Time-of-flight estimation using binary search system identification technique

( ) ( ) ( ) t gs D t r t s + − = , (1b) where the x(t) consists of a reference signal r(t), and Gaussian noise gx(t), while the s(t) consists of the time delayed version of the reference signal r(t-D), and Gaussian noise gs(t). Additionally let us assume that the noise signals are uncorrelated with each other and with the reference signal. The TOF lies at the core of many modern signalprocessing algorithms. In medical ultrasound for example, the TOF is employed in blood flow estimation, tissue motion measurement, tissue elasticity estimation and a number of other algorithms. To these and numerous other algorithms the TOF accuracy and computational cost are critical important. The TOF has been widely and meticulously studied over the past forty years. Early work focused on applications in radar and sonar. While efforts over the past two decades have broadened to include speech processing, medical imaging, and a broad array of other applications, classical TOF there are a few approaches depending on the reference signal and other conditions. TOF measurement methods when the reference signal is random or when TOF measurement is based on direct time-to-digital conversion have been analyzed in studied literature [12-16]. A some kind of “critical point” inside the signal, where the signal energy have maximum value or other conditions are detected, is applied to the signal for determining a point of measurement (positive or negative slope zero crossing, maximum value, a special marker, etc.). The disadvantage of the method is that a signal-tonoise ratio could be changed only by increasing the power of used signals. There are physical and other limitations on a maximal energy used in the measurement. For the case of a deterministic reference signal, the classical methods are generally based on the second order statistics [2], notably computing the lag for which the cross-correlation between the reference and the delayed signal have a maximum value. Another popular method involves the minimization of the squared error (a least squares approach) between the signals for different lags. The advantage of the statistical methods is so called “process gain” means that the signal-to-noise ratio could be increased by increasing the length (or bandwidth) of the reference signal [1]. Up to 60 dB “process gain” is available in practical situations. The higher gain is limited by a sampling jitter and clock stability. A popular method to estimate the time delay is to search for the global extreme ( ) m R τ of the crosscorrelation function [3]: