This paper considers the exploitation of temporal correlation in incident sources in a narrowband array processing scenario. The MLE and CRB are derived for parameter estimation of spatially uncorrelated first order Gaussian autoregressive source signals with additive Gaussian spatially and temporally uncorrelated sensor noise. These are compared to the MLE and CRB for the usual uncorrelated (WN) sources model. The paper deals with the case where the number of data snapshots is small. Numerical simulations show that (i) there is no significant performance gain in the correlated signal case, and significantly, (ii) the WN MLE performance does degrade in the presence of source correlation, which appears to be in contrast to some recently published work.

The influence of a point spectrum on large sample statistics of the autoregressive (AR) spectral estimator is addressed. In particular, the asymptotic distributions of the AR coefficients, the innovations variance, and the spectral density estimator of a finite-order AR(p) model to a mixed spectrum process are presented. Various asymptotic results regarding AR modeling of a regular process with a continuous spectrum are arrived at as special cases of the results for the mixed spectrum setting. Finally, numerical simulations are performed to verify the analytical results.

This work addresses the influence of the point spectrum on large sample statistics of the autoregressive spectral estimator. In particular, the asymptotic distributions of the AR coefficients, the innovations variance, and the spectral density estimator of a finite order AR(p) model for a mixed spectrum process are presented. Numerical simulations are performed to verify the analytical results.

This work addresses the problem of trying to take advantage of the nominally periodic nature of a diesel engine running at constant speed to obtain a time-varying spectral description of vibration data over the shaft period. It requires addressing a number of issues, most notably period estimation and removal of tonal components whose presence in a time-varying spectrum is redundant and undesirable. Use of a recently designed method to identify sinusoids, in conjunction with an adaptive tracking algorithm, results in significant improvement in simulations, and reasonably good improvement in the case of the diesel vibration data, especially when considering the complexity of the stochastic structure of this data.>

A simple proof of the convergence of the minimum variance (MV) spectral estimator to the point spectrum, as the order of the covariance matrix goes to infinity, is presented. This is done in the multichannel setting where the corrupting unknown noise process is allowed to be nonstationary. Also obtained are explicit bounds on the rate of convergence. The results suggest that the MV(n) spectrum is robust with respect to the type of contaminating noise. While the results are obtained in the multichannel random process setting, the same arguments hold in the random field setting.>

A simple proof is presented of the convergence of the minimum variance spectral estimator to the point spectrum, as the order of the covariance matrix goes to infinity. This is done in the multichannel setting where the corrupting unknown noise process is allowed to be nonstationary. Explicit bounds are also obtained on the rate of convergence. >

A novel method for point power spectrum identification is presented. It involves a refinement of a recently developed scheme and achieves measurable performance improvement. It utilizes two families of spectral estimators and a pseudolinearity property to arrive at the final point spectrum estimate. Two examples are included.>

The practical aspects of the convergence properties of the family of maximum-likelihood (ML) estimators are investigated in the context of harmonic signal estimation. Specifically, the consequences of having only a finite number of correlation lags and of performing finite-resolution computations are addressed. The results of this investigation include guidelines for assessing the available frequency resolution and for improved estimates of signal power. Finally, an example is presented which demonstrates the advantages of using autoregressive and ML estimates jointly in harmonic signal estimation.>

The problem of estimating sinusoids that have been corrupted by additive stationary noise is addressed. It is shown how the Naimark dilation for the data correlation sequence can be used to provide additional insight into some fundamental results on orthogonal polynomials and to give a new interpretation of the maximum-likelihood (ML) spectral estimator.>

A method of recovering sinusoids from additive arbitrary colored noise is presented. It was a Hankel matrix formulation to recover the frequencies, and reduces to the Pisarenko decomposition for the case of white noise.