Related papers: Quantized Innovations Bayesian Filtering

Estimating the statistics of the state of a dynamical system, from partial and noisy observations, is both mathematically challenging and finds wide application. Furthermore, the applications are of great societal importance, including…

Sequential fine-tuning of transformers is useful when new data arrive sequentially, especially with shifting distributions. Unlike batch learning, sequential learning demands that training be stabilized despite a small amount of data by…

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 article discusses a partially adapted particle filter for estimating the likelihood of a nonlinear structural econometric state space models whose state transition density cannot be expressed in closed form. The filter generates the…

The Ensemble Kalman Filter method can be used as an iterative particle numerical scheme for state dynamics estimation and control--to--observable identification problems. In applications it may be required to enforce the solution to satisfy…

In this paper the Bayesian analysis is applied to assign a probability density to the value of a quantity having a definite sign. This analysis is logically consistent with the results, positive or negative, of repeated measurements.…

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…

We address the problem of observation noise misspecification in Bayesian filtering of dynamical systems via recent advances in generalised Bayesian inference. Mis-match in tail decay between the true data generating process and an assumed…

Model-based filtering is often carried out while subject to an imperfect model, as learning partially-observable stochastic systems remains a challenge. Recent work on Bayesian inference found that tempering the likelihood or full posterior…

We obtain a class of higher-degree stochastic integration filters (SIF) for nonlinear filtering applications. SIF are based on stochastic spherical-radial integration rules that achieve asymptotically exact evaluations of Gaussian weighted…

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…

We describe a measurement device principle based on discrete iterations of Bayesian updating of system state probability distributions. Although purely classical by nature, these measurements are accompanied with a progressive collapse of…

Bayesian experimental design is a technique that allows to efficiently select measurements to characterize a physical system by maximizing the expected information gain. Recent developments in deep neural networks and normalizing flows…

The design of informatively rich input signals is essential for accurate system identification, yet classical Fisher-information-based methods are inherently local and often inadequate in the presence of significant model uncertainty and…

A Bayesian data assimilation scheme is formulated for advection-dominated or hyperbolic evolutionary problems, and observations. The method is referred to as the dynamic likelihood filter because it exploits the model physics to dynamically…

As an example of the recently-introduced concept of rate of innovation, signals that are linear combinations of a finite number of Diracs per unit time can be acquired by linear filtering followed by uniform sampling. However, in reality,…

We consider the problem of randomly choosing the sensors of a linear time-invariant dynamical system subject to process and measurement noise. We sample the sensors independently and from the same distribution. We measure the performance of…

Bayesian inference is a powerful paradigm for quantum state tomography, treating uncertainty in meaningful and informative ways. Yet the numerical challenges associated with sampling from complex probability distributions hampers Bayesian…

Once upon a time, predictions for the accuracy of inference on gravitational-wave signals relied on computationally inexpensive but often inaccurate techniques. Recently, the approach has shifted to actual inference on noisy signals with…

Many dynamical systems are subjected to stochastic influences, such as random excitations, noise, and unmodeled behavior. Tracking the system's state and parameters based on a physical model is a common task for which filtering algorithms,…