Variable step LMS algorithm using the accumulated instantaneous error concept

The convergence speed of the standard Least Mean Square adaptive array may be degraded in mobile communication environments. Different conventional variable step size LMS algorithms were proposed to enhance the convergence speed while maintaining low steady state error. In this paper, a new variable step LMS algorithm, using the accumulated instantaneous error concept is proposed. In the proposed algorithm, the accumulated instantaneous error is used to update the step size parameter of standard LMS is varied. Simulation results show that the proposed algorithm is simpler and yields better performance than conventional variable step LMS.

An LMS style variable tap-length algorithm for structure adaptation

Searching for the optimum tap-length that best balances the complexity and steady-state performance of an adaptive filter has attracted attention recently. Among existing algorithms that can be found in the literature, two of which, namely the segmented filter (SF) and gradient descent (GD) algorithms, are of particular interest as they can search for the optimum tap-length quickly. In this paper, at first, we carefully compare the SF and GD algorithms and show that the two algorithms are equivalent in performance under some constraints, but each has advantages/disadvantages relative to the other. Then, we propose an improved variable tap-length algorithm using the concept of the pseudo fractional tap-length (FT). Updating the tap-length with instantaneous errors in a style similar to that used in the stochastic gradient [or least mean squares (LMS)] algorithm, the proposed FT algorithm not only retains the advantages from both the SF and the GD algorithms but also has significantly less complexity than existing algorithms. Both performance analysis and numerical simulations are given to verify the new proposed algorithm.

A customizable multi-agent system for distributed data mining

We present a general Multi-Agent System framework for distributed data mining based on a Peer-to-Peer model. Agent protocols are implemented through message-based asynchronous communication. The framework adopts a dynamic load balancing policy that is particularly suitable for irregular search algorithms. A modular design allows a separation of the general-purpose system protocols and software components from the specific data mining algorithm. The experimental evaluation has been carried out on a parallel frequent subgraph mining algorithm, which has shown good scalability performances.

A mixture of experts network structure construction algorithm for modelling and control

This paper introduces a new fast, effective and practical model structure construction algorithm for a mixture of experts network system utilising only process data. The algorithm is based on a novel forward constrained regression procedure. Given a full set of the experts as potential model bases, the structure construction algorithm, formed on the forward constrained regression procedure, selects the most significant model base one by one so as to minimise the overall system approximation error at each iteration, while the gate parameters in the mixture of experts network system are accordingly adjusted so as to satisfy the convex constraints required in the derivation of the forward constrained regression procedure. The procedure continues until a proper system model is constructed that utilises some or all of the experts. A pruning algorithm of the consequent mixture of experts network system is also derived to generate an overall parsimonious construction algorithm. Numerical examples are provided to demonstrate the effectiveness of the new algorithms. The mixture of experts network framework can be applied to a wide variety of applications ranging from multiple model controller synthesis to multi-sensor data fusion.

Data assimilation for state and parameter estimation: application to morphodynamic modelling

Data assimilation is predominantly used for state estimation; combining observational data with model predictions to produce an updated model state that most accurately approximates the true system state whilst keeping the model parameters fixed. This updated model state is then used to initiate the next model forecast. Even with perfect initial data, inaccurate model parameters will lead to the growth of prediction errors. To generate reliable forecasts we need good estimates of both the current system state and the model parameters. This paper presents research into data assimilation methods for morphodynamic model state and parameter estimation. First, we focus on state estimation and describe implementation of a three dimensional variational(3D-Var) data assimilation scheme in a simple 2D morphodynamic model of Morecambe Bay, UK. The assimilation of observations of bathymetry derived from SAR satellite imagery and a ship-borne survey is shown to significantly improve the predictive capability of the model over a 2 year run. Here, the model parameters are set by manual calibration; this is laborious and is found to produce different parameter values depending on the type and coverage of the validation dataset. The second part of this paper considers the problem of model parameter estimation in more detail. We explain how, by employing the technique of state augmentation, it is possible to use data assimilation to estimate uncertain model parameters concurrently with the model state. This approach removes inefficiencies associated with manual calibration and enables more effective use of observational data. We outline the development of a novel hybrid sequential 3D-Var data assimilation algorithm for joint state-parameter estimation and demonstrate its efficacy using an idealised 1D sediment transport model. The results of this study are extremely positive and suggest that there is great potential for the use of data assimilation-based state-parameter estimation in coastal morphodynamic modelling.

