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The Kalman filter is an established tool for the analysis of dynamic systems with normally distributed noise, and it has been successfully applied in numerous application areas. It provides sequentially calculated estimates of the system…
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)…
Stability analysis of the Kalman filter under randomly lost measurements has been widely studied. We revisit this problem in a general continuous-time framework, where both the measurement matrix and noise covariance evolve as random…
Learning in a non-stationary environment is an inevitable problem when applying machine learning algorithm to real world environment. Learning new tasks without forgetting the previous knowledge is a challenge issue in machine learning. We…
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…
In this paper, we investigate stable patterns of electroencephalogram (EEG) over time for emotion recognition using a machine learning approach. Up to now, various findings of activated patterns associated with different emotions have been…
Measuring brain activity with electroencephalography (EEG) is mature enough to assess mental states. Combined with existing methods, such tool can be used to strengthen the understanding of user experience. We contribute a set of methods to…
Traditional statements of the celebrated Kalman filter algorithm focus on the estimation of state, but not the output. For any outputs, measured or auxiliary, it is usually assumed that the posterior state estimates and known inputs are…
Tracking algorithms such as the Kalman filter aim to improve inference performance by leveraging the temporal dynamics in streaming observations. However, the tracking regularizers are often based on the $\ell_p$-norm which cannot account…
Electroencephalography (EEG) is a method to record the electrical signals in the brain. Recognizing the EEG patterns in the sleeping brain gives insights into the understanding of sleeping disorders. The dataset under consideration contains…
In this study, we address the challenges associated with accurately determining gaze location on a screen, which is often compromised by noise from factors such as eye tracker limitations, calibration drift, ambient lighting changes, and…
One-shot pose estimation for tasks such as body joint localization, camera pose estimation, and object tracking are generally noisy, and temporal filters have been extensively used for regularization. One of the most widely-used methods 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…
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…
Accurate estimation of noise parameters is critical for optimal filter performance, especially in systems where true noise parameter values are unknown or time-varying. This article presents a quaternion left-invariant extended Kalman…
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…
We present a single-channel phase-sensitive speech enhancement algorithm that is based on modulation-domain Kalman filtering and on tracking the speech phase using circular statistics. With Kalman filtering, using that speech and noise are…
Electroencephalography foundation models (EEG-FMs) have advanced brain signal analysis, but the lack of standardized evaluation benchmarks impedes model comparison and scientific progress. Current evaluations rely on inconsistent protocols…
In the process of reproducing the state dynamics of parameter dependent distributed systems, data from physical measurements can be incorporated into the mathematical model to reduce the parameter uncertainty and, consequently, improve the…
The extended Kalman filter is perhaps the most standard tool to estimate in real time the state of a dynamical system from noisy measurements of some function of the system, with extensive practical applications (such as position tracking…