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**1 - 7**of**7**### Introduction to the Algebra of Separators with Application to Path Planning

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### Robust Localisation Using Separators

"... Abstract. Contractor algebra is a numerical tool based on interval anal-ysis often used to solve localization problems. This paper proposes to use the separators which is a pair of complementary contractors and recalls the corresponding algebra. Separator algebra inside a paver will allow us to get ..."

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Abstract. Contractor algebra is a numerical tool based on interval anal-ysis often used to solve localization problems. This paper proposes to use the separators which is a pair of complementary contractors and recalls the corresponding algebra. Separator algebra inside a paver will allow us to get an inner and an outer approximation of the solution set in a very easy way. An application to robust localization is presented in order to illustrate the principle of the approach. 1

### Strong Consistency of the Sign-Perturbed Sums Method

"... Abstract—Sign-Perturbed Sums (SPS) is a recently developed non-asymptotic system identification algorithm that constructs confidence regions for parameters of dynamical systems. It works under mild statistical assumptions, such as symmetric and independent noise terms. The SPS confidence region incl ..."

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Abstract—Sign-Perturbed Sums (SPS) is a recently developed non-asymptotic system identification algorithm that constructs confidence regions for parameters of dynamical systems. It works under mild statistical assumptions, such as symmetric and independent noise terms. The SPS confidence region includes the least-squares estimate, and, for any finite sample and user-chosen confidence probability, the constructed region contains the true system parameter with exactly the given probability. The main contribution in this paper is to prove that SPS is strongly consistent, in case of linear regression based models, in the sense that any false parameter will almost surely be excluded from the confidence region as the sample size tends to infinity. The asymptotic behavior of the confidence regions constructed by SPS is also illustrated by numerical experiments.

### Closed-Loop Applicability of the Sign-Perturbed Sums Method

"... Abstract — Sign-Perturbed Sums (SPS) is a non-asymptotic system identification method that can construct confidence regions for general linear systems. It works under mild sta-tistical assumptions, such as symmetric and independent noise terms. The SPS confidence region includes the prediction error ..."

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Abstract — Sign-Perturbed Sums (SPS) is a non-asymptotic system identification method that can construct confidence regions for general linear systems. It works under mild sta-tistical assumptions, such as symmetric and independent noise terms. The SPS confidence region includes the prediction error estimate (PEM) and, for any finite sample and user-chosen con-fidence probability, it contains the true system parameter with exactly the given probability. Originally, SPS was introduced for open-loop systems, this paper overviews its applicability in closed-loop setups. The three main PEM approaches of closed-loop identification are addressed: direct, indirect and joint input-output, and it is discussed whether SPS can be applied to construct guaranteed finite sample confidence regions around these PEM estimates. Some parametrization issues are also highlighted and, finally, two numerical experiments are presented demonstrating SPS for closed-loop systems. I.

### IEEE TRANSACTIONS ON SIGNAL PROCESSING 1 Sign-Perturbed Sums: A New System Identification Approach for Constructing Exact Non-Asymptotic Confidence Regions in Linear Regression Models

"... Abstract—We propose a new system identification method, called Sign- Perturbed Sums (SPS), for constructing non-asymptotic confidence regions under mild statistical assumptions. SPS is introduced for linear regression models, including but not limited to FIR systems, and we show that the SPS confide ..."

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Abstract—We propose a new system identification method, called Sign- Perturbed Sums (SPS), for constructing non-asymptotic confidence regions under mild statistical assumptions. SPS is introduced for linear regression models, including but not limited to FIR systems, and we show that the SPS confidence regions have exact confidence probabilities, i.e., they contain the true parameter with a user-chosen exact probability for any finite data set. Moreover, we also prove that the SPS regions are star convex with the Least-Squares (LS) estimate as a star center. The main assumptions of SPS are that the noise terms are independent and symmetrically distributed about zero, but they can be nonstationary, and their distributions need not be known. The paper also proposes a computationally efficient ellipsoidal outer approximation algorithm for SPS. Finally, SPS is demonstrated through a number of simulation experiments. Index Terms—system identication, finite sample properties, parameter estimation, linear regression models, least squares methods, statistics. I.

### Efficient Distributed Non-Asymptotic Confidence Regions Computation over Wireless Sensor Networks

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"... Guaranteed characterization of exact confidence regions for FIR models under mild assumptions on the noise via interval analysis ..."

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Guaranteed characterization of exact confidence regions for FIR models under mild assumptions on the noise via interval analysis