Related papers: The Kalman Filter: a didactical overview
Estimating parameters of a diffusion process given continuous-time observations of the process via maximum likelihood approaches or, online, via stochastic gradient descent or Kalman filter formulations constitutes a well-established…
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…
In this paper, we consider the task of designing a Kalman Filter (KF) for an unknown and partially observed autonomous linear time invariant system driven by process and sensor noise. To do so, we propose studying the following two step…
Uncertain parameters of state-space models have always been a considerable problem. Consider Kalman filter (CKF) and desensitized Kalman filter (DKF) are two methods to solve this problem. Based on the sensitivity matrix respected to the…
Marginalization techniques are presented for the Bayesian filtering problem under the assumption of Gaussian priors and posteriors and a set of sequentially more constraining state space model assumptions. The techniques provide the…
There is a growing interest in using Kalman-filter models in brain modelling. In turn, it is of considerable importance to make Kalman-filters amenable for reinforcement learning. In the usual formulation of optimal control it is computed…
In order for biomass drying processes to be efficient, it is crucial to achieve the target residual water content within a close margin, since more conservative drying would result in a waste of energy. A method for a reliable estimation of…
Among the class of nonlinear particle filtering methods, the Ensemble Kalman Filter (EnKF) has gained recent attention for its use in solving inverse problems. We review the original method and discuss recent developments in particular in…
This paper presents a new filter for state-space models based on Bellman's dynamic-programming principle, allowing for nonlinearity, non-Gaussianity and degeneracy in the observation and/or state-transition equations. The resulting Bellman…
The Kalman filter is the most powerful tool for estimation of the states of a linear Gaussian system. In addition, using this method, an expectation maximization algorithm can be used to estimate the parameters of the model. However, this…
A new application of duality relations of stochastic processes is demonstrated. Although conventional usages of the duality relations need analytical solutions for the dual processes, we here employ numerical solutions of the dual processes…
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…
In this paper, the ensemble consider Kalman filter is proposed to mitigate the negative effects of uncertain parameters in nonlinear dynamic and measurement models. The ensemble Kalman filter can avoid using the Jacobian matrices and reduce…
The Kalman filter (KF) is an optimal linear state estimator for linear systems, and numerous extensions, including the extended Kalman filter (EKF), unscented Kalman filter (UKF), and cubature Kalman filter (CKF), have been developed for…
Detailed dynamical systems' models used in the life sciences may include hundreds of state variables and many input parameters, often with physical meaning. Therefore, efficient and unique input parameter identification, from experimental…
The implicit particle filter seeks to mitigate particle degeneracy by identifying particles in the target distribution's high-probability regions. This study is motivated by the need to enhance computational tractability in implementing…
We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and…
The problem of multisensor multitarget state estimation in the presence of constant but unknown sensor biases is investigated. The classical approach to this problem is to augment the state vector to include the states of all the targets…
Inverse problems are more challenging when only partial data are available in general. In this paper, we propose a two-step approach combining the extended sampling method and the ensemble Kalman filter to reconstruct an elastic rigid…
We consider the problem of estimating the means $\mu_i$ of $n$ random variables $Y_i \sim N(\mu_i,1)$, $i=1,\ldots ,n$. Assuming some structure on the $\mu$ process, e.g., a state space model, one may use a summary statistics for the…