Data assimilation with correlated observation errors: experiments with a 1-D shallow water model

Remote sensing observations often have correlated errors, but the correlations are typically ignored in data assimilation for numerical weather prediction. The assumption of zero correlations is often used with data thinning methods, resulting in a loss of information. As operational centres move towards higher-resolution forecasting, there is a requirement to retain data providing detail on appropriate scales. Thus an alternative approach to dealing with observation error correlations is needed. In this article, we consider several approaches to approximating observation error correlation matrices: diagonal approximations, eigendecomposition approximations and Markov matrices. These approximations are applied in incremental variational assimilation experiments with a 1-D shallow water model using synthetic observations. Our experiments quantify analysis accuracy in comparison with a reference or ‘truth’ trajectory, as well as with analyses using the ‘true’ observation error covariance matrix. We show that it is often better to include an approximate correlation structure in the observation error covariance matrix than to incorrectly assume error independence. Furthermore, by choosing a suitable matrix approximation, it is feasible and computationally cheap to include error correlation structure in a variational data assimilation algorithm.

A simple column model to explore anticipated problems in variational assimilation of satellite observations

We investigate a simplified form of variational data assimilation in a fully nonlinear framework with the aim of extracting dynamical development information from a sequence of observations over time. Information on the vertical wind profile, w(z ), and profiles of temperature, T (z , t), and total water content, qt (z , t), as functions of height, z , and time, t, are converted to brightness temperatures at a single horizontal location by defining a two-dimensional (vertical and time) variational assimilation testbed. The profiles of T and qt are updated using a vertical advection scheme. A basic cloud scheme is used to obtain the fractional cloud amount and, when combined with the temperature field, this information is converted into a brightness temperature, using a simple radiative transfer scheme. It is shown that our model exhibits realistic behaviour with regard to the prediction of cloud, but the effects of nonlinearity become non-negligible in the variational data assimilation algorithm. A careful analysis of the application of the data assimilation scheme to this nonlinear problem is presented, the salient difficulties are highlighted, and suggestions for further developments are discussed.

Gaussian quadrature 4D-VAR

A new incremental four-dimensional variational (4D-Var) data assimilation algorithm is introduced. The algorithm does not require the computationally expensive integrations with the nonlinear model in the outer loops. Nonlinearity is accounted for by modifying the linearization trajectory of the observation operator based on integrations with the tangent linear (TL) model. This allows us to update the linearization trajectory of the observation operator in the inner loops at negligible computational cost. As a result the distinction between inner and outer loops is no longer necessary. The key idea on which the proposed 4D-Var method is based is that by using Gaussian quadrature it is possible to get an exact correspondence between the nonlinear time evolution of perturbations and the time evolution in the TL model. It is shown that J-point Gaussian quadrature can be used to derive the exact adjoint-based observation impact equations and furthermore that it is straightforward to account for the effect of multiple outer loops in these equations if the proposed 4D-Var method is used. The method is illustrated using a three-level quasi-geostrophic model and the Lorenz (1996) model.

The error of representation: basic understanding

Representation error arises from the inability of the forecast model to accurately simulate the climatology of the truth. We present a rigorous framework for understanding this kind of error of representation. This framework shows that the lack of an inverse in the relationship between the true climatology (true attractor) and the forecast climatology (forecast attractor) leads to the error of representation. A new gain matrix for the data assimilation problem is derived that illustrates the proper approaches one may take to perform Bayesian data assimilation when the observations are of states on one attractor but the forecast model resides on another. This new data assimilation algorithm is the optimal scheme for the situation where the distributions on the true attractor and the forecast attractors are separately Gaussian and there exists a linear map between them. The results of this theory are illustrated in a simple Gaussian multivariate model.

A new algorithm for OFDM joint data detection and phase noise cancellation

This paper proposes a new iterative algorithm for OFDM joint data detection and phase noise (PHN) cancellation based on minimum mean square prediction error. We particularly highlight the problem of "overfitting" such that the iterative approach may converge to a trivial solution. Although it is essential for this joint approach, the overfitting problem was relatively less studied in existing algorithms. In this paper, specifically, we apply a hard decision procedure at every iterative step to overcome the overfitting. Moreover, compared with existing algorithms, a more accurate Pade approximation is used to represent the phase noise, and finally a more robust and compact fast process based on Givens rotation is proposed to reduce the complexity to a practical level. Numerical simulations are also given to verify the proposed algorithm.

