Simo Särkkä

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Filtering and smoothing methods are used to produce an accurate estimate of the state of a time-varying system based on multiple observational inputs (data). Interest in these methods has exploded in recent years, with numerous applications emerging in fields such as navigation, aerospace engineering, telecommunications, and medicine. This compact, informal(More)
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 unscented Kalman filter (UKF) to continuous-time filtering problems, where both the state and measurement processes are modeled 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 unscented(More)
This article considers the application of the unscented 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 twofilter formulation based unscented Kalman smoother in the sense that(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)
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)
Nonlinear Kalman filter and Rauch-Tung-Striebel smoother type recursive estimators for nonlinear discrete-time state space models with multivariate Student's t-distributed measurement noise are presented. The methods approximate the posterior state at each time step using the variational Bayes method. The nonlinearities in the dynamic and measurement models(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)
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)