BAYESIAN INFERENCE OF ROOM GEOMETRY FROM ROOM IMPULSE RESPONSES UNDER ACOUSTIC AND SPATIAL UNCERTAINTIES

Abstract

Reconstructing the geometric structure of a room from indoor acoustic signals (such as room impulse response, RIR) has significant application value in fields such as spatial audio, active sound field control, and virtual reality. However, in real physical measurement environments, inevitable acoustic environmental noise and spatial uncertainty in the placement of equipment (such as minor perturbations in the positions of microphones and sound sources) make deterministic inference methods based on traditional time-domain waveform matching face serious model mismatch and multi-peak posterior distributions. To address this challenge, this thesis proposes a Bayesian robust inference framework for room geometry under acoustic and spatial uncertainties.
Firstly, this thesis thoroughly analyzes the vulnerability of the traditional waveform residual likelihood function when dealing with geometric perturbations, and proposes a likelihood construction method based on early reflection energy binning (Energy-Bin). This method effectively absorbs the time offset error at the sub-sampling level and reduces the model’s sensitivity to high-frequency phase mismatch, thereby significantly enhancing the robustness of the inference. Secondly, in response to the problem of excessively high computational cost of forward acoustic rendering in Markov Chain Monte Carlo (MCMC) posterior sampling, this thesis explores a highly optimized fast mirror source method (Fast ISM), which achieves an order of magnitude acceleration in computation while maintaining the accuracy of macroscopic acoustic energy characteristics.
Furthermore, in order to overcome the complex local modes and multi-peak posterior structures in the joint posterior distribution of multiple microphones, this thesis introduces the multi-start simulated annealing Markov Chain Monte Carlo (SAMH) joint sampling strategy, effectively avoiding the local deadlock of the sampling chain. Finally, this thesis extends the inference model from the simple 3D estimation of room size to the 6D joint Bayesian inference of room geometry and sound source position, and conducts a systematic robustness test for the random perturbation of misspecified sensor positions.
Simulations and experimental results show that, even under complex physical conditions with low signal-to-noise ratios and centimeter-level device-position perturbations, the Bayesian inference framework proposed in this thesis can recover room geometric parameters with improved stability, and can further estimate the source position under the tested 6D settings. It demonstrates significant advantages in system robustness and computational efficiency

Popular Abstract

When we enter a room in daily life, we can easily notice differences in sound. For instance, speaking in an empty classroom will produce a slight echo; in a corridor, the sound will be prolonged; and in a small room filled with furniture, the sound will seem shorter and more muffled. These sound variations are actually closely related to the room itself. The length, width, and height of the room, the position of the walls, and even where the sound source and the microphone are placed, all affect the way sound propagates.

When sound travels in a room, it does not simply travel directly from the sound source to the microphone. It will also encounter walls, floors, and ceilings, and then reflect back. What the microphone finally receives is the result of the superposition of direct sound and many reflected sounds. In acoustics, this response is called room impulse response, or RIR for short. In simple terms, if we give the room a very short sound, the room will "answer" with a series of echoes.

This "answer" actually contains information about the room. Because sound propagation takes time, the time when the reflected sound returns depends on how far it has traveled. If the room gets larger, some reflected sounds will travel a longer path; if the position of the walls changes slightly, the time when the reflected sound reaches the microphone will also change. Therefore, as long as we can understand these echoes, it is possible to infer the length, width, and height of the room.

This paper studies this issue: Can we estimate the geometric dimensions of a room only from the sound recorded by a microphone? That is to say, whether a computer can estimate the size of a room by "listening to the echoes".

However, this is not simple. In real measurements, there will always be errors. The positions of the microphone and the sound source may not be completely accurate, and there may also be background noise in the surrounding environment. More importantly, the original waveform of RIR is very sensitive. If there is a small change in the room size, the arrival time of some early reflected sounds will slightly shift. This change may seem very small to us, but if the computer compares the two waveforms point by point, it may consider them to be very different, thus obtaining unstable results.

Therefore, the paper does not rely solely on the original waveform, but adopts a more stable method: observing the energy distribution of early reflections. Specifically, the early part of the sound is divided into many small time periods, and then the amount of sound energy in each period is calculated. This method is called Energy-Bin, which can be understood as "energy binning". Although it discards some very fine waveform details, it can retain more stable and useful reflection patterns for the room size.

The paper also uses Bayesian inference. In simple terms, the Bayesian method does not just believe one measurement, but combines the existing reasonable judgments with new sound observations. For example, we may know that the room is approximately five meters long, four meters wide, and three meters high, but the specific values are uncertain. The Bayesian method will judge which dimensions are more likely based on the recorded sound.

In experiments, when directly comparing the original RIR waveforms, some results seem close to the actual size, but the sampling process is not stable, and it may just be "getting the right answer by chance". Using Energy-Bin, the algorithm is more likely to find stable results. The paper also incorporates the information of multiple microphones, which is equivalent to listening to the room from different positions, making the judgment more reliable. In simple terms, this paper studies how to "hear" the size of a room without using a ruler, but by using sound.

• author: Wang, Xiaohan and Gu, Junjie
• supervisor: Andreas Jakobsson; David Sundström
• organization: Mathematical Statistics
• course: MASM02 20261
• year: 2026
• type: H2 - Master's Degree (Two Years)
• subject: Mathematics and Statistics
• keywords: Room geometry inference, Bayesian inference, Room impulse response, Energy binning, Markov Chain Monte Carlo, Fast Mirror Source Method
• publication/series: Master's Theses in Mathematical Sciences
• report number: LUNFMS-3140-2026
• ISSN: 1404-6342
• other publication id: 2026:E26
• language: English
• id: 9227685
• date added to LUP: 2026-05-27 09:53:25
• date last changed: 2026-05-27 09:53:25