Time-of-Flight Estimation in the Presence of Outliers Part I—Single Echo Processing

When the signal-to-noise ratio (SNR) falls below a certain level, the error of the time-of-flight (ToF) maximum likelihood estimator abruptly increases due to the well-known threshold effect. Nevertheless, operating near and below the threshold SNR value might be necessary for many remote sensing applications due to power-related constraints. These constraints may include a limit on the maximum power of a single source pulse or a limit on the total power used by multiple signals transmitted during a single measurement. For narrow-band signals, the threshold effect emerges mostly due to outliers induced by local maxima of the autocorrelation function of a source signal. Following the previously explored path of biosonar-inspired echo processing, this paper introduces a new method for ToF estimation in the presence of outliers. The proposed method employs a bank of phase-shifted unmatched filters for generating multiple biased but only partially correlated estimators (multiple experts). Using machine learning techniques, the information from the multiple experts is combined together for improving the near-the-threshold ToF estimation from a single echo.