Related papers: An Efficient Approximation of the Kalman Filter fo…
Since the innovation of the ubiquitous Kalman filter more than five decades back it is well known that to obtain the best possible estimates the tuning of its statistics $X_0$, $P_0$, $\Theta$, $R$ and $Q$ namely initial state and…
State estimation is a fundamental problem in control and signal processing, for which the Kalman Filter provides an optimal solution under linear dynamics, Gaussian noise, and known noise covariances. However, these assumptions often fail…
We introduce the inverse Kalman filter, which enables exact matrix-vector multiplication between a covariance matrix from a dynamic linear model and any real-valued vector with linear computational cost. We integrate the inverse Kalman…
The Derivative-free nonlinear Kalman Filter is proposed for state estimation and fault diagnosis in distributed parameter systems and particularly in dynamical systems described by partial differential equations of the nonlinear wave type.…
Recently, it has been demonstrated experimentally that adaptive estimation of a continuously varying optical phase provides superior accuracy in the phase estimate compared to static estimation. Here, we show that the mean-square error in…
The Kalman-Bucy filter is extensively utilized across various applications. However, its computational complexity increases significantly in large-scale systems. To mitigate this challenge, a low-rank approximated Kalman--Bucy filter was…
This paper proposes control approaches for discrete-time linear systems subject to stochastic disturbances. It employs Kalman filter to estimate the mean and covariance of the state propagation, and the worst-case conditional value-at-risk…
Estimating the state of a dynamical system from partial and noisy observations is a ubiquitous problem in a large number of applications, such as probabilistic weather forecasting and prediction of epidemics. Particle filters are a widely…
We consider the problem of randomly choosing the sensors of a linear time-invariant dynamical system subject to process and measurement noise. We sample the sensors independently and from the same distribution. We measure the performance of…
We develop a fast algorithm for Kalman Filter applied to the random walk forecast model. The key idea is an efficient representation of the estimate covariance matrix at each time-step as a weighted sum of two contributions - the process…
In this article, we propose a new filtering algorithm based in the Koopman operator, showing that a nonlinear filtering problem can be seen as an equivalent problem where the dynamics is infinite dimensional, but linear. Using Extended…
Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state of the system is high dimensional, ensemble Kalman filters are often the method of choice.…
We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and…
Fueled by applications in sensor networks, these years have witnessed a surge of interest in distributed estimation and filtering. A new approach is hereby proposed for the Distributed Kalman Filter (DKF) by integrating a local covariance…
In this paper, we propose a new model reduction technique for linear stochastic systems that builds upon knowledge filtering and utilizes optimal Kalman filtering techniques. This new technique will reduce the dimension of the noise…
This paper presents an LMI-based design framework for multirate steady-state Kalman filters in systems with sensors operating at different sampling rates. The multirate system is formulated as a periodic time-varying system, where the…
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…
Parametric filters, such as the Extended Kalman Filter and the Unscented Kalman Filter, typically scale well with the dimensionality of the problem, but they are known to fail if the posterior state distribution cannot be closely…
The problem of system identification for the Kalman filter, relying on the expectation-maximization (EM) procedure to learn the underlying parameters of a dynamical system, has largely been studied assuming that observations are sampled at…
The paper is devoted to synthesis of recurrent algorithms for detection of stochastic signals given in state space. The structure of the algorithms synthesized is shown to be close to that of the Kalman filter. Analysis of one of the…