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This paper introduces a novel state estimation framework for robots using differentiable ensemble Kalman filters (DEnKF). DEnKF is a reformulation of the traditional ensemble Kalman filter that employs stochastic neural networks to model…

In many physical applications, the system's state varies with spatial variables as well as time. The state of such systems is modelled by partial differential equations and evolves on an infinite-dimensional space. Systems modelled by…

Extracting time-varying latent variables from computational cognitive models is a key step in model-based neural analysis, which aims to understand the neural correlates of cognitive processes. However, existing methods only allow…

Predicting the behavior of a dynamical system from noisy observations of its past outputs is a classical problem encountered across engineering and science. For linear systems with Gaussian inputs, the Kalman filter -- the best linear…

The ensemble Kalman filter (EnKF) is a recursive filter suitable for problems with a large number of variables, such as discretizations of partial differential equations in geophysical models. The EnKF originated as a version of the Kalman…

We consider the problem of learning time-varying functions in a distributed fashion, where agents collect local information to collaboratively achieve a shared estimate. This task is particularly relevant in control applications, whenever…

This paper derives the extended Kalman filter (EKF) for continuous-time systems on matrix Lie groups observed through discrete-time measurements. By modeling the system noise on the Lie algebra and adopting a Stratonovich interpretation for…

Invariant extended Kalman filter (InEKF) possesses excellent trajectory-independent property and better consistency compared to conventional extended Kalman filter (EKF). However, when applied to scenarios involving both global-frame and…

The ensemble Kalman filter (EnKF) is a Monte Carlo approximation of the Kalman filter for high dimensional linear Gaussian state space models. EnKF methods have also been developed for parameter inference of static Bayesian models with a…

Sequential Bayesian filters in non-linear dynamic systems require the recursive estimation of the predictive and posterior distributions. This paper introduces a Bayesian filter called the adaptive kernel Kalman filter (AKKF). With this…

Real-time nonlinear Bayesian filtering algorithms are overwhelmed by data volume, velocity and increasing complexity of computational models. In this paper, we propose a novel ensemble based nonlinear Bayesian filtering approach which only…

State estimation of dynamical systems in real-time is a fundamental task in signal processing. For systems that are well-represented by a fully known linear Gaussian state space (SS) model, the celebrated Kalman filter (KF) is a low…

The iterative ensemble Kalman filter (IEnKF) is widely used in inverse problems to estimate system parameters from limited observations. However, the IEnKF, when applied to nonlinear systems, can be plagued by poor convergence. Here we…

Recent advances in counter-adversarial systems have garnered significant research attention to inverse filtering from a Bayesian perspective. For example, interest in estimating the adversary's Kalman filter tracked estimate with the…

A stochastic filter uses a series of measurements over time to produce estimates of unknown variables based on a dynamic model. For a quantum system, such an algorithm is provided by a quantum filter, which is also known as a stochastic…

In Online Continual Learning (OCL) a learning system receives a stream of data and sequentially performs prediction and training steps. Important challenges in OCL are concerned with automatic adaptation to the particular non-stationary…

Because of physical assumptions and numerical approximations, low-order models are affected by uncertainties in the state and parameters, and by model biases. Model biases, also known as model errors or systematic errors, are difficult to…

Extended Kalman Filtering (EKF) can be used to propagate and quantify input uncertainty through a Deep Neural Network (DNN) assuming mild hypotheses on the input distribution. This methodology yields results comparable to existing methods…

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…

Ensemble Kalman filter (EnKF) is an important data assimilation method for high dimensional geophysical systems. Efficient implementation of EnKF in practice often involves the localization technique, which updates each component using only…