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Counter-adversarial system design problems have lately motivated the development of inverse Bayesian filters. For example, inverse Kalman filter (I-KF) has been recently formulated to estimate the adversary's Kalman-filter-tracked estimates…

We investigate a stochastic version of the synthetic multicellular clock model proposed by Garcia-Ojalvo, Elowitz and Strogatz. By introducing dynamical noise in the model and assuming that the partial observations of the system can be…

The ensemble Kalman filter (EnKF) and ensemble square root filter (ESRF) are data assimilation methods used to combine high dimensional, nonlinear dynamical models with observed data. Despite their widespread usage in climate science and…

The robust estimation of dynamically changing features, such as the position of prey, is one of the hallmarks of perception. On an abstract, algorithmic level, nonlinear Bayesian filtering, i.e. the estimation of temporally changing signals…

This paper tackles the intricate task of jointly estimating state and parameters in data assimilation for stochastic dynamical systems that are affected by noise and observed only partially. While the concept of ``optimal filtering'' serves…

Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…

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…

State estimation of dynamical systems from noisy observations is a fundamental task in many applications. It is commonly addressed using the linear Kalman filter (KF), whose performance can significantly degrade in the presence of outliers…

The Derivative-free nonlinear Kalman Filter is proposed for state estimation and fault diagnosis in distributed parameter systems and particularly in dynamical systems described by partial differential equations of the nonlinear wave type.…

We present a practical implementation of the ensemble Kalman (EnKF) filter based on an iterative Sherman-Morrison formula. The new direct method exploits the special structure of the ensemble-estimated error covariance matrices in order to…

Objective: Mixtures of temporally nonstationary signals are very common in biomedical applications. The nonstationarity of the source signals can be used as a discriminative property for signal separation. Herein, a semi-blind source…

Identifying parameters in a system of nonlinear, ordinary differential equations is vital for designing a robust controller. However, if the system is stochastic in its nature or if only noisy measurements are available, standard…

In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…

This work presents a fast, uncertainty-aware sequential data assimilation framework for estimating key aerodynamic states (e.g., instantaneous vorticity fields and aerodynamic loads) during severe gust encounters, where vortex-gust…

This paper is concerned with the filtering problem in continuous-time. Three algorithmic solution approaches for this problem are reviewed: (i) the classical Kalman-Bucy filter which provides an exact solution for the linear Gaussian…

The phase-field approach to brittle fracture provides a continuum framework for modeling crack initiation and propagation without explicit representation of discrete crack surfaces, provided the spatial discretization is fine enough to…

We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…

We consider inference for a collection of partially observed, stochastic, interacting, nonlinear dynamic processes. Each process is identified with a label called its unit, and our primary motivation arises in biological metapopulation…

An Ensemble Kalman Filter (EnKF, the predictor) is used make a large change in the state, followed by a Particle Filer (PF, the corrector) which assigns importance weights to describe non-Gaussian distribution. The weights are obtained by…

This paper focuses on developing a method to obtain an uncertain linear fractional transformation (LFT) system that adequately captures the dynamics of a nonlinear time-invariant system over some desired envelope. First, the nonlinear…