Enhanced stochastic mobility prediction with multi-output Gaussian processes

Outdoor robots such as planetary rovers must be able to navigate safely and reliably in order to successfully perform missions in remote or hostile environments. Mobility prediction is critical to achieving this goal due to the inherent control uncertainty faced by robots traversing natural terrain. We propose a novel algorithm for stochastic mobility prediction based on multi-output Gaussian process regression. Our algorithm considers the correlation between heading and distance uncertainty and provides a predictive model that can easily be exploited by motion planning algorithms. We evaluate our method experimentally and report results from over 30 trials in a Mars-analogue environment that demonstrate the effectiveness of our method and illustrate the importance of mobility prediction in navigating challenging terrain.

Sensitivity of an Elekta iView GT a-Si EPID model to delivery errors for pre-treatment verification of IMRT fields

A Monte Carlo model of an Elekta iViewGT amorphous silicon electronic portal imaging device (a-Si EPID) has been validated for pre-treatment verification of clinical IMRT treatment plans. The simulations involved the use of the BEAMnrc and DOSXYZnrc Monte Carlo codes to predict the response of the iViewGT a-Si EPID model. The predicted EPID images were compared to the measured images obtained from the experiment. The measured EPID images were obtained by delivering a photon beam from an Elekta Synergy linac to the Elekta iViewGT a-Si EPID. The a-Si EPID was used with no additional build-up material. Frame averaged EPID images were acquired and processed using in-house software. The agreement between the predicted and measured images was analyzed using the gamma analysis technique with acceptance criteria of 3% / 3 mm. The results show that the predicted EPID images for four clinical IMRT treatment plans have a good agreement with the measured EPID signal. Three prostate IMRT plans were found to have an average gamma pass rate of more than 95.0 % and a spinal IMRT plan has the average gamma pass rate of 94.3 %. During the period of performing this work a routine MLC calibration was performed and one of the IMRT treatments re-measured with the EPID. A change in the gamma pass rate for one field was observed. This was the motivation for a series of experiments to investigate the sensitivity of the method by introducing delivery errors, MLC position and dosimetric overshoot, into the simulated EPID images. The method was found to be sensitive to 1 mm leaf position errors and 10% overshoot errors.

Bayesian hierarchical models for analysing spatial point-based data at a grid level: A comparison of approaches

Spatial data are now prevalent in a wide range of fields including environmental and health science. This has led to the development of a range of approaches for analysing patterns in these data. In this paper, we compare several Bayesian hierarchical models for analysing point-based data based on the discretization of the study region, resulting in grid-based spatial data. The approaches considered include two parametric models and a semiparametric model. We highlight the methodology and computation for each approach. Two simulation studies are undertaken to compare the performance of these models for various structures of simulated point-based data which resemble environmental data. A case study of a real dataset is also conducted to demonstrate a practical application of the modelling approaches. Goodness-of-fit statistics are computed to compare estimates of the intensity functions. The deviance information criterion is also considered as an alternative model evaluation criterion. The results suggest that the adaptive Gaussian Markov random field model performs well for highly sparse point-based data where there are large variations or clustering across the space; whereas the discretized log Gaussian Cox process produces good fit in dense and clustered point-based data. One should generally consider the nature and structure of the point-based data in order to choose the appropriate method in modelling a discretized spatial point-based data.

Dosimetry of cone-defined stereotactic radiosurgery fields with a commercial synthetic diamond detector

