Ambiguity Acceptance Testing : A Comparison of the Ratio Test and Difference Test

Integer ambiguity resolution is an indispensable procedure for all high precision GNSS applications. The correctness of the estimated integer ambiguities is the key to achieving highly reliable positioning, but the solution cannot be validated with classical hypothesis testing methods. The integer aperture estimation theory unifies all existing ambiguity validation tests and provides a new prospective to review existing methods, which enables us to have a better understanding on the ambiguity validation problem. This contribution analyses two simple but efficient ambiguity validation test methods, ratio test and difference test, from three aspects: acceptance region, probability basis and numerical results. The major contribution of this paper can be summarized as: (1) The ratio test acceptance region is overlap of ellipsoids while the difference test acceptance region is overlap of half-spaces. (2) The probability basis of these two popular tests is firstly analyzed. The difference test is an approximation to optimal integer aperture, while the ratio test follows an exponential relationship in probability. (3) The limitations of the two tests are firstly identified. The two tests may under-evaluate the failure risk if the model is not strong enough or the float ambiguities fall in particular region. (4) Extensive numerical results are used to compare the performance of these two tests. The simulation results show the ratio test outperforms the difference test in some models while difference test performs better in other models. Particularly in the medium baseline kinematic model, the difference tests outperforms the ratio test, the superiority is independent on frequency number, observation noise, satellite geometry, while it depends on success rate and failure rate tolerance. Smaller failure rate leads to larger performance discrepancy.

A new ambiguity acceptance test threshold determination method with controllable failure rate

The ambiguity acceptance test is an important quality control procedure in high precision GNSS data processing. Although the ambiguity acceptance test methods have been extensively investigated, its threshold determine method is still not well understood. Currently, the threshold is determined with the empirical approach or the fixed failure rate (FF-) approach. The empirical approach is simple but lacking in theoretical basis, while the FF-approach is theoretical rigorous but computationally demanding. Hence, the key of the threshold determination problem is how to efficiently determine the threshold in a reasonable way. In this study, a new threshold determination method named threshold function method is proposed to reduce the complexity of the FF-approach. The threshold function method simplifies the FF-approach by a modeling procedure and an approximation procedure. The modeling procedure uses a rational function model to describe the relationship between the FF-difference test threshold and the integer least-squares (ILS) success rate. The approximation procedure replaces the ILS success rate with the easy-to-calculate integer bootstrapping (IB) success rate. Corresponding modeling error and approximation error are analysed with simulation data to avoid nuisance biases and unrealistic stochastic model impact. The results indicate the proposed method can greatly simplify the FF-approach without introducing significant modeling error. The threshold function method makes the fixed failure rate threshold determination method feasible for real-time applications.

A novel ambiguity acceptance test threshold determination method with controllable failure rate

Ambiguity validation as an important procedure of integer ambiguity resolution is to test the correctness of the fixed integer ambiguity of phase measurements before being used for positioning computation. Most existing investigations on ambiguity validation focus on test statistic. How to determine the threshold more reasonably is less understood, although it is one of the most important topics in ambiguity validation. Currently, there are two threshold determination methods in the ambiguity validation procedure: the empirical approach and the fixed failure rate (FF-) approach. The empirical approach is simple but lacks of theoretical basis. The fixed failure rate approach has a rigorous probability theory basis, but it employs a more complicated procedure. This paper focuses on how to determine the threshold easily and reasonably. Both FF-ratio test and FF-difference test are investigated in this research and the extensive simulation results show that the FF-difference test can achieve comparable or even better performance than the well-known FF-ratio test. Another benefit of adopting the FF-difference test is that its threshold can be expressed as a function of integer least-squares (ILS) success rate with specified failure rate tolerance. Thus, a new threshold determination method named threshold function for the FF-difference test is proposed. The threshold function method preserves the fixed failure rate characteristic and is also easy-to-apply. The performance of the threshold function is validated with simulated data. The validation results show that with the threshold function method, the impact of the modelling error on the failure rate is less than 0.08%. Overall, the threshold function for the FF-difference test is a very promising threshold validation method and it makes the FF-approach applicable for the real-time GNSS positioning applications.

