An Error Analysis Method for Correlation-Based Parameter Estimators in Discrete-Time Signals Under Gaussian Noise

In this study, we expand on a previously introduced method for computing the error statistics associated with estimating the time of arrival of a known signal in sampled data with additive white Gaussian noise (AWGN). When matched filtering techniques are used to localize sampled signals, there is a probability of error, which takes the form of a sample index offset from the true time of arrival. This method allows us to fully calculate the probability mass function for the estimation error, which at lower signal to noise ratios (SNR) does not fit a Gaussian shape and depends heavily on the shape of the signal being detected. We show that the method can be extended to work on cases involving complex signals, interpolated signals, and signals that undergo pre-filtering steps. In addition, we demonstrate that the same method can be used to characterize frequency of arrival error probabilities, and the joint estimation of frequency and time of arrival.