Efficient and robust Levenberg–Marquardt Algorithm based on damping parameters for parameter inversion in underground metal target detection

Abstract

The Levenberg–Marquardt (LM) algorithm has been widely used to solve nonlinear least-squares problems in underground target detection. However, the LM algorithm has an unsatisfactory performance of convergence due to the influence of noise in the environment. Therefore, a new modified LM (NMLM) algorithm has been proposed in this paper to improve its accuracy and efficiency of parameter estimation with low SNR. The NMLM algorithm can also converge globally under certain conditions and converge quadratically under the error-bound condition, which updates based on the gain ratio and determines the damping factor based on the gradient value. An experimental investigation has been conducted under different SNRs and the amount of data, and the results indicate the new algorithm can accurately and quickly estimate the parameters of underground metal targets under the lower SNRs and smaller amounts of data. More specifically, the estimation accuracy of position, principal axes polarizability, and orientation of the metal target can be increased by up to 1.6 cm, 0.00013, and 2.31 degree, respectively. This paper also verifies that the new algorithm finds the optimal solution for standard numerical problems with low errors and a finite number of iterations.