| Summary: | This thesis addresses the problem of impact localization on rigid surfaces using vibration signals. This allows conversion of daily objects, such as tabletops and glass panels, into human-computer touch interfaces using low-cost piezoelectric sensors. Determination of the impact location is achieved via location-template matching (LTM) and/or time-difference-
of-arrival (TDOA)-based localization.
LTM algorithms utilize location-dependent features of the signal to perform localization. Extraction of such features, however, requires high signal-to-noise ratio (SNR) to avoid any noise-induced alteration to the features, which may affect the matching results. In this interdisciplinary research, we propose an LTM algorithm that is robust to band-limited
noises. We first analyze the mechanical model for vibrations due to impacts on plate surface and show that band-limited components (BLCs) of a signal can be employed as its location-dependent features. A measure for signal matching is then proposed based on the cross correlation of BLCs. The measure exploits velocity dispersion among the BLCs to discriminate the library data that matches the test signal from those that do not match. Experiment results show that under noisy environments the proposed BLC-LTM outperform existing LTM techniques when the environment noise is band-limited.
TDOA-based localization on rigid surfaces suffers from dispersion and multipath. To mitigate the effect of these phenomena, the time of arrival (TOA) is first estimated for a component of each sensor-received signal within a narrow frequency band. The TDOA is then subsequently computed as the difference in TOAs. TOA estimation is highly challenging when the sensor is far from the impact location causing the signal to arrive at the sensor gradually. In this thesis, we propose three algorithms to address the problem of gradual transition. In our proposed TOA-HAD algorithm, the short-time-Fourier-transform coefficients of the signal is first converted into Hermitian angle distributions (HADs). Although the resultant HADs vary with time, significant variation is exhibited only within the transition period. We then determine this period by proposing a statistical measure to quantify the time variation of HADs. This facilitates TOA estimation even when the noise-to-signal transition is gradual. Inaddition, the proposed framework allows simultaneous TOA estimation across all the sensors to minimize TDOA estimation errors. Experiment results show that the proposed algorithm outperforms existing techniques for source localization on solid surfaces of different materials.
For longer propagation distances such as that in large surfaces, the noise-to-signal transition occurs gradually over a relatively longer duration. Since the number of spikes introduced by noise increases with the duration of the transition period, estimation of TOA from such spurious transition is therefore prone to error, resulting in poor TDOA estimates. In our proposed STFT-Logistic algorithm, we employ a smooth parametrized function to model the gradual noise-to-signal energy transition at each sensor. Specifically, the noise-to-signal transition is modeled by a four-parameter logistic function. The TDOA is then estimated as the difference in time shifts of the functions fitted to the sensor data. While the TOAs estimated from existing techniques are severely affected by spurious spikes, the proposed fitting procedure involves received signal over the noise-to-signal transition period hence mitigating such detrimental effects. In our final algorithm, to avoid the uncertainty due to gradual noise-to-signal transition, its starting point is estimated as the arrival time. This is achieved by characterizing the arrival of each sensor-received signal by the arrival times of its frequency components. To estimate the arrival time of each frequency component, we first model each component as a harmonic random process. A kurtosis sequence, which exhibits a
sharp rising edge when the signal starts to deviate from the background noise, can then be obtained for each component. Experiment results show that the proposed algorithms significantly outperforms existing techniques which adopt the abrupt change model for time-of-arrival estimation on large surfaces.
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