In this paper fast algorithms for adaptive Capon and amplitude and phase estimation (APES) methods for spectral analysis of time varying signals, are derived. Fast, stable, nonrecursive formulae are derived, based on time shifting properties of the pertinent variables. As a consequence, efficient frequency domain recursive least squares (RLS) based, as well as fast RLS based algorithms for the adaptive estimation of the power spectra are developed. Stability issues of the frequency domain estimators are considered, and stabilization procedures are proposed. The computational complexity of the proposed algorithms is lower than relevant existing methods. The performance of the proposed algorithms is demonstrated through extensive simulations.

The coherence spectrum is of notable interest as a bivariate spectral measure in a variety of application, and the topic has lately attracted interest with the recent formulation of several high-resolution data adaptive estimators. In this work, we further this development with the presentation of computationally efficient implementations of the Capon- and APES-based MSC estimators. The presented implementations furthers the recent development of exploiting the estimators' inherently low displacement rank of the necessary products of Toeplitz-like matrices to include also the required cross-correlation covariance matrices for the mentioned coherence algorithms. Numerical simulations together with theoretical complexity measures illustrate the performance of the proposed implementations.

In this paper, the acoustic leak noise correlation method is applied for the measurement of the sound velocity of the propagated acoustic signal in water filled metallic pipes. Artificially introduced leaks are used as out-of-bracket excitation signal sources. The standard time domain correlation method is adopted for the computation of the required difference time of arrival between noise leakage signals propagating in the pipeline network, which are collected by the use of accelerometers mounted on the surface of the pipe. A new method is proposed for the improvement of the accuracy of the measured sound velocity, introducing a technique of estimation fusion, based upon results obtained from multiple measurements. A simple to use formula is derived for the enhancement of the accuracy of the estimation, introducing a weighted mean of the estimations over various realizations, with the weighting coefficients depending upon the the quality of each estimator and on the geometric characteristics of each experiment. The effectiveness of the proposed method is demonstrated using experimental data for (a) the measurement of the sound velocity and (b) the localization of artificially introduced in-bracket leaks using the measured sound velocity.

Sample Covariance Matrix (SCM) is widely used in the design of array signal processing algorithms that perform well for Circular Complex Gaussian (CCG) distributed samples. However, SCM-based Direction of Arrival (DOA) estimation algorithms are inaccurate for Complex Elliptically Symmetric (CES) data models. This paper aims to extend the conventional SCM-based iterative sparse Stochastic Maximum Likelihood Approaches (SMLA) for DOA estimation to encompass more general circular CES distributed observations. These extended Robust Stochastic Maximum Likelihood Approaches (RSMLA) use robust CES-based Maximum Likelihood (ML)- estimators of the Covariance Matrix (CM) instead of SCM, or more generally M-estimators. Joint and interleaved computation of M-Estimators and the RSMLA are also proposed (denoted as Interleaved Robust Stochastic Maximum Likelihood Approaches (IRSMLA) algorithms) when the size of the observed CES vector, M, is of the same order as the samples size, N, or when $N < M$ . To improve DOA estimation accuracy and eliminate grid mismatch, refined approaches (referred to as RSMLA-RML) that combines the power-based RSMLA and robust ML (RML) methods are also proposed, in which an alternative RML cost function is minimized over a scalar DOA parameter. Performance comparisons are made between the developed approaches and existing DOA estimation algorithms as well as Cramér-Rao Bound (CRB) in terms of sample size, Signal to Noise Ratio (SNR), DOA separation, signal source correlation parameters, and computational cost, demonstrating superior performance over existing schemes for heavy-tailed CES distributed observations. Moreover, it is experimentally demonstrated that the proposed algorithms perform effectively even when the encountered source signals are coherent, despite being derived under the assumption of uncorrelated sources.