An adaptive linear equalizer with optimum filter length and decision delay

The power of an adaptive equalizer is maximized when the structural parameters including the tap-length and decision delay can be optimally chosen. Although the method for adjusting either the tap-length or decision delay has been proposed, adjusting both simultaneously becomes much more involved as they interact with each other. In this paper, this problem is solved by putting a linear prewhitener before the equalizer, with which the equivalent channel becomes maximum-phase. This implies that the optimum decision delay can be simply ¯xed at the tap-length minus one, while the tap-length can then be chosen using a similar approach as that proposed in our previous work.

Ensemble prediction for nowcasting with a convection-permitting model - II: forecast error statistics

A 24-member ensemble of 1-h high-resolution forecasts over the Southern United Kingdom is used to study short-range forecast error statistics. The initial conditions are found from perturbations from an ensemble transform Kalman filter. Forecasts from this system are assumed to lie within the bounds of forecast error of an operational forecast system. Although noisy, this system is capable of producing physically reasonable statistics which are analysed and compared to statistics implied from a variational assimilation system. The variances for temperature errors for instance show structures that reflect convective activity. Some variables, notably potential temperature and specific humidity perturbations, have autocorrelation functions that deviate from 3-D isotropy at the convective-scale (horizontal scales less than 10 km). Other variables, notably the velocity potential for horizontal divergence perturbations, maintain 3-D isotropy at all scales. Geostrophic and hydrostatic balances are studied by examining correlations between terms in the divergence and vertical momentum equations respectively. Both balances are found to decay as the horizontal scale decreases. It is estimated that geostrophic balance becomes less important at scales smaller than 75 km, and hydrostatic balance becomes less important at scales smaller than 35 km, although more work is required to validate these findings. The implications of these results for high-resolution data assimilation are discussed.

State estimation using the particle filter with mode tracking

A particle filter is a data assimilation scheme that employs a fully nonlinear, non-Gaussian analysis step. Unfortunately as the size of the state grows the number of ensemble members required for the particle filter to converge to the true solution increases exponentially. To overcome this Vaswani [Vaswani N. 2008. IEEE Trans Signal Process 56:4583–97] proposed a new method known as mode tracking to improve the efficiency of the particle filter. When mode tracking, the state is split into two subspaces. One subspace is forecast using the particle filter, the other is treated so that its values are set equal to the mode of the marginal pdf. There are many ways to split the state. One hypothesis is that the best results should be obtained from the particle filter with mode tracking when we mode track the maximum number of unimodal dimensions. The aim of this paper is to test this hypothesis using the three dimensional stochastic Lorenz equations with direct observations. It is found that mode tracking the maximum number of unimodal dimensions does not always provide the best result. The best choice of states to mode track depends on the number of particles used and the accuracy and frequency of the observations.

Results of a DSP based adaptive cancellation filter system for the chirp, pulsar and localiser sirens

Sirens’ used by police, fire and paramedic vehicles generate noise that propagates inside the vehicle cab that subsequently corrupts intelligibility of voice communications from the emergency vehicle to the control room. It is even common for the siren to be turned off to enable the control room to hear what is being said. Both fixed filter and adaptive filter systems have previously been developed to help cancel the transmission of the siren noise over the radio. Previous cancellation systems have only concentrated on the traditional 2-tone, wail and yelp sirens. This paper discusses an improvement to a previous adaptive filter system and presents the cancellation results to three new types of sirens; being chirp pulsar and localiser. A siren noise filter system has the capability to improve the response time for an emergency vehicle and thus help save lives. To date, this system has been tested using live recordings taken from a nonemergency situation with good results.

Altitude acts as an environmental filter on phylogenetic composition, traits and diversity in bee communities.

Knowledge about the phylogeny and ecology of communities along environmental gradients helps to disentangle the role of competition-driven processes and environmental filtering for community assembly. In this study, we evaluated patterns in species richness, phylogenetic structure and life-history traits of bee communities along altitudinal gradients in the Alps, Germany. We found a linear decline in species richness and abundance but increasing phylogenetic clustering in communities with increasing altitude. The proportion of social- and ground-nesting species, as well as mean body size and altitudinal range of bee communities, increased with increasing altitude, whereas the mean geographical distribution decreased. Our results suggest that community assembly at high altitudes is dominated by environmental filtering effects, whereas the relative importance of competition increases at low altitudes. We conclude that inherent phylogenetic and ecological species attributes at high altitudes pose a threat for less competitive alpine specialists with ongoing climate change.

