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Practical Bayes filters often assume the state distribution of each time step to be Gaussian for computational tractability, resulting in the so-called Gaussian filters. When facing nonlinear systems, Gaussian filters such as extended…
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…
Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We…
Parameter estimation is a major challenge in computational modeling of biological processes. This is especially the case in image-based modeling where the inherently quantitative output of the model is measured against image data, which is…
The Bayesian decision-theoretic approach to design of experiments involves specifying a design (values of all controllable variables) to maximise the expected utility function (expectation with respect to the distribution of responses and…
We propose an input design method for a general class of parametric probabilistic models, including nonlinear dynamical systems with process noise. The goal of the procedure is to select inputs such that the parameter posterior distribution…
In this paper, the problem of state estimation, in the context of both filtering and smoothing, for nonlinear state-space models is considered. Due to the nonlinear nature of the models, the state estimation problem is generally intractable…
The crucial step in designing a particle filter for a particular application is the choice of importance density. The optimal scheme is to use the conditional posterior density of the state, but this cannot be sampled or calculated…
Recursive estimation of nonlinear dynamical systems is an important problem that arises in several engineering applications. Consistent and accurate propagation of uncertainties is important to ensuring good estimation performance. It is…
Bayesian filtering is a general framework for recursively estimating the state of a dynamical system. Classical solutions such that Kalman filter and Particle filter are introduced in this report. Gaussian processes have been introduced as…
We study the linear filtering problem for systems driven by continuous Gaussian processes with memory described by two parameters. The driving processes have the virtue that they possess stationary increments and simple semimartingale…
This paper introduces a novel approach to system identification for nonlinear input-output models that minimizes the simulation error and frames the problem as a constrained optimization task. The proposed method addresses vanishing…
Current experimental design techniques for dynamical systems often only incorporate measurement noise, while dynamical systems also involve process noise. To construct experimental designs we need to quantify their information content. The…
Implicit particle filtering is a sequential Monte Carlo method for data assim- ilation, designed to keep the number of particles manageable by focussing attention on regions of large probability. These regions are found by min- imizing, for…
Design of experiments is a fundamental topic in applied statistics with a long history. Yet its application is often limited by the complexity and costliness of constructing experimental designs, which involve searching a high-dimensional…
When classical particle filtering algorithms are used for maximum likelihood parameter estimation in nonlinear state-space models, a key challenge is that estimates of the likelihood function and its derivatives are inherently noisy. The…
This paper proposes a new framework for the optimization of excitation inputs for system identification. The optimization problem considered is to maximize a reduced Fisher information matrix in any of the classical D-, E-, or A-optimal…
The paper deals with the problem of output regulation of nonlinear systems by presenting a learning-based adaptive internal model-based design strategy. We borrow from the adaptive internal model design technique recently proposed in [1]…
We propose an algorithm to actively estimate the parameters of a linear dynamical system. Given complete control over the system's input, our algorithm adaptively chooses the inputs to accelerate estimation. We show a finite time bound…
Bayesian filtering is a well-known problem that aims to estimate plausible states of a dynamical system from observations. Among existing approaches to solve this problem, particle filters are theoretically exact for non-linear dynamics and…