Alessandro Chiuso

Dynamic Textures

Dynamic textures are sequences of images of moving scenes that exhibit certain stationarity properties in time; these include sea-waves, smoke, foliage, whirlwind etc. We present a characterization of dynamic textures that poses the problems of modeling, learning, recognizing and synthesizing dynamic textures on a firm analytical footing. We borrow tools from system identification to capture the “essence” of dynamic textures; we do so by learning (i.e. identifying) models that are optimal in the sense of maximum likelihood or minimum prediction error variance. For the special case of second-order stationary processes, we identify the model sub-optimally in closed-form. Once learned, a model has predictive power and can be used for extrapolating synthetic sequences to infinite length with negligible computational cost. We present experimental evidence that, within our framework, even low-dimensional models can capture very complex visual phenomena.

Distributed Kalman filtering based on consensus strategies

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 on the 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 for scalar systems. 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 show 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 relevant scenarios. We also provide some numerical examples to clarify some of the analytical results and compare them with alternative estimation strategies.

Observability of linear hybrid systems

We analyze the observability of the continuous and discrete states of continuous-time linear hybrid systems. For the class of jump-linear systems, we derive necessary and sufficient conditions that the structural parameters of the model must satisfy in order for filtering and smoothing algorithms to operate correctly. Our conditions are simple rank tests that exploit the geometry of the observability subspaces. For linear hybrid systems, we derive weaker rank conditions that are sufficient to guarantee the uniqueness of the reconstruction of the state trajectory, even when the individual linear systems are unobservable.

Consistency analysis of some closed-loop subspace identification methods

We study statistical consistency of two recently proposed subspace identification algorithms for closed-loop systems. These algorithms may be seen as implementations of an abstract state-space construction procedure described by the authors in previous work on stochastic realization of closed-loop systems. A detailed error analysis is undertaken which shows that both algorithms are biased due to an unavoidable mishandling of initial conditions which occurs in closed-loop identification. Instability of the open loop system may also be a cause of trouble.

Observability and identifiability of jump linear systems

We analyze the observability of the continuous and discrete states of a class of linear hybrid systems. We derive rank conditions that the structural parameters of the model must satisfy in order for filtering and smoothing algorithms to operate correctly. We also study the identifiability of the model parameters by characterizing the set of models that produce the same output measurements. Finally, when the data are generated by a model in the class, we give conditions under which the true model can be identified.

Recognition of human gaits

We pose the problem of recognizing different types of human gait in the space of dynamical systems where each gait is represented Established techniques are employed to track a kinematic model of a human body in motion, and the trajectories of the parameters are used to learn a representation of a dynamical system, which defines a gait. Various types of distance between models are then computed These computations are non trivial due to the fact that, even for the case of linear systems, the space of canonical realizations is not linear.

Prediction error identification of linear systems: A nonparametric Gaussian regression approach

A novel Bayesian paradigm for the identification of output error models has recently been proposed in which, in place of postulating finite-dimensional models of the system transfer function, the system impulse response is searched for within an infinite-dimensional space. In this paper, such a nonparametric approach is applied to the design of optimal predictors and discrete-time models based on prediction error minimization by interpreting the predictor impulse responses as realizations of Gaussian processes. The proposed scheme describes the predictor impulse responses as the convolution of an infinite-dimensional response with a low-dimensional parametric response that captures possible high-frequency dynamics. Overparameterization is avoided because the model involves only a few hyperparameters that are tuned via marginal likelihood maximization. Numerical experiments, with data generated by ARMAX and infinite-dimensional models, show the definite advantages of the new approach over standard parametric prediction error techniques and subspace methods both in terms of predictive capability on new data and accuracy in reconstruction of system impulse responses.

On the Relation Between CCA and Predictor-Based Subspace Identification

In this paper, we investigate the relation between a recently proposed subspace method based on predictor identification (PBSID), known also as ldquowhitening filter algorithm,rdquo and the classical CCA algorithm. The comparison is motivated by i) the fact that CCA is known to be asymptotically efficient for time series identification and optimal for white measured inputs and ii) some recent results showing that a number of recently developed algorithms are very closely related to PBSID. We show that PBSID is asymptotically equivalent to CCA precisely in the situations in which CCA is optimal while an ldquooptimizedrdquo version of PBSID behaves no worse than CCA also for nonwhite inputs. Even though PBSID (and its optimized version) are consistent regardless of the presence of feedback, in this paper we work under the assumption that there is no feedback to make the comparison with CCA meaningful. The results of this paper imply that the ldquooptimizedrdquo PBSID, besides being able to handle feedback, is to be preferred to CCA also when there is no feedback; only in very specific cases (white or no inputs) are the two algorithms (asymptotically) equivalent.

Optimal Synchronization for Networks of Noisy Double Integrators

In this technical note, we present a novel synchronization protocol to synchronize a network of controlled discrete-time double integrators which are nonidentical, with unknown model parameters and subject to additive measurement and process noise. This framework is motivated by the typical problem of synchronizing a network of clocks whose speeds are nonidentical and are subject to variations. This synchronization protocol is formally studied in its synchronous implementation. In particular, we provide a completely distributed strategy that guarantees convergence for any undirected connected communication graph and we also propose an optimal design strategy when the underlaying communication graph is known. Moreover, this protocol can be readily used to study the effect of noise and external disturbances on the steady-state performance. Finally, some simulations including also randomized implementation of the proposed algorithm are presented.

Distributed Kalman filtering using consensus strategies

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 message exchange per sampling time is small. Moreover, we prove that under certain conditions the optimal consensus matrix should be doubly stochastic. We also provide some numerical examples to clarify some of the analytical results.