Related papers: Smoothing Dynamic Systems with State-Dependent Cov…

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…

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…

The possible methodologies to handle the uncertain parameter are reviewed. The core idea of the desensitized Kalman filter is introduced. A new cost function consisting of a posterior covariance trace and trace of a weighted norm of the…

We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP)…

This paper presents a novel identification approach of Koopman models of nonlinear systems with inputs under rather general noise conditions. The method uses deep state-space encoders based on the concept of state reconstructability and an…

Low dimensional representations of words allow accurate NLP models to be trained on limited annotated data. While most representations ignore words' local context, a natural way to induce context-dependent representations is to perform…

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…

A new type of ensemble Kalman filter is developed, which is based on replacing the sample covariance in the analysis step by its diagonal in a spectral basis. It is proved that this technique improves the aproximation of the covariance when…

We present a scalable and robust Bayesian inference method for linear state space models. The method is applied to demand forecasting in the context of a large e-commerce platform, paying special attention to intermittent and bursty target…

In the classical Kalman filter(KF), the estimated state is a linear combination of the one-step predicted state and measurement state, their confidence level change when the prediction mean square error matrix and covariance matrix of…

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…

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…

Inference tasks with time series over graphs are of importance in applications such as urban water networks, economics, and networked neuroscience. Addressing these tasks typically relies on identifying a computationally affordable model…

We study the filtering and smoothing problem for continuous-time linear Gaussian systems. While classical approaches such as the Kalman-Bucy filter and the Rauch-Tung-Striebel (RTS) smoother provide recursive formulas for the conditional…

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…

In order to integrate uncertainty estimates into deep time-series modelling, Kalman Filters (KFs) (Kalman et al., 1960) have been integrated with deep learning models, however, such approaches typically rely on approximate inference…

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…

Matrix factorization from a small number of observed entries has recently garnered much attention as the key ingredient of successful recommendation systems. One unresolved problem in this area is how to adapt current methods to handle…

This work introduces the Gaussian integration to address a smoothing problem of a nonlinear stochastic state space model. The probability densities of states at each time instant are assumed to be Gaussian, and their means and covariances…

This paper is considered with joint estimation of state and time-varying noise covariance matrices in non-linear stochastic state space models. We present a variational Bayes and Gaussian filtering based algorithm for efficient computation…