The TAMORA algorithm: satellite rainfall estimates over West Africa using multi-spectral SEVIRI data

A multi-spectral rainfall estimation algorithm has been developed for the Sahel region of West Africa with the purpose of producing accumulated rainfall estimates for drought monitoring and food security. Radar data were used to calibrate multi-channel SEVIRI data from MSG, and a probability of rainfall at several different rain-rates was established for each combination of SEVIRI radiances. Radar calibrations from both Europe (the SatPrecip algorithm) and Niger (TAMORA algorithm) were used. 10 day estimates were accumulated from SatPrecip and TAMORA and compared with kriged gauge data and TAMSAT satellite rainfall estimates over West Africa. SatPrecip was found to produce large overestimates for the region, probably because of its non-local calibration. TAMORA was negatively biased for areas of West Africa with relatively high rainfall, but its skill was comparable to TAMSAT for the low-rainfall region climatologically similar to its calibration area around Niamey. These results confirm the high importance of local calibration for satellite-derived rainfall estimates. As TAMORA shows no improvement in skill over TAMSAT for dekadal estimates, the extra cloud-microphysical information provided by multi-spectral data may not be useful in determining rainfall accumulations at a ten day timescale. Work is ongoing to determine whether it shows improved accuracy at shorter timescales.

Blind equalisation of multilevel PAM data for nonminimum phase channels via second- and fourth-order cumulants

This paper introduces a new blind equalisation algorithm for the pulse amplitude modulation (PAM) data transmitted through nonminimum phase (NMP) channels. The algorithm itself is based on a noncausal AR model of communication channels and the second- and fourth-order cumulants of the received data series, where only the diagonal slices of cumulants are used. The AR parameters are adjusted at each sample by using a successive over-relaxation (SOR) scheme, a variety of the ordinary LMS scheme, but with a faster convergence rate and a greater robustness to the selection of the ‘step-size’ in iterations. Computer simulations are implemented for both linear time-invariant (LTI) and linear time-variant (LTV) NMP channels, and the results show that the algorithm proposed in this paper has a fast convergence rate and a potential capability to track the LTV NMP channels.

Use of the LMS adaptive signal processing technique to improve signal data rates from practical oil well logging equipment

The simulation and development work that has been undertaken to produce a signal equaliser used to improve the data rates from oil well logging instruments is presented. The instruments are lowered into the drill bore hole suspended by a cable which has poor electrical characteristics. The equaliser described in the paper corrects for the distortions that occur from the cable (dispersion and attenuation) with the result that the instrument can send data at 100 K.bits/second down its own suspension cable of 12 Km in length. The use of simulation techniques and tools were invaluable in generating a model for the distortions and proved to be a useful tool when site testing was not available.

eRules: a modular adaptive classification rule learning algorithm for data streams

Advances in hardware and software in the past decade allow to capture, record and process fast data streams at a large scale. The research area of data stream mining has emerged as a consequence from these advances in order to cope with the real time analysis of potentially large and changing data streams. Examples of data streams include Google searches, credit card transactions, telemetric data and data of continuous chemical production processes. In some cases the data can be processed in batches by traditional data mining approaches. However, in some applications it is required to analyse the data in real time as soon as it is being captured. Such cases are for example if the data stream is infinite, fast changing, or simply too large in size to be stored. One of the most important data mining techniques on data streams is classification. This involves training the classifier on the data stream in real time and adapting it to concept drifts. Most data stream classifiers are based on decision trees. However, it is well known in the data mining community that there is no single optimal algorithm. An algorithm may work well on one or several datasets but badly on others. This paper introduces eRules, a new rule based adaptive classifier for data streams, based on an evolving set of Rules. eRules induces a set of rules that is constantly evaluated and adapted to changes in the data stream by adding new and removing old rules. It is different from the more popular decision tree based classifiers as it tends to leave data instances rather unclassified than forcing a classification that could be wrong. The ongoing development of eRules aims to improve its accuracy further through dynamic parameter setting which will also address the problem of changing feature domain values.