Purpose Small field x-ray beam dosimetry is difficult due to a lack of lateral electronic equilibrium, source occlusion, high dose gradients and detector volume averaging. Currently there is no single definitive detector recommended for small field dosimetry. The objective of this work was to evaluate the performance of a new commercial synthetic diamond detector, namely the PTW 60019 microDiamond, for the dosimetry of small x-ray fields as used in stereotactic radiosurgery (SRS). Methods Small field sizes were defined by BrainLAB circular cones (4 – 30 mm diameter) on a Novalis Trilogy linear accelerator and using the 6 MV SRS x-ray beam mode for all measurements. Percentage depth doses were measured and compared to an IBA SFD and a PTW 60012 E diode. Cross profiles were measured and compared to an IBA SFD diode. Field factors, Ω_(Q_clin,Q_msr)^(f_clin,f_msr ), were calculated by Monte Carlo methods using BEAMnrc and correction factors, k_(Q_clin,Q_msr)^(f_clin,f_msr ), were derived for the PTW 60019 microDiamond detector. Results For the small fields of 4 to 30 mm diameter, there were dose differences in the PDDs of up to 1.5% when compared to an IBA SFD and PTW 60012 E diode detector. For the cross profile measurements the penumbra values varied, depending upon the orientation of the detector. The field factors, Ω_(Q_clin,Q_msr)^(f_clin,f_msr ), were calculated for these field diameters at a depth of 1.4 cm in water and they were within 2.7% of published values for a similar linear accelerator. The corrections factors, k_(Q_clin,Q_msr)^(f_clin,f_msr ), were derived for the PTW 60019 microDiamond detector. Conclusions We conclude that the new PTW 60019 microDiamond detector is generally suitable for relative dosimetry in small 6 MV SRS beams for a Novalis Trilogy linear equipped with circular cones.

The use of penumbrae to define and analyse non-standard fields

Aim A new method of penumbral analysis is implemented which allows an unambiguous determination of field size and penumbra size and quality for small fields and other non-standard fields. Both source occlusion and lateral electronic disequilibrium will affect the size and shape of cross-axis profile penumbrae; each is examined in detail. Method A new method of penumbral analysis is implemented where the square of the derivative of the cross-axis profile is plotted. The resultant graph displays two peaks in the place of the two penumbrae. This allows a strong visualisation of the quality of a field penumbra, as well as a mathematically consistent method of determining field size (distance between the two peak’s maxima), and penumbra (full-widthtenth-maximum of peak). Cross-axis profiles were simulated in a water phantom at a depth of 5 cm using Monte Carlo modelling, for field sizes between 5 and 30 mm. The field size and penumbra size of each field was calculated using the method above, as well as traditional definitions set out in IEC976. The effect of source occlusion and lateral electronic disequilibrium on the penumbrae was isolated by repeating the simulations removing electron transport and using an electron spot size of 0 mm, respectively. Results All field sizes calculated using the traditional and proposed methods agreed within 0.2 mm. The penumbra size measured using the proposed method was systematically 1.8 mm larger than the traditional method at all field sizes. The size of the source had a larger effect on the size of the penumbra than did lateral electronic disequilibrium, particularly at very small field sizes. Conclusion Traditional methods of calculating field size and penumbra are proved to be mathematically adequate for small fields. However, the field size definition proposed in this study would be more robust amongst other nonstandard fields, such as flattening filter free. Source occlusion plays a bigger role than lateral electronic disequilibrium in small field penumbra size.

A new approach to spatial data interpolation using higher-order statistics

Interpolation techniques for spatial data have been applied frequently in various fields of geosciences. Although most conventional interpolation methods assume that it is sufficient to use first- and second-order statistics to characterize random fields, researchers have now realized that these methods cannot always provide reliable interpolation results, since geological and environmental phenomena tend to be very complex, presenting non-Gaussian distribution and/or non-linear inter-variable relationship. This paper proposes a new approach to the interpolation of spatial data, which can be applied with great flexibility. Suitable cross-variable higher-order spatial statistics are developed to measure the spatial relationship between the random variable at an unsampled location and those in its neighbourhood. Given the computed cross-variable higher-order spatial statistics, the conditional probability density function (CPDF) is approximated via polynomial expansions, which is then utilized to determine the interpolated value at the unsampled location as an expectation. In addition, the uncertainty associated with the interpolation is quantified by constructing prediction intervals of interpolated values. The proposed method is applied to a mineral deposit dataset, and the results demonstrate that it outperforms kriging methods in uncertainty quantification. The introduction of the cross-variable higher-order spatial statistics noticeably improves the quality of the interpolation since it enriches the information that can be extracted from the observed data, and this benefit is substantial when working with data that are sparse or have non-trivial dependence structures.

