Walter E. Lillo

NEURAL NETWORKS FOR CONSTRAINED OPTIMIZATION PROBLEMS

This paper is concerned with utilizing neural networks and analogue circuits to solve constrained optimization problems. We propose a novel neural network architecture for solving a class of non-linear programming problems. the proposed neural network is then used, and if necessary modified, to solve minimum norm problems subject to linear constraints. Minimum norm problems have many applications in various areas, but we focus on their applications to the control of discrete dynamic processes. the applicability of the proposed neural network is demonstrated on numerical examples.

Solving minimum norm problems using penalty functions and the gradient method

Abstract We use a penalty function approach and the gradient method to solve minimum norm problems. A class of penalty functions is introduced that allows one to transform constrained optimization minimum norm problems to unconstrained optimization problems. The sharp bound on the weight parameter is given for which constrained and unconstrained problems are equivalent. We also give a computationally efficient bound on the weight parameter. Numerical examples and computer simulations illustrate the results obtained.

Navigation Message Bit Identification Using Coherent Code Processing

A navigation message bit stream is modulated on each of the GPS L1 C/A-, L1 P-, and the L2 P-code signals. To demodulate the bit stream in low noise conditions, it is su!cien t to track any one of these signals with a phase-locked loop and to apply an arc-tangent rule to the inphase and quadrature correlations. Coherent replica generation, made possible by ultra-tight processing, in which all code and carrier replica signals are generated directly from the best estimate of the navigation state, allows the fusion of power from all signals for improved bit demodulation in high-noise conditions. A statistical analysis of the bit estimation problem, cast as a binary hypothesis test, predicts a 1.2 dB improvement when L1 C/A- and L1 P-codes are processed coherently. Studies performed using carefully calibrated, recorded GPS signals with applied broad-band jamming, confirm this analytical prediction. Statistical analysis also predicts a 1.8 dB improvement when the L2 P-code is added. An empirical verification of this prediction will be done soon. Performance is also improved when early, prompt, and late correlation weightings are chosen via a generalized eigenvector problem. In particular, only the prompt is used when in code lock.

Bayesian closely spaced object resolution with application to real data.

A technique is presented for resolving closely spaced objects when the point spread function is not well known . The technique uses a Bayesian approach without the use of contrived penalty terms for model complexity.