Undersampling for parameter estimation with application to time of arrival estimation

This paper deals with the effect of sampling the continuous observations on parameter estimation errors. In particular, we study the problem of estimating the time of arrival (TOA) of a continuous, deterministic signal in noise. For this problem, the sampling procedure transforms the continuous parameter space into a discrete one, resulting in inherent estimation errors. We introduce a general tool for evaluating the achievable performance for any parameter estimation problem at a given sampling rate. For TOA estimation with a Gaussian-shaped signal, we show that one can undersample with a factor up to 3 times the Nyquist rate with an average TOA estimation performance reduction of less than 3 dB