A noise autocovariance model for SAR altimeter measurements with implications for optimal sampling. Issue 10 (15th May 2023) - Ehlers, Frithjof; Slobbe, Cornelis; Verlaan, Martin; Kleinherenbrink, Marcel
Abstract: Earlier work has empirically demonstrated some advantages of an increased posting rate of Synthetic Aperture Radar (SAR) altimeters beyond the expected ground resolution of about 320 m in Delay-Doppler (unfocused SAR, UFSAR) processing, corresponding to ∼ 20 Hz sampling. Higher posting rates of 40–80 Hz were shown to prevent spectral aliasing of the signal, enable to measure swell wave related signal distortions and may lead to a reduced root mean square error of 1 Hz estimates of Sea Surface Heights (SSH), radar cross section (sigma0) and Significant Wave Heights (SWH) from current SAR altimeters. These improvements were explained by the narrow noise autocovariance function of the waveform signal's power speckle noise in along-track direction on one hand, and frequency doubling by power detection (squaring of the signal) on the other. It has not been explained, however, why the power speckle noise decorrelates faster than anticipated by the predicted Doppler resolution, and whether this decorrelation depends on the altimeter and processing configuration. Also, it has not been shown explicitly that the estimates of SSH, SWH and sigma0 decorrelate in the same way. Describing the noise autocovariance function – or equivalently the noise power spectral density via the Wiener-Kintchin theorem – is necessary on two counts: Knowing the noise autocovariance allows to apply optimal filtering strategies that maximize precision on one hand, while the noise power spectral density predicts the frequencies contained in the noise (and signals), which in turn determines the required sampling frequency according to the Nyquist theorem. Using a newly derived analytic noise autocovariance model for UFSAR-processed altimeter data, we show that the swift signal decorrelation is mainly due to the observation geometry. Furthermore, our results demonstrate that the noise autocovariance functions of power speckle, SSH, SWH and sigma0 estimates in along-track direction are different and depend on the sea state. On top of that, the noise autocovariance functions are strongly dependent on the number of Doppler beams used for multilooking, the used retracker, and the processing choices such as antenna gain pattern compensation and windowing within the UFSAR processing (Level-1b). We validated our noise autocovariance model with segments of 42 Sentinel-3B overpasses. Our findings are in accordance to all earlier work, but indicate that the reported precision improvements with respect to 20 Hz may have been too optimistic and that the SSH, SWH and sigma0 generally decorrelate slower than the power speckle noise. We found that the required posting rate is always higher or equal to 40 Hz. Our results will potentially enable improved spectral analysis and optimal filtering of any UFSAR altimetry data. More importantly, our results can be used to trade off different aspects for determining an optimal posting rate in UFSAR altimeter processing in different sea states and with changing processing parameters, which is necessary in view of strict precision requirements of existing and future SAR altimetry missions.