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As a burgeoning medical imaging method based on hybrid fusion of light and ultrasound, photoacoustic imaging (PAI) has demonstrated high potential in various biomedical applications recently, especially in revealing the functional and…

Ensemble Kalman filter (EnKF) has been widely used in state estimation and parameter estimation for the dynamic system where observational data is obtained sequentially in time. To reduce uncertainty and accelerate posterior inference, a…

Data assimilation is a method of uncertainty quantification to estimate the hidden true state by updating the prediction owing to model dynamics with observation data. As a prediction model, we consider a class of nonlinear dynamical…

We make modifications to the unscented Kalman filter (UKF) which bestow almost complete practical identifiability upon a lumped-parameter cardiovascular model with 10 parameters and 4 output observables - a highly non-linear, stiff problem…

The ensemble Kalman filter is a well-known and celebrated data assimilation algorithm. It is of particular relevance as it used for high-dimensional problems, by updating an ensemble of particles through a sample mean and covariance…

We present the collaborative Kalman filter (CKF), a dynamic model for collaborative filtering and related factorization models. Using the matrix factorization approach to collaborative filtering, the CKF accounts for time evolution by…

Data assimilation (DA) for compressible flows with shocks is challenging because many classical DA methods generate spurious oscillations and nonphysical features near uncertain shocks. We focus here on the ensemble Kalman filter (EnKF). We…

Recent researches in data assimilation lead to the introduction of the parametric Kalman filter (PKF): an implementation of the Kalman filter, where the covariance matrices are approximated by a parameterized covariance model. In the PKF,…

This paper develops efficient ensemble Kalman filter (EnKF) implementations based on shrinkage covariance estimation. The forecast ensemble members at each step are used to estimate the background error covariance matrix via the…

This paper investigates the control barrier function (CBF) based safety-critical control for continuous nonlinear control affine systems using the more efficient online algorithms through time-varying optimization. The idea lies in that…

High fidelity behavior prediction of human drivers is crucial for efficient and safe deployment of autonomous vehicles, which is challenging due to the stochasticity, heterogeneity, and time-varying nature of human behaviors. On one hand,…

The Unscented Kalman Filter (UKF) is a ubiquitous tool for nonlinear state estimation; however, its performance is limited by the static parameterization of the Unscented Transform (UT). Conventional weighting schemes, governed by fixed…

In this paper we propose a novel observer-based method for anomaly detection in connected and automated vehicles (CAVs). The proposed method utilizes an augmented extended Kalman filter (AEKF) to smooth sensor readings of a CAV based on a…

The extended Kalman filter (EKF) has been the industry standard for state estimation problems over the past sixty years. The Invariant Extended Kalman Filter (IEKF) is a recent development of the EKF for the class of group-affine systems on…

Accurate structural response prediction forms a main driver for structural health monitoring and control applications. This often requires the proposed model to adequately capture the underlying dynamics of complex structural systems. In…

The sample covariance matrix of a random vector is a good estimate of the true covariance matrix if the sample size is much larger than the length of the vector. In high-dimensional problems, this condition is never met. As a result, in…

Markov chain Monte Carlo (MCMC) methods are powerful computational tools for analysis of complex statistical problems. However, their computational efficiency is highly dependent on the chosen proposal distribution, which is generally…

For an improper complex signal x, its complementary covariance ExxT is not zero and thus it carries useful statistical information about x. Widely linear processing exploits Hermitian and complementary covariance to improve performance. In…

We propose a method to account for model error due to unresolved scales in the context of the ensemble transform Kalman filter (ETKF). The approach extends to this class of algorithms the deterministic model error formulation recently…

We describe an application of the Invariant Extended Kalman Filter (IEKF) design methodology to the scan matching SLAM problem. We review the theoretical foundations of the IEKF and its practical interest of guaranteeing robustness to poor…