Related papers: A summary on the UD Kalman Filter

The implicit particle filter seeks to mitigate particle degeneracy by identifying particles in the target distribution's high-probability regions. This study is motivated by the need to enhance computational tractability in implementing…

In this paper, we revisit the Kalman filter theory. After giving the intuition on a simplified financial markets example, we revisit the maths underlying it. We then show that Kalman filter can be presented in a very different fashion using…

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…

We elucidate the mathematical structure of Bayesian filtering, and Bayesian inference more broadly, by applying recent work on category theoretical probability, specifically the concept of a strongly representable Markov category. We show…

Kalman filter is a best linear unbiased state estimator. It is also comprehensible from the point view of the Bayesian estimation. However, this note gives a detailed derivation of Kalman filter from the mutual information perspective for…

In this paper, we enhance a recent algorithm for approximate spectral factorization of matrix functions, extending its capabilities to precisely factorize rational matrices when an exact lower-upper triangular factorization is available.…

We formulate a recursive estimation problem for multiple dynamical systems coupled through a low dimensional stochastic input, and we propose an efficient sub-optimal solution. The suggested approach is an approximation of the Kalman filter…

Common filters are usually based on the linear approximation of the optimal minimum mean square error estimator. The Extended and Unscented Kalman Filters handle nonlinearity through linearization and unscented transformation, respectively,…

We survey recent progress on efficient algorithms for approximately diagonalizing a square complex matrix in the models of rational (variable precision) and finite (floating point) arithmetic. This question has been studied across several…

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 revisit implicit regularization from the ground up using notions from dynamical systems and invariant subspaces of Morse functions. The key contributions are a new criterion for implicit regularization---a leading…

This paper presents a systematic review of recent advances in nonlinear filtering algorithms, structured into three principal categories: Kalman-type methods, Monte Carlo methods, and the Yau-Yau algorithm. For each category, we provide a…

Studying the stability of the Kalman filter whose measurements are randomly lost has been an active research topic for over a decade. In this paper we extend the existing results to a far more general setting in which the measurement…

This paper aims to introduce an application to Kalman Filtering Theory, which is rather unconventional. Recent experiments have shown that many natural phenomena, especially from ecology or meteorology, could be monitored and predicted more…

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…

This study considers the object localization problem and proposes a novel multiparticle Kalman filter to solve it in complex and symmetric environments. Two well-known classes of filtering algorithms to solve the localization problem are…

A common assumption when applying the Kalman filter is a priori knowledge of the system parameters. These parameters are not necessarily known, and this may limit real-world applications of the Kalman filter. The well-established Model…

Some key features of the overlap operator with a UV-filtered Wilson kernel are discussed. The first part concerns spectral properties of the underlying shifted hermitean Wilson operator and the relation to the observed speedup of the…

The Ensemble Kalman Filter (EnKF) is a widely used method for data assimilation in high-dimensional systems, with an ensemble update step equivalent to an empirical version of the Matheron update popular in Gaussian process regression -- a…

Let A, B, C, D be given finite sets of pairs of n-by-n complex matrices. We describe an algorithm to determine, with finitely many computations, whether there is a single unitary matrix U such that each pair of matrices in A is unitarily…