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Transformer models have shown great success in natural language processing; however, their potential remains mostly unexplored for dynamical systems. In this work, we investigate the optimal output estimation problem using transformers,…
This work extends a previous study that introduced an algorithm for state estimation on manifolds within the framework of the Kalman filter. Its objective is to address the limitations of the earlier approach. The reversible Kalman filter…
Robustness and adaptivity are two competing objectives in Kalman filters (KF). Robustness involves temporarily inflating prior estimates of noise covariances, while adaptivity updates prior beliefs by exploiting measurements. In practical…
We consider the solution of inverse problems in dynamic contrast-enhanced imaging by means of Ensemble Kalman Filters. Our quantity of interest is blood perfusion, i.e. blood flow rates in tissue. While existing approaches to compute blood…
In this paper, we study the sensor selection problem for remote state estimation under the Quality-of-Service (QoS) requirement constraints. Multiple sensors are employed to observe a linear time-invariant system, and their measurements…
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…
A recently developed data-driven Kalman filter requires offline measurement of the process disturbance; a requirement that is often unmet for many practical applications. We propose a solution that parametrizes the Kalman filter exclusively…
The literature dealing with data-driven analysis and control problems has significantly grown in the recent years. Most of the recent literature deals with linear time-invariant systems in which the uncertainty (if any) is assumed to be…
The estimation of non-Gaussian measurement noise models is a significant challenge across various fields. In practical applications, it often faces challenges due to the large number of parameters and high computational complexity. This…
The Koopman operator enables simplified representations for nonlinear systems in data-driven optimal control, but the accompanying uncertainties inevitably induce deviations in the optimal controller and associated value function. This…
We consider the problem of optimal power allocation in a sensor network where the sensors observe a dynamic parameter in noise and coherently amplify and forward their observations to a fusion center (FC). The FC uses the observations in a…
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…
Since the innovation of the ubiquitous Kalman filter more than five decades back it is well known that to obtain the best possible estimates the tuning of its statistics $X_0$, $P_0$, $\Theta$, $R$ and $Q$ namely initial state and…
We introduce Kalman Gradient Descent, a stochastic optimization algorithm that uses Kalman filtering to adaptively reduce gradient variance in stochastic gradient descent by filtering the gradient estimates. We present both a theoretical…
Sensor selection is an important design problem in large-scale sensor networks. Sensor selection can be interpreted as the problem of selecting the best subset of sensors that guarantees a certain estimation performance. We focus on…
We consider the problem of finding optimal piecewise constant approximations of one-dimensional signals. These approximations should consist of a specified number of segments (samples) and minimise the mean squared error to the original…
We consider the problem of distributed Kalman filtering for sensor networks in the case there are constraints in data transmission and there is model uncertainty. More precisely, we propose two distributed filtering strategies with…
We present a systematic approach to the optimal placement of finitely many sensors in order to infer a finite-dimensional parameter from point evaluations of the solution of an associated parameter-dependent elliptic PDE. The quality of the…
Filtering is a widely used methodology for the incorporation of observed data into time-evolving systems. It provides an online approach to state estimation inverse problems when data is acquired sequentially. The Kalman filter plays a…
In standard treatments of stochastic filtering one first has to estimate the values of the parameters of the model. Simply running the filter without considering the reliability of this estimate does not take into account this additional…