The Influence of Digital Domain on Time of Flight Estimation Performance

Analysis of the time of flight estimation performance when signal digitization is used is presented. The cross-correlation function peak position was used as time-of-flight estimator. In order to cope with the discrete nature of the cross-correlation the time of flight subsample estimates used interpolation techniques: parabolic peak, derivative's zero crossing, zero crossing of imaginary of Hilbert transform, double zero crossing and frequency domain phase. Noise density component of the Cramer-Rao lower error bound was modified to include the jittering and quantization noise. Basing the real amplifier noise density theoretical analysis concluded that taking the 180 nV/root Hz as lowest noise density at ADC input, 10 bit is needed for 100 MHz sampling. Numerical experiments have been conducted using Matlab to investigate the standard deviation of ToF in presence of additive white Gaussian noise and signal's digitization. It has been concluded that systematic errors are related to subsample interpolation and are in cubic relation to sampling frequency and in inverse quadratic relation to carrier. Random errors are in opposite relation: little influence by sampling frequency and direct proportion to carrier frequency. Investigation on the digital filtering influence revealed that digital filtering does not improve the time-of-flight estimation accuracy.