We propose two nonlinear Kalman smoothers that rely on Student’s t distributions. The T-Robust smoother finds the maximum a posteriori likelihood (MAP) solution for Gaussian process noise and Student’s t observation noise, and is extremely robust against outliers, outperforming the recently proposed `1-Laplace smoother in extreme situations (e.g. 50% or more outliers). The second estimator, whi...

A distribution is a linear functional on a space of test functions. Distributions include all locally integrable functions and have derivatives of all orders (great for linear problems) but cannot be multiplied in any natural way (not so great for nonlinear problems). One can use many different spaces of test functions. We will consider distributions on the space D(Ω) of smooth compactly suppor...

Solutions of the wave equation in a space-time containing a thin cosmic string are examined in the context of non-linear generalised functions. Existence and uniqueness of solutions to the wave equation in the Colombeau algebra G is established for a conical space-time and this solution is shown to be associated to a distributional solution. A concept of generalised hyperbolicity, based on test...

The aim of this paper is to investigate geometrically nonlinear static analysis of axially functionally graded cantilever beam subjected to transversal non follower load. The considered problem is solved by finite element method with total Lagrangian kinematic approach. The material properties of the beam vary along the longitudinal direction according to the power law function. The finite elem...

This paper proposes a method for extracting realistic textures from real-world reference spheres. The BRDF parameters of fundamental materials, as well as a material weight map for the sphere are obtained through a non-linear optimization process. The material weight map can be used as a conventional texture for relighting. With the BRDF models recovered, the real and natural appearances of 3D ...

Ω |Du| + f(AdjDu) + g(detDu), where u : Ω ⊂ IR → IR, f grows like |AdjDu|p, g grows like |detDu|q and 1 < q < p < 2, is C on an open subset Ω0 of Ω such that meas(Ω \ Ω0) = 0. Such functionals naturally arise from nonlinear elasticity problems. The key point in order to obtain the partial regularity result is to establish an energy estimate of Caccioppoli type, which is based on an appropriate ...

A new method has been proposed to introduce an extra parameter to a family of distributions for more flexibility. A special case has been considered in details namely; one parameter exponential distribution. Various properties of the proposed distribution, including explicit expressions for the moments, quantiles, mode, moment generating function, mean residual lifetime, stochastic orders, orde...

This paper presents a procedure for time variant nonlinear system identification based on distribution theory. Some of the system parameters change in time according to unknown laws. These laws are expressed as finite degree time polynomials whose parameters are included in the set of parameters to be identified. Mainly it is an extension of the procedure developed in (Marin et al., 2005). Cons...

Reserve design is concerned with optimal selection of sites for new conservation areas. Spatial reserve design explicitly considers the spatial pattern of the proposed reserve network and the effects of that pattern on reserve cost and/or ability to maintain species there. The vast majority of reserve selection formulations have assumed a linear problem structure, which effectively means that t...

We demonstrate data rates above the threshold imposed by nonlinearity on conventional optical signals by applying novel probability distribution, which we call ripple distribution, adapted to the properties of the fiber channel. Our results offer a new direction for signal coding, modulation and practical nonlinear distortions compensation algorithms.