Technical report associated with the paper “A Semi-Analytical Model for Delay/Doppler Altimetry and its Estimation Algorithm”

TECHNICAL REPORT – 2013, April Abstract The concept of delay/Doppler altimetry has been under study since the mid 90’s, aiming at reducing the measurement noise and increasing the along-track resolution in comparison with the conventional pulse limited altimetry. This paper introduces a new model for the mean backscattered power waveform acquired by a radar altimeter operating in SAR mode, as well as an associated least squares estimation algorithm. As in conventional altimetry, the mean power can be expressed as the convolution of three terms: the flat surface impulse response, the probability density function of the heights of the specular scatterers and the time/frequency point target response of the radar. An important contribution of this paper is to derive an analytical formula for the flat surface impulse response associated with delay/Doppler altimetry. This analytical formula is obtained for circular antenna pattern, no mispointing, no vertical speed effect and a uniform scattering. The double convolution defining the mean echo power can then be computed numerically resulting in a two dimensional semi-analytical model called delay/Doppler map. This delay/Doppler map depends on three altimetric parameters: the epoch, the sea surface wave height and the amplitude. A multi-look model is obtained by summing all the reflected echoes from the same along track surface location of interest after applying appropriate delay compensation (range migration) to align the delay/Doppler map on the same reference. The second contribution of this paper concerns the estimation of the parameters associated with the multilook semi-analytical model. A least squares approach is investigated by means of the LevenbergMarquardt algorithm. Simulations conducted on simulated altimetric waveforms allow the performance of the proposed estimation algorithm to be appreciated. The analysis of Cryosat-2 waveforms shows an improvement in parameter estimation when compared to the conventional altimetry.