Acoustic Setup for Object Localization

Overview

This project aims to localize 3 foam cylinders located inside a disk. The setup utilizes sound transmitters and receivers placed around the cylinders. The localization relies on the assumption that there is no significant reflection or absorption and the signal goes in a straight line. Because sound moving through the cylinder foam has a different velocity than it does moving in air, measuring these different arrival times allows us to identify the location of the cylinders.

Data

• The provided data includes sound signals recorded at 64 receivers.
• These signals originate from 3 transmitters located at positions 1, 24, and 43.
• Simulated data recorded without the cylinders is also included for calibration.

Methodology

The problem is solved using the following three main steps:

1. Estimate Signal Arrival Time

Arrival times are estimated from the recorded data using two methods:

• Integration Method: Computes the signal's energy (the square of the signal) and defines the arrival time as the moment the cumulative energy reaches a certain threshold, such as 10% of total signal energy.
• AIC Method: Identifies two phases of the signal (before and after arrival) with different variances, finding the phase divider that yields the minimum Akaike Information Criterion (AIC). This algorithm is implemented in aic_picker.m.

2. Forward Problem

An algorithm generates signal arrival time data given the coordinates of the 3 cylinders.

• This step utilizes a modified implementation of algorithms from a ground layers permittivity problem.
• The forward matrix A is computed in the circle_ground_layer_matrix_with_comment.m file.
• Maps based on cylinder coordinates are drawn using the forward_map_of_x.m function.

3. Backward Problem

Gibbs sampling is used to find the most likely coordinates of the 3 cylinders from the recorded data.

• Individual sampling processes are separated into specific scripts: Gibb_sampling_for_x.m, Gibb_sampling_for_alpha.m, Gibb_sampling_for_beta.m, and Gibb_sampling_for_offset.m.

Key Findings & Discussion

• Sampling Stability: Attempting Gibbs sampling on all variables (coordinates, alpha, beta, offset) simultaneously is very unstable and fails to converge.
• Parameter Tuning: Simulated data is used to estimate beta to avoid having to sample for it, which dictates how stretched out the forward signal is in the vertical direction.
• Impact of Alpha: Using a large alpha (e.g., set to 1) is critical to stabilize the process; if alpha is too small, the effect of the cylinders' coordinates mixes with noise. A larger alpha amplifies the signal involving the cylinders, helping to match it with real measured data.
• Results: By setting a large alpha and a beta of 1.40, the shape of the calculated solution fit the real data much better than lower beta values, yielding final coordinates that were quite near to the true solution.

Order to read this report:

1. Read MY_REPORT.html or MY_REPORT.pdf
2. Read Present.mlx
3. Read other *.m files