Performance analysis of multi image subspace algorithm for source localization in shallow water

Abstract

In this thesis, the performance analysis of a subspace method for source localization (range and depth) in shallow water is discussed. The performance of a subspace method naturally depends on the quality of the subspace obtained from a covariance matrix computed with a finite number of snapshots. The thesis quantifies the sensitivity of the method to errors in the covariance matrix and incomplete channel information. Expressions for the mean and variance of the null spectrum have been derived. They are proportional to the number of snapshots, as in the DOA estimation case.

Computer simulation results are provided in support of the theoretical predictions. We have also derived the MSE (Mean Squared Error) expressions for range and depth. Simulation results are then provided to support these theoretical predictions. The source position estimates are unbiased. For an unbiased estimate, the variance is bounded below by the CR bound. It is shown that both theoretical and simulation MSE values attain the CR bound either for a large number of dipoles, high SNR (Signal-to-Noise Ratio), large number of snapshots, or sensor elements.

Lastly, we consider the uncertainties in channel parameters, namely the sound speed uncertainty and the channel depth uncertainty, on the source position estimates. It is shown that the range estimate is affected by variations in the sound speed. It is further observed that the source appears to be closer or farther depending on whether the sound speed variation is positive or negative. The error in the depth estimate is, however, marginal. The channel depth uncertainty, on the contrary, is found to seriously affect the source range and depth estimates. It is shown that the source appears to be deeper and farther when the depth uncertainty is positive (overestimate of channel height).