A New Wideband Spread Target Maximum Likelihood Estimator for Blood Velocity Estimation: Part One - Theory
The derivation and theoretical evaluation of new wideband maximum likelihood strategies for the estimation of blood velocity using acoustic signals are presented. A model for the received signal from blood scatterers, using a train of short wideband pulses, is described. Evaluation of the autocorrelation of the signal based on this model shows that the magnitude, periodicity and phase of the autocorrelation are affected by the mean scatterer velocity, and the presence of a velocity spread target. New velocity estimators are then derived that exploit the effect of the scatterer velocity on both the signal delay and the shift in frequency. The wideband range spread estimator is derived using a statistical model of the target. Based on the point target assumption, a simpler wideband maximum likelihood estimator is also obtained. These new estimation strategies are analyzed for their local and global performance. Evaluation of the Cramer-Rao bound shows that the bound on the estimator variance is reduced using these estimators, in comparison with narrowband strategies. In order to study global accuracy, the expected estimator output is evaluated, and it is determined that the width of the mainlobe is reduced. In addition, it is shown that the height of subsidiary velocity peaks is reduced through the use of these new estimators.