Performance Analysis Of Matched-Field Source Localization Under Complex Ocean Environments

As one of the main techniques for passive source localization, matched-field processing (MFP) is a continuation and generalization of the matched filter/ beamforming in underwater acoustics. In a complex oceanic waveguide environment, sound propagation is characterized by standing wave vertically and traveling wave horizontally. Although it is constrained, more information could be utilized compared to a plane-wave model. Advantages of the MFP are doubled by exploiting a full-field wave structure and an effective combination of both sound propagation physics and advanced signal processing techniques.MFP for passive source localization is a comprehensive application of signal processing techniques in extremely complex environments. In essence, it is a parameter estimation processor, which includes two parts, the implementation algorithm and the performance metrics. Particularly, performance analysis quantitatively evaluates both the optimality and limitations of the algorithm, which could provide important guidances for practical applications. However, it is rather challenging especially in a complex environment, since acoustic, environmental and statistical modeling are all involved.This thesis mainly concerns performance analysis of matched field localization. Previously, MFP performance has been intensively investigated under spatially white noise field. On the contrary, we develop approaches to study MFP performance in the presence of spatially correlated noises. Both the discrete interference and surface-generated noise are considered, and the results are compared with that under spatially white noise field. Performances in both Fisher and Bayesian schemes are analyzed, with the mean square error (MSE) as the metric. We consider two local performance bounds—Cramer-rao bound (CRB) and Bayesian Cramer-rao bound (BCRB), and two global performance analysis methods—method of interval errors (MIE) and Ziv-Zakai bound (ZZB). As a non-linear estimator. MFP often shows two main features in its MSE:1) when the signal-to-noise ration (SNR) is lower than a threshold SNR, MSE increases dramatically, caused mostly by the ambiguities surrounding the prominent sidelobes of the output; 2) when some environmental mismatch is present, the estimation can be seriously biased even in the high SNR region, holding MSE almost no gain.In this thesis, performance analysis is conducted in three increasingly complicated situations:known covariance matrix, unknown covariance matrix, and unknown covariance matrix with mismatched Green's function. All the theoretic developments are validated via simulations. Both the Pekeris waveguide and a practical shallow water environment inversed from the 2001 Asian Seas International Acoustic Experiment (ASIAEX) are considered, and the main results include the following three aspects.1) When the covariance matrix is known, without loss of generality, we study the maximum likelihood (ML) estimation. Its performance can achieve the CRB, since it is of asymptotically minimum variance and unbiased (MVU). However, CRB is a local performance bound, which considers the mainlobe ambiguity only. On the contrary, MIE displays obvious threshold behavior, and agrees well with the Monte Carlo simulations in most of the SNR levels. It is the sum of the asymptotic local performance and the probabilistic square error (PSE), requiring that the probability errors associated with the mainlobe and some prominent sidelobes be evaluated. In the Bayesian scheme, BCRB is the inverse of the global information matrix, which is the weighted sum of the Fisher information matrix across the parameter distribution space. When the Fisher information matrix is a function of the parameter of interest, BCRB is no longer achievable, with a little gap below the practical performance. ZZB uses all the probability errors associated with two arbitrary points in the distribution space. Note that the probability error is different from the Fisher matrix, since it is related to the specific algorithm.2) When the covariance matrix is unknown, the Capon algorithm is studied. The Capon algorithm has a high resolution, however, it can not achieve the CRB, because of the biased statistics and the effect of sample matrix inversion (SMI). In this thesis, we modify the CRB to redefine the asymptotic local bound of the Capon algorithm here, and develop the corresponding MIE approach. The BCRB redefined by the same way also has tighter performance. Simulation results show the same characteristics as that when covariance matrix is known:Adding spatially correlated noise, threshold SNR is somehow higher than that under spatially white noise field. The results demonstrate that, MFP has a good suppressing capability with a point interference; while with surface-generated noises, MSE decreases in a slower pace in the high SNR region. When some environmental parameter is mismatched, both MIE and ZZB calculated by modified probability errors also agree with Monte Carlo simulation well, and MSE converges to the bias-square in the high SNR region.3) Robust matched-field processing sacrifices high resolution for robustness, with the aim to improve output signal-to-interference and noise ratio (SINR). Uncertainty of the steering vector is considered directly, modeled by an uncertain sphere whose radius is an uncertainty factor. We make sure that the signal could pass without distortion even in the worst case. With mismatch, the estimation corresponding to the peak output is biased, and a robust algorithm can not change this behavior, thus MSE performance scheme is no longer applicable. We present the analysis in term of both the beampattern and output SINR, and the results show that those performances can be improved with a large uncertainty factor.Finally, experimental data from a waveguide tank test are processed to validate some of the theoretical developments. With known environmental parameters, ML MFP can be implemented to find the source location. However, the MSE evaluation results demonstrate that the steering vector is always mismatched with the real waveguide environment, and hence the estimation is a little biased in the high SNR region. Robust matched-field processing is also validated using real data from the North-Sea Experiment in 1993.In summary, this thesis has further developed numerous performance analysis methods for MFP. Through analyzing the optimality and limitations of the MFP in typical ocean environments, we expect that the results can be used to guide the practical applications of the MFP.