The composite-tendency RAW filter in semi-implicit integrations

The time discretization in weather and climate models introduces truncation errors that limit the accuracy of the simulations. Recent work has yielded a method for reducing the amplitude errors in leapfrog integrations from first-order to fifth-order. This improvement is achieved by replacing the Robert--Asselin filter with the RAW filter and using a linear combination of the unfiltered and filtered states to compute the tendency term. The purpose of the present paper is to apply the composite-tendency RAW-filtered leapfrog scheme to semi-implicit integrations. A theoretical analysis shows that the stability and accuracy are unaffected by the introduction of the implicitly treated mode. The scheme is tested in semi-implicit numerical integrations in both a simple nonlinear stiff system and a medium-complexity atmospheric general circulation model, and yields substantial improvements in both cases. We conclude that the composite-tendency RAW-filtered leapfrog scheme is suitable for use in semi-implicit integrations.

The composite-tendency Robert-Asselin-Williams (RAW) filter in semi-implicit integrations

Timediscretization in weatherandclimate modelsintroduces truncation errors that limit the accuracy of the simulations. Recent work has yielded a method for reducing the amplitude errors in leap-frog integrations from first-order to fifth-order.This improvement is achieved by replacing the Robert–Asselin filter with the Robert–Asselin–Williams (RAW) filter and using a linear combination of unfiltered and filtered states to compute the tendency term. The purpose of the present article is to apply the composite-tendency RAW-filtered leapfrog scheme to semi-implicit integrations. A theoretical analysis shows that the stability and accuracy are unaffected by the introduction of the implicitly treated mode. The scheme is tested in semi-implicit numerical integrations in both a simple nonlinear stiff system and a medium-complexity atmospheric general circulation model and yields substantial improvements in both cases. We conclude that the composite-tendency RAW-filtered leap-frog scheme is suitable for use in semi-implicit integrations.

The equivalent-weights particle filter in a high-dimensional system

In general, particle filters need large numbers of model runs in order to avoid filter degeneracy in high-dimensional systems. The recently proposed, fully nonlinear equivalent-weights particle filter overcomes this requirement by replacing the standard model transition density with two different proposal transition densities. The first proposal density is used to relax all particles towards the high-probability regions of state space as defined by the observations. The crucial second proposal density is then used to ensure that the majority of particles have equivalent weights at observation time. Here, the performance of the scheme in a high, 65 500 dimensional, simplified ocean model is explored. The success of the equivalent-weights particle filter in matching the true model state is shown using the mean of just 32 particles in twin experiments. It is of particular significance that this remains true even as the number and spatial variability of the observations are changed. The results from rank histograms are less easy to interpret and can be influenced considerably by the parameter values used. This article also explores the sensitivity of the performance of the scheme to the chosen parameter values and the effect of using different model error parameters in the truth compared with the ensemble model runs.

Twin experiments with the equivalent weights particle filter and HadCM3

This paper investigates the use of a particle filter for data assimilation with a full scale coupled ocean–atmosphere general circulation model. Synthetic twin experiments are performed to assess the performance of the equivalent weights filter in such a high-dimensional system. Artificial 2-dimensional sea surface temperature fields are used as observational data every day. Results are presented for different values of the free parameters in the method. Measures of the performance of the filter are root mean square errors, trajectories of individual variables in the model and rank histograms. Filter degeneracy is not observed and the performance of the filter is shown to depend on the ability to keep maximum spread in the ensemble.

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

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.

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.

Robust extended Kalman filter based technique for location management in PCS networks

Provisioning of real-time multimedia sessions over wireless cellular network poses unique challenges due to frequent handoff and rerouting of a connection. For this reason, the wireless networks with cellular architecture require efficient user mobility estimation and prediction. This paper proposes using Robust Extended Kalman Filter as a location heading altitude estimator of mobile user for next cell prediction in order to improve the connection reliability and bandwidth efficiency of the underlying system. Through analysis we demonstrate that our algorithm reduces the system complexity (compared to existing approach using pattern matching and Kalman filter) as it requires only two base station measurements or only the measurement from the closest base station. Further, the technique is robust against system uncertainties due to inherent deterministic nature in the mobility model. Through simulation, we show the accuracy and simplicity in implementation of our prediction algorithm.

Robust extended kalman filter applied to location tracking and trajectory prediction for PCS networks

Provisioning of real-time multimedia sessions over wireless cellular network poses unique challenges due to frequent handoff and rerouting of a connection. For this reason, the wireless networks with cellular architecture require efficient user mobility estimation and prediction. This paper proposes using robust extended Kalman filter (REKF) as a location heading altitude estimator of mobile user for next cell prediction in order to improve the connection reliability and bandwidth efficiency of the underlying system. Through analysis we demonstrate that our algorithm reduces the system complexity (compared to existing approach using pattern matching and Kalman filter) as it requires only two base station measurements or only the measurement from the closest base station. Further, the technique is robust against system uncertainties due to inherent deterministic nature in the mobility model and more effective in comparison with the standard Kalman filter.

