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Dynamic models are, in a broad sense, probabilistic models that describe a set of observable measurements conditionally on a set of latent or hidden state-space variables whose time and/or space dynamics are driven by a set of time-invariant parameters. This inherently hierarchical description renders dynamic models to the status of one of the most popular statistical structures in many areas of applied science, including neuroscience, marketing, oceanography, financial markets, target-tracking, signal process, climatology and text analysis, to name just a few. The Kalman filter is one of the most popular algorithms for the sequential update of hidden/latent states in dynamic systems. Numerical integration, in fact, is only realistically feasible for very low dimensional settings. Time series of counts are often encountered in ecological and environmental problems. It is well known that the Poisson distribution assumes …