## 1 Introduction
used the concept of the magnetic polarizability tensor to reduce the number of nonlinear parameters from six to three in the traditional model [15]. [PERSON] et al. used a linearized model to solve the problem of underground metal detection [16]. However, one problem that cannot be avoided in the current research is that the performance of filter algorithms is extremely sensitive to the initial value of the filter. In the case of a large initial value error, the precision is low, and the results sometimes are divergent. In [17], [PERSON] et al. used a least squares estimator to yield an estimation of the acceleration input vector for maneuvering targets. In [18], [PERSON] used maximum likelihood estimation to solve the initialization problem of the KF. Based on their research, the least squares method and two image processing algorithms are combined to obtain initial values for the filter algorithm in underground metal detection. Early research in the underground metal detection is mostly based on the assumption of Gaussian noise distribution. [PERSON] et al. investigate KF and EKF for the inversion of unexploded ordnance (UXO) polarizabilities and positions under the dipole model approximation and the assumption of Gaussian noise distribution, respectively [19]. There are also some researchers studied the application of detection algorithm in non-Gaussian noise. [PERSON] et al. studied the effects of assuming i.i.d. white Gaussian noise on the performance of likelihood ratio detectors and maximum likelihood classifiers implemented in a non-Gaussian noise environment. In addition, they had illustrated the effects of mismatch between the assumed and actual noise distributions on detection and classification performance for likelihood ratio processors derived under several assumptions regarding the noise distribution [20]. [PERSON] et al. had proposed the bootstrap filter for implementing recursive Bayesian filters [21]. In addition, the method is not restricted by assumptions of linearity or Gaussian noise. In [22], [PERSON] et al. derived a theoretical expression of the optimum non-Gaussian radar detector. The researchers above had made certain research about non-Gaussian noise. In this paper, we focus on the improvement of the filter algorithm's performance in the environment of non-Gaussian noise. In this paper, we propose an initial value estimation method for the KF and the EKF (IVE-KF) for underground metal detection. In IVE-KF, the horizontal position of the target is estimated by the first-order central moments of the map that are composed of secondary field data, the depth of the target is estimated by the full width at half maximum (FWHM), and the initial states of the other six linear parameters are estimated by the least square method combined with Tikhonov regularization. Finally, these initial states are used as the initial values of the filter algorithm, and the parameters of the metal target are solved simultaneously by combining the KF and the EKF algorithms. To evaluate the performance of IVE-KF, a simulation platform for EMI detection is built in this paper. The simulation results show that the convergence of IVE-KF is better than that of the filter algorithm with random initial values in the application of underground metal detection, and the detection accuracy is close to that of the Levenberg-Marquardt (LM) algorithm of inversion when the signal-to-noise ratio (SNR) is greater than 30 dB; in addition, the computational complexity of IVE-KF is lower than that of the LM algorithm. The detailed content of this paper is arranged as follows: Section 2 introduces the system model. Section 3 introduces the IVE-KF algorithm, which includes the initial value estimation algorithm and the filter algorithm. Section 4 introduces the simulation system and evaluates the performance of the IVE-KF algorithm. Section 5 concludes the paper.