Practical stability of approximating discrete-time filters with respect to model mismatch using relative entropy concepts

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Using local consistency assumption, the practical stability established is in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Significantly, these practical stability results do not require the approximating model to be of the same model type as the true system. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.

Relative entropy rate based design for linear hybrid system models

Hybrid system representations have been applied to many challenging modeling situations. In these hybrid system representations, a mixture of continuous and discrete states is used to capture the dominating behavioural features of a nonlinear, possible uncertain, model under approximation. Unfortunately, the problem of how to best design a suitable hybrid system model has not yet been fully addressed. This paper proposes a new joint state measurement relative entropy rate based approach for this design purpose. Design examples and simulation studies are presented which highlight the benefits of our proposed design approaches.

An infinite-horizon robust filter for uncertain hidden Markov Models with conditional relative entropy constraints

We consider a robust filtering problem for uncertain discrete-time, homogeneous, first-order, finite-state hidden Markov models (HMMs). The class of uncertain HMMs considered is described by a conditional relative entropy constraint on measures perturbed from a nominal regular conditional probability distribution given the previous posterior state distribution and the latest measurement. Under this class of perturbations, a robust infinite horizon filtering problem is first formulated as a constrained optimization problem before being transformed via variational results into an unconstrained optimization problem; the latter can be elegantly solved using a risk-sensitive information-state based filtering.

See-and-avoid quadcopter using fuzzy control optimized by cross-entropy

In this work we present an optimized fuzzy visual servoing system for obstacle avoidance using an unmanned aerial vehicle. The cross-entropy theory is used to optimise the gains of our controllers. The optimization process was made using the ROS-Gazebo 3D simulation with purposeful extensions developed for our experiments. Visual servoing is achieved through an image processing front-end that uses the Camshift algorithm to detect and track objects in the scene. Experimental flight trials using a small quadrotor were performed to validate the parameters estimated from simulation. The integration of cross- entropy methods is a straightforward way to estimate optimal gains achieving excellent results when tested in real flights.

HMM triangle relative entropy concepts in sequential change detection applied to vision-based dim target manoeuvre detection

The quick detection of abrupt (unknown) parameter changes in an observed hidden Markov model (HMM) is important in several applications. Motivated by the recent application of relative entropy concepts in the robust sequential change detection problem (and the related model selection problem), this paper proposes a sequential unknown change detection algorithm based on a relative entropy based HMM parameter estimator. Our proposed approach is able to overcome the lack of knowledge of post-change parameters, and is illustrated to have similar performance to the popular cumulative sum (CUSUM) algorithm (which requires knowledge of the post-change parameter values) when examined, on both simulated and real data, in a vision-based aircraft manoeuvre detection problem.

Relative entropy rate based model selection for linear hybrid system filters of uncertain nonlinear systems

Hybrid system representations have been exploited in a number of challenging modelling situations, including situations where the original nonlinear dynamics are too complex (or too imprecisely known) to be directly filtered. Unfortunately, the question of how to best design suitable hybrid system models has not yet been fully addressed, particularly in the situations involving model uncertainty. This paper proposes a novel joint state-measurement relative entropy rate based approach for design of hybrid system filters in the presence of (parameterised) model uncertainty. We also present a design approach suitable for suboptimal hybrid system filters. The benefits of our proposed approaches are illustrated through design examples and simulation studies.

Novel methods and the maximum likelihood estimation technique for estimating traffic critical gap

Most unsignalised intersection capacity calculation procedures are based on gap acceptance models. Accuracy of critical gap estimation affects accuracy of capacity and delay estimation. Several methods have been published to estimate drivers’ sample mean critical gap, the Maximum Likelihood Estimation (MLE) technique regarded as the most accurate. This study assesses three novel methods; Average Central Gap (ACG) method, Strength Weighted Central Gap method (SWCG), and Mode Central Gap method (MCG), against MLE for their fidelity in rendering true sample mean critical gaps. A Monte Carlo event based simulation model was used to draw the maximum rejected gap and accepted gap for each of a sample of 300 drivers across 32 simulation runs. Simulation mean critical gap is varied between 3s and 8s, while offered gap rate is varied between 0.05veh/s and 0.55veh/s. This study affirms that MLE provides a close to perfect fit to simulation mean critical gaps across a broad range of conditions. The MCG method also provides an almost perfect fit and has superior computational simplicity and efficiency to the MLE. The SWCG method performs robustly under high flows; however, poorly under low to moderate flows. Further research is recommended using field traffic data, under a variety of minor stream and major stream flow conditions for a variety of minor stream movement types, to compare critical gap estimates using MLE against MCG. Should the MCG method prove as robust as MLE, serious consideration should be given to its adoption to estimate critical gap parameters in guidelines.

