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.

Effects of acute multinutrient supplementation on rugby union game performance and recovery

Purpose: To investigate the effects of an acute multinutrient supplement on game-based running performance, peak power output, anaerobic by-products, hormonal profiles, markers of muscle damage, and perceived muscular soreness before, immediately after, and 24 h following competitive rugby union games. Methods: Twelve male rugby union players ingested either a comprehensive multinutrient supplement (SUPP), [RE-ACTIVATE:01], or a placebo (PL) for 5 d. Participants then performed a competitive rugby union game (with global positioning system tracking), with associated blood draws and vertical jump assessments pre, immediately post and 24 h following competition. Results: SUPP ingestion resulted in moderate to large effects for augmented 1st half very high intensity running (VHIR) mean speed (5.9 ± 0.4 vs 4.8 ± 2.3 m·min–1; d= 0.93). Further, moderate increases in 2nd half VHIR distance (137 ± 119 vs 83 ± 89 m; d= 0.73) and VHIR mean speed (5.9 ± 0.6 v 5.3 ± 1.7 m·min–1; d= 0.56) in SUPP condition were also apparent. Postgame aspartate aminotransferase (AST; 44.1 ± 11.8 vs 37.0 ± 3.2 UL; d= 1.16) and creatine kinase (CK; 882 ± 472 vs. 645 ± 123 UL; d= 0.97) measures demonstrated increased values in the SUPP condition, while AST and CK values correlated with 2nd half VHIR distance (r= –0.71 and r= –0.76 respectively). Elevated C-reactive protein (CRP) was observed postgame in both conditions; however, it was significantly blunted with SUPP (P= .05). Conclusions: These findings suggest SUPP may assist in the maintenance of VHIR during rugby union games, possibly via the buffering qualities of SUPP ingredients. However, correlations between increased work completed at very high intensities and muscular degradation in SUPP conditions, may mask any anticatabolic properties of the supplement.

Telephone support to rural and remote patients with heart failure : the Chronic Heart failure Assessment by Telephone (CHAT) study

Background Heart failure (HF) remains a condition with high morbidity and mortality. We tested a telephone support strategy to reduce major events in rural and remote Australians with HF, who have limited healthcare access. Telephone support comprised an interactive telecommunication software tool (TeleWatch) with follow-up by trained cardiac nurses. Methods Patients with a general practice (GP) diagnosis of HF were randomised to usual care (UC) or UC and telephone support intervention (UC+I) using a cluster design involving 143 GPs throughout Australia. Patients were followed for 12 months. The primary end-point was the Packer clinical composite score. Secondary end-points included hospitalisation for any cause, death or hospitalisation, as well as HF hospitalisation. Results Four hundred and five patients were randomised into CHAT. Patients were well matched at baseline for key demographic variables. The primary end-point of the Packer Score was not different between the two groups (P=0.98), although more patients improved with UC+I. There were fewer patients hospitalised for any cause (74 versus 114, adjusted HR 0.67 [95% CI 0.50-0.89], p=0.006) and who died or were hospitalised (89 versus 124, adjusted HR 0.70 [95% CI 0.53 – 0.92], p=0.011), in the UC+I vs UC group. HF hospitalisations were reduced with UC+I (23 versus 35, adjusted HR 0.81 [95% CI 0.44 – 1.38]), although this was not significant (p=0.43). There were 16 deaths in the UC group and 17 in the UC+I group (p=0.43). Conclusions Although no difference was observed in the primary end-point of CHAT (Packer composite score), UC+I significantly reduced the number of HF patients hospitalised amongst a rural and remote cohort. These data suggest that telephone support may be an efficacious approach to improve clinical outcomes in rural and remote HF patients.