Identification of the state of a moving object by observation of geophysical fields

Problems of identification of the state of a moving object by observation of the geophysical fields are considered. To correct the errors accumulated in the inertial navigation system of the object, the extremal comparison of the information about the outer geophysical fields with the a priori information about them stored in the onboard computer is used (the correlation-extremal approach). The general principles for investigation of the systems for navigation of moving objects by the outer informational fields are described. A model of navigation by the geophysical field and a method for a priori estimation of the local informativeness of the field are suggested.     

Generalized polynomial approximation providing the best reference

We pose the extremum problem of finding a polynomial approximation for a function of several variables so that this approximation by a fragment of the function provides the best reference. We obtain an upper bound for the modulus of informativity of polynomials and rational functions.Translated fromMatematickeskie Zametki, Vol. 60, No. 5, pp. 658–669, November, 1996.The author wishes to thank Yu. N. Subbotin for valuable discussions.This research was supported by the Russian Foundation for Basic Research under grant No. 93-011-196.     

Ray transforms in hyperbolic geometry

We derive explicit inversion formulae for the attenuated geodesic and horocyclic ray transforms of functions and vector fields on two-dimensional manifolds equipped with the hyperbolic metric. The inversion formulae are based on a suitable complexification of the associated vector fields so as to recast the reconstruction as a Riemann–Hilbert problem. The inversion formulae have a very similar structure to their counterparts in Euclidean geometry and may therefore be amenable to efficient discretizations and numerical inversions. An important field of application is geophysical imaging when absorption effects are accounted for.     

Satellite navigation. Raw data processing for geophysical applications

Satellite navigation systems are widely used in geophysical applications for precise trajectory determination of a vehicle-carrier of geophysical equipment. In particular, in airborne gravimetry it is necessary to determine the velocity and acceleration of the vehicle in addition to the position determination. Mathematical models and algorithms for the solution of these problems are described. The source data consists of differential Doppler and carrier phase GPS observations. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 7, pp. 181–196, 2005.     

Estimation of intrinsic processes affected by additive fractal noise

Fractal Gaussian models have been widely used to represent the singular behavior of phenomena arising in different applied fields; for example, fractional Brownian motion and fractional Gaussian noise are considered as monofractal models in subsurface hydrology and geophysical studies Mandelbrot [The Fractal Geometry of Nature, Freeman Press, San Francisco, 1982 [13]]. In this paper, we address the problem of least-squares linear estimation of an intrinsic fractal input random field from the observation of an output random field affected by fractal noise (see Angulo et al. [Estimation and filtering of fractional generalised random fields, J. Austral. Math. Soc. A 69 (2000) 1-26 [2]], Ruiz-Medina et al. [Fractional generalized random fields on bounded domains, Stochastic Anal. Appl. 21 (2003a) 465-492], Ruiz-Medina et al. [Fractional-order regularization and wavelet approximation to the inverse estimation problem for random fields, J. Multivariate Anal. 85 (2003b) 192-216]. Conditions on the fractality order of the additive noise are studied to obtain a bounded inversion of the associated Wiener-Hopf equation. A stable solution is then obtained in terms of orthogonal bases of the reproducing kernel Hilbert spaces associated with the random fields involved. Such bases are constructed from orthonormal wavelet bases (see Angulo and Ruiz-Medina [Multiresolution approximation to the stochastic inverse problem, Adv. in Appl. Probab. 31 (1999) 1039-1057], Angulo et al. [Wavelet-based orthogonal expansions of fractional generalized random fields on bounded domains, Theoret. Probab. Math. Stat. (2004), in press]). A simulation study is carried out to illustrate the influence of the fractality orders of the output random field and the fractal additive noise on the stability of the solution derived.     

Enhanced FEM-based modeling of brain shift deformation in Image-Guided Neurosurgery

We consider the problem of improving outcomes for neurosurgery patients by enhancing intraoperative navigation and guidance. Current navigation systems do not accurately account for intraoperative brain deformation. We focus on the brain shift deformation that occurs just after the opening of the skull and dura. The heart of our system is a nonrigid registration technique using a biomechanical model. We specifically work on two axes: the representation of the structures in the biomechanical model and the evaluation of the surface landmark displacement fields between intraoperative MR images. Using the modified Hausdorff distance as an image similarity measure, we demonstrate that our approach significantly improves the alignment of the intraoperative images.     

Neuro-fuzzy technique for navigation of multiple mobile robots

In this paper, navigation techniques for several mobile robots are investigated in a totally unknown environment. In the beginning, Fuzzy logic controllers (FLC) using different membership functions are developed and used to navigate mobile robots. First a fuzzy controller has been used with four types of input members, two types of output members and three parameters each. Next two types of fuzzy controllers have been developed having same input members and output members with five parameters each. Each robot has an array of sensors for measuring the distances of obstacles around it and an image sensor for detecting the bearing of the target. It is found that the FLC having Gaussian membership function is best suitable for navigation of multiple mobile robots. Then a hybrid neuro-fuzzy technique has been designed for the same problem. The neuro-fuzzy technique being used here comprises a neural network, which is acting as a pre processor for a fuzzy controller. The neural network considered for neuro-fuzzy technique is a multi-layer perceptron, with two hidden layers. These techniques have been demonstrated in simulation mode, which depicts that the robots are able to avoid obstacles and reach the targets efficiently. Amongst the techniques developed neuro-fuzzy technique is found to be most efficient for mobile robots navigation. Experimental verifications have been done with the simulation results to prove the authenticity of the developed neuro-fuzzy technique.     

