Error analysis of a Monte Carlo algorithm for computing bilinear forms of matrix powers

In this paper we present error analysis for a Monte Carlo algorithm for evaluating bilinear forms of matrix powers. An almost Optimal Monte Carlo (MAO) algorithm for solving this problem is formulated. Results for the structure of the probability error are presented and the construction of robust and interpolation Monte Carlo algorithms are discussed. Results are presented comparing the performance of the Monte Carlo algorithm with that of a corresponding deterministic algorithm. The two algorithms are tested on a well balanced matrix and then the effects of perturbing this matrix, by small and large amounts, is studied.

OFDM joint data detection and phase noise cancellation based on minimum mean square prediction error

This paper proposes a new iterative algorithm for orthogonal frequency division multiplexing (OFDM) joint data detection and phase noise (PHN) cancellation based on minimum mean square prediction error. We particularly highlight the relatively less studied problem of "overfitting" such that the iterative approach may converge to a trivial solution. 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 PHN, 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. (C) 2008 Elsevier B.V. All rights reserved.

A general model of error-prone PCR

In this paper, we generalise a previously-described model of the error-prone polymerase chain reaction (PCR) reaction to conditions of arbitrarily variable amplification efficiency and initial population size. Generalisation of the model to these conditions improves the correspondence to observed and expected behaviours of PCR, and restricts the extent to which the model may explore sequence space for a prescribed set of parameters. Error-prone PCR in realistic reaction conditions is predicted to be less effective at generating grossly divergent sequences than the original model. The estimate of mutation rate per cycle by sampling sequences from an in vitro PCR experiment is correspondingly affected by the choice of model and parameters. (c) 2005 Elsevier Ltd. All rights reserved.

Error estimates for a fully discrete spectral scheme for a class of nonlinear, nonlocal dispersive wave equations

We analyze a fully discrete spectral method for the numerical solution of the initial- and periodic boundary-value problem for two nonlinear, nonlocal, dispersive wave equations, the Benjamin–Ono and the Intermediate Long Wave equations. The equations are discretized in space by the standard Fourier–Galerkin spectral method and in time by the explicit leap-frog scheme. For the resulting fully discrete, conditionally stable scheme we prove an L2-error bound of spectral accuracy in space and of second-order accuracy in time.

A note on the analysis error associated with 3D-FGAT

The analysis-error variance of a 3D-FGAT assimilation is examined analytically using a simple scalar equation. It is shown that the analysis-error variance may be greater than the error variances of the inputs. The results are illustrated numerically with a scalar example and a shallow-water model.

Threshold-free object and ground point separation in LIDAR data

Light Detection And Ranging (LIDAR) is an important modality in terrain and land surveying for many environmental, engineering and civil applications. This paper presents the framework for a recently developed unsupervised classification algorithm called Skewness Balancing for object and ground point separation in airborne LIDAR data. The main advantages of the algorithm are threshold-freedom and independence from LIDAR data format and resolution, while preserving object and terrain details. The framework for Skewness Balancing has been built in this contribution with a prediction model in which unknown LIDAR tiles can be categorised as “hilly” or “moderate” terrains. Accuracy assessment of the model is carried out using cross-validation with an overall accuracy of 95%. An extension to the algorithm is developed to address the overclassification issue for hilly terrain. For moderate terrain, the results show that from the classified tiles detached objects (buildings and vegetation) and attached objects (bridges and motorway junctions) are separated from bare earth (ground, roads and yards) which makes Skewness Balancing ideal to be integrated into geographic information system (GIS) software packages.

