Multiresolution optimal interpolation and statistical analysis of TOPEX/POSEIDON satellite altimetry

A recently developed multiresolution estimation framework offers the possibility of highly efficient statistical analysis, interpolation, and smoothing of extremely large data sets in a multiscale fashion. This framework enjoys a number of advantages not shared by other statistically-based methods. In particular, the algorithms resulting from this framework have complexity that scales only linearly with problem size, yielding constant complexity load per grid point independent of problem size. Furthermore these algorithms directly provide interpolated estimates at multiple resolutions, accompanying error variance statistics of use in assessing resolution / accuracy tradeoffs and in detecting statistically significant anomalies, and maximum likelihood estimates of parameters such as spectral power law coefficients. Moreover, the efficiency of these algorithms is completely insensitive to irregularities in the sampling or spatial distribution of measurements and to heterogeneities in measurement errors or model parameters. For these reasons this approach has the potential of being an effective tool in a variety of remote sensing problems. In this paper, we demonstrate a realization of this potential by applying the multiresolution framework to a problem of considerable current interest – the interpolation and statistical analysis of ocean surface data from the TOPEX / POSEIDON altimeter. Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science; MIT, Cambridge MA, 02139 USA. Research support provided in part by the Office of Naval Research under Grant N00014-91-J-1004, by the Draper Laboratory under Grant DL-H-467133, and by the Air Force Office of Scientific Research under Grant F49620-92-J-0002. P.W.F. was also supported by an NSERC-67 fellowship of the Natural Sciences and Engineering Research Council of Canada. Department of Earth, Atmospheric, and Planetary Sciences; MIT, Cambridge MA, 02139 USA. Research supported in part by NASA under Grant NAGW-1048.