This paper concerns the dynamical behavior, in probabilistic sense, of a simple perceptron network with sigmoidal output units performing autoassociation for novelty filtering. Networks of retinotopic topology having a one-to-one correspondence between input and output units can be readily trained using the delta learning rule, to perform autoassociative mappings. A novelty filter is obtained by subtracting the network output from the input vector. Then the presentation of a "familiar" pattern tends to evoke a null response; but any anomalous component is enhanced. Such a behavior exhibits a promising feature for enhancement of weak signals in additive noise. As an analysis of the novelty filtering, this paper shows that the probability density function of the weight converges to Gaussian when the input time series is statistically characterized by nonsymmetrical probability density functions. After output units are locally linearized, the recursive relation for updating the weight of the neural network is converted into a first-order random differential equation. Based on this equation it is shown that the probability density function of the weight satisfies the Fokker-Planck equation. By solving the Fokker-Planck equation, it is found that the weight is Gaussian distributed with time dependent mean and variance.

The range focused beamformer (RFB) and the triple aperture crosscorrelator (TAC) are the two primary wavefront curvature ranging techniques used in fielded sonar systems. Theoretical performance bounds have been presented in the past for both approaches. This paper develops unified array processing performance bounds where the RFB and the TAC are special cases. Specifically, general Cramer-Rao lower bounds (CRLB) on range and bearing estimation for a linear array of directional elements are developed, where the CRLB for the RFB and the TAC are shown to be special cases of the general theory. The ranging performance of the two techniques are then compared.

The theoretical classification performance of a Hopfield neural network is presented. An important link between empirically based investigations of neural network classification models and the correct application of these models to AI-based systems is established. General expressions are derived relating the performance of the Hopfield model to the number and dimensionality of code vectors stored in memory. The average performance of the network is analyzed by randomizing the subsequent code vectors and examining classification relative to the output bit errors. An exact probabilistic description of the network is derived for the first iteration, and an approximate second-moment analysis generalizable to multiple iterations examines performance near a fixed point. Degradations generated by noisy or incomplete input data are analyzed. The results show that the Hopfield net has major limitations when applied to fixed pattern classification problems because of its sensitivity to the number of code vectors stored in memory and the signal-to-noise ratio of the input data.>