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.

Expected value, reward outcome, and temporal difference error representations in a probabilistic decision task

In probabilistic decision tasks, an expected value (EV) of a choice is calculated, and after the choice has been made, this can be updated based on a temporal difference (TD) prediction error between the EV and the reward magnitude (RM) obtained. The EV is measured as the probability of obtaining a reward x RM. To understand the contribution of different brain areas to these decision-making processes, functional magnetic resonance imaging activations related to EV versus RM (or outcome) were measured in a probabilistic decision task. Activations in the medial orbitofrontal cortex were correlated with both RM and with EV and confirmed in a conjunction analysis to extend toward the pregenual cingulate cortex. From these representations, TD reward prediction errors could be produced. Activations in areas that receive from the orbitofrontal cortex including the ventral striatum, midbrain, and inferior frontal gyrus were correlated with the TD error. Activations in the anterior insula were correlated negatively with EV, occurring when low reward outcomes were expected, and also with the uncertainty of the reward, implicating this region in basic and crucial decision-making parameters, low expected outcomes, and uncertainty.

Prediction of metabolisable energy concentrations of fresh cut grass using digestibility data measured with non-pregnant non-lactating cows

Pasture-based ruminant production systems are common in certain areas of the world, but energy evaluation in grazing cattle is performed with equations developed, in their majority, with sheep or cattle fed total mixed rations. The aim of the current study was to develop predictions of metabolisable energy (ME) concentrations in fresh-cut grass offered to non-pregnant non-lactating cows at maintenance energy level, which may be more suitable for grazing cattle. Data were collected from three digestibility trials performed over consecutive grazing seasons. In order to cover a range of commercial conditions and data availability in pasture-based systems, thirty-eight equations for the prediction of energy concentrations and ratios were developed. An internal validation was performed for all equations and also for existing predictions of grass ME. Prediction error for ME using nutrient digestibility was lowest when gross energy (GE) or organic matter digestibilities were used as sole predictors, while the addition of grass nutrient contents reduced the difference between predicted and actual values, and explained more variation. Addition of N, GE and diethyl ether extract (EE) contents improved accuracy when digestible organic matter in DM was the primary predictor. When digestible energy was the primary explanatory variable, prediction error was relatively low, but addition of water-soluble carbohydrates, EE and acid-detergent fibre contents of grass decreased prediction error. Equations developed in the current study showed lower prediction errors when compared with those of existing equations, and may thus allow for an improved prediction of ME in practice, which is critical for the sustainability of pasture-based systems.

Comparison of energy evaluation systems and a mechanistic model for milk production by dairy cattle offered fresh grass-based diets

Grass-based diets are of increasing social-economic importance in dairy cattle farming, but their low supply of glucogenic nutrients may limit the production of milk. Current evaluation systems that assess the energy supply and requirements are based on metabolisable energy (ME) or net energy (NE). These systems do not consider the characteristics of the energy delivering nutrients. In contrast, mechanistic models take into account the site of digestion, the type of nutrient absorbed and the type of nutrient required for production of milk constituents, and may therefore give a better prediction of supply and requirement of nutrients. The objective of the present study is to compare the ability of three energy evaluation systems, viz. the Dutch NE system, the agricultural and food research council (AFRC) ME system, and the feed into milk (FIM) ME system, and of a mechanistic model based on Dijkstra et al. [Simulation of digestion in cattle fed sugar cane: prediction of nutrient supply for milk production with locally available supplements. J. Agric. Sci., Cambridge 127, 247-60] and Mills et al. [A mechanistic model of whole-tract digestion and methanogenesis in the lactating dairy cow: model development, evaluation and application. J. Anim. Sci. 79, 1584-97] to predict the feed value of grass-based diets for milk production. The dataset for evaluation consists of 41 treatments of grass-based diets (at least 0.75 g ryegrass/g diet on DM basis). For each model, the predicted energy or nutrient supply, based on observed intake, was compared with predicted requirement based on observed performance. Assessment of the error of energy or nutrient supply relative to requirement is made by calculation of mean square prediction error (MSPE) and by concordance correlation coefficient (CCC). All energy evaluation systems predicted energy requirement to be lower (6-11%) than energy supply. The root MSPE (expressed as a proportion of the supply) was lowest for the mechanistic model (0.061), followed by the Dutch NE system (0.082), FIM ME system (0.097) and AFRCME system(0.118). For the energy evaluation systems, the error due to overall bias of prediction dominated the MSPE, whereas for the mechanistic model, proportionally 0.76 of MSPE was due to random variation. CCC analysis confirmed the higher accuracy and precision of the mechanistic model compared with energy evaluation systems. The error of prediction was positively related to grass protein content for the Dutch NE system, and was also positively related to grass DMI level for all models. In conclusion, current energy evaluation systems overestimate energy supply relative to energy requirement on grass-based diets for dairy cattle. The mechanistic model predicted glucogenic nutrients to limit performance of dairy cattle on grass-based diets, and proved to be more accurate and precise than the energy systems. The mechanistic model could be improved by allowing glucose maintenance and utilization requirements parameters to be variable. (C) 2007 Elsevier B.V. All rights reserved.

