Related papers: Nonlinear Kalman Filtering with Reparametrization …
The Kalman filter (KF) provides optimal recursive state estimates for linear-Gaussian systems and underpins applications in control, signal processing, and others. However, it is vulnerable to outliers in the measurements and process noise.…
Kalman filtering can provide an optimal estimation of the system state from noisy observation data. This algorithm's performance depends on the accuracy of system modeling and noise statistical characteristics, which are usually challenging…
This paper describes a method to filter oscillatory transients from measurements of a time series which were at least an order of magnitude larger than the signal to be measured. Based on a Kalman filter, it has an optimality property and a…
The Kalman filter and its extensions are used in a vast number of aerospace and navigation applications for nonlinear state estimation of time series. In the literature, different approaches have been proposed to exploit the structure of…
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…
Transmission electron microscopes (TEMs) enable atomic-scale imaging but suffer from aberrations caused by lens imperfections and environmental conditions, reducing image quality. These aberrations can be compensated by adjusting…
We present a novel approach to approximate Gaussian and mixture-of-Gaussians filtering. Our method relies on a variational approximation via a gradient-flow representation. The gradient flow is derived from a Kullback--Leibler discrepancy…
Differential equations are used to model and predict the behaviour of complex systems in a wide range of fields, and the ability to solve them is an important asset for understanding and predicting the behaviour of these systems.…
This paper addresses the problem of optimal linear filtering in a network of local estimators, commonly referred to as distributed Kalman filtering (DKF). The DKF problem is formulated within a distributed optimization framework, where…
An optimal estimator of quantum states based on a modified Kalman's Filter is proposed in this work. Such estimator acts after state measurement, allowing obtain an optimal estimation of quantum state resulting in the output of any quantum…
The extended Kalman filter is perhaps the most standard tool to estimate in real time the state of a dynamical system from noisy measurements of some function of the system, with extensive practical applications (such as position tracking…
We consider approximate maximum likelihood parameter estimation in nonlinear state-space models. We discuss both direct optimization of the likelihood and expectation--maximization (EM). For EM, we also give closed-form expressions for the…
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…
Experimental data is costly to obtain, which makes it difficult to calibrate complex models. For many models an experimental design that produces the best calibration given a limited experimental budget is not obvious. This paper introduces…
We derive a decomposition for the gradient of the innovation loss with respect to the filter gain in a linear time-invariant system, decomposing as a product of an observability Gramian and a term quantifying the ``non-orthogonality"…
Autonomous vehicles have gained significant attention due to technological advancements and their potential to transform transportation. A critical challenge in this domain is precise localization, particularly in LiDAR-based map matching,…
The unscented Kalman filter is an algorithm capable of handling nonlinear scenarios. Uncertainty in process noise covariance may decrease the filter estimation performance or even lead to its divergence. Therefore, it is important to adjust…
Kalman filtering and smoothing are the foundational mechanisms for efficient inference in Gauss-Markov models. However, their time and memory complexities scale prohibitively with the size of the state space. This is particularly…
A theoretical framework for non-negative matrix factorization based on generalized dual Kullback-Leibler divergence, which includes members of the exponential family of models, is proposed. A family of algorithms is developed using this…
Training of autoencoders using the back-propagation algorithm is challenging for non-differential channel models or in an experimental environment where gradients cannot be computed. In this paper, we study a gradient-free training method…