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Switching Kalman Filters (SKF) are well known for their ability to solve the piecewise linear dynamic system estimation problem using the standard Kalman Filter (KF). Practical SKFs are heuristic, approximate filters that are not guaranteed…

The contraction properties of the Extended Kalman Filter, viewed as a deterministic observer for nonlinear systems, are analyzed. This yields new conditions under which exponential convergence of the state error can be guaranteed. As…

Accurate estimation of the dynamic states of a synchronous machine (e.g., rotor s angle and speed) is essential in monitoring and controlling transient stability of a power system. It is well known that the covariance matrixes of process…

Heavy tails is a common feature of filtering distributions that results from the nonlinear dynamical and observation processes as well as the uncertainty from physical sensors. In these settings, the Kalman filter and its ensemble version -…

Probabilistic forecasting of multivariate time series is essential for various downstream tasks. Most existing approaches rely on the sequences being uniformly spaced and aligned across all variables. However, real-world multivariate time…

The Kalman filter computes the optimal variable-gain using prior knowledge of the initial state and random (process and measurement) noise distributions, which are assumed to be Gaussian with known variance. However, when these…

Some real-world decision-making problems require making probabilistic forecasts over multiple steps at once. However, methods for probabilistic forecasting may fail to capture correlations in the underlying time-series that exist over long…

We study state estimation for discrete-time linear stochastic systems under distributional ambiguity in the initial state, process noise, and measurement noise. We propose a noise-centric distributionally robust Kalman filter (DRKF) based…

When machine learning systems meet real world applications, accuracy is only one of several requirements. In this paper, we assay a complementary perspective originating from the increasing availability of pre-trained and regularly…

This paper investigates the state estimation problem for unknown linear systems subject to both process and measurement noise. Based on a prior input-output trajectory sampled at a higher frequency and a prior state trajectory sampled at a…

Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions…

Stability analysis of the Kalman filter under randomly lost measurements has been widely studied. We revisit this problem in a general continuous-time framework, where both the measurement matrix and noise covariance evolve as random…

Several particle algorithms admit a Feynman-Kac representation such that the potential function may be expressed as a recursive function which depends on the complete state trajectory. An important example is the mixture Kalman filter, but…

We consider the problem of high-dimensional filtering of state-space models (SSMs) at discrete times. This problem is particularly challenging as analytical solutions are typically not available and many numerical approximation methods can…

Despite the widespread usage of discrete generation Ensemble Kalman particle filtering methodology to solve nonlinear and high dimensional filtering and inverse problems, little is known about their mathematical foundations. As genetic-type…

Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system's time evolution. Rather than solving the…

This paper proposes an Extended-Kalman-Filter-like observer for parameter estimation during synchronization of chaotic systems. The exponential stability of the observer is guaranteed by a persistent excitation condition. This approach is…

The main objective of Prognostics and Health Management is to estimate the Remaining Useful Lifetime (RUL), namely, the time that a system or a piece of equipment is still in working order before starting to function incorrectly. In recent…

This paper studies an output feedback stabilization control framework for discrete-time linear systems with stochastic dynamics determined by an independent and identically distributed (i.i.d.) process. The controller is constructed with an…

This article is concerned with the convergence of the state estimate obtained from the discrete time Kalman filter to the continuous time estimate as the temporal discretization is refined. We derive convergence rate estimates for different…