Digital signal processing of optical monitoring by means of a Kalman filter

A Kalman filter algorithm has been applied to interpret the optical reflectance excursions during vacuum deposition of infrared coatings and multilayer thin-film filters. The application has been described in detail elsewhere and this paper now reports on-line experience for estimating deposition rate and thickness. The estimation proved sufficiently reliable to firstly 'navigate' regular manufacture (as controlled by a skilled operator) and to subsequently reproduce the skill without interpretation or intervention whilst maintaining exemplary product quality. Optical control by means of this Kalman filter application is therefore considered suitable as a basis for the automated manufacture of infrared coatings and multilayer thin-film filters.

Dual-orthogonal radial basis function networks for nonlinear time series prediction

A new structure of Radial Basis Function (RBF) neural network called the Dual-orthogonal RBF Network (DRBF) is introduced for nonlinear time series prediction. The hidden nodes of a conventional RBF network compare the Euclidean distance between the network input vector and the centres, and the node responses are radially symmetrical. But in time series prediction where the system input vectors are lagged system outputs, which are usually highly correlated, the Euclidean distance measure may not be appropriate. The DRBF network modifies the distance metric by introducing a classification function which is based on the estimation data set. Training the DRBF networks consists of two stages. Learning the classification related basis functions and the important input nodes, followed by selecting the regressors and learning the weights of the hidden nodes. In both cases, a forward Orthogonal Least Squares (OLS) selection procedure is applied, initially to select the important input nodes and then to select the important centres. Simulation results of single-step and multi-step ahead predictions over a test data set are included to demonstrate the effectiveness of the new approach.

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.

Applying the extended Kalman filter to systems described by nonlinear differential-algebraic equations

This paper describes a method for the state estimation of nonlinear systems described by a class of differential-algebraic equation models using the extended Kalman filter. The method involves the use of a time-varying linearisation of a semi-explicit index one differential-algebraic equation. The estimation technique consists of a simplified extended Kalman filter that is integrated with the differential-algebraic equation model. The paper describes a simulation study using a model of a batch chemical reactor. It also reports a study based on experimental data obtained from a mixing process, where the model of the system is solved using the sequential modular method and the estimation involves a bank of extended Kalman filters.

The effects of the RAW filter on the climatology and forecast skill of the SPEEDY model

In a recent study, Williams introduced a simple modification to the widely used Robert–Asselin (RA) filter for numerical integration. The main purpose of the Robert–Asselin–Williams (RAW) filter is to avoid the undesired numerical damping of the RA filter and to increase the accuracy. In the present paper, the effects of the modification are comprehensively evaluated in the Simplified Parameterizations, Primitive Equation Dynamics (SPEEDY) atmospheric general circulation model. First, the authors search for significant changes in the monthly climatology due to the introduction of the new filter. After testing both at the local level and at the field level, no significant changes are found, which is advantageous in the sense that the new scheme does not require a retuning of the parameterized model physics. Second, the authors examine whether the new filter improves the skill of short- and medium-term forecasts. January 1982 data from the NCEP–NCAR reanalysis are used to evaluate the forecast skill. Improvements are found in all the model variables (except the relative humidity, which is hardly changed). The improvements increase with lead time and are especially evident in medium-range forecasts (96–144 h). For example, in tropical surface pressure predictions, 5-day forecasts made using the RAW filter have approximately the same skill as 4-day forecasts made using the RA filter. The results of this work are encouraging for the implementation of the RAW filter in other models currently using the RA filter.

Grey-box radial basis function modelling

A fundamental principle in data modelling is to incorporate available a priori information regarding the underlying data generating mechanism into the modelling process. We adopt this principle and consider grey-box radial basis function (RBF) modelling capable of incorporating prior knowledge. Specifically, we show how to explicitly incorporate the two types of prior knowledge: (i) the underlying data generating mechanism exhibits known symmetric property, and (ii) the underlying process obeys a set of given boundary value constraints. The class of efficient orthogonal least squares regression algorithms can readily be applied without any modification to construct parsimonious grey-box RBF models with enhanced generalisation capability.

On combination of SMOTE and particle swarm optimization based radial basis function classifier for imbalanced problems

The combination of the synthetic minority oversampling technique (SMOTE) and the radial basis function (RBF) classifier is proposed to deal with classification for imbalanced two-class data. In order to enhance the significance of the small and specific region belonging to the positive class in the decision region, the SMOTE is applied to generate synthetic instances for the positive class to balance the training data set. Based on the over-sampled training data, the RBF classifier is constructed by applying the orthogonal forward selection procedure, in which the classifier structure and the parameters of RBF kernels are determined using a particle swarm optimization algorithm based on the criterion of minimizing the leave-one-out misclassification rate. The experimental results on both simulated and real imbalanced data sets are presented to demonstrate the effectiveness of our proposed algorithm.

Multi-layer radial basis function networks: an extension to the radial basis function

This paper presents the initial research carried out into a new neural network called the multilayer radial basis function network (MRBF). The network extends the radial basis function (RBF) in a similar way to that in which the multilayer perceptron extends the perceptron. It is hoped that by connecting RBFs together in a layered fashion, an equivalent increase in ability can be gained, as is gained from using MLPs instead of single perceptrons. The results of a practical comparison between individual RBFs and MRBF's are also given.

An introduction to radial basis functions for system identification: a comparison with other neural network methods

A look is taken at the use of radial basis functions (RBFs), for nonlinear system identification. RBFs are firstly considered in detail themselves and are subsequently compared with a multi-layered perceptron (MLP), in terms of performance and usage.

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.