Zur simultanen Diophantischen Approximation. I

An important problem in the field of Diophantine Approximation was solved in 1891 byHurwitz. He could show that any irrational number can be approximated by infinitely many rationals in such a way that the modulus of the difference multiplied with the square of the denominator is less than 5^–1/2, and there 5^–1/2 is best possible.-The generalization of this problem in the direction of simultaneous Diophantine Approximation is still unsolved.Furtwängler in 1925 gave lower bounds for the maximum difference, conjecturing that these were best possible.-Here it is shown that in the two dimensional caseFurtwängler's bounds are indeed best possible for certain irrationals lying in cubic number fields which are not totally real. Yet by considering totally real cubic fields we are led to replaceFurtwängler's conjecture by a new one.     

Simple-motion pursuit-evasion differential games,part 2: Optimal evasion from proportional navigation guidance in the deterministic and stochastic cases

The problem of the optimal evasion from a pursuer employing proportional navigation guidance is considered. Thus, we consider the problem of maximizing the time-to-capture when the problem parameters, namely, the speed ratio and the proportional navigation constant, are such that capturability of the evader is guaranteed.     

Exact geophysical waves in stratified fluids

When studying water waves travelling over an inviscid fluid at the Earth's surface there are additional Coriolis and centrifugal forces which influence the motion of the fluid particles. In particular, for waves propagating near the Equator the geophysical wave problem can be modelled by the so-called f-plane approximation. In this paper, we provide an explicit exact solution to the edge wave problem for stratified geophysical flows in the equatorial f-plane approximation.     

Asymptotic theory of parameter estimation by a contrast function based on interpolation error

Interpolation is an important issue for a variety fields of statistics (e.g., missing data analysis). In time series analysis, the best interpolator for missing points problem has been investigated in several ways. In this paper, the asymptotics of a contrast function estimator defined by pseudo interpolation error for stationary process are investigated. We estimate parameters of the process by minimizing the pseudo interpolation error written in terms of a fitted parametric spectral density and the periodogram based on observed stretch. The estimator has the consistency and asymptotical normality. Although the criterion for the interpolation problem is known as the best in the sense of smallest mean square error for past and future extrapolation, it is shown that the estimator is asymptotically inefficient in general parameter estimation, which leads to an unexpected result.     

Cryptography in Quadratic Function Fields

We describe severalcryptographic schemes in quadratic function fields of odd characteristic.In both the real and the imaginary representation of such a field,we present a Diffie-Hellman-like key exchange protocol as wellas a public-key cryptosystem and a signature scheme of ElGamaltype. Several of these schemes are improvements of systems previouslyfound in the literature, while others are new. All systems arebased on an appropriate discrete logarithm problem. In the imaginarysetting, this is the discrete logarithm problem in the idealclass group of the field, or equivalently, in the Jacobian ofthe curve defining the function field. In the real case, theproblem in question is the task of computing distances in theset of reduced principal ideals, which is a monoid under a suitableoperation. Currently, the best general algorithms for solvingboth discrete logarithm problems are exponential (subexponentialonly in fields of high genus), resulting in a possibly higherlevel of security than that of conventional discrete logarithmbased schemes.     

An extension of Chevalley's theorem to congruences modulo prime powers

Olson determined, for each finite abelian p-group G, the maximal length of a sequence of elements of G such that no subsequence has zero sum, thus settling (at least for these groups) a problem raised by Davenport in connection with factorization in number fields. This problem is equivalent to one on simultaneous linear congruences to which one seeks solutions with the variables restricted to the values 0 and 1. In the present note, the analogous problem for forms of arbitrary degree is settled, again with best possible results. The main tool is an extension of Chevalley's theorem on finite fields to congruences modulo prime powers. This in turn is deduced from Chevalley's theorem by a simple device which circumvents the use of Witt vectors.     

Investigating pedestrian navigation in indoor open space environments using big data

Reliable empirical data are required to understand and model realistic pedestrian navigation behaviours at public crowd-gathering places such as public transportation hubs and shopping malls. Naturalistic walking big data could provide reliable information for investigating realistic pedestrian behaviours and to overcome critical shortcomings of the data collected through controlled laboratory experiments. In this work, we investigate pedestrian navigation in indoor open spaces using naturalistic walking big data collected through video recordings. The extracted data include 299,082 trajectories of individual pedestrians who navigated through the atrium of the Informatics Forum building of the University of Edinburgh. We compare several pedestrian vector fields by calibrating several cellular automaton (CA) models and we finally identify a generalized vector field for pedestrians who are walking in indoor open space environments under normal walking conditions.The output of this study could be useful in enhancing CA-based pedestrian simulation models by representing pedestrian navigation as well as route-choice behaviours more realistically in those models. Simulation tools based on such enhanced models can facilitate practitioners, such as public building designers, to optimize designs considering naturalistic pedestrian behaviours in open spaces.     

