Time-of-Flight Estimation in the Presence of Outliers. Part II—Multiple Echo Processing

The mean squared error of the classical maximum likelihood time-of-flight (ToF) estimator increases dramatically when the signal-to-noise ratio falls below a certain threshold. For narrow-band signals, this well-known threshold effect occurs largely due to the biased outliers which are induced by the local maxima of the source signal autocorrelation function. In our previous work (Part I), we have described a machine learning biosonar-inspired method for reducing the effect of the outlier bias on the accuracy of a single-echo estimate. In this paper, we extend this approach by introducing a method for combining multiple echo signals into a robust ToF estimator which is resilient to outliers. The individual bias-corrected estimates are combined together using the optimal weighted averaging (OWA) scheme which takes into account the uncertainties associated with inlier and outlier measurements. As in the single-echo case, a weak classifier and a bank of phase-shifted unmatched filters are used for estimating the probabilities of appearance of a specific outlier class in a single-echo estimate. Combined with the previously introduced single-echo bias-reduction method, the OWA scheme results in significant improvement in the ToF estimation accuracy.