Alternative approaches to predicting methane emissions from dairy cows

Previous attempts to apply statistical models, which correlate nutrient intake with methane production, have been of limited. value where predictions are obtained for nutrient intakes and diet types outside those. used in model construction. Dynamic mechanistic models have proved more suitable for extrapolation, but they remain computationally expensive and are not applied easily in practical situations. The first objective of this research focused on employing conventional techniques to generate statistical models of methane production appropriate to United Kingdom dairy systems. The second objective was to evaluate these models and a model published previously using both United Kingdom and North American data sets. Thirdly, nonlinear models were considered as alternatives to the conventional linear regressions. The United Kingdom calorimetry data used to construct the linear models also were used to develop the three. nonlinear alternatives that were ball of modified Mitscherlich (monomolecular) form. Of the linear models tested,, an equation from the literature proved most reliable across the full range of evaluation data (root mean square prediction error = 21.3%). However, the Mitscherlich models demonstrated the greatest degree of adaptability across diet types and intake level. The most successful model for simulating the independent data was a modified Mitscherlich equation with the steepness parameter set to represent dietary starch-to-ADF ratio (root mean square prediction error = 20.6%). However, when such data were unavailable, simpler Mitscherlich forms relating dry matter or metabolizable energy intake to methane production remained better alternatives relative to their linear counterparts.

Modelling the partitioning of evapotranspiration in a maize-sunflower intercrop

The primary purpose of this study was to model the partitioning of evapotranspiration in a maize-sunflower intercrop at various canopy covers. The Shuttleworth-Wallace (SW) model was extended for intercropping systems to include both crop transpiration and soil evaporation and allowing interaction between the two. To test the accuracy of the extended SW model, two field experiments of maize-sunflower intercrop were conducted in 1998 and 1999. Plant transpiration and soil evaporation were measured using sap flow gauges and lysimeters, respectively. The mean prediction error (simulated minus measured values) for transpiration was zero (which indicated no overall bias in estimation error), and its accuracy was not affected by the plant growth stages, but simulated transpiration during high measured transpiration rates tended to be slightly underestimated. Overall, the predictions for daily soil evaporation were also accurate. Model estimation errors were probably due to the simplified modelling of soil water content, stomatal resistances and soil heat flux as well as due to the uncertainties in characterising the 2 micrometeorological conditions. The SW’s prediction of transpiration was most sensitive to parameters most directly related to the canopy characteristics such as the partitioning of captured solar radiation, canopy resistance, and bulk boundary layer resistance.

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.

OFDM joint data detection and phase noise cancellation for constant modulus modulations

This correspondence proposes a new algorithm for the OFDM joint data detection and phase noise (PHN) cancellation for constant modulus modulations. We highlight that it is important to address the overfitting problem since this is a major detrimental factor impairing the joint detection process. In order to attack the overfitting problem we propose an iterative approach based on minimum mean square prediction error (MMSPE) subject to the constraint that the estimated data symbols have constant power. The proposed constrained MMSPE algorithm (C-MMSPE) significantly improves the performance of existing approaches with little extra complexity being imposed. Simulation results are also given to verify the proposed algorithm.

Neurofuzzy design and model construction of nonlinear dynamical processes from data

A common problem in many data based modelling algorithms such as associative memory networks is the problem of the curse of dimensionality. In this paper, a new two-stage neurofuzzy system design and construction algorithm (NeuDeC) for nonlinear dynamical processes is introduced to effectively tackle this problem. A new simple preprocessing method is initially derived and applied to reduce the rule base, followed by a fine model detection process based on the reduced rule set by using forward orthogonal least squares model structure detection. In both stages, new A-optimality experimental design-based criteria we used. In the preprocessing stage, a lower bound of the A-optimality design criterion is derived and applied as a subset selection metric, but in the later stage, the A-optimality design criterion is incorporated into a new composite cost function that minimises model prediction error as well as penalises the model parameter variance. The utilisation of NeuDeC leads to unbiased model parameters with low parameter variance and the additional benefit of a parsimonious model structure. Numerical examples are included to demonstrate the effectiveness of this new modelling approach for high dimensional inputs.

Parameter estimation based on stacked regression and evolutionary algorithms

A new parameter-estimation algorithm, which minimises the cross-validated prediction error for linear-in-the-parameter models, is proposed, based on stacked regression and an evolutionary algorithm. It is initially shown that cross-validation is very important for prediction in linear-in-the-parameter models using a criterion called the mean dispersion error (MDE). Stacked regression, which can be regarded as a sophisticated type of cross-validation, is then introduced based on an evolutionary algorithm, to produce a new parameter-estimation algorithm, which preserves the parsimony of a concise model structure that is determined using the forward orthogonal least-squares (OLS) algorithm. The PRESS prediction errors are used for cross-validation, and the sunspot and Canadian lynx time series are used to demonstrate the new algorithms.

