Cramer-RAO lower bounds for sinusoidal models from Topex/Poseidon data in the Indian Ocean

Abstract

The Cramer-Rao lower bound (CRLB) for the estimations of the cosine and sine amplitudes of multi-tone sinusoidal model is derived and applied on TOPEX/Poseidon satellite altimetry data sets covering the Indian Ocean. The CRLB depends on the variance of the White Gaussian Noise that it is computed by Modern Parametric Autoregressive Adaptative Spectral Analysis. Determining CRLB parameters it is possible to establish the minimal error associated to any model built to work in the study area what improves the intrinsic bias of the generated time series. The noise that appears in the altimetric data depends strongly on the errors from the atmospheric and geophysical corrections, so the role of the inverted barometer and tidal corrections are also analyzed. The results is summarized as: a) the spatial structure of the order of the parametric model considering the application or not of the above corrections and its relationship to the surface dynamical system of currents in Indian Ocean; b) the spatial structure of the variance of the WGN in the area and its meaning; c) the CRLB for the Geoid's estimators and the CRLB for the estimators of the semiannual and annual waves.