Audio recordings from crime scenes often involve multiple gunshots shots fired from multiple firearms. To further complicate crime scene audio analysis, there may be multiple recordings from spatially distributed recorders that are not time synchronized and have uncertain locations. In this paper we describe the general Time Difference of Arrival (TDOA) problem with multiple sources and multiple receivers. From these equations, we show that for each source location, the time differences between any two impulsive events are identical for all non-synchronized (uncalibrated) receivers, assuming all locations remain stationary. Assuming the receivers are not collinear, the time differences between events from different sources are not identical at different receivers, and can be used to identify the presence of multiple sources. This timing analysis method is shown to be applicable in some cases where the recordings are noisy, distorted, and have interference.
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