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Fast sampling is desirable to describe signal transmission through wide-bandwidth systems. The delta-operator provides an ideal discrete-time modeling description for such fast-sampled systems. However, the estimation of delta-domain model parameters is usually biased by directly applying the delta-transformations to a sampled signal corrupted by additive measurement noise. This problem is solved here by expectation-maximization, where the delta-transformations of the true signal are estimated and then used to obtain the model parameters. The method is demonstrated on a numerical example to improve on the accuracy of using a shift operator approach when the sample rate is fast. [ABSTRACT FROM AUTHOR]

The maximum likelihood estimation of a dynamic spatiotemporal model is introduced, centred around the inclusion of a prior arbitrary spatiotemporal neighborhood description. The neighborhood description defines a specific parameterization of the state transition matrix, chosen on the basis of prior knowledge about the system. The model used is inspired by the spatiotemporal ARMA (STARMA) model, but the representation used is based on the standard state-space model. The inclusion of the neighborhood into an expectation-maximization based joint state and parameter estimation algorithm allows for accurate characterization of the spatiotemporal model. The process of including the neighborhood, and the effect it has on the maximum likelihood parameter estimate is described and demonstrated in this paper. [ABSTRACT FROM AUTHOR]

An adaptive receiver based on hybrid system theory is developed for a multiuser multiple-input multiple-output (MIMO) fading code-division multiple-access (CDMA) system. The basic idea is to treat the transmitted symbols and channel gains as unknown states (discrete and continuous) within a hybrid systems framework. The Bayesian-inference-based state estimation is derived using multiple model theory resulting in an optimal joint sequence estimator, which is shown to be intractable in its computational complexity. A suboptimal receiver (IMM-SIC) is then derived based on the well-known Interacting Multiple Model (IMM) algorithm and successive interference cancellation (SIC) scheme. This paper shows the specific approximations made to the probability densities of the optimal receiver in deriving the IMM-SIC receiver with complexity linear in number of users. This receiver design is well suited for online recursive processing of space-time coded CDMA system, where the decoding stage is incorporated within the multiple model framework. [ABSTRACT FROM AUTHOR]

Spatiotemporal models are ubiquitous in science and engineering, yet estimation in these models from discrete observations remains computationally challenging. We propose a practical novel approach to inference in spatiotemporal processes, both from continuous and from discrete (point-process) observations. The method is based on a finite-dimensional reduction of the spatiotemporal model, followed by a mean field variational approximate inference approach. To cater for the point-process case, a variational-Laplace approach is proposed which yields tractable computations of approximate variational posteriors. Results show that variational Bayes is a viable and practical alternative to statistical methods such as expectation maximization or Markov chain Monte Carlo. [ABSTRACT FROM PUBLISHER]

A state space model of the stochastic spatio-temporal Integro-Difference Equation (IDE) is derived. Based on multidimensional sampling theory, the dimensions of the state space and parameter space of the model are identified from the spatial band- width of the system and the support of the redistribution kernel of the IDE. When both the bandwidth and the kernel support are unknown, a method to propose a number of state space and parameter space dimensions is presented. These chosen dimensions result in a number of candidate model structures. Bayesian model selection, making use of Bayes factor, the data augmentation algorithm and importance sampling, is then used to identify the model best suited to represent the data in a maximum a posteriori sense. [ABSTRACT FROM AUTHOR]

A continuous-in-space, discrete-in-time dynamic spatio-temporal model known as the Integro-Difference Equation (IDE) model is presented in the context of data-driven modeling. A novel decomposition of the IDE is derived, leading to state-space representation that does not couple the number of states with the number of observation locations or the number of parameters. Based on this state-space model, an expectation-maximization (EM) algorithm is developed in order to jointly estimate the IDE model's spatial field and spatial mixing kernel. The resulting modeling framework is demonstrated on a set of examples. [ABSTRACT FROM AUTHOR]