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Bayesian optimization is a popular and versatile approach that is well suited to solve challenging optimization problems. Their popularity comes from their effective minimization of expensive function evaluations, their capability to…
Non-Gaussian Bayesian filtering is a core problem in stochastic filtering. The difficulty of the problem lies in parameterizing the state estimates. However the existing methods are not able to treat it well. We propose to use power moments…
In this letter, a new filtering technique to solve a nonlinear state estimation problem has been developed. It is well known that for a nonlinear system, the prior and posterior probability density functions (pdf) are non-Gaussian in…
Data-informed predictive maintenance planning largely relies on stochastic deterioration models. Monitoring information can be utilized to update sequentially the knowledge on time-invariant deterioration model parameters either within an…
Kalman filtering is a classic state estimation technique used in application areas such as signal processing and autonomous control of vehicles. It is now being used to solve problems in computer systems such as controlling the voltage and…
Filtering is a widely used methodology for the incorporation of observed data into time-evolving systems. It provides an online approach to state estimation inverse problems when data is acquired sequentially. The Kalman filter plays a…
Gaussian process regression is a machine learning approach which has been shown its power for estimation of unknown functions. However, Gaussian processes suffer from high computational complexity, as in a basic form they scale cubically…
The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation…
Inference and simulation in the context of high-dimensional dynamical systems remain computationally challenging problems. Some form of dimensionality reduction is required to make the problem tractable in general. In this paper, we propose…
Bayesian Optimization using Gaussian Processes is a popular approach to deal with the optimization of expensive black-box functions. However, because of the a priori on the stationarity of the covariance matrix of classic Gaussian…
We consider Bayesian inference for large scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. This renders most Markov chain Monte Carlo approaches infeasible,…
In this paper we consider the behavior of Kalman Filter state estimates in the case of distribution with heavy tails .The simulated linear state space models with Gaussian measurement noises were used. Gaussian noises in state equation are…
We tackle the problem of system identification, where we select inputs, observe the corresponding outputs from the true system, and optimize the parameters of our model to best fit the data. We propose a practical and computationally…
This paper presents a performance comparison of different estimation and prediction techniques applied to the problem of tracking multiple robots. The main performance criteria are the magnitude of the estimation or prediction error, the…
Gaussian Processes (GPs) are powerful kernelized methods for non-parameteric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs…
Stochastic filtering is defined as the estimation of a partially observed dynamical system. A massive scientific and computational effort is dedicated to the development of numerical methods for approximating the solution of the filtering…
Autonomous platforms require accurate positioning to complete their tasks. To this end, a Kalman filter-based algorithms, such as the extended Kalman filter or invariant Kalman filter, utilizing inertial and external sensor fusion are…
In this paper we address the problem of estimating the posterior distribution of the static parameters of a continuous time state space model with discrete time observations by an algorithm that combines the Kalman filter and a particle…
We introduce a novel nonlinear Kalman filter that utilizes reparametrization gradients. The widely used parametric approximation is based on a jointly Gaussian assumption of the state-space model, which is in turn equivalent to minimizing…
This paper introduces a Gaussian Bayesian Network-based Extended Kalman Filter (GBN-EKF) for non-linear state estimators on stiff and ill-conditioned continuous-discrete stochastic systems, with a further analysis on systems with…