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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.…
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…
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…
The Kalman filter is a fundamental filtering algorithm that fuses noisy sensory data, a previous state estimate, and a dynamics model to produce a principled estimate of the current state. It assumes, and is optimal for, linear models and…
Based on Bellman's dynamic-programming principle, Lange (2024) presents an approximate method for filtering, smoothing and parameter estimation for possibly non-linear and/or non-Gaussian state-space models. While the approach applies more…
This paper studies the distributed state estimation problem for a class of discrete-time stochastic systems with nonlinear uncertain dynamics over time-varying topologies of sensor networks. An extended state vector consisting of the…
The unscented Kalman filter is an algorithm capable of handling nonlinear scenarios. Uncertainty in process noise covariance may decrease the filter estimation performance or even lead to its divergence. Therefore, it is important to adjust…
Koopman spectral analysis plays a crucial role in understanding and modeling nonlinear dynamical systems as it reveals key system behaviors and long-term dynamics. However, the presence of measurement noise poses a significant challenge to…
Classical discriminant analysis assumes identically distributed training data, yet in many applications observations are collected over time and the class-conditional distributions drift. This population drift renders stationary classifiers…
We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to…
We present a Kalman smoothing framework based on modeling errors using the heavy tailed Student's t distribution, along with algorithms, convergence theory, open-source general implementation, and several important applications. The…
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 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 application of neural networks in modeling dynamic systems has become prominent due to their ability to estimate complex nonlinear functions. Despite their effectiveness, neural networks face challenges in long-term predictions, where…
The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode…
We present an efficient and practical (polynomial time) algorithm for online prediction in unknown and partially observed linear dynamical systems (LDS) under stochastic noise. When the system parameters are known, the optimal linear…
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.…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…
Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us…
Predicting the behavior of a dynamical system from noisy observations of its past outputs is a classical problem encountered across engineering and science. For linear systems with Gaussian inputs, the Kalman filter -- the best linear…