Title :
Error propagation bounds in dual and triple beam vector Doppler ultrasound
Author :
Steel, R. ; Fish, P.J.
Author_Institution :
Sch. of Informatics, Univ. of North Wales, Bangor, UK
Abstract :
Measurement of the velocity components along two (three) directions enables the two (three)dimensional velocity vector to be estimated exactly. However, in practical systems employing such multiple beam techniques, there will usually be errors in the measured velocity components along each beam, which will lead to errors in the estimated velocity magnitude and direction. This error propagation problem is analyzed in both two and three dimensions by decomposition of the velocity estimation matrix, and exact upper and lower bounds are derived for both the magnitude and angle bias as a function of the angle between the beams. The bias in triple beam systems is shown to have identical bounds to that in dual beam systems with an equivalent interbeam angle. It is found that small errors in the individual beam velocity components can be magnified in the final determination of velocity magnitude and angle. Plots are presented to assist system designers to specify the interbeam angle(s) to avoid gross velocity estimation errors.
Keywords :
Doppler measurement; errors; flow measurement; matrix algebra; ultrasonic applications; ultrasonic propagation; Doppler US flow measurement systems; angle between beams; angle bias; dual beam systems; dual beam vector Doppler ultrasound; equivalent interbeam angle; error propagation bounds; lower bounds; magnitude bias; measured velocity components errors; multiple beam techniques; triple beam systems; triple beam vector Doppler ultrasound; upper bounds; velocity components; velocity estimation errors; velocity estimation matrix decomposition; Doppler radar; Estimation error; Matrix decomposition; Medical services; Structural beams; Ultrasonic imaging; Velocity measurement; Blood Flow Velocity; Ultrasonography, Doppler;
Journal_Title :
Ultrasonics, Ferroelectrics, and Frequency Control, IEEE Transactions on
DOI :
10.1109/TUFFC.2002.1041538