We have three key observations on the result shown in Fig. 3. • For stable environments, the difference between the two temperature measurements is smaller than 0.5 ◦C. For example, before we start the air conditioner and after we close the window, the sound-based temperature measurement is stable and very close to the readings of BME280 sensor. Therefore, our system can provide accurate temperature readings that are comparable to commercial sensors. • We observe that VECTOR responses to temperature changes much faster than traditional sensors. This can be seen from the differences in the two temperature curves when we turn on/off the heating. For example, when we stopped heating, the measurement of VECTOR drops by 0.5 ◦C within 5 seconds, while BME280 takes 30 seconds to detect the same temperature change. The output of sound-based sensing agrees with human perceptions, since human beings could notice temperature change caused by such events within seconds. The low latency feedback provided by VECTOR could potentially improve the performance of control algorithms in HVAC systems. We further study this phenomenon with detailed experiments in Section 6.6. • When the temperature is unstable, VECTOR observes larger short-term variance in the measurements. For example, when the air conditioner is on or the window is opening, the sound-based measurements have higher fluctuation than the BME280 sensor’s readings as shown in Fig. 3. This phenomenon is consistent with our daily experience. When the air conditioner is on, human can perceive the fluctuation of temperatures due to the cool/warm air from the air-conditioner, which is quite different to natural stable environments. However, traditional sensors only perceive smooth temperature changes as shown by Fig. 3. We can leverage Proc. ACM Interact. Mob. Wearable Ubiquitous Technol., Vol. 6, No. 3, Article 144. Publication date: September 2022
144:10·Wan et al.. -VECTOR Stop Air-con and -BME280 open window 24 -Filtered 22 920 Close window Start Air-con 16 0 1200 2400 3600 4800 6000 Time(s) Fig.3.Preliminary experiment of temperature sensing. this new capability provided by VECTOR to capture human perceived-temperature for better thermal comfort experience,or to identify the heating source as discussed in Section 6.6. In our extensive experiments,we also observe that when traditional temperature sensors are exposed to the radiation heating source closely(30~50cm)or sunlight,the temperature reading will exhibit a large mismatch with the air temperature felt by human.For example,the measured ground temperature could be much higher than air temperature in summer.This might be caused by the different thermal transmission types,e.g.,radiation in air and heat conduction in the solid sensor probe.If we want to get the air temperature in these scenarios,the sound-based temperature sensing is much more reliable than the probe-based temperature sensing. 4 TEMPERATURE DISTRIBUTION RECONSTRUCTION As stated in the previous sections,the estimation of air temperature distribution is quite important in many practical scenarios.However,as far as we know,there are few works to measure the actual air temperature distribution.Based on our preliminary experiments of sound-based temperature sensing,we can extend the single path temperature measurements to temperature distribution estimation,using the fact that we are actually measuring the temperature's harmonic mean along the propagation path.In this section,we first introduce the problem of estimating the air temperature distribution and propose a dRadon transform algorithm to solve this problem. 4.1 Problem Statements We consider the temperature distribution estimation problem in the 2-D scenario.Suppose that there is a target area where each point(x,y)has a temperature of T(x,y),where x and y are Cartesian coordinates.Hence,based on the Eq.(1),the sound speed at the point (x,y)is (x,y)=0+0.606(T(x,-T0), (7) where vo is the sound speed at a reference temperature To,e.g.0C. In our system,we can measure the ToF r along the given path using cross-correlation and signal phases.For a path L that passes through different points in the target area,the ToF along the path is a line integral: dl f 1 1 L= JL0(x,y)JL001+ .06((dl, (8) Proc.ACM Interact.Mob.Wearable Ubiquitous Technol.,Vol.6,No.3,Article 144.Publication date:September 2022
144:10 • Wan et al. 0 1200 2400 3600 4800 6000 Time (s) 16 18 20 22 24 26 Temperature (°C) VECTOR BME280 Filtered Start Air-con Close window Stop Air-con and open window Fig. 3. Preliminary experiment of temperature sensing. this new capability provided by VECTOR to capture human perceived-temperature for better thermal comfort experience, or to identify the heating source as discussed in Section 6.6. In our extensive experiments, we also observe that when traditional temperature sensors are exposed to the radiation heating source closely (30 ∼ 50𝑐𝑚) or sunlight, the temperature reading will exhibit a large mismatch with the air temperature felt by human. For example, the measured ground temperature could be much higher than air temperature in summer. This might be caused by the different thermal transmission types, e.g., radiation in air and heat conduction in the solid sensor probe. If we want to get the air temperature in these scenarios, the sound-based temperature sensing is much more reliable than the probe-based temperature sensing. 4 TEMPERATURE DISTRIBUTION RECONSTRUCTION As stated in the previous sections, the estimation of air temperature distribution is quite important in many practical scenarios. However, as far as we know, there are few works to measure the actual air temperature distribution. Based on our preliminary experiments of sound-based temperature sensing, we can extend the single path temperature measurements to temperature distribution estimation, using the fact that we are actually measuring the temperature’s harmonic mean along the propagation path. In this section, we first introduce the problem of estimating the air temperature distribution and propose a dRadon transform algorithm to solve this problem. 4.1 Problem Statements We consider the temperature distribution estimation problem in the 2-D scenario. Suppose that there is a target area where each point (𝑥, 𝑦) has a temperature of 𝑇 (𝑥, 𝑦), where 𝑥 and 𝑦 are Cartesian coordinates. Hence, based on the Eq. (1), the sound speed at the point (𝑥, 𝑦) is 𝑣(𝑥, 𝑦) = 𝑣0 + 0.606(𝑇 (𝑥, 𝑦) −𝑇0), (7) where 𝑣0 is the sound speed at a reference temperature 𝑇0, e.g., 0◦C. In our system, we can measure the ToF 𝜏 along the given path using cross-correlation and signal phases. For a path 𝐿 that passes through different points in the target area, the ToF along the path is a line integral: 𝜏 𝐿 = ∫ 𝐿 d𝑙 𝑣(𝑥, 𝑦) = ∫ 𝐿 1 𝑣0 1 1 + 0.606(𝑇 (𝑥,𝑦)−𝑇0) 𝑣0 d𝑙, (8) Proc. ACM Interact. Mob. Wearable Ubiquitous Technol., Vol. 6, No. 3, Article 144. Publication date: September 2022