Cooperative Recurrent Neural Networks for the Constrained $L_{1}$ Estimator

The constrained least absolute deviation (L
₁
) estimator is an attractive alternative to both the unconstrained L
₁
estimator and the least-square estimator. This paper introduces a constrained L
₁
method and proposes two cooperative recurrent neural networks (CRNNs) for the constrained L
₁
estimator. Unlike existing cooperative neural networks, the proposed two CRNNs have a novel weighting cooperation scheme to integrate individual neural network information automatically. As a special case, the proposed continuous-time CRNN includes the existing continuous- time neural network for unconstrained L
₁
estimator. Compared with existing continuous-time neural networks for the constrained L
₁
estimator, the proposed continuous-time CRNN has a lower model complexity and the finite-time convergence to the exact optimal solution without any additional condition. Furthermore, compared with existing numerical algorithms for the constrained L
₁
estimator, in addition to a low computational complexity, the proposed two CRNNs are suitable for parallel implementation and can deal with the L
₁
estimation problem with degeneracy. The proposed two CRNNs are applied to parameter estimation problems under non-Gaussian noise environments. Simulation results demonstrate that the proposed CRNNs are indeed effective in dealing with the L
₁
estimation problem with nonunique solutions and in obtaining a better solution than relevant algorithms.