Multivariate acoustic detection of small explosions using Fisher's combined probability test

Abstract

A methodology for the combined acoustic detection and discrimination of explosions, which uses three discriminants, is developed for the purpose of identifying weak explosion signals embedded in complex background noise. By utilizing physical models for simple explosions that are formulated as statistical hypothesis tests, the detection/discrimination approach does not require a model for the background noise, which can be highly complex and variable in practice. Fisher's Combined Probability Test is used to combine the p-values from all multivariate discriminants. This framework is applied to acoustic data from a 400 g explosion conducted at Los Alamos National Laboratory.

Development of a matched filter detector for acoustic signals at local distances from small explosions

“…In this paper, the coupling of a matched filter with a p-value representing the conditional probability of detection under the single hypothesis of signal plus additive noise is advocated. Further, when combined with other detectors under the same hypothesis, detection performance can be improved by combining with other p-values from different detectors constructed under the same hypothesis that each measure different (orthogonal) aspects of the observed signal: For example, using Fisher's Combined Probability test as suggested by Arrowsmith and Taylor (2013).…”

“…The simple Gaussian monopulse can easily fit filtered Gaussian noise (especially if a short window is used), so the window length specified should be long enough to hopefully contain a signal (e.g., 1 h). The key to the matched filter detector is that it operates in tandem with other detectors all constructed under the same hypothesis as described in Arrowsmith and Taylor (2013). As will be shown below, the test statistic used to compute the p-value is dependent on the estimated signal energy.…”

“…As mentioned above, we do not address the choice of a threshold since our purpose is simply to develop the p-value formulation for a matched filter approach. In practice, we would combine these p-values with other techniques using the method discussed by Arrowsmith and Taylor (2013).…”

“…In our formulation, we summarize the hypothesis test with a p-value and not a decision rule involving a threshold (c 0 ) derived from the specification of a false alarm rate (a). We take this approach to enable combined multi-phenomenology detections (e.g., Arrowsmith and Taylor, 2013). In order for the likelihood ratio in Eq.…”

“…Rather, it is the development of an N-wave detector p-value formulation that can naturally be combined with other detectors (each measuring different signal aspects) all under the same single hypothesis. The p-values from each detector can then be effectively combined into a multivariate detector (e.g., Arrowsmith and Taylor, 2013).…”