This paper studies the nonlinear vibration analysis of a simply supported Euler-Bernoulli beam resting on a nonlinear elastic foundation under compressive axial load using nonlinear normal modes concept in the case of three-to-one (3:1) internal resonance. The beam’s governing nonlinear PDE of motion and also its boundary conditions are derived and then solved using the method of Multiple Time ...

A localization algorithm is developed to assist automated landing on unknown planetary surface. Classically, using a vision-sensor only, the vehicle states are subject to an observability issue. In order to overcome this problem, relative motion estimates were used as measurements in addition to image-plane data of the feature points. Using these data as measurements, a nonlinear least square e...

This paper is concerned with path planning for under-sensed vehicles, where the vehicle has insufficient sensors to estimate its state without active control. One such system is an autonomous underwater vehicle, which typically does not have complete inertial position information. Using the condition number of the observability gramian as a cost functional, we develop an observability optimal c...

This paper investigates a method for the state estimation of nonlinear systems described by a class of differentialalgebraic equation (DAE) models using the extended Kalman filter. The method involves the use of a transformation from a DAE to ordinary differential equation (ODE). A relevant dynamic power systems model using decoupled techniques will be proposed. The estimation technique consist...

The Iterated Extended Kalman smoother (IEKS) is shown to be equivalent to one iteration of the Expectation Maximisation (EM)-based SAGE algorithm for the class of nonlinear signal models containing polynomial dynamics. Thus the IEKS is a maximum a posteriori (MAP) state sequence estimator for this class of systems. The Iterated Extended Kalman filter (IEKF) can be thought of as a heuristic, onl...

Multilayer bootstrap network builds a gradually narrowed multilayer nonlinear network from bottom up for unsupervised nonlinear dimensionality reduction. Each layer of the network is a nonparametric density estimator. It consists of a group of k-centroids clusterings. Each clustering randomly selects data points with randomly selected features as its centroids, and learns a one-hot encoder by o...

We introduce the antiparticle filter, AF, a new type of recursive Bayesian estimator that is unlike either the extended Kalman Filter, EKF, unscented Kalman Filter, UKF or the particle filter PF. We show that for a classic problem of robot localization the AF can substantially outperform these other filters in some situations. The AF estimates the posterior distribution as an auxiliary variable...

Generally, blind separation of sources from their nonlinear mixtures is rather difficult. This nonlinear mapping, constituted by unsupervised linear mixing followed by unknown and invertible nonlinear distortion, is found in many signal processing cases. We propose using a kernel density estimator incorporated within an equivariant gradient algorithm to separate the nonlinear mixed sources. The...

We propose Gaussian processes (GPs) as a novel nonlinear receiver for digital communication systems. The GPs framework can be used to solve both classification (GPC) and regression (GPR) problems. The minimum mean squared error solution is the expectation of the transmitted symbol given the information at the receiver, which is a nonlinear function of the received symbols for discrete inputs. G...

This paper discusses some asymptotic uniform linearity results of randomly weighted empirical processes based on long range dependent random variables+ These results are subsequently used to linearize nonlinear regression quantiles in a nonlinear regression model with long range dependent errors, where the design variables can be either random or nonrandom+ These, in turn, yield the limiting be...