Undersampling for parameter estimation with application to time of arrival estimation
Hagit Messer · 2002
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.