Visual motion interferes with lexical decision on motion words

Embodied theories of cognition propose that neural substrates used in experiencing the referent of a word, for example perceiving upward motion, should be engaged in weaker form when that word, for example ‘rise’, is comprehended. Motivated by the finding that the perception of irrelevant background motion at near-threshold, but not supra-threshold, levels interferes with task execution, we assessed whether interference from near-threshold background motion was modulated by its congruence with the meaning of words (semantic content) when participants completed a lexical decision task (deciding if a string of letters is a real word or not). Reaction times for motion words, such as ‘rise’ or ‘fall’, were slower when the direction of visual motion and the ‘motion’ of the word were incongruent — but only when the visual motion was at nearthreshold levels. When motion was supra-threshold, the distribution of error rates, not reaction times, implicated low-level motion processing in the semantic processing of motion words. As the perception of near-threshold signals is not likely to be influenced by strategies, our results support a close contact between semantic information and perceptual systems.

Synchronisation error resistant CDMA detection

A bit-level linear CDMA detector is presented which is based on the minimum variance distortionless response (MVDR) principle. Owing to the interference suppression capability made possible by basing the detector on the MVDR principle and the fact that no inversion of the user correlation matrix is involved, the influence of synchronisation errors is greatly suppressed.

Synchronisation error resistant multiuser detection for asynchronous CDMA

Linear CDMA detectors have emerged as a promising solution to multiple access interference (MAI) suppression. Unfortunately, most existing linear detectors suffer from high sensitivity to synchronisation errors (also termed parameter estimation error), and synchronisation error resistant detectors have so far not been as widely investigated as they should have. This paper extends the minimum variance distortionless response (MVDR) detector, proposed previously by this author (Zheng 2000) for synchronous systems, to asynchronous systems. It has been shown that the MVDR structure is equally effective for asynchronous systems, especially for the weaker users.

Detecting the number of signals using antenna array: a single threshold solution

A new approach is presented to identify the number of incoming signals in antenna array processing. The new method exploits the inherent properties existing in the noise eigenvalues of the covariance matrix of the array output. A single threshold has been established concerning information about the signal and noise strength, data length, and array size. When the subspace-based algorithms are adopted the computation cost of the signal number detector can almost be neglected. The performance of the threshold is robust against low SNR and short data length.

Forecast impact of targeted observations: sensitivity to observation error and proximity to steep orography

For a targeted observations case, the dependence of the size of the forecast impact on the targeted dropsonde observation error in the data assimilation is assessed. The targeted observations were made in the lee of Greenland; the dependence of the impact on the proximity of the observations to the Greenland coast is also investigated. Experiments were conducted using the Met Office Unified Model (MetUM), over a limited-area domain at 24-km grid spacing, with a four-dimensional variational data assimilation (4D-Var) scheme. Reducing the operational dropsonde observation errors by one-half increases the maximum forecast improvement from 5% to 7%–10%, measured in terms of total energy. However, the largest impact is seen by replacing two dropsondes on the Greenland coast with two farther from the steep orography; this increases the maximum forecast improvement from 5% to 18% for an 18-h forecast (using operational observation errors). Forecast degradation caused by two dropsonde observations on the Greenland coast is shown to arise from spreading of data by the background errors up the steep slope of Greenland. Removing boundary layer data from these dropsondes reduces the forecast degradation, but it is only a partial solution to this problem. Although only from one case study, these results suggest that observations positioned within a correlation length scale of steep orography may degrade the forecast through the anomalous upslope spreading of analysis increments along terrain-following model levels.

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.

A method for merging flow-dependent forecast error statistics from an ensemble with static statistics for use in high resolution variational data assimilation

The background error covariance matrix, B, is often used in variational data assimilation for numerical weather prediction as a static and hence poor approximation to the fully dynamic forecast error covariance matrix, Pf. In this paper the concept of an Ensemble Reduced Rank Kalman Filter (EnRRKF) is outlined. In the EnRRKF the forecast error statistics in a subspace defined by an ensemble of states forecast by the dynamic model are found. These statistics are merged in a formal way with the static statistics, which apply in the remainder of the space. The combined statistics may then be used in a variational data assimilation setting. It is hoped that the nonlinear error growth of small-scale weather systems will be accurately captured by the EnRRKF, to produce accurate analyses and ultimately improved forecasts of extreme events.