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Augusto Ferrante

Publications and source records attributed to Augusto Ferrante.

At least 37 records · Page 2Linked to original sources
arXiv2019

Fusion of Sensors Data in Automotive Radar Systems: A Spectral Estimation Approach

To accurately estimate locations and velocities of surrounding targets (cars) is crucial for advanced driver assistance systems based on radar sensors. In this paper we derive methods for fusing data from multiple radar sensors in order to improve the accuracy and robustness of such estimates. First we pose the target estimation problem as a multivariate multidimensional spectral estimation problem. The problem is multivariate since each radar sensor gives rise to a measurement channel. Then we investigate how the use of the cross-spectra affects target estimates. We see that the use of the magnitude of the cross-spectrum significantly improves the accuracy of the target estimates, whereas an attempt to compensate the phase lag of the cross-spectrum only gives marginal improvement. This paper may be viewed as a first step towards applying high-resolution methods that builds on multidimensional multivariate spectral estimation for sensor fusion.

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arXiv2019

Robust Identification of "Sparse Plus Low-rank" Graphical Models: An Optimization Approach

Motivated by graphical models, we consider the "Sparse Plus Low-rank" decomposition of a positive definite concentration matrix -- the inverse of the covariance matrix. This is a classical problem for which a rich theory and numerical algorithms have been developed. It appears, however, that the results rapidly degrade when, as it happens in practice, the covariance matrix must be estimated from the observed data and is therefore affected by a certain degree of uncertainty. We discuss this problem and propose an alternative optimization approach that appears to be suitable to deal with robustness issues in the "Sparse Plus Low-rank" decomposition problem.The variational analysis of this optimization problem is carried over and discussed.

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arXiv2018

A Scalable Strategy for the Identification of Latent-variable Graphical Models

In this paper we propose an identification method for latent-variable graphical models associated to autoregressive (AR) Gaussian stationary processes. The identification procedure exploits the approximation of AR processes through stationary reciprocal processes thus benefiting of the numerical advantages of dealing with block-circulant matrices. These advantages become more and more significant as the order of the process gets large. We show how the identification can be cast in a regularized convex program and we present numerical examples that compares the performances of the proposed method with the existing ones.

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arXiv2018

Factor Models with Real Data: a Robust Estimation of the Number of Factors

Factor models are a very efficient way to describe high dimensional vectors of data in terms of a small number of common relevant factors. This problem, which is of fundamental importance in many disciplines, is usually reformulated in mathematical terms as follows. We are given the covariance matrix Sigma of the available data. Sigma must be additively decomposed as the sum of two positive semidefinite matrices D and L: D | that accounts for the idiosyncratic noise affecting the knowledge of each component of the available vector of data | must be diagonal and L must have the smallest possible rank in order to describe the available data in terms of the smallest possible number of independent factors. In practice, however, the matrix Sigma is never known and therefore it must be estimated from the data so that only an approximation of Sigma is actually available. This paper discusses the issues that arise from this uncertainty and provides a strategy to deal with the problem of robustly estimating the number of factors.

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arXiv2018

Identification of Sparse Reciprocal Graphical Models

In this paper we propose an identification procedure of a sparse graphical model associated to a Gaussian stationary stochastic process. The identification paradigm exploits the approximation of autoregressive processes through reciprocal processes in order to improve the robustness of the identification algorithm, especially when the order of the autoregressive process becomes large. We show that the proposed paradigm leads to a regularized, circulant matrix completion problem whose solution only requires computations of the eigenvalues of matrices of dimension equal to the dimension of the process.

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arXiv2018

An alternating minimization algorithm for Factor Analysis

The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem. This algorithm appears to perform extremely well and is extremely fast even when the given covariance matrix has a very large dimension. The effectiveness of the algorithm is assessed through simulation studies and by applications to three real datasets that are considered as benchmark for the problem. A local convergence analysis of the algorithm is also presented.

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arXiv2018

Conal Distances Between Rational Spectral Densities

The paper generalizes Thompson and Hilbert metric to the space of spectral densities. The resulting complete metric space has the differentiable structure of a Finsler manifold with explicit geodesics. The resulting distances are filtering invariant, can be computed efficiently, and admit geodesic paths that preserve rationality; these are properties of fundamental importance in many engineering applications.

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arXiv2018

Families of Solutions of Algebraic Riccati Equations

We consider Homogeneous Algebraic Riccati Equations in the general situation when the matrix of the dynamics can be "mixed". We show that in this case the equation may have infinitely many families of solutions. An analysis of these families is carried over and explicit formulas are derived. We also derive sufficient conditions under which the union of the families covers the whole set of solutions.

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arXiv2018

On the state space and dynamics selection in linear stochastic models: a spectral factorization approach

Matrix spectral factorization is traditionally described as finding spectral factors having a fixed analytic pole configuration. The classification of spectral factors then involves studying the solutions of a certain algebraic Riccati equation which parametrizes their zero structure. The pole structure of the spectral factors can be also parametrized in terms of solutions of another Riccati equation. We study the relation between the solution sets of these two Riccati equations and describe the construction of general spectral factors which involve both zero- and pole-flipping on an arbitrary reference spectral factor.

