Determining Time of Arrival
We developed five algorithms for finding the time of arrival of a signal from an experiment . The start of the simulation signal is clear, but the start of the signal in the experimental data is not. Therefore, registering the simulation with the experimental signal for comparison is hard. We developed methods that, combined, agreed with expert opinion 95% of the time.
Chris Orum - Kolomogorov-Smirnov goodness-of-fit
Time of arrival based on a Kolomogorov-Smirnov goodness-of-fit hypothesis test.
Tom Asaki - Time of Arrival via Onset of Non-Noise Signal Frequencies
The goal of this algorithm is to detect the time of arrival of a signal of interest in a 1D noisy back- ground time series. The basic concept is to monitor non-noise frequency components using a windowed FFT scheme. The time of arrival of the signal should correspond to the time of arrival of non-noise frequencies. One potential benefit of working in the frequency space is that the signal to noise ratio can be greater. A second benefit is that one can monitor any subset of frequencies that are considered relevant. Potential difficulties include the need for significant pre-signal data, the presence of non-noise features in the pre-signal, and the use of a user-determined sensitivity parameter.
The routine is based on the assumption that the time series data behaves like Gaussian noise for some period of time, until the arrival of a signal whose peak amplitude is greater than the amplitude of the background noise. It attempts to give an answer to the question of when the time series ceases to behave like Gaussian noise.
Rick Chartrand - Time of Arrival via Total-Variation Regularized Differentiat
The time of arrival is when the signal ceases to be essentially flat. Noise keeps the signal from being flat, but noise is fluctuation of a smaller scale than that of the signal proper. The method for identifying the time of arrival is to find where the derivative is essentially zero. The problem with doing this in a straightforward way is that noise in the signal will be magnified by numerical differentiation. Denoising either the result or the initial signal (or both) does not give satisfactory results. What does work is to regularize the differentiation process itself. We use total- variation regularization to find a function that is both regular and consistent with the original data. Once this is found, the time of arrival can be identified by thresholding.
Brendt Wohlbert - Time of Arrival by Determining the Detection Threshold
The algorithm attempts to identify an initial region of stationary noise, and uses the maximum value within that region to construct a detection threshold. code
Code for the above methods.