Gabriel Schamberg

Gabriel Schamberg, Demba Ba, Todd P. Coleman

We present a compartmentalized approach to finding the maximum a-posteriori (MAP) estimate of a latent time series that obeys a dynamic stochastic model and is observed through noisy measurements. We specifically consider modern signal processing problems with non-Markov signal dynamics (e.g. group sparsity) and/or non-Gaussian measurement models (e.g. point process observation models used in neuroscience). Through the use of auxiliary variables in the MAP estimation problem, we show that a consensus formulation of the alternating direction method of multipliers (ADMM) enables iteratively computing separate estimates based on the likelihood and prior and subsequently "averaging" them in an appropriate sense using a Kalman smoother. As such, this can be applied to a broad class of problem settings and only requires modular adjustments when interchanging various aspects of the statistical model. Under broad log-concavity assumptions, we show that the separate estimation problems are convex optimization problems and that the iterative algorithm converges to the MAP estimate. As such, this framework can capture non-Markov latent time series models and non-Gaussian measurement models. We provide example applications involving (i) group-sparsity priors, within the context of electrophysiologic specrotemporal estimation, and (ii) non-Gaussian measurement models, within the context of dynamic analyses of learning with neural spiking and behavioral observations.

Blake Cole, Gabriel Schamberg

This paper describes a novel tracking filter, designed primarily for use in collision avoidance systems on autonomous surface vehicles (ASVs). The proposed methodology leverages real-time kinematic information broadcast via the Automatic Information System (AIS) messaging protocol, in order to estimate the position, speed, and heading of nearby cooperative targets. The state of each target is recursively estimated in geodetic coordinates using an unscented Kalman filter (UKF) with kinematic equations derived from the spherical law of cosines. This improves upon previous approaches, many of which employ the extended Kalman filter (EKF), and thus require the specification of a local planar coordinate frame, in order to describe the state kinematics in an easily differentiable form. The proposed geodetic UKF obviates the need for this local plane. This feature is particularly advantageous for long-range ASVs, which must otherwise periodically redefine a new local plane to curtail linearization error. In real-world operations, this recurring redefinition can introduce error and complicate mission planning. It is shown through both simulation and field testing that the proposed geodetic UKF performs as well as, or better than, the traditional plane-Cartesian EKF, both in terms of estimation error and stability.