arXiv subjects

Mattia Zorzi

Publications and source records attributed to Mattia Zorzi.

At least 19 recordsLinked to original sources

arXiv2026

Identification of forward models: a nonparametric approach

In this paper we propose a new kernel-based method for the identification of the impulse responses of forward models. The resulting estimator leads to a nonlinear Tikhonov regularization problem for which we prove the existence of a solution. The latter result makes legitimate to approximate the forward model through a high-order Moving Average with eXogenous input (MAX) model, i.e. the numerical solution found using this model introduces only a negligible bias in the estimate. The optimization of the marginal likelihood to estimate the kernel hyperparameters is also taken into account. Since there does not exist a closed-form expression for the marginal likelihood, we present an evaluation method that relies on the Laplace approximation of the marginal likelihood. Finally, some numerical experiments are discussed to show the effectiveness of the proposed method.

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arXiv2026

A robust approach to sigma point Kalman filtering

We propose a robust estimator for nonlinear state-space models and provide a clear interpretation of it as the minimizer of a minimax game. The corresponding maximizer searches for the least favorable model over an ambiguity set whose center is obtained by approximating the nominal model through a sigma-point transformation. Moreover, we develop a Markov Chain Monte Carlo (MCMC) scheme for generating adversarial data from it, thereby allowing the assessment of the resulting uncertainty.

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arXiv2026

An update-resilient Kalman filtering approach

We propose a new robust filtering paradigm considering the situation in which model uncertainty, described through an ambiguity set, is present only in the observations. We derive the corresponding robust estimator, referred to as update-resilient Kalman filter, which appears to be novel compared to existing minimax game-based filtering approaches. Moreover, we characterize the corresponding least favorable state space model and analyze the filter stability. Finally, some numerical examples show the effectiveness of the proposed estimator.

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arXiv2025

Distributionally Robust LQG with Kullback-Leibler Ambiguity Sets

The Linear Quadratic Gaussian (LQG) controller is known to be inherently fragile to model misspecifications common in real-world situations. We consider discrete-time partially observable stochastic linear systems and provide a robustification of the standard LQG against distributional uncertainties on the process and measurement noise. Our distributionally robust formulation specifies the admissible perturbations by defining a relative entropy based ambiguity set individually for each time step along a finite-horizon trajectory, and minimizes the worst-case cost across all admissible distributions. We prove that the optimal control policy is still linear, as in standard LQG, and derive a computational scheme grounded on iterative best response that provably converges to the set of saddle points. Finally, we consider the case of endogenous uncertainty captured via decision-dependent ambiguity sets and we propose an approximation scheme based on dynamic programming.

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arXiv2025

Data-driven robust UAV position estimation in GPS signal-challenged environment

In this paper, we consider a position estimation problem for an unmanned aerial vehicle (UAV) equipped with both proprioceptive sensors, i.e. IMU, and exteroceptive sensors, i.e. GPS and a barometer. We propose a data-driven position estimation approach based on a robust estimator which takes into account that the UAV model is affected by uncertainties and thus it belongs to an ambiguity set. We propose an approach to learn this ambiguity set from the data.

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arXiv2024

Identification of Non-causal Graphical Models

The paper considers the problem to estimate non-causal graphical models whose edges encode smoothing relations among the variables. We propose a new covariance extension problem and show that the solution minimizing the transportation distance with respect to white noise process is a double-sided autoregressive non-causal graphical model. Then, we generalize the paradigm to a class of graphical autoregressive moving-average models. Finally, we test the performance of the proposed method through some numerical experiments.

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arXiv2024

A kernel-based PEM estimator for forward models

This paper addresses the problem of learning the impulse responses characterizing forward models by means of a regularized kernel-based Prediction Error Method (PEM). The common approach to accomplish that is to approximate the system with a high-order stable ARX model. However, such choice induces a certain undesired prior information in the system that we want to estimate. To overcome this issue, we propose a new kernel-based paradigm which is formulated directly in terms of the impulse responses of the forward model and leading to the identification of a high-order MAX model. The most challenging step is the estimation of the kernel hyperparameters optimizing the marginal likelihood. The latter, indeed, does not admit a closed form expression. We propose a method for evaluating the marginal likelihood which makes possible the hyperparameters estimation. Finally, some numerical results showing the effectiveness of the method are presented.

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arXiv2024

Distributionally Robust LQG control under Distributed Uncertainty

A new paradigm is proposed for the robustification of the LQG controller against distributional uncertainties on the noise process. Our controller optimizes the closed-loop performances in the worst possible scenario under the constraint that the noise distributional aberrance does not exceed a certain threshold limiting the relative entropy pseudo-distance between the actual noise distribution the nominal one. The main novelty is that the bounds on the distributional aberrance can be arbitrarily distributed along the whole disturbance trajectory. We discuss why this can, in principle, be a substantial advantage and we provide simulation results that substantiate such a principle.