Balance model for equatorial long waves

Geophysical fluid models often support both fast and slow motions. As the dynamics are often dominated by the slow motions, it is desirable to filter out the fast motions by constructing balance models. An example is the quasi geostrophic (QG) model, which is used widely in meteorology and oceanography for theoretical studies, in addition to practical applications such as model initialization and data assimilation. Although the QG model works quite well in the mid-latitudes, its usefulness diminishes as one approaches the equator. Thus far, attempts to derive similar balance models for the tropics have not been entirely successful as the models generally filter out Kelvin waves, which contribute significantly to tropical low-frequency variability. There is much theoretical interest in the dynamics of planetary-scale Kelvin waves, especially for atmospheric and oceanic data assimilation where observations are generally only of the mass field and thus do not constrain the wind field without some kind of diagnostic balance relation. As a result, estimates of Kelvin wave amplitudes can be poor. Our goal is to find a balance model that includes Kelvin waves for planetary-scale motions. Using asymptotic methods, we derive a balance model for the weakly nonlinear equatorial shallow-water equations. Specifically we adopt the ‘slaving’ method proposed by Warn et al. (Q. J. R. Meteorol. Soc., vol. 121, 1995, pp. 723–739), which avoids secular terms in the expansion and thus can in principle be carried out to any order. Different from previous approaches, our expansion is based on a long-wave scaling and the slow dynamics is described using the height field instead of potential vorticity. The leading-order model is equivalent to the truncated long-wave model considered previously (e.g. Heckley & Gill, Q. J. R. Meteorol. Soc., vol. 110, 1984, pp. 203–217), which retains Kelvin waves in addition to equatorial Rossby waves. Our method allows for the derivation of higher-order models which significantly improve the representation of Rossby waves in the isotropic limit. In addition, the ‘slaving’ method is applicable even when the weakly nonlinear assumption is relaxed, and the resulting nonlinear model encompasses the weakly nonlinear model. We also demonstrate that the method can be applied to more realistic stratified models, such as the Boussinesq model.

Automated algorithms for multilayer thin film filter design using metamaterials

Currently, infrared filters for astronomical telescopes and satellite radiometers are based on multilayer thin film stacks of alternating high and low refractive index materials. However, the choice of suitable layer materials is limited and this places limitations on the filter performance that can be achieved. The ability to design materials with arbitrary refractive index allows for filter performance to be greatly increased but also increases the complexity of design. Here a differential algorithm was used as a method for optimised design of filters with arbitrary refractive indices, and then materials are designed to these specifications as mono-materials with sub wavelength structures using Bruggeman’s effective material approximation (EMA).

Estimating correlated observation error statistics using an ensemble transform Kalman filter

For certain observing types, such as those that are remotely sensed, the observation errors are correlated and these correlations are state- and time-dependent. In this work, we develop a method for diagnosing and incorporating spatially correlated and time-dependent observation error in an ensemble data assimilation system. The method combines an ensemble transform Kalman filter with a method that uses statistical averages of background and analysis innovations to provide an estimate of the observation error covariance matrix. To evaluate the performance of the method, we perform identical twin experiments using the Lorenz ’96 and Kuramoto-Sivashinsky models. Using our approach, a good approximation to the true observation error covariance can be recovered in cases where the initial estimate of the error covariance is incorrect. Spatial observation error covariances where the length scale of the true covariance changes slowly in time can also be captured. We find that using the estimated correlated observation error in the assimilation improves the analysis.

On the application of optimal wavelet filter banks for ECG signal classification

This paper discusses ECG signal classification after parametrizing the ECG waveforms in the wavelet domain. Signal decomposition using perfect reconstruction quadrature mirror filter banks can provide a very parsimonious representation of ECG signals. In the current work, the filter parameters are adjusted by a numerical optimization algorithm in order to minimize a cost function associated to the filter cut-off sharpness. The goal consists of achieving a better compromise between frequency selectivity and time resolution at each decomposition level than standard orthogonal filter banks such as those of the Daubechies and Coiflet families. Our aim is to optimally decompose the signals in the wavelet domain so that they can be subsequently used as inputs for training to a neural network classifier.

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.