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This paper focuses on target localization in a widely distributedmultiple-input-multiple-output (MIMO) radar system. In this system, rangemeasurements, which include the sum of distances between transmitter and targetand the distances from the target to receivers, are used. We can obtain anaccurate estimated position of the target by minimizing the measurement errors.In order to make our model come closer to reality, we introduce two kinds ofnoises, namely, Gaussian noise and outliers. When we evaluate a targetlocalization algorithm, its localization accuracy and computational complexityare two main criteria. To improve the positioning accuracy, the originalproblem is formulated as solving a non-smooth constrained optimization problemin which the objective function is either l1-norm or l0-norm term. To achieve areal-time solution, the Lagrange programming neural network (LPNN) is utilizedto solve this problem. However, it is well known that LPNN requirestwice-differentiable objective function and constraints. Obviously, the l1-normor l0-norm term in the objective function does not satisfy this requirement. Toaddress this non-smooth optimization problem, this paper proposes twomodifications based on the LPNN framework. In the first method, adifferentiable proximate l1-norm function is introduced. While in the secondmethod, locally competitive algorithm is utilized. Simulation and experimentalresults demonstrate that the performance of the proposed algorithms outperformsseveral existing schemes.

Robust MIMO Radar Target Localization based on Lagrange Programming Neural Network