A Variance-Minimizing Filter for Large-Scale Applications

A truly variance-minimizing filter is introduced and its per for mance is demonstrated with the Korteweg– DeV ries (KdV) equation and with a multilayer quasigeostrophic model of the ocean area around South Africa. It is recalled that Kalman-like filters are not variance minimizing for nonlinear model dynamics and that four - dimensional variational data assimilation (4DV AR)-like methods relying on per fect model dynamics have dif- ficulty with providing error estimates. The new method does not have these drawbacks. In fact, it combines advantages from both methods in that it does provide error estimates while automatically having balanced states after analysis, without extra computations. It is based on ensemble or Monte Carlo integrations to simulate the probability density of the model evolution. When obser vations are available, the so-called importance resampling algorithm is applied. From Bayes’ s theorem it follows that each ensemble member receives a new weight dependent on its ‘ ‘distance’ ’ t o the obser vations. Because the weights are strongly var ying, a resampling of the ensemble is necessar y. This resampling is done such that members with high weights are duplicated according to their weights, while low-weight members are largely ignored. In passing, it is noted that data assimilation is not an inverse problem by nature, although it can be for mulated that way . Also, it is shown that the posterior variance can be larger than the prior if the usual Gaussian framework is set aside. However , i n the examples presented here, the entropy of the probability densities is decreasing. The application to the ocean area around South Africa, gover ned by strongly nonlinear dynamics, shows that the method is working satisfactorily . The strong and weak points of the method are discussed and possible improvements are proposed.

Analysis Scheme in the Ensemble Kalman Filter

This paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter . I t i s shown that the obser vations must be treated as random variables at the analysis steps. That is, one should add random perturbations with the correct statistics to the obser vations and generate an ensemble of obser vations that then is used in updating the ensemble of model states. T raditionally , this has not been done in previous applications of the ensemble Kalman filter and, as will be shown, this has resulted in an updated ensemble with a variance that is too low . This simple modification of the analysis scheme results in a completely consistent approach if the covariance of the ensemble of model states is interpreted as the prediction error covariance, and there are no further requirements on the ensemble Kalman filter method, except for the use of an ensemble of sufficient size. Thus, there is a unique correspondence between the error statistics from the ensemble Kalman filter and the standard Kalman filter approach

Assimilation of Geosat Altimeter Data for the Agulhas Current Using the Ensemble Kalman Filter with a Quasigeostrophic Model

The ring-shedding process in the Agulhas Current is studied using the ensemble Kalman filter to assimilate geosat altimeter data into a two-layer quasigeostrophic ocean model. The properties of the ensemble Kalman filter are further explored with focus on the analysis scheme and the use of gridded data. The Geosat data consist of 10 fields of gridded sea-surface height anomalies separated 10 days apart that are added to a climatic mean field. This corresponds to a huge number of data values, and a data reduction scheme must be applied to increase the efficiency of the analysis procedure. Further, it is illustrated how one can resolve the rank problem occurring when a too large dataset or a small ensemble is used.

Why cancer patients choose in-patient complementary therapy in palliative care: a qualitative study at Arokhayasala Hospice in Thailand

Cancer patients often choose complementary and alternative medicine (CAM) in palliative care, often in addition to conventional treatment and without medical advice or approval. Herbal medicines (HM) are the most commonly used type of CAM, but rarely available on an in-patient basis for palliative care. The motivations which lead very ill patients to travel far to receive such therapies are not clear. A qualitative study was therefore carried out to investigate influences on choosing to attend a CAM herbal hospice, to identify cancer patients’ main concerns about end-of-life care. Semi-structured interviews with 32 patients were conducted and analysed using thematic analysis. Patients were recruited from Arokhayasala, a Buddhist cancer hospice in Thailand which provides CAM, in the form of HM, a restricted diet, Thai yoga, deep-breathing exercises, meditation, chanting, Dhamma, laughter and music therapy, free-of-charge. The main factors influencing decision-making were a positive attitude towards HMs and previous use of them, dissatisfaction with conventional treatment, the home environment and their relationships with hospital doctors. Patients’ own perceptions and experiences were more important in making the decision to use CAM, and especially HM, in palliative cancer care than referral by healthcare professionals or scientific evidence of efficacy. Patients were prepared to travel far and live away from home to receive such care, especially as it was cost-free. In view of patients’ previously stated satisfaction with the regime at the Arokhayasala, these findings may be relevant to the provision of in-patient cancer palliative care to other patients.

