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Kalman Filter (KF) is an optimal linear state prediction algorithm, with applications in fields as diverse as engineering, economics, robotics, and space exploration. Here, we develop an extension of the KF, called a Pathspace Kalman Filter…
Traditional statements of the celebrated Kalman filter algorithm focus on the estimation of state, but not the output. For any outputs, measured or auxiliary, it is usually assumed that the posterior state estimates and known inputs are…
Sliding window-factor graph optimization (SW-FGO) has gained more and more attention in navigation research due to its robust approximation to non-Gaussian noises and nonlinearity of measuring models. There are lots of works focusing on its…
State estimation that combines observational data with mathematical models is central to many applications and is commonly addressed through filtering methods, such as ensemble Kalman filters. In this article, we examine the signal-tracking…
The Gaussian process state-space models (GPSSMs) represent a versatile class of data-driven nonlinear dynamical system models. However, the presence of numerous latent variables in GPSSM incurs unresolved issues for existing variational…
Metric descriptions of gravitation, among them general relativity as today's established theory, are founded on assumptions summarized by the Einstein equivalence principle (EEP). Its violation would hint at unknown physics and could be a…
In general relativity, the picture of spacetime assigns an ideal clock to each worldline. Being ideal, gravitational effects due to these clocks are ignored and the flow of time according to one clock is not affected by the presence of…
A quantum error correcting protocol can be substantially improved by taking into account features of the physical noise process. We present an efficient decoder for the surface code which can account for general noise features, including…
Data assimilation schemes are confronted with the presence of model errors arising from the imperfect description of atmospheric dynamics. These errors are usually modeled on the basis of simple assumptions such as bias, white noise, first…
Ensemble Kalman Filtering (EnKF) is a popular technique for data assimilation, with far ranging applications. However, the vanilla EnKF framework is not well-defined when perturbations are nonlinear. We study two non-linear extensions of…
We describe a collective state atomic clock with Ramsey fringes narrowed by a factor of $\sqrt{N}$ compared to a conventional clock, N being the number of non-interacting atoms, without violating the uncertainty relation. This narrowing is…
This brief technical note elaborates three well-known state estimators, which are used extensively in practice. These are the rather old-fashioned extended Kalman filter (EKF) and the recently-designed cubature Kalman filtering (CKF) and…
This paper proposes a novel global optimization algorithm, Particle Filter-Based Optimization (PFO), designed for a class of stochastic optimization problems in which the objective function lacks an analytical form and is subject to noisy…
The ensemble Kalman filter (EnKF) (Evensen, 2009) has proven effective in quantifying uncertainty in a number of challenging dynamic, state estimation, or data assimilation, problems such as weather forecasting and ocean modeling. In these…
The Kalman Filter is a widely used approach for the linear estimation of dynamical systems and is frequently employed within nuclear and particle physics experiments for the reconstruction of charged particle trajectories, known as tracks.…
Kalman filter-based algorithms are fundamental for mobile robots, as they provide a computationally efficient solution to the challenging problem of state estimation. However, they rely on two main assumptions that are difficult to satisfy…
This report derives a generalized, converted measurement Kalman filter for the class of filtering problems with a linear state equation and nonlinear measurement equation, for which a bijective mapping exists between the state and…
This paper derives a \emph{distributed} Kalman filter to estimate a sparsely connected, large-scale, $n-$dimensional, dynamical system monitored by a network of $N$ sensors. Local Kalman filters are implemented on the ($n_l-$dimensional,…
Recently, there has been a growing literature exploring the generalization of quantum algorithms, such that different quantum algorithms are special examples of a more fundamental structure. In this short paper, we provide a general…
In this paper, we investigate a distributed estimation problem for multi-agent systems with state equality constraints (SEC). First, under a time-based consensus communication protocol, applying a modified projection operator and the…