Empirical Interferometric Phase Variance Formulas for Bathymetric Applications

Current sonar and radar applications use interferometry to estimate the arrival angles of backscattered signals. This direction-finding method is based on a phase-difference measurement between two close receiving arrays. To model the associated bathymetric error, it is necessary to know the second-order moment of the interferometric phase estimator. This paper explains the connection between bathymetric variance and interferometric phase variance and the difficulty in the evaluation of the phase second-order estimation. Thus, a brief statistical overview of the interferometric phase estimator for fully developed speckle signals (called here RMPC for random modulus partially correlated signals) is introduced in this paper. The focus of this paper is the derivation of simple empirical variance that matches the exact values in both single-look and multilook cases. For the sake of constituency, the construction of these empirical approximations is based on a modified asymptotic expression of the second order for the phase estimator assuming high signal-to-noise ratio. In order to perform these derivations, it appears necessary to introduce a new kind of signal (namely, CMPC for constant modulus partially correlated signal) whose modulus is assumed constant. This family of signals, whose physical existence is also investigated, appears as an alternative way to derive RMPC empirical formulas. The link between RMPC and CMPC signals is established through the conditional expectation of the signal modulus. Finally, the existence of these two statistical behaviors is tested over real underwater data.