A singular vector perspective of 4D-Var: Filtering and interpolation

Four-dimensional variational data assimilation (4D-Var) combines the information from a time sequence of observations with the model dynamics and a background state to produce an analysis. In this paper, a new mathematical insight into the behaviour of 4D-Var is gained from an extension of concepts that are used to assess the qualitative information content of observations in satellite retrievals. It is shown that the 4D-Var analysis increments can be written as a linear combination of the singular vectors of a matrix which is a function of both the observational and the forecast model systems. This formulation is used to consider the filtering and interpolating aspects of 4D-Var using idealized case-studies based on a simple model of baroclinic instability. The results of the 4D-Var case-studies exhibit the reconstruction of the state in unobserved regions as a consequence of the interpolation of observations through time. The results also exhibit the filtering of components with small spatial scales that correspond to noise, and the filtering of structures in unobserved regions. The singular vector perspective gives a very clear view of this filtering and interpolating by the 4D-Var algorithm and shows that the appropriate specification of the a priori statistics is vital to extract the largest possible amount of useful information from the observations. Copyright © 2005 Royal Meteorological Society

Particle filtering in geophysical systems

The application of particle filters in geophysical systems is reviewed. Some background on Bayesian filtering is provided, and the existing methods are discussed. The emphasis is on the methodology, and not so much on the applications themselves. It is shown that direct application of the basic particle filter (i.e., importance sampling using the prior as the importance density) does not work in high-dimensional systems, but several variants are shown to have potential. Approximations to the full problem that try to keep some aspects of the particle filter beyond the Gaussian approximation are also presented and discussed.

Far-red light filtering by plastic film, greenhouse-cladding materials: effects on growth and flowering in Petunia and Impatiens

Photoselective plastic films with low transmission to far-red (FR) light (700-800 nm) are now available so that plants grown in greenhouses clad with such plastics exhibit reduced stem extension and, consequently, plant height. Here we compare the action of three FR-absorbing polythene films on extension growth of Petunia (Petunia X hybrida) cv. 'Express Blue' and Impatiens walleriana cv. 'Accent Deep Pink' with plants grown under a control polythene film (standard UVI/EVA film). Half of the plants under the control film were treated with a chemical plant growth regulator (PGR; diaminozide, B-Nine) and half were sprayed with water alone. Possible negative effects of such film plastics on flowering, and on fresh and dry weight accumulation, were also quantified. Plants were harvested destructively when all plants in each treatment had reached the first open flower stage. In Petunia, plant height was reduced by all three FR-filtering films and by PGR-treatment. The FR-filtering films giving the highest R:FR ratios also reduced plant height in Impatiens. Leaf number, leaf area and total dry Weight in both species. were greatest in the controls and smallest under films with the lowest PAR transmission. The film giving the highest R:FR ratio and PAR transmission also produced the most compact Petunia plants;, while the film. with. the lowest PAR transmission produced the least compact plants in both species. There was no significant effect of treatments on time to first flower in Impatiens. However, Petunia plants under low PAR transmission films took longer to flower. Plastic-films which filter out FR light to increase the R:FR ratio, combined With high PAR transmission, can therefore be used as an alternative to conventional PGRs.

Reach & grasp therapy: Design and control of a 9-DOF robotic neuro-rehabilitation system

This paper presents the Gentle/G integrated system for reach & grasp therapy retraining following brain injury. The design, control and integration of an experimental grasp assistance unit is described for use in robot assisted stroke rehabilitation. The grasp assist unit is intended to work with the hardware and software of the Gentle/S robot although the hardware could be adapted to other rehabilitation applications. When used with the Gentle/S robot a total of 6 active and 3 passive degrees of freedom are available to provide active, active assist or passive grasp retraining in combination with reaching movements in a reach-grasp-transfer-release sequence.

Perceptual cues for orientation in a two finger haptic grasp task

Single point interaction haptic devices do not provide the natural grasp and manipulations found in the real world, as afforded by multi-fingered haptics. The present study investigates a two-fingered grasp manipulation involving rotation with and without force feedback. There were three visual cue conditions: monocular, binocular and projective lighting. Performance metrics of time and positional accuracy were assessed. The results indicate that adding haptics to an object manipulation task increases the positional accuracy but slightly increases the overall time taken.

Reach and grasp therapy: effects of the Gentle/G System assessing sub-acute stroke whole-arm rehabilitation

This paper reports preliminary results of a reach and grasp study of robot mediated neurorehabilitation. These results are presented on a case-by-case basis and give a good indication of a positive effect of robot mediated therapy. The study investigated both reach and grasp assistance and although it is not possible to attribute the response to the benefits of providing assistance of both modalities the study is a good indicator that this strategy should be pursued. The paper also reports on the benefits of motivational queues such as exercise scores and on subject attitudes to the robot mediated therapy.

