A practical constraint that comes in the way of spectrum estimation of a continuous time stationary stochastic process is the minimum separation between successively observed samples of the process. When the underlying process is not band-limited, sampling at any uniform rate leads to aliasing, while certain stochastic sampling schemes, including Poisson process sampling, are rendered infeasible by the constraint of minimum separation. It is shown in this paper that, subject to this constraint, no point process sampling scheme is alias-free for the class of all spectra. It turns out that point process sampling under this constraint can be alias-free for band-limited spectra. However, the usual construction of a consistent spectrum estimator does not work in such a case. Simulations indicate that a commonly used estimator, which is consistent in the absence of this constraint, performs poorly when the constraint is present. These results should help practitioners in rationalizing their expectations from point process sampling as far as spectrum estimation is concerned, and motivate researchers to look for appropriate estimators of bandlimited spectra.

In the matter of selection of sample time points for the estimation of the power spectral density of a continuous time stationary stochastic process, irregular sampling schemes such as Poisson sampling are often preferred over regular (uniform) sampling. A major reason for this preference is the well-known problem of inconsistency of estimators based on regular sampling, when the underlying power spectral density is not bandlimited. It is argued in this paper that, in consideration of a large sample property like consistency, it is natural to allow the sampling rate to go to infinity as the sample size goes to infinity. Through appropriate asymptotic calculations under this scenario, it is shown that the smoothed periodogram based on regularly spaced data is a consistent estimator of the spectral density, even when the latter is not band-limited. It transpires that, under similar assumptions, the estimators based on uniformly sampled and Poisson-sampled data have about the same rate of convergence. Apart from providing this reassuring message, the paper also gives a guideline for practitioners regarding appropriate choice of the sampling rate. Theoretical calculations for large samples and Monte-Carlo simulations for small samples indicate that the smoothed periodogram based on uniformly sampled data have less variance and more bias than its counterpart based on Poisson sampled data.

This paper considers the problem of estimating the direction of arrival of plane waves from sensor array data. It is shown through a multivariate generalization of Whittle's inequality that the least squares estimator and its subspace-based approximations are inefficient when the noise distribution is non-Gaussian. In order to improve efficiency, two computationally elegant extensions of the MUSIC algorithm are suggested. Computer simulations indicate that the proposed methods perform much better than MUSIC for non-Gaussian noise, while the performances of all the three methods are comparable for Gaussian noise.>

The joint probabilistic data association (JPDA) algorithm previously reported by T.E. Fortmann et al. (1983) for tracking multiple targets in the presence of clutter has the drawback that its complexity increases rapidly with the number of targets and returns. An approximation of the JPDA is suggested that solves this problem by using an analog computational network to solve the data association problem. The problem is viewed as that of optimizing a suitably chosen objective function. Simple neural-network structures for the approximate minimization of such functions have been proposed by other researchers. The analog network used here offers a significant degree of parallelism and thus can compute the association probabilities more rapidly. Computer simulations indicate the ability of the algorithm to track many targets simultaneously in the presence of moderate density clutter.>

A new technique for the estimation of autoregressive filter parameters of a non-Gaussian autoregressive process is proposed. The probability density function of the driving noise is assumed to be known. The new technique is a two-stage procedure motivated by maximum likelihood estimation. It is computationally much simpler than the maximum likelihood estimator and does not suffer from convergence prroblems. Computer simulations indicate that unlike the least squares or linear prediction estimators, the proposed estimator is nearly eifficient, even for moderately Sized data records.

The problem of detecting a signal known except for amplitude in incompletely characterized non-Gaussian noise is addressed. The use of a generalized likelihood ratio test or its asymptotically equivalent form, the Rao test, is shown to produce a detector that has the identical asymptotic performance as a generalized likelihood ratio test designed with a priori knowledge of the unknown noise parameters. Since the latter clairvoyant detector always produces an upper bound on performance, the generalized likelihood ratio test is optimum. An example is given in which the noise is modeled as an autoregressive process with a mixed-Gaussian noise excitation. Results of a computer simulation are described which verify the theory.