Dynamical matched filters for transient detection and classification

We have recently generalized a global model fitting procedure to a temporally local adaptive method which can model the evolution of nonstationary systems. Here we present applications of these temporally localized estimates of system dynamics to detection and classification of short duration (`transient') signals in the presence of noise. The method involves generating a library of dynamic models of signals of interest. These dynamic templates are used to generate temporally evolving estimates of system dynamic coefficients, invariants, and goodness of fit to a vector system reconstructed from incoming data using some appropriate method. These estimated values form a time- varying vector space in which signal classification (of which detection is a special case) can be performed. The classification method is based on measuring short term variations in the geometry of the reconstructed state space by their impact on the distributions of derived quantities such as system parameters, degree of predictability, and invariants. The method provides for the generation of performance measures such as probability of detection vs. probability of false alarm (pD/pFA) curves, constant false alarm rates, etc. We provide results for several model systems in varying amounts of noise, including detection of transient dynamics at input signal to noise ratios as low as -10 dB (nearly 320% noise).

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