TOA and TDOA Based Asynchronous Self-Localization: Three Stage Framework for Simultaneous Localization of Microphones and Audio Sources

Cao, Faxian

Abstract

Self-localization, a pivotal aspect explored in this research, holds significant relevance across various applications, including human-robot interaction and surveillance for aging individuals. Traditional localization methods relying on GPS signals or visual information face limitations in poorly illuminated environments or areas with obstructed GPS signals. In these situations, audio signals emerge as a promising alternative. When localizing both devices/microphones and ambient objects using audio signals from sources, typically two types of information are used: time of arrival (TOA) and time difference of arrival (TDOA). TOA measures the distance between microphones and sources, while TDOA measures the range difference between pairs of microphones relative to the audio source. However, there are three challenges in localizing both microphones and sources with TOA and TDOA measurements, which limit the efficiency and accuracy of self-localization, regardless of whether the microphones and sources are synchronous or asynchronous.
In scenarios where both microphones and sources are asynchronous, both TOA and TDOA contain unknown timing information (UTIm). The unknown start time for the microphones and the emission time for the sources are embedded in the TOA measurements. Additionally, there is an unknown time offset between pairs of microphones in TDOA measurements. Under this scenario, there are at least two challenges for self-localization. Firstly, TOA requires estimation from both microphone and source signals, whereas TDOA requires estimation from microphone signals only. Even if the UTIm in TOA and TDOA is accurately estimated, asynchronous TOA provides range measurements between microphones and sources, while asynchronous TDOA only provides range differences. Range measurements contain richer and more efficient information than range difference measurements for self-localization, as range differences can be derived directly from range measurements. Therefore, when audio source signals are absent, it is crucial to find a way to use microphone signals alone for efficient self-localization before estimating UTIm. Secondly, UTIm in both TOA and TDOA pose significant challenges for self-localization. Traditional methods for estimating UTIm (synchronizing microphones and sources) in TOA/TDOA measurements often get stuck in local minima due to the randomness of UTIm, leading to inaccuracies in range measurements and substantial localization errors. Therefore, it’s paramount to design a method to improve the accuracy of range measurements for self-localization.
The third challenge arises in scenarios where both microphones and sources are synchronized, and range measurements between them are available. Traditional methods require a minimum number of microphones and sources to achieve effective self-localization. Typically, at least six, five, or four microphones are required along with four, five, or six sources, respectively. This requirement is based on the principle that the number of equations (known range measurements) should be greater than or equal to the number of unknowns (location variables for microphones and sources). When the number of microphones and sources is below this minimum threshold, traditional state-of-the-art methods fail. Unfortunately, this issue has not been adequately explored, significantly limiting the efficiency of self-localization. This poses the third challenge to find a way to reduce the number of microphones and sources required for self-localization.
To address above three challenges, this PhD thesis proposes a three stage framework (TSF) designed to simultaneously localize both microphones and audio sources, improving both accuracy and efficiency for self-localization. The initial stage focuses on developing a mapping function that can transform between TOA and TDOA formulas, demonstrating their potential equivalence for the first time. This breakthrough reveals that microphone signals alone are adequate for self-localization, eliminating the need for source signal waveforms and providing richer information for localization once UTIm is estimated in asynchronous TOA/TDOA measurements. This advancement could revolutionize self-localization techniques, greatly expanding their use in challenging environments. Backed by solid mathematical proof and compelling experimental results, this research makes a significant contribution to the current discourse on audio self-localization. In the second stage, an innovative combined low-rank approximation (CLRA) technique aimed at estimating UTIm is introduced. This involves developing three novel low-rank property (LRP) variants, each of which is backed by mathematical proof, allowing UTIm to utilize a broader range of low-rank structural information. By leveraging this augmented low-rank information from both the LRP and the proposed variants, I formulate four linear constraints on UTIm. Employing the CLRA algorithm, global optimal solutions for UTIm based on these constraints are derived. Experimental results showcase proposed method’s superior performance over current state-of-the-art approaches, as demonstrated by higher recovery numbers and lower estimation errors for UTIm. In the third stage, the proposed TSF relaxes the minimal configurations required for self-localization by presenting a novel numerical method. Based on the laws of cosine, the localization problem is transformed to estimate four unknown pairs of distances pertaining to one pair of microphones and three pairs of sources. Using the triangle inequality, both the lower and upper boundaries of these four unknown pairs of distances can be obtained, enabling the determination of the numerical method by searching for candidates within the corresponding boundaries. This approach shows that self-localization in 3D space is achievable with only four microphones and four sources, relaxing the minimal configurations required by traditional methods, improving the efficiency for self-localization. Both theory and simulation results validate the feasibility of this new numerical method.
In summary, the impact of the proposed TSF in this PhD thesis extends to providing a comprehensive understanding of self-localization, enhancing accuracy and efficiency in challenging environments. The proposed methodologies contribute to the advancement of signal and audio processing, paving the way for more intelligent and flexible solutions in real-world scenarios.

Citation

Cao, F. (2025). TOA and TDOA Based Asynchronous Self-Localization: Three Stage Framework for Simultaneous Localization of Microphones and Audio Sources. (Thesis). University of Hull. https://hull-repository.worktribe.com/output/5086296

• Thesis Type: Thesis
• Deposit Date: Mar 20, 2025
• Publicly Available Date: Apr 14, 2025
• Keywords: Computer science
• Public URL: https://hull-repository.worktribe.com/output/5086296
• Additional Information: School of Computer Science; University of Hull
• Award Date: Jan 16, 2025