Related papers: Desensitized Kalman Filtering with Analytical Gain

Kalman filter is a best linear unbiased state estimator. It is also comprehensible from the point view of the Bayesian estimation. However, this note gives a detailed derivation of Kalman filter from the mutual information perspective for…

This article presents an up-to-date tutorial review of nonlinear Bayesian estimation. State estimation for nonlinear systems has been a challenge encountered in a wide range of engineering fields, attracting decades of research effort. To…

Stochastic parameterizations are increasingly being used to represent the uncertainty associated with model errors in ensemble forecasting and data assimilation. One of the challenges associated with the use of these parameterizations is…

Kalman filtering can provide an optimal estimation of the system state from noisy observation data. This algorithm's performance depends on the accuracy of system modeling and noise statistical characteristics, which are usually challenging…

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…

We consider Kalman filtering problems when the observations are intermittently erased or lost. It was known that the estimates are mean-square unstable when the erasure probability is larger than a certain critical value, and stable…

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…

Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…

Traditional statements of the celebrated Kalman filter algorithm focus on the estimation of state, but not the output. For any outputs, measured or auxiliary, it is usually assumed that the posterior state estimates and known inputs are…

We present a novel quantum tomographic reconstruction method based on Bayesian inference via the Kalman filter update equations. The method not only yields the maximum likelihood/optimal Bayesian reconstruction, but also a covariance matrix…

We introduce the inverse Kalman filter, which enables exact matrix-vector multiplication between a covariance matrix from a dynamic linear model and any real-valued vector with linear computational cost. We integrate the inverse Kalman…

State estimation when only a partial model of a considered system is available remains a major challenge in many engineering fields. This work proposes a joint, square-root unscented Kalman filter to estimate states and model uncertainties…

The characteristics of the model dynamics are critical in the performance of (ensemble) Kalman filters. In particular, as emphasized in the seminal work of Anna Trevisan and co-authors, the error covariance matrix is asymptotically…

This paper is concerned with the problem of distributed Kalman filtering in a network of interconnected subsystems with distributed control protocols. We consider networks, which can be either homogeneous or heterogeneous, of linear…

The extraction of weak signals plays a crucial role in quantum precision measurement, where the estimation results are often limited by low signal-to-noise ratios. Here, we demonstrate a parameter-estimation framework based on the adaptive…

The ensemble Kalman filter (EnKF) is a data assimilation technique that uses an ensemble of models, updated with data, to track the time evolution of a usually non-linear system. It does so by using an empirical approximation to the…

Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of…

Conventional Bayesian estimation requires an accurate stochastic model of a system. However, this requirement is not always met in many practical cases where the system is not completely known or may differ from the assumed model. For such…

The Kalman filter is extensively used for state estimation for linear systems under Gaussian noise. When non-Gaussian L\'evy noise is present, the conventional Kalman filter may fail to be effective due to the fact that the non-Gaussian…

Contemporary data assimilation often involves millions of prediction variables. The classical Kalman filter is no longer computationally feasible in such a high dimensional context. This problem can often be resolved by exploiting the…