Error Analysis of Correlation Methods for Estimation of Time Delays in Sensor Signals

To avoid false alarms in many failure detection schemes, it is important to be able to align time-shifted sensor signals in real-time. If finite-window cross-correlation techniques are used to estimate the time delay between two signals, the estimate can often be in error even if the signals are identical and there is no sensor noise. In this paper, we characterize this estimation error for smooth signals. A graph relating correlation window length and delay estimation error for bandlimited signals obtained by low-pass filtering a Gaussian process is generated using a Monte Carlo simulation. These results are compared to experimental data obtained with an instrumented mechanical manipulator.