An approach to benchmarking of loosely coupled low-cost navigation systems

New solutions to the navigation problem related to low-cost integrated navigation systems (INS) are often published. Since these new solutions are generally compared with ad hoc mathematical models that are not fully exposed, one cannot be sure of the relative improvements. In this work, complete mathematical model for a low-cost INS is suggested to be used as a benchmarking. As far as the authors’ knowledge, a benchmarking for low-cost INS has not been previously reported. Shown INS comprises a strapdown inertial navigation system, loosely coupled to a GPS receiver. The INS mathematical model is based upon classical navigation equations and classical sensor models, both from recognized authors. The algorithm that details the INS operation is also presented. The benchmarking is provided as an open-source toolbox for MATLAB. Additionally, this work can be taken as a starting point for new practitioners in the INS field. To validate the INS mathematical model, real-world data sets from three different Micro Electro-Mechanical Systems (MEMS) inertial measurement units (IMU) and a GPS receiver are processed. It is observed that obtained RMS errors from the three INS are coherent with the quality of corresponding MEMS IMU. This confirms that the proposed benchmarking is a suitable tool to evaluate objectively new solutions to low-cost INS.     

Scheduling workover rigs for onshore oil production

Many oil wells in Brazilian onshore fields rely on artificial lift methods. Maintenance services such as cleaning, reinstatement, stimulation and others are essential to these wells. These services are performed by workover rigs, which are available on a limited number with respect to the number of wells demanding service. The decision of which workover rig should be sent to perform some maintenance service is based on factors such as the well production, the current location of the workover rig in relation to the demanding well, and the type of service to be performed. The problem of scheduling workover rigs consists in finding the best schedule for the available workover rigs, so as to minimize the production loss associated with the wells awaiting for service. We propose a variable neighborhood search (VNS) heuristic for this problem. Computational results on real-life problems are reported and their economic impacts are evaluated.     

Time-optimal solutions of Parallel navigation and Finsler geodesics

A geometric approach to kinematics in control theory is illustrated. A non-linear control system is derived for the problem and the Pontryagin maximum principle is used to find the time-optimal trajectories of the Parallel navigation. It is proved that the time-optimal relative trajectories of the Parallel navigation are geodesics of a Finsler metric. It is notable that the approach has the advantages using feedback.     

Representations of the optimal filter in the context of nonlinear filtering of random fields with fractional noise

The problem of nonlinear filtering of multiparameter random fields, observed in the presence of a long-range dependent spatial noise, is considered. When the observation noise is modelled by a persistent fractional Wiener sheet, several pathwise representations of the optimal filter are derived. The representations involve series of multiple stochastic integrals of different types and are particularly important since the evolution equations, satisfied by the best mean-square estimate of the signal random field, have a complicated analytical structure and fail to be proper (measure-valued) stochastic partial differential equations. Several of the above optimal filter representations involve a new family of strong martingale transforms associated to the multiparameter fractional Brownian sheet; the latter martingale family is of independent interest in fractional stochastic calculus of multiparameter random fields.     

Numerical-analytical simulation of wave fields for complex subsurface geometries and structures

In this paper, we propose an analytical method of modeling seismic wave fields over a wide range of geophysical media: elastic, inelastic, anisotropic, anisotropic-inelastic, porous, random-inhomogeneous, etc., at very large distances. Since no finite-difference approximations are used, no grid dispersion occurs in computing wave fields for arbitrary media models and observation points. An analytical solution representation in the spectral domain makes it possible to analyze the wave field by parts, specifically, to obtain primary waves. A program of computing the wave fields has been developed, and a simulation of water waves and seismic “ringing” of the Moon has been carried out. The phenomenon of a monotonic shift of the resonance to the lower frequency area with increasing distance of recording is explained. This phenomenon was detected in some experiments with a seismic vibrator.     

Limit analysis decomposition and finite element mixed method

This paper proposes an original decomposition approach to the upper bound method of limit analysis. It is based on a mixed finite element approach and on a convex interior point solver, using linear or quadratic discontinuous velocity fields. Presented in plane strain, this method appears to be rapidly convergent, as verified in the Tresca compressed bar problem in the linear velocity case. Then, using discontinuous quadratic velocity fields, the method is applied to the celebrated problem of the stability factor of a Tresca vertical slope: the upper bound is lowered to 3.7776-value to be compared to the best published lower bound 3.7752-by succeeding in solving a nonlinear optimization problem with millions of variables and constraints.