Related papers: Stochastic Formulation of Causal Digital Twin: Kal…

We examine the problem of time delay estimation, or temporal calibration, in the context of multisensor data fusion. Differences in processing intervals and other factors typically lead to a relative delay between measurement updates from…

This paper introduces two new algorithms to accurately estimate the process noise covariance of a discrete-time Kalman filter online for robust orbit determination in the presence of dynamics model uncertainties. Common orbit determination…

The Recursive KalmanNet, recently introduced by the authors, is a recurrent neural network guided by a Kalman filter, capable of estimating the state variables and error covariance of stochastic dynamic systems from noisy measurements,…

Causal discovery between collections of time-series data can help diagnose causes of symptoms and hopefully prevent faults before they occur. However, reliable causal discovery can be very challenging, especially when the data acquisition…

We consider the problem of forecasting multivariate time series by a Seemingly Unrelated Time Series Equations (SUTSE) model. The SUTSE model usually assumes that error variables are correlated. A crucial issue is that the model estimation…

This report provides a brief historical evolution of the concepts in the Kalman filtering theory since ancient times to the present. A brief description of the filter equations its aesthetics, beauty, truth, fascinating perspectives and…

This paper describes the development of a causal diagnosis approach for troubleshooting an industrial environment on the basis of the technical language expressed in Return on Experience records. The proposed method leverages the vectorized…

Forecasting driving behavior or other sensor measurements is an essential component of autonomous driving systems. Often real-world multivariate time series data is hard to model because the underlying dynamics are nonlinear and the…

Online joint estimation of unknown parameters and states in a dynamical system with uncertainty quantification is crucial in many applications. For example, digital twins dynamically update their knowledge of model parameters and states to…

Many state estimation algorithms must be tuned given the state space process and observation models, the process and observation noise parameters must be chosen. Conventional tuning approaches rely on heuristic hand-tuning or gradient-based…

Kalman filtering is a cornerstone of estimation theory, yet learning the optimal filter under unknown and potentially singular noise covariances remains a fundamental challenge. In this paper, we revisit this problem through the lens of…

In this paper is proposed a novel incremental iterative Gauss-Newton-Markov-Kalman filter method for state estimation of dynamic models given noisy measurements. The mathematical formulation of the proposed filter is based on the…

This paper addresses the mathematical modeling and compensation of stochastic discrete-time clock jitter in analog-to-digital converters (ADCs). We model the stochastic clock jitter as a first-order autoregressive (AR(1)) process, and we…

Researchers collecting intensive longitudinal data (ILD) are increasingly looking to model psychological processes, such as emotional dynamics, that organize and adapt across time in complex and meaningful ways. This is also the case for…

Many estimation problems in aerospace navigation and robotics involve measurements that depend on prior states. A prominent example is odometry, which measures the relative change between states over time. Accurately handling these…

Uncertainty quantification in digital twins is critical to enable reliable and credible predictions beyond available data. A key challenge is that ensemble-based approaches can become prohibitively expensive when embedded in control and…

We employ the variational formulation and the Euler-Lagrange equations to study the steady-state error in linear non-causal estimators (smoothers). We give a complete description of the steady-state error for inputs that are polynomial in…

Smoothing algorithms for state-space models, i.e., fixed-interval smoothing, fixed-lag smoothing, and two-filter formula for smoothing, are examined using real examples. For linear and Gaussian state-space models, it is observed that…

State estimation in heavy-tailed process and measurement noise is an important challenge that must be addressed in, e.g., tracking scenarios with agile targets and outlier-corrupted measurements. The performance of the Kalman filter (KF)…

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…