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METHODOLOGY PUBLISHED FORENSIC ACOUSTICS

FA-2026-001: Muzzle Blast Source Localization

TDOA Multilateration Analysis — Charlie Kirk Shooting, Utah Valley University

September 10, 2025 | Analysis completed February 2026

EXECUTIVE SUMMARY

Forensic acoustic analysis of four cell phone recordings captured during the shooting of Charlie Kirk at UVU's Fountain Courtyard. Using Time Difference of Arrival (TDOA) multilateration on muzzle blast onset times, the analysis localizes the shot origin within the audience area in front of the speaker tent, with a 95% confidence ellipse of 2.42 × 1.01 meters.

▸ Muzzle blast source located within the audience area in front of the speaker tent (95% confidence ellipse: 2.42 × 1.01m)
▸ Supersonic projectile confirmed — the crack arrives ahead of the muzzle blast at all 4 receivers
▸ Synchronization accuracy: ±0.021ms (±21μs) — negligible position error contribution
▸ Solution stable under jackknife leave-one-out (max shift 2.4m when R4 dropped)
▸ PA correction uncertainty bounded to <0.7 meter across 5 independent models

WHY THIS ISN'T CRACK-TO-BANG ANALYSIS

This analysis localizes the muzzle blast using TDOA multilateration — the arrival-time differences of the same blast across four synchronized receivers, intersected geometrically. It needs only receiver positions, synchronized onsets, and the speed of sound; it does not assume the bullet's velocity or trajectory.

Crack-to-bang (crack-thump) ranging is a different method: it measures the gap between the supersonic crack and the muzzle blast at a single sensor and must assume the round's velocity and trajectory to turn that gap into a distance. Here the crack is filtered out and used only to confirm the projectile was supersonic — it never enters the localization.

→ What crack-to-bang analysis can and can't do (ranging vs localization)
4
Synced Recordings
349.7
m/s Speed of Sound
±21μs
Sync Accuracy
2.4×1.0m
95% CI Ellipse
10K
Monte Carlo Runs

Local coordinate system: receivers (green), speakers (blue), TDOA solution (diamond), 95% confidence ellipse (dashed).

ANALYSIS SECTIONS

01

Methodology

10-phase forensic pipeline from evidence intake through TDOA multilateration to uncertainty quantification.
02

Evidence

4 cell phone recordings, environmental parameters, receiver positions, and chain of custody documentation.
03

Analysis

Synchronization, spectral decomposition, onset picking, and PA correction walkthrough.
04

Results

TDOA solution with interactive visualizations, confidence bounds, and stability analysis.
05

Technical Appendix

Complete equations, parameters, data tables, and Monte Carlo methodology reference.

This analysis presents only the physical acoustics. It locates where a sound originated. It does not address who, why, or any other investigative questions beyond the acoustic evidence.