Real-time assessment of GNSS observation noise with single receivers

Stochastic modelling is critical in GNSS data processing. Currently, GNSS data processing commonly relies on the empirical stochastic model which may not reflect the actual data quality or noise characteristics. This paper examines the real-time GNSS observation noise estimation methods enabling to determine the observation variance from single receiver data stream. The methods involve three steps: forming linear combination, handling the ionosphere and ambiguity bias and variance estimation. Two distinguished ways are applied to overcome the ionosphere and ambiguity biases, known as the time differenced method and polynomial prediction method respectively. The real time variance estimation methods are compared with the zero-baseline and short-baseline methods. The proposed method only requires single receiver observation, thus applicable to both differenced and un-differenced data processing modes. However, the methods may be subject to the normal ionosphere conditions and low autocorrelation GNSS receivers. Experimental results also indicate the proposed method can result on more realistic parameter precision.

Exploring accuracy factors in cost estimating practice towards implementing Building Information Modelling (BIM)

Cost estimating has been acknowledged as a crucial component of construction projects. Depending on available information and project requirements, cost estimates evolve in tandem with project lifecycle stages; conceptualisation, design development, execution and facility management. The premium placed on the accuracy of cost estimates is crucial to producing project tenders and eventually in budget management. Notwithstanding the initial slow pace of its adoption, Building Information Modelling (BIM) has successfully addressed a number of challenges previously characteristic of traditional approaches in the AEC, including poor communication, the prevalence of islands of information and frequent reworks. Therefore, it is conceivable that BIM can be leveraged to address specific shortcomings of cost estimation. The impetus for leveraging BIM models for accurate cost estimation is to align budgeted and actual cost. This paper hypothesises that the accuracy of BIM-based estimation, as more efficient, process-mirrors of traditional cost estimation methods, can be enhanced by simulating traditional cost estimation factors variables. Through literature reviews and preliminary expert interviews, this paper explores the factors that could potentially lead to more accurate cost estimates for construction projects. The findings show numerous factors that affect the cost estimates ranging from project information and its characteristic, project team, clients, contractual matters, and other external influences. This paper will make a particular contribution to the early phase of BIM-based project estimation.

Global, regional, and national disability-adjusted life years (DALYs) for 306 diseases and injuries and healthy life expectancy (HALE) for 188 countries, 1990–2013: Quantifying the epidemiological transition