A Gaussian pseudolikelihood approach for quantile regression with repeated measurements

To enhance the efficiency of regression parameter estimation by modeling the correlation structure of correlated binary error terms in quantile regression with repeated measurements, we propose a Gaussian pseudolikelihood approach for estimating correlation parameters and selecting the most appropriate working correlation matrix simultaneously. The induced smoothing method is applied to estimate the covariance of the regression parameter estimates, which can bypass density estimation of the errors. Extensive numerical studies indicate that the proposed method performs well in selecting an accurate correlation structure and improving regression parameter estimation efficiency. The proposed method is further illustrated by analyzing a dental dataset.

Predicting flow and transport in highly heterogeneous alluvial aquifers

Successful prediction of groundwater flow and solute transport through highly heterogeneous aquifers has remained elusive due to the limitations of methods to characterize hydraulic conductivity (K) and generate realistic stochastic fields from such data. As a result, many studies have suggested that the classical advective-dispersive equation (ADE) cannot reproduce such transport behavior. Here we demonstrate that when high-resolution K data are used with a fractal stochastic method that produces K fields with adequate connectivity, the classical ADE can accurately predict solute transport at the macrodispersion experiment site in Mississippi. This development provides great promise to accurately predict contaminant plume migration, design more effective remediation schemes, and reduce environmental risks. Key Points Non-Gaussian transport behavior at the MADE site is unraveledADE can reproduce tracer transport in heterogeneous aquifers with no calibrationNew fractal method generates heterogeneous K fields with adequate connectivity

Autonomous vehicle path planning for persistence monitoring under uncertainty using Gaussian based Markov decision process

One of the main challenges facing online and offline path planners is the uncertainty in the magnitude and direction of the environmental energy because it is dynamic, changeable with time, and hard to forecast. This thesis develops an artificial intelligence for a mobile robot to learn from historical or forecasted data of environmental energy available in the area of interest which will help for a persistence monitoring under uncertainty using the developed algorithm.

Exploiting parallax in panoramic capture to construct light fields

We show that the parallax motion resulting from non-nodal rotation in panorama capture can be exploited for light field construction from commodity hardware. Automated panoramic image capture typically seeks to rotate a camera exactly about its nodal point, for which no parallax motion is observed. This can be difficult or impossible to achieve due to limitations of the mounting or optical systems, and consequently a wide range of captured panoramas suffer from parallax between images. We show that by capturing such imagery over a regular grid of camera poses, then appropriately transforming the captured imagery to a common parameterisation, a light field can be constructed. The resulting four-dimensional image encodes scene geometry as well as texture, allowing an increasingly rich range of light field processing techniques to be applied. Employing an Ocular Robotics REV25 camera pointing system, we demonstrate light field capture,refocusing and low-light image enhancement.

An efficient DSE using conditional multivariate complex Gaussian distribution

This paper presents an efficient noniterative method for distribution state estimation using conditional multivariate complex Gaussian distribution (CMCGD). In the proposed method, the mean and standard deviation (SD) of the state variables is obtained in one step considering load uncertainties, measurement errors, and load correlations. In this method, first the bus voltages, branch currents, and injection currents are represented by MCGD using direct load flow and a linear transformation. Then, the mean and SD of bus voltages, or other states, are calculated using CMCGD and estimation of variance method. The mean and SD of pseudo measurements, as well as spatial correlations between pseudo measurements, are modeled based on the historical data for different levels of load duration curve. The proposed method can handle load uncertainties without using time-consuming approaches such as Monte Carlo. Simulation results of two case studies, six-bus, and a realistic 747-bus distribution network show the effectiveness of the proposed method in terms of speed, accuracy, and quality against the conventional approach.