Cramer-Rao bounds for shallow water environmental parameter estimation

Abstract

This paper demonstrates a technique for solving the Cramer-Rao lower estimation bounds of environmental parameters applied to matched field tomography (MFT) and ocean acoustic tomography (OAT). MFT is a parameter estimation method which processes narrowband signals, using the interference pattern generated between elements in a sonar array. OAT, another estimation technique, relies on acoustic travel times between a source and receiver; consequently, wideband signals are used to provide high time resolution. OAT exploits signal coherence over a selected bandwidth, while MFT does not. With knowledge of the Cramer-Rao bounds, one can determine the minimum variance attainable for an estimator of any environmental parameter, as well as determining the coupling between any set of parameters in the ocean environment. This information is useful for evaluating present estimation techniques, determining the feasibility and expected performance of new estimators, and finding how changes in one parameter can affect the estimation of other parameters in the ocean. Attention was focused on modeling a range independent shallow water environment with a sediment layer and hard bottom. For a source and receiver spaced 15 km apart, four sound velocity profile parameters were estimated. A comparison was made between the relative performance of MFT and OAT. At low SNR levels, OAT has superior performance over MFT. Above certain SNR levels, similar performance was observed for both MFT and OAT. Under constant energy conditions, minimum standard deviations decrease as signal bandwidth increases. Coupling between parameters appears to be independent of SNR and inversion method (OAT vs. MFT), and only slightly influenced by signal bandwidth. Parameter selection is very important in determining the CRB; improper selection leads to artificially high estimation bounds, due to strong coupling across parameters.