Background The Global Burden of Disease Study 2013 (GBD 2013) aims to bring together all available epidemiological data using a coherent measurement framework, standardised estimation methods, and transparent data sources to enable comparisons of health loss over time and across causes, age–sex groups, and countries. The GBD can be used to generate summary measures such as disability-adjusted life-years (DALYs) and healthy life expectancy (HALE) that make possible comparative assessments of broad epidemiological patterns across countries and time. These summary measures can also be used to quantify the component of variation in epidemiology that is related to sociodemographic development. Methods We used the published GBD 2013 data for age-specific mortality, years of life lost due to premature mortality (YLLs), and years lived with disability (YLDs) to calculate DALYs and HALE for 1990, 1995, 2000, 2005, 2010, and 2013 for 188 countries. We calculated HALE using the Sullivan method; 95% uncertainty intervals (UIs) represent uncertainty in age-specific death rates and YLDs per person for each country, age, sex, and year. We estimated DALYs for 306 causes for each country as the sum of YLLs and YLDs; 95% UIs represent uncertainty in YLL and YLD rates. We quantified patterns of the epidemiological transition with a composite indicator of sociodemographic status, which we constructed from income per person, average years of schooling after age 15 years, and the total fertility rate and mean age of the population. We applied hierarchical regression to DALY rates by cause across countries to decompose variance related to the sociodemographic status variable, country, and time. Findings Worldwide, from 1990 to 2013, life expectancy at birth rose by 6·2 years (95% UI 5·6–6·6), from 65·3 years (65·0–65·6) in 1990 to 71·5 years (71·0–71·9) in 2013, HALE at birth rose by 5·4 years (4·9–5·8), from 56·9 years (54·5–59·1) to 62·3 years (59·7–64·8), total DALYs fell by 3·6% (0·3–7·4), and age-standardised DALY rates per 100 000 people fell by 26·7% (24·6–29·1). For communicable, maternal, neonatal, and nutritional disorders, global DALY numbers, crude rates, and age-standardised rates have all declined between 1990 and 2013, whereas for non–communicable diseases, global DALYs have been increasing, DALY rates have remained nearly constant, and age-standardised DALY rates declined during the same period. From 2005 to 2013, the number of DALYs increased for most specific non-communicable diseases, including cardiovascular diseases and neoplasms, in addition to dengue, food-borne trematodes, and leishmaniasis; DALYs decreased for nearly all other causes. By 2013, the five leading causes of DALYs were ischaemic heart disease, lower respiratory infections, cerebrovascular disease, low back and neck pain, and road injuries. Sociodemographic status explained more than 50% of the variance between countries and over time for diarrhoea, lower respiratory infections, and other common infectious diseases; maternal disorders; neonatal disorders; nutritional deficiencies; other communicable, maternal, neonatal, and nutritional diseases; musculoskeletal disorders; and other non-communicable diseases. However, sociodemographic status explained less than 10% of the variance in DALY rates for cardiovascular diseases; chronic respiratory diseases; cirrhosis; diabetes, urogenital, blood, and endocrine diseases; unintentional injuries; and self-harm and interpersonal violence. Predictably, increased sociodemographic status was associated with a shift in burden from YLLs to YLDs, driven by declines in YLLs and increases in YLDs from musculoskeletal disorders, neurological disorders, and mental and substance use disorders. In most country-specific estimates, the increase in life expectancy was greater than that in HALE. Leading causes of DALYs are highly variable across countries. Interpretation Global health is improving. Population growth and ageing have driven up numbers of DALYs, but crude rates have remained relatively constant, showing that progress in health does not mean fewer demands on health systems. The notion of an epidemiological transition—in which increasing sociodemographic status brings structured change in disease burden—is useful, but there is tremendous variation in burden of disease that is not associated with sociodemographic status. This further underscores the need for country-specific assessments of DALYs and HALE to appropriately inform health policy decisions and attendant actions.

Stochastic growth models for analyzing crustacean data

The contemporary methodology for growth models of organisms is based on continuous trajectories and thus it hinders us from modelling stepwise growth in crustacean populations. Growth models for fish are normally assumed to follow a continuous function, but a different type of model is needed for crustacean growth. Crustaceans must moult in order for them to grow. The growth of crustaceans is a discontinuous process due to the periodical shedding of the exoskeleton in moulting. The stepwise growth of crustaceans through the moulting process makes the growth estimation more complex. Stochastic approaches can be used to model discontinuous growth or what are commonly known as "jumps" (Figure 1). However, in stochastic growth model we need to ensure that the stochastic growth model results in only positive jumps. In view of this, we will introduce a subordinator that is a special case of a Levy process. A subordinator is a non-decreasing Levy process, that will assist in modelling crustacean growth for better understanding of the individual variability and stochasticity in moulting periods and increments. We develop the estimation methods for parameter estimation and illustrate them with the help of a dataset from laboratory experiments. The motivational dataset is from the ornate rock lobster, Panulirus ornatus, which can be found between Australia and Papua New Guinea. Due to the presence of sex effects on the growth (Munday et al., 2004), we estimate the growth parameters separately for each sex. Since all hard parts are shed too often, the exact age determination of a lobster can be challenging. However, the growth parameters for the aforementioned moult processes from tank data being able to estimate through: (i) inter-moult periods, and (ii) moult increment. We will attempt to derive a joint density, which is made up of two functions: one for moult increments and the other for time intervals between moults. We claim these functions are conditionally independent given pre-moult length and the inter-moult periods. The variables moult increments and inter-moult periods are said to be independent because of the Markov property or conditional probability. Hence, the parameters in each function can be estimated separately. Subsequently, we integrate both of the functions through a Monte Carlo method. We can therefore obtain a population mean for crustacean growth (e. g. red curve in Figure 1). [GRAPHICS]

