Related papers: Smoothing and Interpolating Noisy GPS Data with Sm…
A noise-reduction algorithm for time-series of non-linear systems is presented. The algorithm smoothes the attractors in phase space using B-splines, allowing a more accurate measure of their dynamics. The algorithm is tested on numerical…
We compare a recently proposed multivariate spline based on mixed partial derivatives with two other standard splines for the scattered data smoothing problem. The splines are defined as the minimiser of a penalised least squares…
This article presents a method for estimating the dynamic driving states (position, velocity, acceleration and heading) from noisy measurement data. The proposed approach is effective with both complete and partial observations, producing…
Surface-based data is commonly observed in diverse practical applications spanning various fields. In this paper, we introduce a novel nonparametric method to discover the underlying signals from data distributed on complex surface-based…
In this paper, we report the development of the generalized proximal smoothing (GPS) algorithm for phase retrieval of noisy data. GPS is a optimization-based algorithm, in which we relax both the Fourier magnitudes and object constraints.…
In this paper, we present the development of a many-knot spline method derived to remove the statistical noise in the spectroscopic data. This method is an expansion of the B-spline method. Compared to the B-spline method, the many-knot…
Splines are a popular and attractive way of smoothing noisy data. Computing splines involves minimizing a functional which is a linear combination of a fitting term and a regularization term. The former is classically computed using a…
Attaining reliable profile gradients is of utmost relevance for many physical systems. In most situations, the estimation of gradient can be inaccurate due to noise. It is common practice to first estimate the underlying system and then…
It is known by the experience gained from the gravitational wave detector proto-types that the interferometric output signal will be corrupted by a significant amount of non-Gaussian noise, large part of it being essentially composed of…
Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us…
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 considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…
Underwater visual-inertial navigation is challenging due to the poor visibility and presence of outliers in underwater environments. The navigation performance is closely related to outlier detection and elimination. Existing methods assume…
Interpolation techniques play a central role in Astronomy, where one often needs to smooth irregularly sampled data into a smooth map. In a previous article (Lombardi & Schneider 2001), we have considered a widely used smoothing technique…
A method is described for the detection and estimation of transient chirp signals that are characterized by smoothly evolving, but otherwise unmodeled, amplitude envelopes and instantaneous frequencies. Such signals are particularly…
This article introduces a method for estimating the smoothness of a stationary, isotropic Gaussian random field from irregularly spaced data. This involves novel constructions of higher-order quadratic variations and the establishment of…
In this paper we address smoothing-that is, optimisation-based-estimation techniques for localisation problems in the case where motion sensors are very accurate. Our mathematical analysis focuses on the difficult limit case where motion…
Transient signals of instrumental and environmental origins ("glitches") in gravitational wave data elevate the false alarm rate of searches for astrophysical signals and reduce their sensitivity. Glitches that directly overlap…
In recent years, passively collected GPS data have been popularly applied in various transportation studies, such as highway performance monitoring, travel behavior analysis, and travel demand estimation. Despite multiple advantages, one of…
Identifying Ordinary Differential Equations (ODEs) from measurement data requires both fitting the dynamics and assimilating, either implicitly or explicitly, the measurement data. The Sparse Identification of Nonlinear Dynamics (SINDy)…