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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…

Numerical Analysis · Mathematics 2025-06-03 J. A. Carrillo , F. Hoffmann , A. M. Stuart , U. Vaes

Optimization techniques play a crucial role in estimating parameters and state information for nonlinear systems. However, some critical aspects of these problems have received little attention in previous research. In this paper, we…

Optimization and Control · Mathematics 2023-06-02 Kaushal Kumar

We present a parameter estimation method in Ordinary Differential Equation (ODE) models. Due to complex relationships between parameters and states the use of standard techniques such as nonlinear least squares can lead to the presence of…

Methodology · Statistics 2018-10-11 Quentin Clairon

Standard battery management systems treat the control and state estimation problems as decoupled objectives, relying on certainty equivalence controllers that are blind to the varying observability induced by nonlinear open-circuit voltage…

Systems and Control · Electrical Eng. & Systems 2026-04-17 Mohammad S. Ramadan , Marfred Barrera , Mihai Anitescu , Sylvia Herbert

Controlling nonlinear dynamical systems remains a central challenge in a wide range of applications, particularly when accurate first-principle models are unavailable. Data-driven approaches offer a promising alternative by designing…

Systems and Control · Electrical Eng. & Systems 2025-12-23 Robin Strässer , Karl Worthmann , Igor Mezić , Julian Berberich , Manuel Schaller , Frank Allgöwer

In this paper we perform an experimental comparison of three different target based 3D-LIDAR camera calibration algorithms. We briefly elucidate the mathematical background behind each method and provide insights into practical aspects like…

Robotics · Computer Science 2020-07-07 Subodh Mishra , Philip R. Osteen , Gaurav Pandey , Srikanth Saripalli

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…

Optimization and Control · Mathematics 2026-01-16 Griffin M. Kearney , Makan Fardad

This paper studies a nonlinear filtering problem over an infinite time interval. The signal to be estimated is driven by a stochastic partial differential equation involves unknown parameters. Based on discrete observation, strongly…

Statistics Theory · Mathematics 2021-07-12 Qizhu Liang , Jie Xiong , Xingqiu Zhao

We present a new calibration scheme based on a non-linear version of Kalman filter that aims at estimating the physical terms appearing in the Radio Interferometry Measurement Equation (RIME). We enrich the filter's structure with a tunable…

Instrumentation and Methods for Astrophysics · Physics 2015-06-19 Cyril Tasse

We review optimization-based approaches to smoothing nonlinear dynamical systems. These approaches leverage the fact that the Extended Kalman Filter and corresponding smoother can be framed as the Gauss-Newton method for a nonlinear least…

Optimization and Control · Mathematics 2025-10-07 Payton Howell , Aleksandr Aravkin

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…

Methodology · Statistics 2025-03-17 Jan Albrecht , Sebastian Reich

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…

Optimization and Control · Mathematics 2015-12-09 Atte Aalto

In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…

Numerical Analysis · Mathematics 2024-12-20 Max Winkler

Water treatment and liquid storage are the two plants implementing the hydraulic three-tank system. Maintaining certain levels is the critical scenario so that the systems run as desired. To deal with, the optimal linear control and the…

Systems and Control · Electrical Eng. & Systems 2026-04-07 Bambang L. Widjiantoro , Katherin Indriawati , Moh Kamalul Wafi

This paper studies the optimal state estimation for a dynamic system, whose transfer function can be nonlinear and the input noise can be of arbitrary distribution. Our algorithm differs from the conventional extended Kalman filter (EKF)…

Signal Processing · Electrical Eng. & Systems 2022-04-22 Xin Liang , Yi Jiang

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…

Optimization and Control · Mathematics 2022-09-12 Davide Ghion , Mattia Zorzi

This paper considers homography estimation in a Bayesian filtering framework using rate gyro and camera measurements. The use of rate gyro measurements facilitates a more reliable estimate of homography in the presence of occlusions, while…

Robotics · Computer Science 2023-10-17 Arturo Del Castillo Bernal , Philippe Decoste , James Richard Forbes

Accurate estimation of the dynamic states of a synchronous machine (e.g., rotor s angle and speed) is essential in monitoring and controlling transient stability of a power system. It is well known that the covariance matrixes of process…

Systems and Control · Computer Science 2017-02-06 Shahrokh Akhlaghi , Ning Zhou , Zhenyu Huang

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…

Statistics Theory · Mathematics 2016-06-30 Andrew J. Majda , Xin T. Tong

Post-selection strategies have been proposed with the aim of amplifying weak signals, which may help to overcome detection thresholds associated with technical noise in high-precision measurements. Here we use an optical setup to…

Quantum Physics · Physics 2017-01-11 G. Bié Alves , A. Pimentel , M. Hor-Meyll , S. P. Walborn , L. Davidovich , R. L. de Matos Filho