Related papers: The Convergence of the Extended Kalman Filter
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…
We consider filtering for a continuous-time, or asynchronous, stochastic system where the full distribution over states is too large to be stored or calculated. We assume that the rate matrix of the system can be compactly represented and…
Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
Complex systems are often described with competing models. Such divergence of interpretation on the system may stem from model fidelity, mathematical simplicity, and more generally, our limited knowledge of the underlying processes.…
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…
This paper revisits the question of duality between minimum variance estimation and optimal control first described for the linear Gaussian case in the celebrated paper of Kalman and Bucy. A duality result is established for nonlinear…
We study a distributed Kalman filtering problem in which a number of nodes cooperate without central coordination to estimate a common state based on local measurements and data received from neighbors. This is typically done by running a…
An important part of system modeling is determining parameter values, particularly for biomolecular systems, where direct measurements of individual parameters are typically hard. While Extended Kalman Filters have been used for this…
Many robotic sensor estimation problems can characterized in terms of nonlinear measurement systems. These systems are contaminated with noise and may be underdetermined from a single observation. In order to get reliable estimation…
Many nonlinear extensions of the Kalman filter, e.g., the extended and the unscented Kalman filter, reduce the state densities to Gaussian densities. This approximation gives sufficient results in many cases. However, this filters only…
The literature dealing with data-driven analysis and control problems has significantly grown in the recent years. Most of the recent literature deals with linear time-invariant systems in which the uncertainty (if any) is assumed to be…
Inertial measurement units are widely used in different fields to estimate the attitude. Many algorithms have been proposed to improve estimation performance. However, most of them still suffer from 1) inaccurate initial estimation, 2)…
This article examines state estimation in discrete-time nonlinear stochastic systems with finite-dimensional states and infinite-dimensional measurements, motivated by real-world applications such as vision-based localization and tracking.…
In this article, we present a structured Kalman filter associated with the transformation matrix for observable Kalman canonical decomposition from conventional Kalman filter (CKF) in order to generate a more accurate time scale. The…
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…
This work concerns the nonlinear filtering problem of multiscale McKean-Vlasov stochastic systems where the whole systems depend on distributions of fast components. First of all, we prove that the slow component of the original system…
A novel approximate Bayesian filter based on backward stochastic differential equations is introduced. It uses a nonlinear Feynman--Kac representation of the filtering problem and the approximation of an unnormalized filtering density using…
The Kalman filter (KF) is an optimal linear state estimator for linear systems, and numerous extensions, including the extended Kalman filter (EKF), unscented Kalman filter (UKF), and cubature Kalman filter (CKF), have been developed for…
We study the Extended Kalman Filter in constant dynamics, offering a bayesian perspective of stochastic optimization. We obtain high probability bounds on the cumulative excess risk in an unconstrained setting. In order to avoid any…