Related papers: Adaptive Continuous Homodyne Phase Estimation Usin…
In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault…
Phase estimation protocols provide a fundamental benchmark for the field of quantum metrology. The latter represents one of the most relevant applications of quantum theory, potentially enabling the capability of measuring unknown physical…
Standard maximum likelihood or Bayesian approaches to parameter estimation for stochastic differential equations are not robust to perturbations in the continuous-in-time data. In this paper, we give a rather elementary explanation of this…
Real-time density estimation is ubiquitous in many applications, including computer vision and signal processing. Kernel density estimation is arguably one of the most commonly used density estimation techniques, and the use of "sliding…
The synchronization problem over the special orthogonal group $SO(d)$ consists of estimating a set of unknown rotations $R_1,R_2,...,R_n$ from noisy measurements of a subset of their pairwise ratios $R_{i}^{-1}R_{j}$. The problem has found…
A robust estimator, namely M-smoother, for piecewise-constant smoothing is revisited in this paper. Starting from its generalized formulation, we propose a numerical scheme/framework for solving it via a series of weighted-average filtering…
Filtering and smoothing algorithms for linear discrete-time state-space models with skewed and heavy-tailed measurement noise are presented. The algorithms use a variational Bayes approximation of the posterior distribution of models that…
In applications such as free-space optical communication, a signal is often recovered after propagation through a turbulent medium. In this setting, it is common to assume that limited information is known about the turbulent medium, such…
Efficient stochastic optimization typically integrates an update direction that performs well in the deterministic regime with a mechanism adapting to stochastic perturbations. While Adam uses adaptive moment estimates to promote stability,…
Temporal imaging systems are outstanding tools for single-shot observation of optical signals that have irregular and ultrafast dynamics. They allow long time windows to be recorded with femtosecond resolution, and do not rely on complex…
Quantum state estimation is important for various quantum information processes, including quantum communications, computation, and metrology, which require the characterization of quantum states for evaluation and optimization. We present…
This paper is an algorithmic study of quantum phase estimation with multiple eigenvalues. We present robust multiple-phase estimation (RMPE) algorithms with Heisenberg-limited scaling. The proposed algorithms improve significantly from the…
Wavelet phase is a critical parameter in seismic processing, where zero-phase wavelets are essential for maximizing temporal resolution and ensuring accurate interpretation of subsurface structures. In practice, however, the seismic wavelet…
Nonparametric estimators for the mean and the covariance functions of functional data are proposed. The setup covers a wide range of practical situations. The random trajectories are, not necessarily differentiable, have unknown regularity,…
We present a numerically-stable parallel-in-time linear Kalman smoother. The smoother uses a novel highly-parallel QR factorization for a class of structured sparse matrices for state estimation, and an adaptation of the SelInv…
Iterative phase estimation has long been used in quantum computing to estimate Hamiltonian eigenvalues. This is done by applying many repetitions of the same fundamental simulation circuit to an initial state, and using statistical…
This article improves on existing methods to estimate the spectral density of stationary and nonstationary time series assuming a Gaussian process prior. By optimising an appropriate eigendecomposition using a smoothing spline covariance…
This article mainly proves the existence of stationary correctors under space-time spectral gap conditions, which exhibit different properties from those of elliptic operator correctors. Additionally, new flux correctors and their…
The detection of anomalies in non-stationary time-series streams is a critical but challenging task across numerous industrial and scientific domains. Traditional models, trained offline, suffer significant performance degradation when…
In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…