Implicit equal-weights particle filter

Filter degeneracy is the main obstacle for the implementation of particle filter in non-linear high-dimensional models. A new scheme, the implicit equal-weights particle filter (IEWPF), is introduced. In this scheme samples are drawn implicitly from proposal densities with a different covariance for each particle, such that all particle weights are equal by construction. We test and explore the properties of the new scheme using a 1,000-dimensional simple linear model, and the 1,000-dimensional non-linear Lorenz96 model, and compare the performance of the scheme to a Local Ensemble Kalman Filter. The experiments show that the new scheme can easily be implemented in high-dimensional systems and is never degenerate, with good convergence properties in both systems.

Optimising mirid control on cocoa farms through complementary monitoring systems

Mirids (Sahlbergella singularis and Distantiella theobroma) are the most important insect pests affecting cocoa production across West Africa. Understanding the population dynamics of mirids is key to their management, however, the current recommended hand-height assessment method is labour intensive. The objective of the study was to compare recently developed mirid sex pheromone trapping and visual hand-height assessment methods as monitoring tools on cocoa farms and to consider implications for a decision support system. Ten farms from the Eastern and Ashanti regions of Ghana were used for the study. Mirid numbers and damage were assessed fortnightly on twenty trees per farm, using both methods, from January 2012 to April 2013. The mirid population increased rapidly in June, reached a peak in September and began to decline in October. There was a significant linear relationship between numbers of mirids sampled to hand-height and mirid damage. High numbers of male mirids were recorded in pheromone traps between January and April 2012 after which there was a gradual decline. There was a significant inverse relationship between numbers of trapped adult mirids and mirids sampled to hand-height (predominantly nymphs). Higher temperatures and lower relative humidities in the first half of the year were associated with fewer mirids at hand-height but larger numbers of adult males were caught in pheromone traps. The study showed that relying solely on one method is not sufficient to provide accurate information on mirid population dynamics and a combination of the two methods is necessary.

The Diffusion Kernel Filter

A particle filter method is presented for the discrete-time filtering problem with nonlinear ItA ` stochastic ordinary differential equations (SODE) with additive noise supposed to be analytically integrable as a function of the underlying vector-Wiener process and time. The Diffusion Kernel Filter is arrived at by a parametrization of small noise-driven state fluctuations within branches of prediction and a local use of this parametrization in the Bootstrap Filter. The method applies for small noise and short prediction steps. With explicit numerical integrators, the operations count in the Diffusion Kernel Filter is shown to be smaller than in the Bootstrap Filter whenever the initial state for the prediction step has sufficiently few moments. The established parametrization is a dual-formula for the analysis of sensitivity to gaussian-initial perturbations and the analysis of sensitivity to noise-perturbations, in deterministic models, showing in particular how the stability of a deterministic dynamics is modeled by noise on short times and how the diffusion matrix of an SODE should be modeled (i.e. defined) for a gaussian-initial deterministic problem to be cast into an SODE problem. From it, a novel definition of prediction may be proposed that coincides with the deterministic path within the branch of prediction whose information entropy at the end of the prediction step is closest to the average information entropy over all branches. Tests are made with the Lorenz-63 equations, showing good results both for the filter and the definition of prediction.

Towards improving cluster-based feature selection with a simplified silhouette filter

This paper proposes a filter-based algorithm for feature selection. The filter is based on the partitioning of the set of features into clusters. The number of clusters, and consequently the cardinality of the subset of selected features, is automatically estimated from data. The computational complexity of the proposed algorithm is also investigated. A variant of this filter that considers feature-class correlations is also proposed for classification problems. Empirical results involving ten datasets illustrate the performance of the developed algorithm, which in general has obtained competitive results in terms of classification accuracy when compared to state of the art algorithms that find clusters of features. We show that, if computational efficiency is an important issue, then the proposed filter May be preferred over their counterparts, thus becoming eligible to join a pool of feature selection algorithms to be used in practice. As an additional contribution of this work, a theoretical framework is used to formally analyze some properties of feature selection methods that rely on finding clusters of features. (C) 2011 Elsevier Inc. All rights reserved.

