In this paper, we consider the problem of estimating the state of a dynamical system from distributed noisy measurements. Each agent constructs a local estimate based on its own measurements and estimates from its neighbors. Estimation is performed via a two stage strategy, the first being a Kalman-like measurement update which does not require communication, and the second being an estimate fusion using a consensus matrix. In particular we study the interaction between the consensus matrix, the number of messages exchanged per sampling time, and the Kalman gain. We prove that optimizing the consensus matrix for fastest convergence and using the centralized optimal gain is not necessarily the optimal strategy if the number of exchanged messages per sampling time is small. Moreover, we showed that although the joint optimization of the consensus matrix and the Kalman gain is in general a non-convex problem, it is possible to compute them under some important scenarios. We also provide some numerical examples to clarify some of the analytical results and compare them with alternative estimation strategies.

ÐWe describe an algorithm for reconstructing three-dimensional structure and motion causally, in real time from monocular sequences of images. We prove that the algorithm is minimal and stable, in the sense that the estimation error remains bounded with probability one throughout a sequence of arbitrary length. We discuss a scheme for handling occlusions (point features appearing and disappearing) and drift in the scale factor. These issues are crucial for the algorithm to operate in real time on real scenes. We describe in detail the implementation of the algorithm, which runs on a personal computer and has been made available to the community. We report the performance of our implementation on a few representative long sequences of real and synthetic images. The algorithm, which has been tested extensively over the course of the past few years, exhibits honest performance when the scene contains at least 20-40 points with high contrast, when the relative motion is ªslowº compared to the sampling frequency of the frame grabber (QHHz), and the lens aperture is ªlarge enoughº (typically more than QH o of visual field).

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Modeling and identification for high dimensional (i.e. signals with many components) data sets poses severe challenges to off-the-shelf techniques for system identification. This is particularly so when relatively small data sets, as compared to the number signal components, have to be used. It is often the case that each component of the measured signal can be described in terms of few other measured variables and these dependence can be encoded in a graphical way via so called "Dynamic Bayesian Networks". Finding the interconnection structure as well as the dynamic models can be posed as a system identification problem which involves variables selection. While this variable selection could be performed via standard selection techniques, computational complexity may however be a critical issue, being combinatorial in the number of inputs and outputs. Parametric estimation techniques which result in sparse models have nowadays become very popular and include, among others, the well known Lasso, LAR and their "grouped" versions Group Lasso and Group LAR. In this paper we introduce two new nonparametric techniques which borrow ideas from a recently introduced Kernel estimator called "stable-spline" as well as from sparsity inducing priors which use 1 -type penalties. Numerical experiments regarding estimation of large scale sparse (ARMAX) models show that this technique provides a definite advantage over a group LAR algorithm and state-of-the-art parametric identification techniques based on prediction error minimization.

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