Cramér-Rao bounds for radar altimeter waveforms

The pseudo maximum likelihood estimator allows one to estimate the unknown parameters of Brown's model for altimeter waveforms. However, the optimality of this estimator, for instance in terms of minimizing the mean square errors of the unknown parameters is not guarantied. Thus it is not clear whether there is some space for developing new estimators for the unknown parameters of altimetric signals. This paper derives the Cramér-Rao lower bounds of the parameters associated to Brown's model. These bounds provide the minimum variances of any unbiased estimator of these parameters, i.e. a reference in terms of estimation error. A comparison between the mean square errors of the standard estimators and Cramér-Rao bounds allows one to evaluate the potential gain (in terms of estimation variance) that could be achieved with new estimation strategies.