Using matrix norms to estimate the direction of arrival of planar waves on an ULA

SEAD method estimates the direction-of-arrival angles on an uniform linear array based on the difference between the two largest singular values, what is called differential spectrum. Although it presented an outstanding performance, the ability to indicate the source positions was not elucidated yet. Inspired by the differential spectrum formulation we derived a total differential spectrum and found out that the matrix norm induced by the vector 2-norm of a modified spatial covariance matrix can be used to estimate the direction-of-arrival of multiple plane waves. Indeed we show that matrix norms are estimators and we propose their use instead of the singular value decomposition in SEAD-based methods. We present a general mathematical expression in order to explicit the operating principles of the proposed methods. Consequently, we were able to explain how the relation between the arriving and the search angles produces the larger peaks on the differential spectrum. To evaluate the important role played by matrix norms, a thousand experiments were carried out. They showed that the proposed approach proved to be as accurate as the previous SEAD-based methods, while providing a significant reduction on runtime. It also outperformed well-established methods like MODEX regarding the estimation error.     

Physiological Correlations With Short,Medium, and Long Cycling Time-Trial Performance

Purpose: Several studies have demonstrated that physiological variables predict cycling endurance performance. However, it is still unclear whether the predictors will change over different performance durations. The aim of this study was to assess the correlations between physiological variables and cycling time trials with different durations. Methods: Twenty trained male cyclists (maximal oxygen uptake [VO₂max] = 60.5 ± 5.6 mL/kg/min) performed 4 separate experimental trials during a 2-week period. Cyclists initially completed an incremental exercise test until volitional exhaustion followed by 3 maximal cycling time trials on separate days. Each time trial consisted of 3 different durations: 5 min, 20 min, and 60 min performed in a randomized order. Results: The main results showed that the physiological measures strongly correlated with long cycling performances rather than short and medium time trials. The time-trial mean power output was moderately high to highly correlated with peak power output and VO_2max (r = .61–.87, r = .72–.89, respectively), and was moderately to highly correlated with the lactate threshold Dmax method and second ventilatory threshold (r = .52–.75, r = .55–.82, respectively). Conclusions: Therefore, trained cyclists should develop maximal aerobic power irrespective of the duration of time trial, as well as enhancements in metabolic thresholds for long-duration time trials.