Lagrange Programming Neural Network Approaches for Robust Time-of-Arrival Localization

Abstract

There are two interesting properties in human brain. One is its massively interconnected structure. Another one is that human can handle outlier data effectively. For instance, human is able to recognize an object from an image with non-Gaussian noise. Artificial neural network is one of biologically inspired techniques. From the structural point of view, many neural network models have massively interconnected structures. Since the traditional analog neural network approach cannot handle an l 1-norm-like objective function, it cannot be used to handle outlier data. This paper proposes two neural network models for the robust source localization problem in the time-of-arrival (TOA) model. Our development is based on the Lagrange programming neural network (LPNN) approach. To alleviate the influence of outliers, this paper introduces an l 1-norm objective function. However, in the traditional LPNN approach, the constraints and the objective function must be differentiable. We devise two methods to handle the non-differentiable l 1-norm term. The first method introduces an approximation to replace the l 1-norm term. The second one uses the concept of hidden state from the locally competitive algorithm (LCA) to avoid the computation of the gradient vector at non-differentiable points. We also present the local stability of the two proposed models. From the simulations, our proposed methods are capable to handle the outliers and their error performances are better than many existing TOA algorithms.