A NEW ALGORITHM FOR NONLINEAR L1-NORM MINIMIZATION WITH NONLINEAR EQUALITY CONSTRAINTS

In this paper a new algorithm for solving the nonlinear L1-norm minimization problem subject to nonlinear equality constraints, is presented. The nonlinear problem and the constraints are linearized using a first order Taylor series expansion. Then, the problem is solved as an overdetermined problem by using the well known left pseudo-inverse technique. A least squares (LS) solution is obtained and the LS residuals are then calculated. In obtaining the LS solution, we use the equality constraints together with the m measurements, m > n, (n is the number of parameters to be estimated). If the column rank of H (H is the m x n Jacobian matrix of the original problem) is k, k less-than-or-equal-to n and l is the number of nonlinear equality constraints then for L1-norm minimization, the estimator fits at least (n - 1) measurements. These measurements are the measurements which have the smallest least squares residuals. The algorithm selects the (n - l) measurements which correspond to the smallest residuals, together with the l equality constraints and obtains a fully determined set of equations. By solving these equations iteratively, an optimal L1 estimate is obtained. It has been shown that this technique requires much less computing time and storage requirements than other available techniques such as linear programming.