Simulating the effects of grassland management and grass ensiling on methane emission from lactating cows

A dynamic, mechanistic model of enteric fermentation was used to investigate the effect of type and quality of grass forage, dry matter intake (DMI) and proportion of concentrates in dietary dry matter (DM) on variation in methane (CH(4)) emission from enteric fermentation in dairy cows. The model represents substrate degradation and microbial fermentation processes in rumen and hindgut and, in particular, the effects of type of substrate fermented and of pH oil the production of individual volatile fatty acids and CH, as end-products of fermentation. Effects of type and quality of fresh and ensiled grass were evaluated by distinguishing two N fertilization rates of grassland and two stages of grass maturity. Simulation results indicated a strong impact of the amount and type of grass consumed oil CH(4) emission, with a maximum difference (across all forage types and all levels of DM 1) of 49 and 77% in g CH(4)/kg fat and protein corrected milk (FCM) for diets with a proportion of concentrates in dietary DM of 0.1 and 0.4, respectively (values ranging from 10.2 to 19.5 g CH(4)/kg FCM). The lowest emission was established for early Cut, high fertilized grass silage (GS) and high fertilized grass herbage (GH). The highest emission was found for late cut, low-fertilized GS. The N fertilization rate had the largest impact, followed by stage of grass maturity at harvesting and by the distinction between GH and GS. Emission expressed in g CH(4)/kg FCM declined oil average 14% with an increase of DMI from 14 to 18 kg/day for grass forage diets with a proportion of concentrates of 0.1, and on average 29% with an increase of DMI from 14 to 23 kg/day for diets with a proportion of concentrates of 0.4. Simulation results indicated that a high proportion of concentrates in dietary DM may lead to a further reduction of CH, emission per kg FCM mainly as a result of a higher DM I and milk yield, in comparison to low concentrate diets. Simulation results were evaluated against independent data obtained at three different laboratories in indirect calorimetry trials with COWS consuming GH mainly. The model predicted the average of observed values reasonably, but systematic deviations remained between individual laboratories and root mean squared prediction error was a proportion of 0.12 of the observed mean. Both observed and predicted emission expressed in g CH(4)/kg DM intake decreased upon an increase in dietary N:organic matter (OM) ratio. The model reproduced reasonably well the variation in measured CH, emission in cattle sheds oil Dutch dairy farms and indicated that oil average a fraction of 0.28 of the total emissions must have originated from manure under these circumstances.

A dynamic mechanistic model of lactic acid metabolism in the rumen

Current feed evaluation systems for ruminants are too imprecise to describe diets in terms of their acidosis risk. The dynamic mechanistic model described herein arises from the integration of a lactic acid (La) metabolism module into an extant model of whole-rumen function. The model was evaluated using published data from cows and sheep fed a range of diets or infused with various doses of La. The model performed well in simulating peak rumen La concentrations (coefficient of determination = 0.96; root mean square prediction error = 16.96% of observed mean), although frequency of sampling for the published data prevented a comprehensive comparison of prediction of time to peak La accumulation. The model showed a tendency for increased La accumulation following feeding of diets rich in nonstructural carbohydrates, although less-soluble starch sources such as corn tended to limit rumen La concentration. Simulated La absorption from the rumen remained low throughout the feeding cycle. The competition between bacteria and protozoa for rumen La suggests a variable contribution of protozoa to total La utilization. However, the model was unable to simulate the effects of defaunation on rumen La metabolism, indicating a need for a more detailed description of protozoal metabolism. The model could form the basis of a feed evaluation system with regard to rumen La metabolism.

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

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.

Representation of model error in a convective-scale ensemble prediction system

In this paper ensembles of forecasts (of up to six hours) are studied from a convection-permitting model with a representation of model error due to unresolved processes. The ensemble prediction system (EPS) used is an experimental convection-permitting version of the UK Met Office’s 24- member Global and Regional Ensemble Prediction System (MOGREPS). The method of representing model error variability, which perturbs parameters within the model’s parameterisation schemes, has been modified and we investigate the impact of applying this scheme in different ways. These are: a control ensemble where all ensemble members have the same parameter values; an ensemble where the parameters are different between members, but fixed in time; and ensembles where the parameters are updated randomly every 30 or 60 min. The choice of parameters and their ranges of variability have been determined from expert opinion and parameter sensitivity tests. A case of frontal rain over the southern UK has been chosen, which has a multi-banded rainfall structure. The consequences of including model error variability in the case studied are mixed and are summarised as follows. The multiple banding, evident in the radar, is not captured for any single member. However, the single band is positioned in some members where a secondary band is present in the radar. This is found for all ensembles studied. Adding model error variability with fixed parameters in time does increase the ensemble spread for near-surface variables like wind and temperature, but can actually decrease the spread of the rainfall. Perturbing the parameters periodically throughout the forecast does not further increase the spread and exhibits “jumpiness” in the spread at times when the parameters are perturbed. Adding model error variability gives an improvement in forecast skill after the first 2–3 h of the forecast for near-surface temperature and relative humidity. For precipitation skill scores, adding model error variability has the effect of improving the skill in the first 1–2 h of the forecast, but then of reducing the skill after that. Complementary experiments were performed where the only difference between members was the set of parameter values (i.e. no initial condition variability). The resulting spread was found to be significantly less than the spread from initial condition variability alone.