Statistical and scientometric analysis of international research in geographical and environmental education

Certain statistic and scientometric features of articles published in the journal “International Research in Geographical and Environmental Education” are examined in this paper, for the period 1992-2009, by applying nonparametric statistics and Shannon’s entropy (diversity) formula. The main findings of this analysis are: a) after 2004 the research priorities of researchers in geographical and environmental education seem to have changed, b) “teacher education” has been the most recurrent theme throughout these 18 years, followed by “values & attitudes” and “inquiry & problem solving” c) the themes “GIS” and “Sustainability” were the most “stable” throughout the 18 years, meaning that they maintained their ranks as publication priorities more than other themes, d) citations of IRGEE increase annually, e) the average thematic diversity of articles published during the period 1992-2009 is 82.7% of the maximum thematic diversity (very high), meaning that the Journal has the capacity to attract a wide readership for the 10 themes it has successfully covered throughout the 18 years of its publication.

Cross-entropy optimization for scaling factors of a fuzzy controller : a see-and-avoid approach for unmanned aerial systems

The Cross-Entropy (CE) is an efficient method for the estimation of rare-event probabilities and combinatorial optimization. This work presents a novel approach of the CE for optimization of a Soft-Computing controller. A Fuzzy controller was designed to command an unmanned aerial system (UAS) for avoiding collision task. The only sensor used to accomplish this task was a forward camera. The CE is used to reach a near-optimal controller by modifying the scaling factors of the controller inputs. The optimization was realized using the ROS-Gazebo simulation system. In order to evaluate the optimization a big amount of tests were carried out with a real quadcopter.

A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations

In Burrage and Burrage [1] it was shown that by introducing a very general formulation for stochastic Runge-Kutta methods, the previous strong order barrier of order one could be broken without having to use higher derivative terms. In particular, methods of strong order 1.5 were developed in which a Stratonovich integral of order one and one of order two were present in the formulation. In this present paper, general order results are proven about the maximum attainable strong order of these stochastic Runge-Kutta methods (SRKs) in terms of the order of the Stratonovich integrals appearing in the Runge-Kutta formulation. In particular, it will be shown that if an s-stage SRK contains Stratonovich integrals up to order p then the strong order of the SRK cannot exceed min{(p + 1)/2, (s - 1)/2), p greater than or equal to 2, s greater than or equal to 3 or 1 if p = 1.

How to achieve maximum charge carrier loading on heteroatom-substituted graphene nanoribbon edges: density functional theory study

The practical number of charge carriers loaded is crucial to the evaluation of the capacity performance of carbon-based electrodes in service, and cannot be easily addressed experimentally. In this paper, we report a density functional theory study of charge carrier adsorption onto zigzag edge-shaped graphene nanoribbons (ZGNRs), both pristine and incorporating edge substitution with boron, nitrogen or oxygen atoms. All edge substitutions are found to be energetically favorable, especially in oxidized environments. The maximal loading of protons onto the substituted ZGNR edges obeys a rule of [8-n-1], where n is the number of valence electrons of the edge-site atom constituting the adsorption site. Hence, a maximum charge loading is achieved with boron substitution. This result correlates in a transparent manner with the electronic structure characteristics of the edge atom. The boron edge atom, characterized by the most empty p band, facilitates more than the other substitutional cases the accommodation of valence electrons transferred from the ribbon, induced by adsorption of protons. This result not only further confirms the possibility of enhancing charge storage performance of carbon-based electrochemical devices through chemical functionalization but also, more importantly, provides the physical rationale for further design strategies.

A quasi-maximum likelihood method for estimating the parameters of multivariate diffusions

A quasi-maximum likelihood procedure for estimating the parameters of multi-dimensional diffusions is developed in which the transitional density is a multivariate Gaussian density with first and second moments approximating the true moments of the unknown density. For affine drift and diffusion functions, the moments are exactly those of the true transitional density and for nonlinear drift and diffusion functions the approximation is extremely good and is as effective as alternative methods based on likelihood approximations. The estimation procedure generalises to models with latent factors. A conditioning procedure is developed that allows parameter estimation in the absence of proxies.