This paper presents a new multi-sensor data fusion method based on the combination of wavelet transform (WT) and extended Kalman filter (EKF). Input data are first filtered by a wavelet transform via Daubechies wavelet “db4” functions and the filtered data are then fused based on variance weights in terms of minimum mean square error. The fused data are finally treated by extended Kalman filter...

This paper presents a distributed bounded-error state estimation algorithm suited, e.g., to measurement processing by a network of sensors. Contrary to centralized estimation, where all data are collected to a central processing unit, here, each data is processed locally by the sensor, the results are broadcasted to the network and taken into account by the other sensors. A first analysis of th...

Machine learning algorithms search a space of possible hypotheses and estimate the error of each hypotheses using a sample. Most often, the goal of classification tasks is to find a hypothesis with a low true (or generalization) misclassification probability (or error rate); however, only the sample (or empirical) error rate can actually be measured and minimized. The true error rate of the ret...

A general framework for weak residual error estimators applying to various types of boundary value problems in connection with finite element and finite volume approximations is developed. Basic ideas commonly shared by various applications in error estimation and adaptive computation are presented and illustrated. Some numerical results are given to show the effectiveness and efficiency of the...

In this paper we consider the topic of model reduction for nonlinear dynamical systems based on kernel expansions. Our approach allows for a full offline/online decomposition and efficient online computation of the reduced model. In particular we derive an a-posteriori state-space error estimator for the reduction error. A key ingredient is a local Lipschitz constant estimation that enables rig...

Methods are developed and analyzed for estimating the distance to a local minimizer of a nonlinear programming problem. One estimate, based on the solution of a constrained convex quadratic program, can be used when strict complementary slackness and the second-order sufficient optimality conditions hold. A second estimate, based on the solution of an unconstrained nonconvex, nonsmooth optimiza...

Estimation of a digital curve’s curvature at any given point is needed for many tasks in computer vision, be it differential invariants or curvature scale space. However, curvature estimation is known to be very susceptible to noise on the contour. We shall show how noise on the contour affects the relative accuracy of the curvature computation. One interesting result is that, contrary to intui...

MOTIVATION In small-sample settings, bolstered error estimation has been shown to perform better than cross-validation and competitively with bootstrap with regard to various criteria. The key issue for bolstering performance is the variance setting for the bolstering kernel. Heretofore, this variance has been determined in a non-parametric manner from the data. Although bolstering based on thi...

It is common, in deconvolution problems, to assume that the measurement errors are identically distributed. In many real life applications however, this condition is not satisfied and the deconvolution estimators developed for homoscedastic errors become inconsistent. In this paper, we introduce a kernel estimator of a density in the case of heteroscedastic contamination. We establish consisten...