The complementary exponential power lifetime model

In this paper we propose a new lifetime distribution which can handle bathtub-shaped unimodal increasing and decreasing hazard rate functions The model has three parameters and generalizes the exponential power distribution proposed by Smith and Bain (1975) with the inclusion of an additional shape parameter The maximum likelihood estimation procedure is discussed A small-scale simulation study examines the performance of the likelihood ratio statistics under small and moderate sized samples Three real datasets Illustrate the methodology (C) 2010 Elsevier B V All rights reserved

The complementary exponential geometric distribution: Model, properties, and a comparison with its counterpart

In this paper, we proposed a new two-parameter lifetime distribution with increasing failure rate, the complementary exponential geometric distribution, which is complementary to the exponential geometric model proposed by Adamidis and Loukas (1998). The new distribution arises on a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the maximum lifetime value among all risks. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its reliability and failure rate functions, moments, including the mean and variance, variation coefficient, and modal value. The parameter estimation is based on the usual maximum likelihood approach. We report the results of a misspecification simulation study performed in order to assess the extent of misspecification errors when testing the exponential geometric distribution against our complementary one in the presence of different sample size and censoring percentage. The methodology is illustrated on four real datasets; we also make a comparison between both modeling approaches. (C) 2011 Elsevier B.V. All rights reserved.

A Floating-point Extended Kalman Filter Implementation for Autonomous Mobile Robots

Localization and Mapping are two of the most important capabilities for autonomous mobile robots and have been receiving considerable attention from the scientific computing community over the last 10 years. One of the most efficient methods to address these problems is based on the use of the Extended Kalman Filter (EKF). The EKF simultaneously estimates a model of the environment (map) and the position of the robot based on odometric and exteroceptive sensor information. As this algorithm demands a considerable amount of computation, it is usually executed on high end PCs coupled to the robot. In this work we present an FPGA-based architecture for the EKF algorithm that is capable of processing two-dimensional maps containing up to 1.8 k features at real time (14 Hz), a three-fold improvement over a Pentium M 1.6 GHz, and a 13-fold improvement over an ARM920T 200 MHz. The proposed architecture also consumes only 1.3% of the Pentium and 12.3% of the ARM energy per feature.

Aerosol inorganic composition at a tropical site: Discrepancies between filter-based sampling and a semi-continuous method

The concentrations of the water-soluble inorganic aerosol species, ammonium (NH4+), nitrate (NO3-), chloride (Cl-), and sulfate (SO42-), were measured from September to November 2002 at a pasture site in the Amazon Basin (Rondnia, Brazil) (LBA-SMOCC). Measurements were conducted using a semi-continuous technique (Wet-annular denuder/Steam-Jet Aerosol Collector: WAD/SJAC) and three integrating filter-based methods, namely (1) a denuder-filter pack (DFP: Teflon and impregnated Whatman filters), (2) a stacked-filter unit (SFU: polycarbonate filters), and (3) a High Volume dichotomous sampler (HiVol: quartz fiber filters). Measurements covered the late dry season (biomass burning), a transition period, and the onset of the wet season (clean conditions). Analyses of the particles collected on filters were performed using ion chromatography (IC) and Particle-Induced X-ray Emission spectrometry (PIXE). Season-dependent discrepancies were observed between the WAD/SJAC system and the filter-based samplers. During the dry season, when PM2.5 (D-p <= 2.5 mu m) concentrations were similar to 100 mu g m(-3), aerosol NH4+ and SO42- measured by the filter-based samplers were on average two times higher than those determined by the WAD/SJAC. Concentrations of aerosol NO3- and Cl- measured with the HiVol during daytime, and with the DFP during day- and nighttime also exceeded those of the WAD/SJAC by a factor of two. In contrast, aerosol NO3- and Cl- measured with the SFU during the dry season were nearly two times lower than those measured by the WAD/SJAC. These differences declined markedly during the transition period and towards the cleaner conditions during the onset of the wet season (PM2.5 similar to 5 mu g m(-3)); when filter-based samplers measured on average 40-90% less than the WAD/SJAC. The differences were not due to consistent systematic biases of the analytical techniques, but were apparently a result of prevailing environmental conditions and different sampling procedures. For the transition period and wet season, the significance of our results is reduced by a low number of data points. We argue that the observed differences are mainly attributable to (a) positive and negative filter sampling artifacts, (b) presence of organic compounds and organosulfates on filter substrates, and (c) a SJAC sampling efficiency of less than 100%.