Determinants of skin self-examination (SSE) in men aged 50 years or older

Background: Queensland men aged 50 years and older are at high risk for melanoma. Early detection via skin self examination (SSE) (particularly whole-body SSE) followed by presentation to a doctor with suspicious lesions, may decrease morbidity and mortality from melanoma. Prevalence of whole-body SSE (wbSSE) is lower in Queensland older men compared to other population subgroups. With the exception of the present study no previous research has investigated the determinants of wbSSE in older men, or interventions to increase the behaviour in this population. Furthermore, although past SSE intervention studies for other populations have cited health behaviour models in the development of interventions, no study has tested these models in full. The Skin Awareness Study: A recent randomised trial, called the Skin Awareness Study, tested the impact of a video-delivered intervention compared to written materials alone on wbSSE in men aged 50 years or older (n=930). Men were recruited from the general population and interviewed over the telephone at baseline and 13 months. The proportion of men who reported wbSSE rose from 10% to 31% in the control group, and from 11% to 36% in the intervention group. Current research: The current research was a secondary analysis of data collected for the Skin Awareness Study. The objectives were as follows: • To describe how men who did not take up any SSE during the study period differed from those who did take up examining their skin. • To determine whether the intervention program was successful in affecting the constructs of the Health Belief Model it was aimed at (self-efficacy, perceived threat, and outcome expectations); and whether this in turn influenced wbSSE. • To determine whether the Health Action Process Approach (HAPA) was a better predictor of wbSSE behaviour compared to the Health Belief Model (HBM). Methods: For objective 1, men who did not report any past SSE at baseline (n=308) were categorised as having ‘taken up SSE’ (reported SSE at study end) or ‘resisted SSE’ (reported no SSE at study end). Bivariate logistic regression, followed by multivariable regression, investigated the association between participant characteristics measured at baseline and resisting SSE. For objective 2 proxy measures of self-efficacy, perceived threat, and outcome expectations were selected. To determine whether these mediated the effect of the intervention on the outcome, a mediator analysis was performed with all participants who completed interviews at both time points (n=830) following the Baron and Kenny approach, modified for use with structural equation modelling (SEM). For objective 3, control group participants only were included (n=410). Proxy measures of all HBM and HAPA constructs were selected and SEM was used to build up models and test the significance of each hypothesised pathway. A likelihood ratio test compared the HAPA to the HBM. Results: Amongst men who did not report any SSE at baseline, 27% did not take up any SSE by the end of the study. In multivariable analyses, resisting SSE was associated with having more freckly skin (p=0.027); being unsure about the statement ‘if I saw something suspicious on my skin, I’d go to the doctor straight away’ (p=0.028); not intending to perform SSE (p=0.015), having lower SSE self-efficacy (p<0.001), and having no recommendation for SSE from a doctor (p=0.002). In the mediator analysis none of the tested variables mediated the relationship between the intervention and wbSSE. In regards to health behaviour models, the HBM did not predict wbSSE well overall. Only the construct of self-efficacy was a significant predictor of future wbSSE (p=0.001), while neither perceived threat (p=0.584) nor outcome expectations (p=0.220) were. By contrast, when the HAPA constructs were added, all three HBM variables predicted intention to perform SSE, which in turn predicted future behaviour (p=0.015). The HAPA construct of volitional self-efficacy was also associated with wbSSE (p=0.046). The HAPA was a significantly better model compared to the HBM (p<0.001). Limitations: Items selected to measure HBM and HAPA model constructs for objectives 2 and 3 may not have accurately reflected each construct. Conclusions: This research added to the evidence base on how best to target interventions to older men; and on the appropriateness of particular health behaviour models to guide interventions. Findings indicate that to overcome resistance those men with more negative pre-existing attitudes to SSE (not intending to do it, lower initial self-efficacy) may need to be targeted with more intensive interventions in the future. Involving general practitioners in recommending SSE to their patients in this population, alongside disseminating an intervention, may increase its success. Comparison of the HBM and HAPA showed that while two of the three HBM variables examined did not directly predict future wbSSE, all three were associated with intention to self-examine skin. This suggests that in this population, intervening on these variables may increase intention to examine skin, but not necessarily the behaviour itself. Future interventions could potentially focus on increasing both the motivational variables of perceived threat and outcome expectations as well as a combination of both action and volitional self-efficacy; with the aim of increasing intention as well as its translation to taking up and maintaining regular wbSSE.

Right-angle crash vulnerability of motorcycles at signalized intersections : mixed logit analysis

