ADMM-Based Algorithm for Training Fault Tolerant RBF Networks and Selecting Centers.

In the training stage of radial basis function (RBF) networks, we need to select some suitable RBF centers first. However, many existing center selection algorithms were designed for the fault-free situation. This brief develops a fault tolerant algorithm that trains an RBF network and selects the RBF centers simultaneously. We first select all the input vectors from the training set as the RBF centers. Afterward, we define the corresponding fault tolerant objective function. We then add an -norm term into the objective function. As the -norm term is able to force some unimportant weights to zero, center selection can be achieved at the training stage. Since the -norm term is nondifferentiable, we formulate the original problem as a constrained optimization problem. Based on the alternating direction method of multipliers framework, we then develop an algorithm to solve the constrained optimization problem. The convergence proof of the proposed algorithm is provided. Simulation results show that the proposed algorithm is superior to many existing center selection algorithms.

Augmented Lagrange Programming Neural Network for Localization Using Time-Difference-of-Arrival Measurements.

A commonly used measurement model for locating a mobile source is time-difference-of-arrival (TDOA). As each TDOA measurement defines a hyperbola, it is not straightforward to compute the mobile source position due to the nonlinear relationship in the measurements. This brief exploits the Lagrange programming neural network (LPNN), which provides a general framework to solve nonlinear constrained optimization problems, for the TDOA-based localization. The local stability of the proposed LPNN solution is also analyzed. Simulation results are included to evaluate the localization accuracy of the LPNN scheme by comparing with the state-of-the-art methods and the optimality benchmark of Cramér-Rao lower bound.