Related papers: A Linear Programming Approach to Attainable Cram\'…
Synchronization of rotations is the problem of estimating a set of rotations R_i in SO(n), i = 1, ..., N, based on noisy measurements of relative rotations R_i R_j^T. This fundamental problem has found many recent applications, most…
We establish Cram\'er-type moderate deviation theorems for sums of locally dependent random variables and combinatorial central limit theorems. Under some mild exponential moment conditions, optimal error bounds and convergence ranges are…
We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute…
The adoption of large-scale antenna arrays at high-frequency bands is widely envisioned in the beyond 5G wireless networks. This leads to the near-field regime where the wavefront is no longer planar but spherical, bringing new…
The quantum Cram\'{e}r-Rao bound (QCRB) as the ultimate lower bound for precision in quantum parameter estimation is only known to be saturable in the multiparameter setting in special cases and under conditions such as full or average…
We consider the problem of estimating the state of a large but finite number $N$ of identical quantum systems. In the limit of large $N$ the problem simplifies. In particular the only relevant measure of the quality of the estimation is the…
We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the…
Parameter estimation is a fundamental problem in science and engineering. In many safety-critical applications, one is not only interested in a {\it point} estimator, but also the uncertainty bound that can self-assess the accuracy of the…
In this note we develop a linear programming framework to produce upper and lower bounds for the lonely runner problem.
The estimation of multiple parameters is a ubiquitous requirement in many quantum metrology applications. However, achieving the ultimate precision limit, i.e. the quantum Cram\'er-Rao bound, becomes challenging in these scenarios compared…
The Cram\'er-Rao bound serves as a crucial lower limit for the mean squared error of an estimator in frequentist parameter estimation. Paradoxically, it requires highly accurate prior knowledge of the estimated parameter for constructing…
The Bayesian Cram\'er-Rao bound (BCRB) is a crucial tool in signal processing for assessing the fundamental limitations of any estimation problem as well as benchmarking within a Bayesian frameworks. However, the BCRB cannot be computed…
For decoherence processes induced by weak interactions with the environment, a general quantum channel with one noise parameter has been formulated. This channel is called low-noise channel and very useful for investigating the parameter…
This paper deals with the scenario approach to robust optimization. This relies on a random sampling of the possibly infinite number of constraints induced by uncertainties in the parameters of an optimization problem. Solving the resulting…
In [1], we proved the asymptotic achievability of the Cram\'{e}r-Rao bound in the compressive sensing setting in the linear sparsity regime. In the proof, we used an erroneous closed-form expression of $\alpha \sigma^2$ for the genie-aided…
This paper presents a new performance bound for estimation problems where the parameter to estimate lies in a Riemannian manifold (a smooth manifold endowed with a Riemannian metric) and follows a given prior distribution. In this setup,…
We propose a certainty-equivalence scheme for adaptive control of scalar linear systems subject to additive, i.i.d. Gaussian disturbances and bounded control input constraints, without requiring prior knowledge of the bounds of the system…
This paper proposes a model, the linear model, for randomly generating logic programs with low density of rules and investigates statistical properties of such random logic programs. It is mathematically shown that the average number of…
Sampling-based motion planners have proven to be efficient solutions to a variety of high-dimensional, geometrically complex motion planning problems with applications in several domains. The traditional view of these approaches is that…
This paper presents a computationally efficient robust model predictive control law for discrete linear time invariant systems subject to additive disturbances that may depend on the state and/or input norms. Despite the dependency being…