Entropy Spectral Estimation Research Articles

Extendability tests for multidimensional covariance sequences

The problem of extendibility of multidimensional covariance sequences and the equivalent problem of the existence of maximum entropy (ME) spectral estimates are analyzed using some recent results on the valid parameter space of Gaussian Markov random fields (GMRFs). For several nontrivial examples, explicit conditions for extendability and, using those conditions, sketches of the space of extendible covariance sequences are obtained. For the general case, a cutting-plane algorithm is proposed as an alternative to the two existing numerical procedures for ascertaining extendibility, namely, the linear programming procedure and the expanding-hull algorithm. The duality between the valid parameter space and the space of extendible covariances, and the relationship between those two spaces and the space of admissible covariances for finite-size data sequences, are examined. The connection between extendability and maximum-likelihood (ML) estimation is established, and some properties extendibility of covariances specified over increasing window sizes are presented. >

Maximum Entropy and Bayesian Spectral Analysis and Estimation Problems.

Maximum Entropy and Bayesian Spectral Analysis and Estimation Problems.

The relationship between maximum entropy and maximum likelihood spectra

Burg (1972) established an analytical relationship between maximum entropy and maximum likelihood spectral density estimates. If [Formula: see text], j = 0, 1,… M − 1 and M successive maximum entropy spectral density estimates at frequency f, then the M‐length maximum likelihood spectral density estimate [Formula: see text] is given by [Formula: see text]. (1) The maximum entropy estimates are made via Burg's well‐known formula,[Formula: see text], (2) where [Formula: see text], k = 0, 1,…,N are the coefficients of the N‐length prediction‐error filter, [Formula: see text] is its error power, and Δt is the sample interval. These estimates can be recursively calculated as shown by Burg (Smylie et al, 1973).

A Sequential Approach to Target Discrimination

The Wald sequential probability ratio test is applied to the discrimination of targets observed by a radar or other sensor and a form for the classifier involving linear predictive filtering is developed. In this sequential approach, a target is illuminated with consecutive pulses until a classification of the target can be made to within a prescribed probability of error. Because of the linear-predictive formulation, the computational and storage requirements for the classifier are related only to the number of returns necessary to predict the target signature and not to the length of signature observed; a classifier with modest storage and computational requirements can be employed to process signatures consisting of an arbitrarily large number of returns. The classifier is based on some well-known results in mean-square filtering theory and has a simple intuitive interpretation. The classifier structure can also be related to autoregressive time series analysis and innovations process concepts and has an interpretation in the frequency domain in terms of the maximum entropy and maximum likelihood spectral estimates for the target signatures.