EMG signal filtering based on Empirical Mode Decomposition

This paper introduces a procedure for filtering electromyographic (EMG) signals. Its key element is the Empirical Mode Decomposition, a novel digital signal processing technique that can decompose my time-series into a set of functions designated as intrinsic mode functions. The procedure for EMG signal filtering is compared to a related approach based on the wavelet transform. Results obtained from the analysis of synthetic and experimental EMG signals show that Our method can be Successfully and easily applied in practice to attenuation of background activity in EMG signals. (c) 2006 Elsevier Ltd. All rights reserved.

Comparison of subspace and ARX models of a waveguide's terahertz transient response after optimal wavelet filtering

A quasi-optical deembedding technique for characterizing waveguides is demonstrated using wide-band time-resolved terahertz spectroscopy. A transfer function representation is adopted for the description of the signal in the input and output port of the waveguides. The time-domain responses were discretized and the waveguide transfer function was obtained through a parametric approach in the z-domain after describing the system with an AutoRegressive with eXogenous input (ARX), as well as with a state-space model. Prior to the identification procedure, filtering was performed in the wavelet domain to minimize both signal distortion, as well as the noise propagating in the ARX and subspace models. The optimal filtering procedure used in the wavelet domain for the recorded time-domain signatures is described in detail. The effect of filtering prior to the identification procedures is elucidated with the aid of pole-zero diagrams. Models derived from measurements of terahertz transients in a precision WR-8 waveguide adjustable short are presented.

Filtering techniques in self-tuning

In the last few years a state-space formulation has been introduced into self-tuning control. This has not only allowed for a wider choice of possible control actions, but has also provided an insight into the theory underlying—and hidden by—that used in the polynomial description. This paper considers many of the self-tuning algorithms, both state-space and polynomial, presently in use, and by starting from first principles develops the observers which are, effectively, used in each case. At any specific time instant the state estimator can be regarded as taking one of two forms. In the first case the most recently available output measurement is excluded, and here an optimal and conditionally stable observer is obtained. In the second case the present output signal is included, and here it is shown that although the observer is once again conditionally stable, it is no longer optimal. This result is of significance, as many of the popular self-tuning controllers lie in the second, rather than first, category.

Neurofuzzy control using Kalman filtering state feedback with coloured noise for unknown non-linear processes

This paper presents a controller design scheme for a priori unknown non-linear dynamical processes that are identified via an operating point neurofuzzy system from process data. Based on a neurofuzzy design and model construction algorithm (NeuDec) for a non-linear dynamical process, a neurofuzzy state-space model of controllable form is initially constructed. The control scheme based on closed-loop pole assignment is then utilized to ensure the time invariance and linearization of the state equations so that the system stability can be guaranteed under some mild assumptions, even in the presence of modelling error. The proposed approach requires a known state vector for the application of pole assignment state feedback. For this purpose, a generalized Kalman filtering algorithm with coloured noise is developed on the basis of the neurofuzzy state-space model to obtain an optimal state vector estimation. The derived controller is applied in typical output tracking problems by minimizing the tracking error. Simulation examples are included to demonstrate the operation and effectiveness of the new approach.

Goal-refinement appraisal of soft projects (GRASP)

Industrial projects are often complex and burdened with time pressures and a lack of information. The term 'soft-project' used here stands for projects where the ‘what’ and/or the ‘how’ is uncertain, which is often the experience in projects involving software intensive systems developments. This thesis intertwines the disciplines of project management and requirements engineering in a goal-oriented application of the maxim ‘keep all objectives satisfied’. It thus proposes a method for appraising projects. In this method, a goal-oriented analysis establishes a framework with which expert judgements are collected so as to construct a confidence profile in regard to the feasibility and adequacy of the project's planned outputs. It is hoped that this appraisal method will contribute to the activities of project ‘shaping’ and aligning stakeholders’ expectations whilst helping project managers appreciate what parts of their project can be progressed and what parts should be held pending further analysis. This thesis offers the following original contribution: an appreciation of appraisal in the project context; a goal-oriented confidence profiling technique; and: a technique to produce goal-refinement diagrams – referred to as Goal Sketching. Collectively these amount to a method for the ‘Goal Refinement Appraisal of Soft-Projects’ (GRASP). The validity of the GRASP method is shown for two projects. In the first it is used for shaping a business investigation project. This is done in real-time in the project. The second case is a retrospective study of an enterprise IT project. This case tests the effectiveness of forecasting project difficulty from an initial confidence profile.