Motorcycles are particularly vulnerable in right-angle crashes at signalized intersections. The objective of this study is to explore how variations in roadway characteristics, environmental factors, traffic factors, maneuver types, human factors as well as driver demographics influence the right-angle crash vulnerability of motorcycles at intersections. The problem is modeled using a mixed logit model with a binary choice category formulation to differentiate how an at-fault vehicle collides with a not-at-fault motorcycle in comparison to other collision types. The mixed logit formulation allows randomness in the parameters and hence takes into account the underlying heterogeneities potentially inherent in driver behavior, and other unobserved variables. A likelihood ratio test reveals that the mixed logit model is indeed better than the standard logit model. Night time riding shows a positive association with the vulnerability of motorcyclists. Moreover, motorcyclists are particularly vulnerable on single lane roads, on the curb and median lanes of multi-lane roads, and on one-way and two-way road type relative to divided-highway. Drivers who deliberately run red light as well as those who are careless towards motorcyclists especially when making turns at intersections increase the vulnerability of motorcyclists. Drivers appear more restrained when there is a passenger onboard and this has decreased the crash potential with motorcyclists. The presence of red light cameras also significantly decreases right-angle crash vulnerabilities of motorcyclists. The findings of this study would be helpful in developing more targeted countermeasures for traffic enforcement, driver/rider training and/or education, safety awareness programs to reduce the vulnerability of motorcyclists.

Orthogonality defect and reduced search-space size for solving integer least-squares problems

In the context of ambiguity resolution (AR) of Global Navigation Satellite Systems (GNSS), decorrelation among entries of an ambiguity vector, integer ambiguity search and ambiguity validations are three standard procedures for solving integer least-squares problems. This paper contributes to AR issues from three aspects. Firstly, the orthogonality defect is introduced as a new measure of the performance of ambiguity decorrelation methods, and compared with the decorrelation number and with the condition number which are currently used as the judging criterion to measure the correlation of ambiguity variance-covariance matrix. Numerically, the orthogonality defect demonstrates slightly better performance as a measure of the correlation between decorrelation impact and computational efficiency than the condition number measure. Secondly, the paper examines the relationship of the decorrelation number, the condition number, the orthogonality defect and the size of the ambiguity search space with the ambiguity search candidates and search nodes. The size of the ambiguity search space can be properly estimated if the ambiguity matrix is decorrelated well, which is shown to be a significant parameter in the ambiguity search progress. Thirdly, a new ambiguity resolution scheme is proposed to improve ambiguity search efficiency through the control of the size of the ambiguity search space. The new AR scheme combines the LAMBDA search and validation procedures together, which results in a much smaller size of the search space and higher computational efficiency while retaining the same AR validation outcomes. In fact, the new scheme can deal with the case there are only one candidate, while the existing search methods require at least two candidates. If there are more than one candidate, the new scheme turns to the usual ratio-test procedure. Experimental results indicate that this combined method can indeed improve ambiguity search efficiency for both the single constellation and dual constellations respectively, showing the potential for processing high dimension integer parameters in multi-GNSS environment.

Reliability of partial ambiguity fixing with multiple GNSS constellations

Reliable ambiguity resolution (AR) is essential to Real-Time Kinematic (RTK) positioning and its applications, since incorrect ambiguity fixing can lead to largely biased positioning solutions. A partial ambiguity fixing technique is developed to improve the reliability of AR, involving partial ambiguity decorrelation (PAD) and partial ambiguity resolution (PAR). Decorrelation transformation could substantially amplify the biases in the phase measurements. The purpose of PAD is to find the optimum trade-off between decorrelation and worst-case bias amplification. The concept of PAR refers to the case where only a subset of the ambiguities can be fixed correctly to their integers in the integer least-squares (ILS) estimation system at high success rates. As a result, RTK solutions can be derived from these integer-fixed phase measurements. This is meaningful provided that the number of reliably resolved phase measurements is sufficiently large for least-square estimation of RTK solutions as well. Considering the GPS constellation alone, partially fixed measurements are often insufficient for positioning. The AR reliability is usually characterised by the AR success rate. In this contribution an AR validation decision matrix is firstly introduced to understand the impact of success rate. Moreover the AR risk probability is included into a more complete evaluation of the AR reliability. We use 16 ambiguity variance-covariance matrices with different levels of success rate to analyse the relation between success rate and AR risk probability. Next, the paper examines during the PAD process, how a bias in one measurement is propagated and amplified onto many others, leading to more than one wrong integer and to affect the success probability. Furthermore, the paper proposes a partial ambiguity fixing procedure with a predefined success rate criterion and ratio-test in the ambiguity validation process. In this paper, the Galileo constellation data is tested with simulated observations. Numerical results from our experiment clearly demonstrate that only when the computed success rate is very high, the AR validation can provide decisions about the correctness of AR which are close to real world, with both low AR risk and false alarm probabilities. The results also indicate that the PAR procedure can automatically chose adequate number of ambiguities to fix at given high-success rate from the multiple constellations instead of fixing all the ambiguities. This is a benefit that multiple GNSS constellations can offer.

