Neural implementation of unconstrained minimum L-1-norm optimization - Least absolute deviation model and its application to time delay estimation

Least absolute deviation (LAD) optimization model, also called the unconstr ained minimum L-1-norm optimization model, has found extensive applications in linear parameter estimations. L-1-norm model is superior to L-p-norm (p > 1) models in non-Gaussian noise environments or even in chaos, especiall y for signals that contain sharp transitions (such as biomedical signals wi th spiky series or motion artifacts) or chaotic dynamic processes. However, its implementation is more difficult due to discontinuous derivatives, esp ecially compared with the least-squares model (L-2-norm). In this paper, ne ural implementation of LAD optimization model is presented, where a new neu ral network is constructed and its performance in LAD optimization is evalu ated theoretically and experimentally, Then, the application of the propose d LAD neural network (LADNN) to time delay estimation (TDE) is presented. I n TDE, a given signal is modeled using the moving average (MA) model. The M A parameters are estimated by using the LADNN and the time delay correspond s to the time index at which the MA coefficients have a peak. Compared with higher order spectra (HOS)-based TDF, methods, the LADNN-based method is f ree of the assumption that the signal is non-Gaussian and the noises are Ga ussian. which is closer to real situations. Experiments under three differ ent noise environments, Gaussian, non-Gaussian and chaotic, are conducted t o compare the proposed TDE method with the existing HOS-based method.