An extended regression approach to estimating loads and their uncertainties in Great Barrier Reef catchments

There are numerous load estimation methods available, some of which are captured in various online tools. However, most estimators are subject to large biases statistically, and their associated uncertainties are often not reported. This makes interpretation difficult and the estimation of trends or determination of optimal sampling regimes impossible to assess. In this paper, we first propose two indices for measuring the extent of sampling bias, and then provide steps for obtaining reliable load estimates by minimizing the biases and making use of possible predictive variables. The load estimation procedure can be summarized by the following four steps: - (i) output the flow rates at regular time intervals (e.g. 10 minutes) using a time series model that captures all the peak flows; - (ii) output the predicted flow rates as in (i) at the concentration sampling times, if the corresponding flow rates are not collected; - (iii) establish a predictive model for the concentration data, which incorporates all possible predictor variables and output the predicted concentrations at the regular time intervals as in (i), and; - (iv) obtain the sum of all the products of the predicted flow and the predicted concentration over the regular time intervals to represent an estimate of the load. The key step to this approach is in the development of an appropriate predictive model for concentration. This is achieved using a generalized regression (rating-curve) approach with additional predictors that capture unique features in the flow data, namely the concept of the first flush, the location of the event on the hydrograph (e.g. rise or fall) and cumulative discounted flow. The latter may be thought of as a measure of constituent exhaustion occurring during flood events. The model also has the capacity to accommodate autocorrelation in model errors which are the result of intensive sampling during floods. Incorporating this additional information can significantly improve the predictability of concentration, and ultimately the precision with which the pollutant load is estimated. We also provide a measure of the standard error of the load estimate which incorporates model, spatial and/or temporal errors. This method also has the capacity to incorporate measurement error incurred through the sampling of flow. We illustrate this approach using the concentrations of total suspended sediment (TSS) and nitrogen oxide (NOx) and gauged flow data from the Burdekin River, a catchment delivering to the Great Barrier Reef. The sampling biases for NOx concentrations range from 2 to 10 times indicating severe biases. As we expect, the traditional average and extrapolation methods produce much higher estimates than those when bias in sampling is taken into account.

Overfitting Bayesian mixture models with an unknown number of components

This paper proposes solutions to three issues pertaining to the estimation of finite mixture models with an unknown number of components: the non-identifiability induced by overfitting the number of components, the mixing limitations of standard Markov Chain Monte Carlo (MCMC) sampling techniques, and the related label switching problem. An overfitting approach is used to estimate the number of components in a finite mixture model via a Zmix algorithm. Zmix provides a bridge between multidimensional samplers and test based estimation methods, whereby priors are chosen to encourage extra groups to have weights approaching zero. MCMC sampling is made possible by the implementation of prior parallel tempering, an extension of parallel tempering. Zmix can accurately estimate the number of components, posterior parameter estimates and allocation probabilities given a sufficiently large sample size. The results will reflect uncertainty in the final model and will report the range of possible candidate models and their respective estimated probabilities from a single run. Label switching is resolved with a computationally light-weight method, Zswitch, developed for overfitted mixtures by exploiting the intuitiveness of allocation-based relabelling algorithms and the precision of label-invariant loss functions. Four simulation studies are included to illustrate Zmix and Zswitch, as well as three case studies from the literature. All methods are available as part of the R package Zmix, which can currently be applied to univariate Gaussian mixture models.

Numerical investigations of linear least squares methods for derivative estimation

The results of a numerical investigation into the errors for least squares estimates of function gradients are presented. The underlying algorithm is obtained by constructing a least squares problem using a truncated Taylor expansion. An error bound associated with this method contains in its numerator terms related to the Taylor series remainder, while its denominator contains the smallest singular value of the least squares matrix. Perhaps for this reason the error bounds are often found to be pessimistic by several orders of magnitude. The circumstance under which these poor estimates arise is elucidated and an empirical correction of the theoretical error bounds is conjectured and investigated numerically. This is followed by an indication of how the conjecture is supported by a rigorous argument.

