Related papers: State and Parameter Estimation from Observed Signa…
We develop a general framework for state estimation in systems modeled with noise-polluted continuous time dynamics and discrete time noisy measurements. Our approach is based on maximum likelihood estimation and employs the calculus of…
We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty.…
Data-driven prediction and physics-agnostic machine-learning methods have attracted increased interest in recent years achieving forecast horizons going well beyond those to be expected for chaotic dynamical systems. In a separate strand of…
In this paper, we consider the filtering problem of an optical parametric oscillator (OPO). The OPO pump power may fluctuate due to environmental disturbances, resulting in uncertainty in the system modeling. Thus, both the state and the…
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 has been traditionally applied in three application areas of estimation, state estimation, parameter estimation (a.k.a. model updating), and dual estimation. However, Kalman filter is often not sufficient when experimenting…
Chaos is ubiquitous in physical systems. The associated sensitivity to initial conditions is a significant obstacle in forecasting the weather and other geophysical fluid flows. Data assimilation is the process whereby the uncertainty in…
Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state is high dimensional, ensemble Kalman filters are often the method of choice. This paper…
The performance of ensemble-based data assimilation techniques that estimate the state of a dynamical system from partial observations depends crucially on the prescribed uncertainty of the model dynamics and of the observations. These are…
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…
Standard maximum likelihood or Bayesian approaches to parameter estimation for stochastic differential equations are not robust to perturbations in the continuous-in-time data. In this paper, we give a rather elementary explanation of this…
State estimation is a fundamental problem in control and signal processing, for which the Kalman Filter provides an optimal solution under linear dynamics, Gaussian noise, and known noise covariances. However, these assumptions often fail…
In this article, we complement recent results on the convergence of the state estimate obtained by applying the discrete-time Kalman filter on a time-sampled continuous-time system. As the temporal discretization is refined, the estimate…
Kalman filtering is a classic state estimation technique used in application areas such as signal processing and autonomous control of vehicles. It is now being used to solve problems in computer systems such as controlling the voltage and…
Motivated by the maneuvering target tracking with sensors such as radar and sonar, this paper considers the joint and recursive estimation of the dynamic state and the time-varying process noise covariance in nonlinear state space models.…
The Kalman(-Bucy) filter is the natural choice for the state reconstruction of disturbed, linear dynamical systems based on flawed and incomplete measurements. Taking a deterministic viewpoint this work investigates possible extensions of…
For continuous-time linear stochastic dynamical systems driven by Wiener processes, we consider the problem of designing ensemble filters when the observation process is randomly time-sampled. We propose a continuous-discrete McKean--Vlasov…
Sparsity constraints on the control inputs of a linear dynamical system naturally arise in several practical applications such as networked control, computer vision, seismic signal processing, and cyber-physical systems. In this work, we…
The paper is devoted to synthesis of recurrent algorithms for detection of stochastic signals given in state space. The structure of the algorithms synthesized is shown to be close to that of the Kalman filter. Analysis of one of the…
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…