We investigate the maximum likelihood (ML) direction-of-arrival (DOA) estimation of multiple wideband sources in the presence of unknown nonuniform sensor noise. New closed-form expression for the direction estimation Cramér-Rao-Bound (CRB) has been derived. The performance of the conventional wideband uniform ML estimator under nonuniform noise has been studied. In order to mitigate the performance degradation caused by the nonuniformity of the noise, a new deterministic wideband nonuniform ML DOA estimator is derived and two associated processing algorithms are proposed. The first algorithm is based on an iterative procedure which stepwise concentrates the log-likelihood function with respect to the DOAs and the noise nuisance parameters, while the second is a noniterative algorithm that maximizes the derived approximately concentrated loglikelihood function. The performance of the proposed algorithms is tested through extensive computer simulations. Simulation results show the stepwise-concentrated ML algorithm (SC-ML) requires only a few iterations to converge and both the SC-ML and the approximately-concentrated ML algorithm (AC-ML) attain a solution close to the derived CRB at high signal-to-noise ratio.
Heart rate (HR) and oxygen uptake (VO2) at the mechanical power (W) corresponding to the capillary blood lactate ([la]cap) of 4 mmol.l-1 (Wlt) were measured in 34 healthy male subjects during incremental exercise (Winc). On the basis of these measurements, the subjects were asked to cycle at Wlt for 60 min (steady-state exercise, Wss). Twenty subjects could not reach the target time (mean exhaustion time, te, 38.2 min, SD 5.3), while 6 of the 14 remaining subjects declared themselves exhausted at the end of exercise. The final [la]cap if the two groups of exhausted subjects were 5.3 mmol.l-1, SD 2.3 and 4.3 mmol.l-1, SD 1.1, respectively. At the end of Wss, [la]cap and HR were significantly lower in the 8 unexhausted subjects than in the other subjects. This group also had a lower HR at Wlt during Winc. The HR and VO2 appeared to be higher during Wss than during Winc. When all subjects were ranked according to their te during Wss, Wlt (expressed per kilogram of body mass) was found to be negatively related to te. In conclusion, during Winc, measurements of physiological variables at fixed [la]cap give a poor prediction of their trends during Wss and of the relative te; at the same work load [la]cap can be quite different in the two experimental conditions. Furthermore, resistance to exercise fatigue at Wlt seems lower in the fitter subjects.
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