Related papers: Optimally (Distributional-)Robust Kalman Filtering

Sparse estimation methods capable of tolerating outliers have been broadly investigated in the last decade. We contribute to this research considering high-dimensional regression problems contaminated by multiple mean-shift outliers which…

Ordinary Differential Equations are a simple but powerful framework for modeling complex systems. Parameter estimation from times series can be done by Nonlinear Least Squares (or other classical approaches), but this can give…

This study addresses the problem of selecting dynamically, at each time instance, the ``optimal'' p-norm to combat outliers in linear adaptive filtering without any knowledge on the potentially time-varying probability distribution function…

We consider the robust filtering problem for a nonlinear state-space model with outliers in measurements. To improve the robustness of the traditional Kalman filtering algorithm, we propose in this work two robust filters based on mixture…

Optimal decision-making under partial observability requires reasoning about the uncertainty of the environment's hidden state. However, most reinforcement learning architectures handle partial observability with sequence models that have…

We address the problem of determining optimal sensor precisions for estimating the states of linear time-varying discrete-time stochastic dynamical systems, with guaranteed bounds on the estimation errors. This is performed in the Kalman…

We study high-dimensional sparse estimation tasks in a robust setting where a constant fraction of the dataset is adversarially corrupted. Specifically, we focus on the fundamental problems of robust sparse mean estimation and robust sparse…

Robust regression models in the presence of outliers have significant practical relevance in areas such as signal processing, financial econometrics, and energy management. Many existing robust regression methods, either grounded in…

Motion planning is a fundamental problem and focuses on finding control inputs that enable a robot to reach a goal region while safely avoiding obstacles. However, in many situations, the state of the system may not be known but only…

We study distributed filtering for a class of uncertain systems over corrupted communication channels. We propose a distributed robust Kalman filter with stochastic gains, through which upper bounds of the conditional mean square estimation…

We study the factor model problem, which aims to uncover low-dimensional structures in high-dimensional datasets. Adopting a robust data-driven approach, we formulate the problem as a saddle-point optimization. Our primary contribution is a…

K-means clustering is a workhorse of unsupervised learning, but it is notoriously brittle to outliers, distribution shifts, and limited sample sizes. Viewing k-means as Lloyd--Max quantization of the empirical distribution, we develop a…

We look at a stochastic time-varying optimization problem and we formulate online algorithms to find and track its optimizers in expectation. The algorithms are derived from the intuition that standard prediction and correction steps can be…

Systems equipped with modern sensing modalities such as vision and lidar gain access to increasingly high-dimensional measurements with which to enact estimation and control schemes. In this article, we examine the continuum limit of…

The increasing availability of sensing techniques provides a great opportunity for engineers to design state estimation methods, which are optimal for the system under observation and the observed noise patterns. However, these patterns…

Good robust estimators can be tuned to combine a high breakdown point and a specified asymptotic efficiency at a central model. This happens in regression with MM- and tau-estimators among others. However, the finite-sample efficiency of…

Many problems in signal processing require finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. When dealing with real-world data, the presence of outliers and impulsive noise must also be accounted…

We consider the problem of optimal control for partially observed dynamical systems. Despite its prevalence in practical applications, there are still very few algorithms available, which take uncertainties in the current state estimates…

We study robust linear regression in high-dimension, when both the dimension $d$ and the number of data points $n$ diverge with a fixed ratio $\alpha=n/d$, and study a data model that includes outliers. We provide exact asymptotics for the…

Spatial perception is the backbone of many robotics applications, and spans a broad range of research problems, including localization and mapping, point cloud alignment, and relative pose estimation from camera images. Robust spatial…