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arXiv2017

Parametrization of Minimal Spectral Factors of Discrete-Time Rational Spectral Densities

In this paper, the problem of providing a complete parametrization of the minimal spectral factors of a discrete-time rational spectral density is considered. The desired parametrization, given in terms of the all-pass divisors of a certain all-pass function, is established in the most general setting: after several partial results, mostly in the continuous-time case, this is indeed the first complete parametrization obtained without resorting to any facilitating assumption. This result provides a positive answer to a conjecture raised in [Baggio and Ferrante, 2016].

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arXiv2017

Factor analysis with finite data

Factor analysis aims to describe high dimensional random vectors by means of a small number of unknown common factors. In mathematical terms, it is required to decompose the covariance matrix $Σ$ of the random vector as the sum of a diagonal matrix $D$ | accounting for the idiosyncratic noise in the data | and a low rank matrix $R$ | accounting for the variance of the common factors | in such a way that the rank of $R$ is as small as possible so that the number of common factors is minimal. In practice, however, the matrix $Σ$ is unknown and must be replaced by its estimate, i.e. the sample covariance, which comes from a finite amount of data. This paper provides a strategy to account for the uncertainty in the estimation of $Σ$ in the factor analysis problem.

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arXiv2016

Foundations of negative imaginary systems theory and relations with positive real systems

In this paper we lay the foundations of a not necessarily rational negative imaginary systems theory and its relations with positive real systems theory and, hence, with passivity. In analogy with the theory of positive real functions, in our general framework, negative imaginary systems are defined in terms of a domain of analyticity of the transfer function and of a sign condition that must be satisfied in such domain. In this way, on the one hand, our theory does not require to restrict the attention to systems with rational transfer function and, on the other hand | just by suitably selecting the domain of analyticity to be either the right half complex plane or the complement of the unit disc in the complex plane | we particularize our theory to both continuous-time and to discrete-time systems. Indeed, to the best of our knowledge, this is first time that discrete-time negative imaginary systems are studied in the literature. In this work, we also aim to provide a unitary view of the different notions that have appeared so far in the literature within the framework of positive real and in the more recent theory of negative imaginary systems, and to show how these notions are characterized and linked to each other. A stability analysis result for the interconnection of discrete-time systems is also derived.

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arXiv2015

On Minimal Spectral Factors with Zeroes and Poles lying on Prescribed Region

In this paper, we consider a general discrete-time spectral factorization problem for rational matrix-valued functions. We build on a recent result establishing existence of a spectral factor whose zeroes and poles lie in any pair of prescribed regions of the complex plane featuring a geometry compatible with symplectic symmetry. In this general setting, uniqueness of the spectral factor is not guaranteed. It was, however, conjectured that if we further impose stochastic minimality, uniqueness can be recovered. The main result of his paper is a proof of this conjecture.

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arXiv2015

Representation and Factorization of Discrete-Time Rational All-Pass Functions

We obtain a general characterization of discrete-time all-pass rational matrix functions from state-space representations. It can be employed to address model reduction problems in the same vein of the theory developed by Glover in the continuous-time. Besides model reduction, this characterization is shown to be useful in a variety of contexts such as studying LMI's and Riccati equations and especially in the factorization of all-pass functions. The results are obtained in the most general setting, without introducing any {\em ad hoc} assumption.

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arXiv2015

On the Factorization of Rational Discrete-Time Spectral Densities

In this paper, we consider an arbitrary matrix-valued, rational spectral density $Φ(z)$. We show with a constructive proof that $Φ(z)$ admits a factorization of the form $Φ(z)=W^\top (z^{-1})W(z)$, where $W(z)$ is stochastically minimal. Moreover, $W(z)$ and its right inverse are analytic in regions that may be selected with the only constraint that they satisfy some symplectic-type conditions. By suitably selecting the analyticity regions, this extremely general result particularizes into a corollary that may be viewed as the discrete-time counterpart of the matrix factorization method devised by Youla in his celebrated work (Youla, 1961).

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arXiv2014

A structural solution to the monotonic tracking control problem

In this paper we present a method for designing a linear time invariant (LTI) state-feedback controller to monotonically track a constant step reference at any desired rate of convergence for any initial condition. Necessary and sufficient constructive conditions are given to deliver a monotonic step response from all initial conditions. This method is developed for multi-input multi-output (MIMO) systems, and can be applied to square and non-square systems, strictly proper and non-strictly proper systems, and, importantly, also minimum and non-minimum phase systems. The framework proposed here shows that for MIMO LTI systems the objectives of achieving a rapid settling time, while at the same time avoiding overshoot and/or undershoot, are not necessarily competing objectives.

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arXiv2014

The Discrete-Time Generalized Algebraic Riccati Equation: Order Reduction and Solutions' Structure

In this paper we discuss how to decompose the constrained generalized discrete-time algebraic Riccati equation arising in optimal control and optimal filtering problems into two parts corresponding to an additive decomposition X=X0+D of each solution X: The first part is an explicit expression of the addend X0 which is common to all solutions, and does not depend on the particular X. The second part can be either a reduced-order discrete-time regular algebraic Riccati equation whose associated closed-loop matrix is non-singular, or a symmetric Stein equation.

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