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We present a novel Rao-Blackwellized multiple particle filtering method for inference of correlated latent states observed via nonlinear functions. We adopt a state-space framework and model the dynamic correlated states using a mixing matrix, embedded in white Gaussian noise. The critical challenges in practice are the lack of knowledge about the mixing parameters and the possibly large dimensionality...
In this paper we consider a set of time-series that are coupled by latent fractional Gaussian processes. Specifically, we address time-series that combine idiosyncratic short-term and shared long-term features. The long-memory is modeled by fractional Gaussian processes, whereas the short-memory properties are captured by linear models of past data. The observations are nonlinear functions of the...
In the past decades, Sequential Monte Carlo (SMC) sampling has proven to be a method of choice in many applications where the dynamics of the studied system are described by nonlinear equations and/or non-Gaussian noises. In this paper, we study the application of SMC sampling to nonlinear state-space models where the state is a fractional Gaussian process. These processes are characterized by long-memory...
Particle filtering has been widely accepted as an important methodology for processing data represented by state-space models characterized by nonlinearities and/or non-Gaussianities. It is also well documented that particle filtering deteriorates quickly in performance when the dimension of the tracked state becomes large. This limits its application in many science/engineering problems. Previously...
In Gaussian particle filtering the distributions of interest are approximated by Gaussians or mixtures of Gaussians. In this paper, we present an approach for using Gaussian particle filtering in high dimensional systems. The approach is based on breaking the high-dimensional systems into smaller-dimensional systems (subsystems) and applying Gaussian particle filtering in each of the subsystems. The...
This paper addresses the problem of indoor tracking of tagged objects with Ultra High Frequency (UHF) Radio Frequency Identification (RFID) systems. A new and more realistic observation model of the system is proposed, where the probability of detecting a tag by a reader is described by a Beta distribution. We model the probability of detection as a function of both the distance and the angle between...
In this paper we model and simulate a biological system describing the evolution of cancer stem cells into tumors. Starting from some basic hypotheses about the behavior of these cells, we develop a model that mimics the evolution of a system of cancer stem cells and show how random-set-theory naturally leads to a generation algorithm. Computer simulations demonstrate the potential of our approach...
In signal processing, it is typical to develop or use a method based on a given model. In practice, however, we almost never know the actual model and we hope that the assumed model is in the neighborhood of the true one. If deviations exist, the method may be more or less sensitive to them. Therefore, it is important to know more about this sensitivity, or in other words, how robust the method is...
In the past decade and a half, particle filtering (PF), has gained considerable popularity in dealing with nonlinear and/or non-Gaussian target tracking problems. However, in problems of high dimensionality, i.e., when many targets are present in the field, a very large number of particles is required for satisfactory performance of the methodology. In this paper we improve our previously proposed...
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