Fixed failure rate ambiguity validation methods for GPS and compass

Ambiguity resolution plays a crucial role in real time kinematic GNSS positioning which gives centimetre precision positioning results if all the ambiguities in each epoch are correctly fixed to integers. However, the incorrectly fixed ambiguities can result in large positioning offset up to several meters without notice. Hence, ambiguity validation is essential to control the ambiguity resolution quality. Currently, the most popular ambiguity validation is ratio test. The criterion of ratio test is often empirically determined. Empirically determined criterion can be dangerous, because a fixed criterion cannot fit all scenarios and does not directly control the ambiguity resolution risk. In practice, depending on the underlying model strength, the ratio test criterion can be too conservative for some model and becomes too risky for others. A more rational test method is to determine the criterion according to the underlying model and user requirement. Miss-detected incorrect integers will lead to a hazardous result, which should be strictly controlled. In ambiguity resolution miss-detected rate is often known as failure rate. In this paper, a fixed failure rate ratio test method is presented and applied in analysis of GPS and Compass positioning scenarios. A fixed failure rate approach is derived from the integer aperture estimation theory, which is theoretically rigorous. The criteria table for ratio test is computed based on extensive data simulations in the approach. The real-time users can determine the ratio test criterion by looking up the criteria table. This method has been applied in medium distance GPS ambiguity resolution but multi-constellation and high dimensional scenarios haven't been discussed so far. In this paper, a general ambiguity validation model is derived based on hypothesis test theory, and fixed failure rate approach is introduced, especially the relationship between ratio test threshold and failure rate is examined. In the last, Factors that influence fixed failure rate approach ratio test threshold is discussed according to extensive data simulation. The result shows that fixed failure rate approach is a more reasonable ambiguity validation method with proper stochastic model.

A Satellite Selection Algorithm for Achieving High Reliability of Ambiguity Resolution with GPS and Beidou Constellations

Reliability of carrier phase ambiguity resolution (AR) of an integer least-squares (ILS) problem depends on ambiguity success rate (ASR), which in practice can be well approximated by the success probability of integer bootstrapping solutions. With the current GPS constellation, sufficiently high ASR of geometry-based model can only be achievable at certain percentage of time. As a result, high reliability of AR cannot be assured by the single constellation. In the event of dual constellations system (DCS), for example, GPS and Beidou, which provide more satellites in view, users can expect significant performance benefits such as AR reliability and high precision positioning solutions. Simply using all the satellites in view for AR and positioning is a straightforward solution, but does not necessarily lead to high reliability as it is hoped. The paper presents an alternative approach that selects a subset of the visible satellites to achieve a higher reliability performance of the AR solutions in a multi-GNSS environment, instead of using all the satellites. Traditionally, satellite selection algorithms are mostly based on the position dilution of precision (PDOP) in order to meet accuracy requirements. In this contribution, some reliability criteria are introduced for GNSS satellite selection, and a novel satellite selection algorithm for reliable ambiguity resolution (SARA) is developed. The SARA algorithm allows receivers to select a subset of satellites for achieving high ASR such as above 0.99. Numerical results from a simulated dual constellation cases show that with the SARA procedure, the percentages of ASR values in excess of 0.99 and the percentages of ratio-test values passing the threshold 3 are both higher than those directly using all satellites in view, particularly in the case of dual-constellation, the percentages of ASRs (>0.99) and ratio-test values (>3) could be as high as 98.0 and 98.5 % respectively, compared to 18.1 and 25.0 % without satellite selection process. It is also worth noting that the implementation of SARA is simple and the computation time is low, which can be applied in most real-time data processing applications.

Intra-cluster correlation structure in longitudinal data analysis: Selection criteria and misspecification tests

Selection criteria and misspecification tests for the intra-cluster correlation structure (ICS) in longitudinal data analysis are considered. In particular, the asymptotical distribution of the correlation information criterion (CIC) is derived and a new method for selecting a working ICS is proposed by standardizing the selection criterion as the p-value. The CIC test is found to be powerful in detecting misspecification of the working ICS structures, while with respect to the working ICS selection, the standardized CIC test is also shown to have satisfactory performance. Some simulation studies and applications to two real longitudinal datasets are made to illustrate how these criteria and tests might be useful.

