Adaptive Trackers Based on Continuous Learning Theory

The theory of ?continuous learning? is applied here to the design of nonlinear sampled-data trackers. This theory provides a continuous-motion approximation of the discrete or sampled motion of the actual tracker. The theory prodicts the transient-response performance of the tracker as well as the mean-square errors caused by noise and statistical fluctuations in the signal. Numerical examples of first-order and second-order trackers designed by this technique are presented. These examples illustrate the adaptive behavior predicted by the technique. In one of these examples the trade-off between transient-response performance and the suppression of noise-induced tracking errors is demonstrated.     

Sonar Array Detection of Gaussian Signals in Gaussian Noise of Unknown Power

A statistical test is postulated for detecting, with an M-element hydrophone array, a Gaussian signal in spatially independent Gaussian noise of unknown power. The test is an extension of the uniformly-most-powerful (UMP) unbiased test for a two-element array. The output signal-to-noise ratio of the test is calculated and, for a large number of independent space-time samples, is shown to be no better than a mean-level detector (MLD). Receiver operating characteristic curves (ROC) for the MLD are computed and compared to the ROC curves for the optimum (Bayes) parametric detector. The input signal-to-noise power ratios required to provide a detection probability of 0.5 differ by less than 0.2 dB for a fifty-element array with wide variation in false-alarm probability and time-bandwidth product. This result suggests that both the extended bivariate UMP unbiased test and the MLD perform close to the unknown UMP unbiased test for independence of a multivariate Gaussian distribution.     

Performance Analysis of Adaptive Processors via Diffusion Model Approximations and the Fokker-Planck Equation

Some results on adaptive array processors and adaptive filters that have been obtainsd by the use of diffusion model approximations and the Fokker-Planck equation are described.