Related papers: Covariance-Intersection-based Distributed Kalman F…
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…
This paper proposes a probabilistic approach to the problem of intrinsic filtering of a system on a matrix Lie group with invariance properties. The problem of an invariant continuous-time model with discrete-time measurements is cast into…
This work presents a notion of strong detectability for linear time varying systems affected by unknown inputs. It is shown that this notion is equivalent to detectability of an auxiliary system without unknown inputs. This allows a…
In this paper we analyze the convergence of a family of robust Kalman filters. For each filter of this family the model uncertainty is tuned according to the so called tolerance parameter. Assuming that the corresponding state-space model…
The Ensemble Kalman filter is a sophisticated and powerful data assimilation method for filtering high dimensional problems arising in fluid mechanics and geophysical sciences. This Monte Carlo method can be interpreted as a mean-field…
In this paper, we analyze the convergence of a risk sensitive like filter where the risk sensitivity parameter is time varying. Such filter has a Kalman like structure and its gain matrix is updated according to a Riccati like iteration. We…
This paper studies a distributed estimation problem for time-varying/time-invariant large-scale interconnected systems (LISs). A fully distributed estimator is presented by recursively solving a distributed modified Riccati equation (DMRE)…
This paper is concerned with optimality and stability analysis of a family of ensemble Kalman filter (EnKF) algorithms. EnKF is commonly used as an alternative to the Kalman filter for high-dimensional problems, where storing the covariance…
In this paper, we consider the problem of quantifying controllability and observability of a nonlinear discrete time dynamical system. We introduce the Koopman operator as a canonical representation of the system and apply a lifting…
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…
This paper presents a novel approach to distributed pose estimation in the multi-agent system based on an invariant Kalman filter with covariance intersection. Our method models uncertainties using Lie algebra and applies object-level…
We prove that for linear, discrete, time-varying, deterministic system (perfect model) with noisy outputs, the Riccati transformation in the Kalman filter asymptotically bounds the rank of the forecast and the analysis error covariance…
Compared with linear time invariant systems, linear periodic system can describe the periodic processes arising from nature and engineering more precisely. However, the time-varying system parameters increase the difficulty of the research…
We develop a self contained stochastic perturbation theory for discrete generation and multivariate Ensemble Kalman filters. Unlike their continuous-time counterparts, discrete EnKF algorithms are defined through a two steps prediction…
The Kalman filter is an established tool for the analysis of dynamic systems with normally distributed noise, and it has been successfully applied in numerous application areas. It provides sequentially calculated estimates of the system…
We analyze the convergence aspects of the invariant extended Kalman filter (IEKF), when the latter is used as a deterministic non-linear observer on Lie groups, for continuous-time systems with discrete observations. One of the main…
The exponential stability and the concentration properties of a class of extended Kalman-Bucy filters are analyzed. New estimation concentration inequalities around partially observed signals are derived in terms of the stability properties…
This work presents a distributionally robust Kalman filter to address uncertainties in noise covariance matrices and predicted covariance estimates. We adopt a distributionally robust formulation using bicausal optimal transport to…
The filtering distribution captures the statistics of the state of a dynamical system from partial and noisy observations. Classical particle filters provably approximate this distribution in quite general settings; however they behave…
The paper presents the gossip interactive Kalman filter (GIKF) for distributed Kalman filtering for networked systems and sensor networks, where inter-sensor communication and observations occur at the same time-scale. The communication…