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The observables of a noisy quantum system can be estimated by appropriately filtering the records of their continuous measurement. Such filtering is relevant for state estimation and measurement-based quantum feedback control. It is…
Practical Bayes filters often assume the state distribution of each time step to be Gaussian for computational tractability, resulting in the so-called Gaussian filters. When facing nonlinear systems, Gaussian filters such as extended…
Accurate modeling is crucial in many engineering and scientific applications, yet obtaining a reliable process model for complex systems is often challenging. To address this challenge, we propose a novel framework, reservoir computing with…
Bayesian filtering is a general framework for recursively estimating the state of a dynamical system. Classical solutions such that Kalman filter and Particle filter are introduced in this report. Gaussian processes have been introduced as…
This paper studies the distributed state estimation problem for a class of discrete time-varying systems over sensor networks. Firstly, it is shown that a networked Kalman filter with optimal gain parameter is actually a centralized filter,…
In this work, we present methods for state estimation in continuous-discrete nonlinear systems involving stochastic differential equations. We present the extended Kalman filter, the unscented Kalman filter, the ensemble Kalman filter, and…
Conventional Kalman filtering (KF) approaches exhibit significant limitations in addressing nonlinear state estimation problems contaminated by non-Gaussian noise disturbances. To overcome these challenges, this work proposes a robust…
Traditional Kalman filter (KF) is derived under the well-known minimum mean square error (MMSE) criterion, which is optimal under Gaussian assumption. However, when the signals are non-Gaussian, especially when the system is disturbed by…
Biomolecular systems are often modeled with partially known nonlinear stochastic dynamics, making state and parameter estimation a central challenge. While Kalman filtering techniques are widely used in this setting, their performance…
Leveraging the unique quantum properties of non-Gaussian states is crucial for advancing continuous variable quantum technologies. Recent experimental advancements in generating non-Gaussian states, coupled with theoretical findings of…
We propose a measure of non-Gaussianity for quantum states of a system of $n$ oscillator modes. Our measure is based on the quasi-probability $Q(\alpha), \alpha\in{\cal C}^n$. Since any measure of non-Gaussianity is necessarily an attempt…
We establish the potential of continuous-variable Gaussian states of linear dynamical systems for machine learning tasks. Specifically, we consider reservoir computing, an efficient framework for online time series processing. As a…
Filtering is a general name for inferring the states of a dynamical system given observations. The most common filtering approach is Gaussian Filtering (GF) where the distribution of the inferred states is a Gaussian whose mean is an affine…
This paper presents a novel adaptive fading cubature Kalman filter (AFCKF) based on double transitive factors. The developed adaptive algorithm is explained in two stages; stage (i) a single transitive factor is used to update the predicted…
Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems is a fundamental yet challenging problem in many fields of science and engineering. Existing methods face significant obstacles: Gaussian-based filters struggle…
Quantum reservoir computing is a machine learning scheme in which a quantum system is used to perform information processing. A prospective approach to its physical realization is a photonic platform in which continuous variable (CV)…
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, the problem of state estimation, in the context of both filtering and smoothing, for nonlinear state-space models is considered. Due to the nonlinear nature of the models, the state estimation problem is generally intractable…
Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The impact is described by the conditional quantile function and its functionals. In this paper we develop the nonparametric…
Consistent state estimation is challenging, especially under the epistemic uncertainties arising from learned (nonlinear) dynamic and observation models. In this work, we propose a set-based estimation algorithm, named Gaussian…