Effect of amblyopia on the developmental eye movement test in children

Purpose. To investigate the functional impact of amblyopia in children, the performance of amblyopic and age-matched control children on a clinical test of eye movements was compared. The influence of visual factors on test outcome measures was explored. Methods. Eye movements were assessed with the Developmental Eye Movement (DEM) test, in a group of children with amblyopia (n = 39; age, 9.1 ± 0.9 years) of different causes (infantile esotropia, n = 7; acquired strabismus, n = 10; anisometropia, n = 8; mixed, n = 8; deprivation, n = 6) and in an age-matched control group (n = 42; age, 9.3 ± 0.4 years). LogMAR visual acuity (VA), stereoacuity, and refractive error were also recorded in both groups. Results. No significant difference was found between the amblyopic and age-matched control group for any of the outcome measures of the DEM (vertical time, horizontal time, number of errors and ratio(horizontal time/vertical time)). The DEM measures were not significantly related to VA in either eye, level of binocular function (stereoacuity), history of strabismus, or refractive error. Conclusions. The performance of amblyopic children on the DEM, a commonly used clinical measure of eye movements, has not previously been reported. Under habitual binocular viewing conditions, amblyopia has no effect on DEM outcome scores despite significant impairment of binocular vision and decreased VA in both the better and worse eye.

The efficacy of the Sortino ratio and other benchmarked performance measures under skewed return distributions

This paper will investigate the suitability of existing performance measures under the assumption of a clearly defined benchmark. A range of measures are examined including the Sortino Ratio, the Sharpe Selection ratio (SSR), the Student’s t-test and a decay rate measure. A simulation study is used to assess the power and bias of these measures based on variations in sample size and mean performance of two simulated funds. The Sortino Ratio is found to be the superior performance measure exhibiting more power and less bias than the SSR when the distribution of excess returns are skewed.

Developing a research method to test a new first-order decision making model for the procurement of public sector major infrastructure

Given global demand for new infrastructure, governments face substantial challenges in funding new infrastructure and simultaneously delivering Value for Money (VfM). The paper begins with an update on a key development in a new early/first-order procurement decision making model that deploys production cost/benefit theory and theories concerning transaction costs from the New Institutional Economics, in order to identify a procurement mode that is likely to deliver the best ratio of production costs and transaction costs to production benefits, and therefore deliver superior VfM relative to alternative procurement modes. In doing so, the new procurement model is also able to address the uncertainty concerning the relative merits of Public-Private Partnerships (PPP) and non-PPP procurement approaches. The main aim of the paper is to develop competition as a dependent variable/proxy for VfM and a hypothesis (overarching proposition), as well as developing a research method to test the new procurement model. Competition reflects both production costs and benefits (absolute level of competition) and transaction costs (level of realised competition) and is a key proxy for VfM. Using competition as a proxy for VfM, the overarching proposition is given as: When the actual procurement mode matches the predicted (theoretical) procurement mode (informed by the new procurement model), then actual competition is expected to match potential competition (based on actual capacity). To collect data to test this proposition, the research method that is developed in this paper combines a survey and case study approach. More specifically, data collection instruments for the surveys to collect data on actual procurement, actual competition and potential competition are outlined. Finally, plans for analysing this survey data are briefly mentioned, along with noting the planned use of analytical pattern matching in deploying the new procurement model and in order to develop the predicted (theoretical) procurement mode.

DEM test, visagraph eye movement recordings, and reading ability in children

Purpose. To determine how Developmental Eye Movement (DEM) test results relate to reading eye movement patterns recorded with the Visagraph in visually normal children, and whether DEM results and recorded eye movement patterns relate to standardized reading achievement scores. Methods. Fifty-nine school-age children (age = 9.7 ± 0.6 years) completed the DEM test and had eye movements recorded with the Visagraph III test while reading for comprehension. Monocular visual acuity in each eye and random dot stereoacuity were measured and standardized scores on independently administered reading comprehension tests [reading progress test (RPT)] were obtained. Results. Children with slower DEM horizontal and vertical adjusted times tended to have slower reading rates with the Visagraph (r = -0.547 and -0.414 respectively). Although a significant correlation was also found between the DEM ratio and Visagraph reading rate (r = -0.368), the strength of the relationship was less than that between DEM horizontal adjusted time and reading rate. DEM outcome scores were not significantly associated with RPT scores. When the relative contribution of reading ability (RPT) and DEM scores was accounted for in multivariate analysis, DEM outcomes were not significantly associated with Visagraph reading rate. RPT scores were associated with Visagraph outcomes of duration of fixations (r = -0.403) and calculated reading rate (r = 0.366) but not with DEM outcomes. Conclusions.DEM outcomes can identify children whose Visagraph recorded eye movement patterns show slow reading rates. However, when reading ability is accounted for, DEM outcomes are a poor predictor of reading rate. Visagraph outcomes of duration of fixation and reading rate relate to standardized reading achievement scores; however, DEM results do not. Copyright © 2011 American Academy of Optometry.

Models of collective cell motion for cell populations with different aspect ratio : diffusion, proliferation and travelling waves

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealizations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data for with varying cell shape.