A multi-resolution image alignment technique based on direct methods for pose estimation of aerial vehicles

In this paper, we seek to expand the use of direct methods in real-time applications by proposing a vision-based strategy for pose estimation of aerial vehicles. The vast majority of approaches make use of features to estimate motion. Conversely, the strategy we propose is based on a MR (Multi- Resolution) implementation of an image registration technique (Inverse Compositional Image Alignment ICIA) using direct methods. An on-board camera in a downwards-looking configuration, and the assumption of planar scenes, are the bases of the algorithm. The motion between frames (rotation and translation) is recovered by decomposing the frame-to-frame homography obtained by the ICIA algorithm applied to a patch that covers around the 80% of the image. When the visual estimation is required (e.g. GPS drop-out), this motion is integrated with the previous known estimation of the vehicles’ state, obtained from the on-board sensors (GPS/IMU), and the subsequent estimations are based only on the vision-based motion estimations. The proposed strategy is tested with real flight data in representative stages of a flight: cruise, landing, and take-off, being two of those stages considered critical: take-off and landing. The performance of the pose estimation strategy is analyzed by comparing it with the GPS/IMU estimations. Results show correlation between the visual estimation obtained with the MR-ICIA and the GPS/IMU data, that demonstrate that the visual estimation can be used to provide a good approximation of the vehicle’s state when it is required (e.g. GPS drop-outs). In terms of performance, the proposed strategy is able to maintain an estimation of the vehicle’s state for more than one minute, at real-time frame rates based, only on visual information.

Using Bayesian methods for the estimation of uncertainty in complex statistical models

The research objectives of this thesis were to contribute to Bayesian statistical methodology by contributing to risk assessment statistical methodology, and to spatial and spatio-temporal methodology, by modelling error structures using complex hierarchical models. Specifically, I hoped to consider two applied areas, and use these applications as a springboard for developing new statistical methods as well as undertaking analyses which might give answers to particular applied questions. Thus, this thesis considers a series of models, firstly in the context of risk assessments for recycled water, and secondly in the context of water usage by crops. The research objective was to model error structures using hierarchical models in two problems, namely risk assessment analyses for wastewater, and secondly, in a four dimensional dataset, assessing differences between cropping systems over time and over three spatial dimensions. The aim was to use the simplicity and insight afforded by Bayesian networks to develop appropriate models for risk scenarios, and again to use Bayesian hierarchical models to explore the necessarily complex modelling of four dimensional agricultural data. The specific objectives of the research were to develop a method for the calculation of credible intervals for the point estimates of Bayesian networks; to develop a model structure to incorporate all the experimental uncertainty associated with various constants thereby allowing the calculation of more credible credible intervals for a risk assessment; to model a single day’s data from the agricultural dataset which satisfactorily captured the complexities of the data; to build a model for several days’ data, in order to consider how the full data might be modelled; and finally to build a model for the full four dimensional dataset and to consider the timevarying nature of the contrast of interest, having satisfactorily accounted for possible spatial and temporal autocorrelations. This work forms five papers, two of which have been published, with two submitted, and the final paper still in draft. The first two objectives were met by recasting the risk assessments as directed, acyclic graphs (DAGs). In the first case, we elicited uncertainty for the conditional probabilities needed by the Bayesian net, incorporated these into a corresponding DAG, and used Markov chain Monte Carlo (MCMC) to find credible intervals, for all the scenarios and outcomes of interest. In the second case, we incorporated the experimental data underlying the risk assessment constants into the DAG, and also treated some of that data as needing to be modelled as an ‘errors-invariables’ problem [Fuller, 1987]. This illustrated a simple method for the incorporation of experimental error into risk assessments. In considering one day of the three-dimensional agricultural data, it became clear that geostatistical models or conditional autoregressive (CAR) models over the three dimensions were not the best way to approach the data. Instead CAR models are used with neighbours only in the same depth layer. This gave flexibility to the model, allowing both the spatially structured and non-structured variances to differ at all depths. We call this model the CAR layered model. Given the experimental design, the fixed part of the model could have been modelled as a set of means by treatment and by depth, but doing so allows little insight into how the treatment effects vary with depth. Hence, a number of essentially non-parametric approaches were taken to see the effects of depth on treatment, with the model of choice incorporating an errors-in-variables approach for depth in addition to a non-parametric smooth. The statistical contribution here was the introduction of the CAR layered model, the applied contribution the analysis of moisture over depth and estimation of the contrast of interest together with its credible intervals. These models were fitted using WinBUGS [Lunn et al., 2000]. The work in the fifth paper deals with the fact that with large datasets, the use of WinBUGS becomes more problematic because of its highly correlated term by term updating. In this work, we introduce a Gibbs sampler with block updating for the CAR layered model. The Gibbs sampler was implemented by Chris Strickland using pyMCMC [Strickland, 2010]. This framework is then used to consider five days data, and we show that moisture in the soil for all the various treatments reaches levels particular to each treatment at a depth of 200 cm and thereafter stays constant, albeit with increasing variances with depth. In an analysis across three spatial dimensions and across time, there are many interactions of time and the spatial dimensions to be considered. Hence, we chose to use a daily model and to repeat the analysis at all time points, effectively creating an interaction model of time by the daily model. Such an approach allows great flexibility. However, this approach does not allow insight into the way in which the parameter of interest varies over time. Hence, a two-stage approach was also used, with estimates from the first-stage being analysed as a set of time series. We see this spatio-temporal interaction model as being a useful approach to data measured across three spatial dimensions and time, since it does not assume additivity of the random spatial or temporal effects.

