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The state-of-the-art tensor network Kalman filter lifts the curse of dimensionality for high-dimensional recursive estimation problems. However, the required rounding operation can cause filter divergence due to the loss of positive…

We demonstrate that the extended Kalman filter converges locally for a broad class of nonlinear systems. If the initial estimation error of the filter is not too large then the error goes to zero exponentially as time goes to infinity. To…

Kalman filtering and smoothing algorithms are used in many areas, including tracking and navigation, medical applications, and financial trend filtering. One of the basic assumptions required to apply the Kalman smoothing framework is that…

We consider the problem of learning time-varying functions in a distributed fashion, where agents collect local information to collaboratively achieve a shared estimate. This task is particularly relevant in control applications, whenever…

The Kalman filter (KF) is an optimal linear state estimator for linear systems, and numerous extensions, including the extended Kalman filter (EKF), unscented Kalman filter (UKF), and cubature Kalman filter (CKF), have been developed for…

Bayesian filtering is a cornerstone of state estimation in complex systems such as aerospace systems, yet exact solutions are available only for linear Gaussian models. In practice,nonlinear systems are handled through tractable…

This paper is concerned with the problem of distributed Kalman filtering in a network of interconnected subsystems with distributed control protocols. We consider networks, which can be either homogeneous or heterogeneous, of linear…

This paper investigates the optimal selection of portfolios for power utility maximizing investors in a financial market where stock returns depend on a hidden Gaussian mean reverting drift process. Information on the drift is obtained from…

In this paper, we propose an approach to address the problems with ambiguity in tuning the process and observation noises for a discrete-time linear Kalman filter. Conventional approaches to tuning (e.g. using normalized estimation error…

This note studies the use of relays to improve the performance of Kalman filtering over packet dropping links. Packet reception probabilities are governed by time-varying fading channel gains, and the sensor and relay transmit powers. We…

This paper studies the distributed state estimation in sensor network, where $m$ sensors are deployed to infer the $n$-dimensional state of a linear time-invariant (LTI) Gaussian system. By a lossless decomposition of optimal steady-state…

This paper considers the Linear Minimum Variance recursive state estimation for the linear discrete time dynamic system with random state transition and measurement matrices, i.e., random parameter matrices Kalman filtering. It is shown…

Ensemble filters implement sequential Bayesian estimation by representing the probability distribution by an ensemble mean and covariance. Unbiased square root ensemble filters use deterministic algorithms to produce an analysis (posterior)…

This paper presents a novel distribution-agnostic Wasserstein distance-based estimation framework. The goal is to determine an optimal map combining prior estimate with measurement likelihood such that posterior estimation error optimally…

The Markowitz model is still the cornerstone of modern portfolio theory. In particular, when focusing on the minimum-variance portfolio, the covariance matrix or better its inverse, the so-called precision matrix, is the only input…

This paper presents a new approach to distributed linear filtering and prediction. The problem under consideration consists of a random dynamical system observed by a multi-agent network of sensors where the network is sparse. Inspired by…

Kalman filtering and smoothing are the foundational mechanisms for efficient inference in Gauss-Markov models. However, their time and memory complexities scale prohibitively with the size of the state space. This is particularly…

A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…

The optimal predictor for a linear dynamical system (with hidden state and Gaussian noise) takes the form of an autoregressive linear filter, namely the Kalman filter. However, a fundamental problem in reinforcement learning and control…

Robustness and adaptivity are two competing objectives in Kalman filters (KF). Robustness involves temporarily inflating prior estimates of noise covariances, while adaptivity updates prior beliefs by exploiting measurements. In practical…