Related papers: Extending the practical applicability of the Kalma…

We study the problem of optimal estimation and control of linear systems using quantized measurements, with a focus on applications over sensor networks. We show that the state conditioned on a causal quantization of the measurements can be…

Researchers collecting intensive longitudinal data (ILD) are increasingly looking to model psychological processes, such as emotional dynamics, that organize and adapt across time in complex and meaningful ways. This is also the case for…

Online estimation of electromechanical oscillation parameters provides essential information to prevent system instability and blackout and helps to identify event categories and locations. We formulate the problem as a state space model…

In this paper, we consider the task of designing a Kalman Filter (KF) for an unknown and partially observed autonomous linear time invariant system driven by process and sensor noise. To do so, we propose studying the following two step…

Current experimental design techniques for dynamical systems often only incorporate measurement noise, while dynamical systems also involve process noise. To construct experimental designs we need to quantify their information content. The…

We analyze the Ensemble and Polynomial Chaos Kalman filters applied to nonlinear stationary Bayesian inverse problems. In a sequential data assimilation setting such stationary problems arise in each step of either filter. We give a new…

Nonlinear Kalman Filters are powerful and widely-used techniques when trying to estimate the hidden state of a stochastic nonlinear dynamic system. In this paper, we extend the Smart Sampling Kalman Filter (S2KF) with a new point symmetric…

Using the array form of numerically stable square-root implementation methods for Kalman filtering formulas, we construct a new square-root algorithm for the log-likelihood gradient (score) evaluation. This avoids the use of the…

Model-based filtering is often carried out while subject to an imperfect model, as learning partially-observable stochastic systems remains a challenge. Recent work on Bayesian inference found that tempering the likelihood or full posterior…

The Kalman filter (KF) is one of the most widely used tools for data assimilation and sequential estimation. In this work, we show that the state estimates from the KF in a standard linear dynamical system setting are equivalent to those…

The kinematics of many systems encountered in robotics, mechatronics, and avionics are naturally posed on homogeneous spaces; that is, their state lies in a smooth manifold equipped with a transitive Lie group symmetry. This paper proposes…

Convergence of the Kalman filter is best analyzed by studying the contraction of the Riccati map in the space of positive definite (covariance) matrices. In this paper, we explore how this contraction property relates to a more fundamental…

The extraction of weak signals plays a crucial role in quantum precision measurement, where the estimation results are often limited by low signal-to-noise ratios. Here, we demonstrate a parameter-estimation framework based on the adaptive…

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…

Motivated by the need for accurate frequency information, a novel algorithm for estimating the fundamental frequency and its rate of change in three-phase power systems is developed. This is achieved through two stages of Kalman filtering.…

This paper develops a new nonlinear filter, called Moment-based Kalman Filter (MKF), using the exact moment propagation method. Existing state estimation methods use linearization techniques or sampling points to compute approximate values…

A central obstacle in nonlinear Bayesian filtering is representing the belief distribution. Moment-based filters address this by propagating polynomial moments and reconstructing a density from them. Recent work completes the predict-update…

A square root approach is considered for the problem of accounting for model noise in the forecast step of the ensemble Kalman filter (EnKF) and related algorithms. The primary aim is to replace the method of simulated, pseudo-random,…

Square-root Kalman filters propagate state covariances in Cholesky-factor form for numerical stability, and are a natural target for gradient-based parameter learning in state-space models. Their core operation, triangularization of a…

The new method of multivariate data analysis based on the complements of classical probability distribution to quantum state and Schmidt decomposition is presented. We considered Schmidt formalism application to problems of statistical…