Novel methods and the maximum likelihood estimation technique for estimating traffic critical gap

Most unsignalised intersection capacity calculation procedures are based on gap acceptance models. Accuracy of critical gap estimation affects accuracy of capacity and delay estimation. Several methods have been published to estimate drivers’ sample mean critical gap, the Maximum Likelihood Estimation (MLE) technique regarded as the most accurate. This study assesses three novel methods; Average Central Gap (ACG) method, Strength Weighted Central Gap method (SWCG), and Mode Central Gap method (MCG), against MLE for their fidelity in rendering true sample mean critical gaps. A Monte Carlo event based simulation model was used to draw the maximum rejected gap and accepted gap for each of a sample of 300 drivers across 32 simulation runs. Simulation mean critical gap is varied between 3s and 8s, while offered gap rate is varied between 0.05veh/s and 0.55veh/s. This study affirms that MLE provides a close to perfect fit to simulation mean critical gaps across a broad range of conditions. The MCG method also provides an almost perfect fit and has superior computational simplicity and efficiency to the MLE. The SWCG method performs robustly under high flows; however, poorly under low to moderate flows. Further research is recommended using field traffic data, under a variety of minor stream and major stream flow conditions for a variety of minor stream movement types, to compare critical gap estimates using MLE against MCG. Should the MCG method prove as robust as MLE, serious consideration should be given to its adoption to estimate critical gap parameters in guidelines.

Permeability estimation conditioned to geophysical downhole log data in sandstones of the northern Galilee Basin, Queensland : methods and application

This study uses borehole geophysical log data of sonic velocity and electrical resistivity to estimate permeability in sandstones in the northern Galilee Basin, Queensland. The prior estimates of permeability are calculated according to the deterministic log–log linear empirical correlations between electrical resistivity and measured permeability. Both negative and positive relationships are influenced by the clay content. The prior estimates of permeability are updated in a Bayesian framework for three boreholes using both the cokriging (CK) method and a normal linear regression (NLR) approach to infer the likelihood function. The results show that the mean permeability estimated from the CK-based Bayesian method is in better agreement with the measured permeability when a fairly apparent linear relationship exists between the logarithm of permeability and sonic velocity. In contrast, the NLR-based Bayesian approach gives better estimates of permeability for boreholes where no linear relationship exists between logarithm permeability and sonic velocity.