A multi-filter enhanced genetic ensemble system for gene selection and sample classification of microarray data

Background: Feature selection techniques are critical to the analysis of high dimensional datasets. This is especially true in gene selection from microarray data which are commonly with extremely high feature-to-sample ratio. In addition to the essential objectives such as to reduce data noise, to reduce data redundancy, to improve sample classification accuracy, and to improve model generalization property, feature selection also helps biologists to focus on the selected genes to further validate their biological hypotheses.
Results: In this paper we describe an improved hybrid system for gene selection. It is based on a recently proposed genetic ensemble (GE) system. To enhance the generalization property of the selected genes or gene subsets and to overcome the overfitting problem of the GE system, we devised a mapping strategy to fuse the goodness information of each gene provided by multiple filtering algorithms. This information is then used for initialization and mutation operation of the genetic ensemble system.
Conclusion: We used four benchmark microarray datasets (including both binary-class and multi-class classification problems) for concept proving and model evaluation. The experimental results indicate that the proposed multi-filter enhanced genetic ensemble (MF-GE) system is able to improve sample classification accuracy, generate more compact gene subset, and converge to the selection results more quickly. The MF-GE system is very flexible as various combinations of multiple filters and classifiers can be incorporated based on the data characteristics and the user preferences.

Mathematical modelling of downflow floating medium filter (DFF) with in-line flocculation arrangement

A laboratory-scale set-up consisting of rapid mixing device and floating medium filter was used to study the use of a downflow floating medium filter (DFF) with an in-line flocculation arrangement as a static flocculator and a prefilter. The semi-empirical mathematical model formulated incorporates flocculation within the filter, particle/floc attachment onto the filter and the detachment of flocs from the medium. The mathematical model for filtration takes into account the expansion of the filter bed. The removal efficiency of DFF and headless development were successfully simulated for different conditions of filtration velocity, filter depth and influent suspended solids (SS). The values of attachment coefficient a(p)β and headless coefficient β1 were found to be independent of filtration velocity, filter depth and influent SS concentration.

Surface coverage of filter medium in deep bed filtration : mathematical modelling and experiments

This paper highlights the importance of surface coverage in modeling the removal of particles in deep bed filtration. A model that considers the saturation of sites on which particle deposition occurs is used. Experimental results obtained with monodispersed suspensions of 0.46 and 0.816 μm latex particles at different influent concentrations and ionic strengths were used to calculate the fraction of filter grain surface (β1) on which actual particle deposition occurs. This will be useful in evaluating the filter performance in terms of the utilization of available surface area of the filter medium. Further, the level of dendrite formation of particles on filter grains during filtration is expressed in terms of β1 and the specific surface coverage, θT (the fraction of a filter grain surface that is covered by particles at time T, assuming that the filter grain is covered by a monolayer of particles). This can be used to compare the contribution of deposited particles in the removal efficiency of deep bed filtration for suspensions with different physical and chemical characteristics.

Identification of nonlinear fMRI models using Auxiliary Particle Filter and kernel smoothing method

Hemodynamic models have a high potential in application to understanding the functional differences of the brain. However, full system identification with respect to model fitting to actual functional magnetic resonance imaging (fMRI) data is practically difficult and is still an active area of research. We present a simulation based Bayesian approach for nonlinear model based analysis of the fMRI data. The idea is to do a joint state and parameter estimation within a general filtering framework. One advantage of using Bayesian methods is that they provide a complete description of the posterior distribution, not just a single point estimate. We use an Auxiliary Particle Filter adjoined with a kernel smoothing approach to address this joint estimation problem.

Incorporating human perception with the motion washout filter using fuzzy logic control

Abstract—Nowadays, classical washout filters are extensively used in commercial motion simulators. Even though there are several advantages for classical washout filters, such as short processing time, simplicity and ease of adjustment, they have several shortcomings. The main disadvantage is the fixed scheme and parameters of the classical washout filter cause inflexibility of the structure and thus the resulting simulator fails to suit all circumstances. Moreover, it is a conservative approach and the platform cannot be fully exploited. The aim of this research is to present a fuzzy logic approach and take the human perception error into account in the classical motion cueing algorithm, in order to improve both the physical limits of restitution and realistic human sensations. The fuzzy compensator signal is applied to adjust the filtered signals on the longitudinal and rotational channels online, as well as the tilt coordination to minimize the vestibular sensation error below the human perception threshold. The results indicate that the proposed fuzzy logic controllers significantly minimize the drawbacks of having fixed parameters and conservativeness in the classical washout filter. In addition, the performance of motion cueing algorithm and human perception for most occasions is improved.