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Abstract:
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Particle filters (PF) used to track dynamical systems from noisy time series observations are known to quickly loose ensemble spread in high-dimensional systems (Snyder at al 2008, Bengtsson et al 2008). For systems of even modest dimension, this lack of variability in the updated (i.e. posterior) ensemble leads to a collapse onto a single particle and consequent filter failure. The construction of sequential importance samplers for high-dimensional systems is therefore inherently challenging. Based on ideas similar to that of the Auxiliary PF (Pitt, 1999), this talk details a sequential importance sampler that does not collapse in high-dimensional model based on a cellular automata scheme to model traffic flow (Helbing, 1998). To understand why the presented high-dimensional PF does not collapse, we explore the effective dimension of the generated and compare the empirical results to theoretical bound set forth in Snyder et al (2015).
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