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arXiv2023

On the identification of ARMA graphical models

The paper considers the problem to estimate a graphical model corresponding to an autoregressive moving-average (ARMA) Gaussian stochastic process. We propose a new maximum entropy covariance and cepstral extension problem and we show that the problem admits an approximate solution which represents an ARMA graphical model whose topology is determined by the selected entries of the covariance lags considered in the extension problem. Then, we show how the corresponding dual problem is connected with the maximum likelihood principle. Such connection allows to design a Bayesian model and characterize an approximate maximum a posteriori estimator of the ARMA graphical model in the case the graph topology is unknown. We test the performance of the proposed method through some numerical experiments.

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arXiv2023

A Weaker Regularity Condition for the Multidimensional $ν$-Moment Problem

We consider the problem of finding a $d$-dimensional spectral density through a moment problem which is characterized by an integer parameter $ν$. Previous results showed that there exists an approximate solution under the regularity condition $ν\geq d/2+1$. To realize the process corresponding to such a spectral density, one would take $ν$ as small as possible. In this letter we show that this condition can be weaken as $ν\geq d/2$.

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arXiv2023

On the Statistical Consistency of a Generalized Cepstral Estimator

We consider the problem to estimate the generalized cepstral coefficients of a stationary stochastic process or stationary multidimensional random field. It turns out that a naive version of the periodogram-based estimator for the generalized cepstral coefficients is not consistent. We propose a consistent estimator for those coefficients. Moreover, we show that the latter can be used in order to build a consistent estimator for a particular class of cascade linear stochastic systems.

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arXiv2023

A Well-Posed Multidimensional Rational Covariance and Generalized Cepstral Extension Problem

In the present paper we consider the problem of estimating the multidimensional power spectral density which describes a second-order stationary random field from a finite number of covariance and generalized cepstral coefficients. The latter can be framed as an optimization problem subject to multidimensional moment constraints, i.e., to search a spectral density maximizing an entropic index and matching the moments. In connection with systems and control, such a problem can also be posed as finding a multidimensional shaping filter (i.e., a linear time-invariant system) which can output a random field that has identical moments with the given data when fed with a white noise, a fundamental problem in system identification. In particular, we consider the case where the dimension of the random field is greater than two for which a satisfying theory is still missing. We propose a multidimensional moment problem which takes into account a generalized definition of the cepstral moments, together with a consistent definition of the entropy. We show that it is always possible to find a rational power spectral density matching exactly the covariances and approximately the generalized cepstral coefficients, from which a shaping filter can be constructed via spectral factorization. In plain words, our theory allows to construct a well-posed spectral estimator for any finite dimension.

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arXiv2022

Hidden Factor estimation in Dynamic Generalized Factor Analysis Models

This paper deals with the estimation of the hidden factor in Dynamic Generalized Factor Analysis via a generalization of Kalman filtering. Asymptotic consistency is discussed and it is shown that the Kalman one-step predictor is not the right tool while the pure filter yields a consistent estimate.

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arXiv2022

Robust fixed-lag smoothing under model perturbations

A robust fixed-lag smoothing approach is proposed in the case there is a mismatch between the nominal model and the actual model. The resulting robust smoother is characterized by a dynamic game between two players: one player selects the least favorable model in a prescribed ambiguity set, while the other player selects the fixed-lag smoother minimizing the smoothing error with respect to least favorable model. We propose an efficient implementation of the proposed smoother. Moreover, we characterize the corresponding least favorable model over a finite time horizon. Finally, we test the robust fixed-lag smoother in two examples. The first one regards a target tracking problem, while the second one regards a parameter estimation problem.

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arXiv2022

Robust Distributed Kalman filtering with Event-Triggered Communication

We consider the problem of distributed Kalman filtering for sensor networks in the case there are constraints in data transmission and there is model uncertainty. More precisely, we propose two distributed filtering strategies with event-triggered communication where the state estimators are computed according to the least favorable model. The latter belongs to a ball about the nominal model. We also show that both the methods are stable in the sense that the mean-square of the state estimation error is bounded in all the nodes.

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arXiv2022

Mean-square consistency of the $f$-truncated $\text{M}^2$-periodogram

The paper deals with the problem of estimating the M$^2$ (i.e. multivariate and multidimensional) spectral density function of a stationary random process or random field. We propose the $f$-truncated periodogram, i.e. a truncated periodogram where the truncation point is a suitable function $f$ of the sample size. We discuss the asymptotic consistency of the estimator and we provide three concrete problems that can be solved using the proposed approach. Simulation results show the effectiveness of the procedure.

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arXiv2022

Nonparametric Identification of Kronecker Networks

We address the problem to estimate a dynamic network whose edges describe Granger causality relations and whose topology has a Kronecker structure. Such a structure arises in many real networks and allows to understand the organization of complex networks. We proposed a kernel-based PEM method to learn such networks. Numerical examples show the effectiveness of the proposed method.

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arXiv2022

Distributed Kalman filtering with event-triggered communication: a robust approach

We consider the problem of distributed Kalman filtering for sensor networks in the case there is a limit in data transmission and there is model uncertainty. More precisely, we propose a distributed filtering strategy with event-triggered communication in which the state estimators are computed according to the least favorable model. The latter belongs to a ball (in Kullback-Leibler topology) about the nominal model. We also present a preliminary numerical example in order to test the performance of the proposed strategy.

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