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In this article we propose a new Rao-Blackwellized particle filtering based algorithm for tracking an unknown number of targets. The algorithm is based on formulating probabilistic stochastic process models for target states, data associations, and birth and death processes. The tracking of these stochastic processes is implemented using sequential Monte(More)
— This article considers the application of the un-scented Kalman filter (UKF) to continuous-time filtering problems , where both the state and measurement processes are mod-eled as stochastic differential equations. The mean and covariance differential equations which result in the continuous-time limit of the UKF are derived. The continuous-discrete(More)
— This article considers the application of the un-scented transform to optimal smoothing of non-linear state space models. In this article, a new Rauch-Tung-Striebel type form of the fixed-interval unscented Kalman smoother is derived. The new smoother differs from the previously proposed two-filter formulation based unscented Kalman smoother in the sense(More)
— This article considers the application of variational Bayesian methods to joint recursive estimation of the dynamic state and the time-varying measurement noise parameters in linear state space models. The proposed adaptive Kalman filtering method is based on forming a separable variational approximation to the joint posterior distribution of states and(More)
—In this paper, we revisit batch state estimation through the lens of Gaussian process (GP) regression. We consider continuous-discrete estimation problems wherein a trajectory is viewed as a one-dimensional GP, with time as the independent variable. Our continuous-time prior can be defined by any linear, time-varying stochastic differential equation driven(More)
In this article we introduce the DRIFTER algorithm, which is a new model based Bayesian method for retrospective elimination of physiological noise from functional magnetic resonance imaging (fMRI) data. In the method, we first estimate the frequency trajectories of the physiological signals with the interacting multiple models (IMM) filter algorithm. The(More)
Gaussian process-based machine learning is a powerful Bayesian paradigm for nonparametric nonlinear regression and classification. In this article, we discuss connections of Gaussian process regression with Kalman filtering and present methods for converting spatiotemporal Gaussian process regression problems into infinite-dimensional state-space models.(More)
– We propose a new Rao-Blackwellized sequential Monte Carlo method for tracking multiple targets in presence of clutter and false alarm measurements. The advantage of the new approach is that Rao-Blackwellization allows the estimation algorithm to be partitioned into single target tracking and data association sub-problems, where the single target tracking(More)
This article considers the application of the unscented transformation to approximate fixed-interval optimal smoothing of continuous-time non-linear stochastic systems. The proposed methodology can be applied to systems, where the dynamics can be modeled with non-linear stochastic differential equations and the noise corrupted measurements are obtained(More)