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Integrity Monitoring for Carrier Phase Ambiguities
- Shaojun Feng, Washington Ochieng, Jaron Samson, Michel Tossaint, Manuel Hernandez-Pajares, J. Miguel Juan, Jaume Sanz, Àngela Aragón-Àngel, Pere Ramos-Bosch, Marti Jofre
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- Journal:
- The Journal of Navigation / Volume 65 / Issue 1 / January 2012
- Published online by Cambridge University Press:
- 25 November 2011, pp. 41-58
- Print publication:
- January 2012
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The determination of the correct integer number of carrier cycles (integer ambiguity) is the key to high accuracy positioning with carrier phase measurements from Global Navigation Satellite Systems (GNSS). There are a number of current methods for resolving ambiguities including the Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) method, which is a combination of least-squares and a transformation to reduce the search space. The current techniques to determine the level of confidence (integrity) of the resolved ambiguities (i.e. ambiguity validation), usually involve the construction of test statistics, characterisation of their distribution and definition of thresholds. Example tests applied include ratio, F-distribution, t-distribution and Chi-square distribution. However, the assumptions that underpin these tests have weaknesses. These include the application of a fixed threshold for all scenarios, and therefore, not always able to provide an acceptable integrity level in the computed ambiguities. A relatively recent technique referred to as Integer Aperture (IA) based on the ratio test with a large number of simulated samples of float ambiguities requires significant computational resources. This precludes the application of IA in real time.
This paper proposes and demonstrates the power of an integrity monitoring technique that is applied at the ambiguity resolution and positioning stages. The technique has the important benefit of facilitating early detection of any potential threat to the position solution, originating in the ambiguity space, while at the same time giving overall protection in the position domain based on the required navigation performance. The proposed method uses the conventional test statistic for ratio testing together with a doubly non-central F distribution to compute the level of confidence (integrity) of the ambiguities. Specifically, this is determined as a function of geometry and the ambiguity residuals from least squares based ambiguity resolution algorithms including LAMBDA. A numerical method is implemented to compute the level of confidence in real time.
The results for Precise Point Positioning (PPP) with simulated and real data demonstrate the power and efficiency of the proposed method in monitoring both the integrity of the ambiguity computation and position solution processes. Furthermore, due to the fact that the method only requires information from least squares based ambiguity resolution algorithms, it is easily transferable to conventional Real Time Kinematic (RTK) positioning.
Concurrent and construct validity of Mediterranean diet scores as assessed by an FFQ
- Alejandra A Benítez-Arciniega, Michelle A Mendez, Jose M Baena-Díez, Maria-Asunción Rovira Martori, Cristina Soler, Jaume Marrugat, Maria-Isabel Covas, Hector Sanz, Alba Llopis, Helmut Schröder
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- Journal:
- Public Health Nutrition / Volume 14 / Issue 11 / November 2011
- Published online by Cambridge University Press:
- 11 July 2011, pp. 2015-2021
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Objective
The aim of the present study was to assess the concurrent and construct validity of two diet-quality indices, a modified Mediterranean diet score (mMDS) and a Mediterranean-like diet score (MLDS) additionally incorporating unhealthy food choices, as determined by an FFQ.
DesignA validation study assessing FFQ intake estimates compared with ten or more unannounced 24 h recalls. Pearson's correlation coefficients, intraclass correlation coefficients (ICC), Bland–Altman plots and the limits of agreement method were used to assess the between-method agreement of scores. Construct validity was shown using associations between nutrient intakes derived from multiple 24 h recalls and the mMDS and MLDS derived from the FFQ.
SettingGerona, Spain.
SubjectsA total of 107 consecutively selected participants from a population-based cross-sectional survey.
ResultsPearson's correlations for the energy-adjusted mMDS and MLDS compared with multiple recalls were 0·48 and 0·62, respectively. The average FFQ energy-adjusted mMDS and MLDS were 102 % and 98 % of the recall-based mMDS and MLDS estimates, respectively. The FFQ under- and overestimated dietary recall estimates of the energy-adjusted MLDS by 28 % and 25 %, respectively, with slightly wider boundaries for the mMDS (31 % and 34 %). The ICC, which assesses absolute agreement, was similar to Pearson's correlations (mMDS = 0·48 and MLDS = 0·61). The mean differences between methods were similar across the range of average ratings for both scores, indicating the absence of bias. The FFQ-derived mMDS and MLDS correlated in the anticipated directions with intakes of eleven (73·3 %) and thirteen of fifteen nutrients (86·7 %), respectively.
ConclusionsThe FFQ provides valid estimates of diet quality as assessed by the mMDS and MLDS.