Bayesian Estimation of Smooth Altimetric Parameters: Application to Conventional and Delay/Doppler Altimetry

Abstract

This paper proposes a new Bayesian strategy for the smooth estimation of altimetric parameters.The altimetric signal is assumed to be corrupted by a thermal and speckle noise distributed according to an independent and non identically Gaussian distribution. We introduce a prior enforcing a smooth temporal evolution of the altimetric parameters which improves their physical interpretation. The posterior distribution of the resulting model is optimized using a gradient descent algorithm which allows us to compute the maximum a posteriori estimator of the unknown model parameters.This algorithm presents a low computational cost which is suitable for real time applications.The proposed Bayesian strategy and the corresponding estimation algorithm are validated on both synthetic and real data associated with conventional and delay/Doppler altimetry. The analysis of real Jason-2 and Cryosat-2 waveforms shows an improvement in parameter estimation when compared to the state-of-the-art estimation algorithms.

Fast Estimation of Covariance Parameters in Least-Squares Collocation by Fisher Scoring with Levenberg–Marquardt Optimization

“…The studies of the atmosphere that are consolidated with meteorology in IUGG investigate important or dangerous phenomena in the atmosphere, like, e.g., fluxes of different atmospheric gases (Michalak et al 2005;Miller et al 2014;Winiarek et al 2012;Zupanski et al 2007). A separate domain in IUGG is the ocean science and ML techniques have been found as helpful also there, in ocean storm studies, sea surface determination and studies on acoustic waves in the water (Bengtsson et al 2005;Halimi et al 2015;Thode et al 2002;Ueno et al 2010). The seismological society analyzes the parameters of earthquakes by ML (Console and Murru 2001;Herak et al 2001;Legrand et al 2012;Segall and Matthews 1997;Segall et al 2000).…”

“…The applications are not so frequent in the literature and the convergence problems are often found as a limitation of a non-optimized form of FS (Grodecki 1999;Pardo-Igúzquiza 1997). The conclusion about the poor convergence of primary FS or converging at most to the local minima is repeated many times in the literature (Green 1984;Halimi et al 2015;Kubik 1970;Sari and Ç elebi 2004). This work attempts to analyze it in more detail, to make it more efficient and more readily used.…”

“…The estimates were often divergent from the global or even from the local minimum of the NLLF. The divergence of the scoring is the most frequently reported problem in the literature (Green 1984;Halimi et al 2015;Kubik 1970;Sari and Ç elebi 2004). Currently, a very promising technique that can overcome this disadvantage is LM optimization.…”

STAR: Spatio-temporal altimeter waveform retracking using sparse representation and conditional random fields

“…SSHs and other sea surface conditions such as wave height are neither independent along tracks, nor between neighboring tracks (Sandwell & Smith (1997)). Spatial information has been used in the analysis, for example, by Maus et al (1998) through simultaneously processing of a sequence of waveforms for tracking of travel times, or Halimi et al (2016) for a smooth estimation of altimetric parameters. This means, the integration of spatial information can be carried out in different parts of the analysis.…”

“…1). In contrast to Halimi et al (2016) where the conditional random field is used as part of an algorithm to enforce a smooth estimation of the retracking parameters, we propose to use the conditional random field at the sub-waveform detection step. Subsequently, any retracking method can be applied to the identified individual sub-waveforms for deriving the SSH, thus effectively ignoring disturbing signals outside the selected sub-waveform.…”