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The Poisson multi-Bernoulli mixture (PMBM) is an unlabelled multi-target distribution for which the prediction and update are closed. It has a Poisson birth process, and new Bernoulli components are generated on each new measurement as a…
A Riemannian geometric framework for Markov chain Monte Carlo (MCMC) is developed where using the Fisher-Rao metric on the manifold of probability density functions (pdfs), informed proposal densities for Metropolis-Hastings (MH) algorithms…
Automatic lane tracking involves estimating the underlying signal from a sequence of noisy signal observations. Many models and methods have been proposed for lane tracking, and dynamic targets tracking in general. The Kalman Filter is a…
This paper uses multi-object tracking methods known from the radar tracking community to address the problem of pedestrian tracking using 2D bounding box detections. The standard point-object (SPO) model is adopted, and the posterior…
This paper presents a new derivation of the variational Poisson multi-Bernoulli (V-PMB) filter for multi-target estimation proposed in [#Williams15]. The proposed derivation is based on considering an augmented space that includes the set…
Increasing availability of vehicle GPS data has created potentially transformative opportunities for traffic management, route planning and other location-based services. Critical to the utility of the data is their accuracy. Map-matching…
An algorithm for the estimation of multiple targets from partial and corrupted observations is introduced based on the concept of partially-distinguishable multi-target system. It combines the advantages of engineering solutions like MHT…
Partially-observable problems pose a trade-off between reducing costs and gathering information. They can be solved optimally by planning in belief space, but that is often prohibitively expensive. Model-predictive control (MPC) takes the…
This paper presents a mathematical framework for causal nonlinear prediction in settings where observations are generated from an underlying hidden Markov model (HMM). Both the problem formulation and the proposed solution are motivated by…
As robotic systems move from highly structured environments to open worlds, incorporating uncertainty from dynamics learning or state estimation into the control pipeline is essential for robust performance. In this paper we present a…
Markov Decision Processes (MDPs) are a popular class of models suitable for solving control decision problems in probabilistic reactive systems. We consider parametric MDPs (pMDPs) that include parameters in some of the transition…
Switching state-space models (SSSM) are a very popular class of time series models that have found many applications in statistics, econometrics and advanced signal processing. Bayesian inference for these models typically relies on Markov…
We consider the approximation of expectations with respect to the distribution of a latent Markov process given noisy measurements. This is known as the smoothing problem and is often approached with particle and Markov chain Monte Carlo…
This paper proposes a novel particle filter for tracking time-varying states of multiple targets jointly from superpositional data, which depend on the sum of contributions of all targets. Many conventional tracking methods rely on…
This paper presents two trajectory Poisson multi-Bernoulli (TPMB) filters for multi-target tracking: one to estimate the set of alive trajectories at each time step and another to estimate the set of all trajectories, which includes alive…
Bayesian inference in the presence of an intractable likelihood function is computationally challenging. When following a Markov chain Monte Carlo (MCMC) approach to approximate the posterior distribution in this context, one typically…
Nonlinear non-Gaussian state-space models arise in numerous applications in statistics and signal processing. In this context, one of the most successful and popular approximation techniques is the Sequential Monte Carlo (SMC) algorithm,…
Hidden Markov models (HMMs) are flexible time series models in which the distributions of the observations depend on unobserved serially correlated states. The state-dependent distributions in HMMs are usually taken from some class of…
In this paper we consider the filtering of a class of partially observed piecewise deterministic Markov processes (PDMPs). In particular, we assume that an ordinary differential equation (ODE) drives the deterministic element and can only…
A challenging problem in probabilistic programming is to develop inference algorithms that work for arbitrary programs in a universal probabilistic programming language (PPL). We present the nonparametric involutive Markov chain Monte Carlo…