## 1 Introduction  
Underground metal detection technology has been widely used in military fields [1] and also plays an important role in archeology [2], prospecting [3], medical positioning [4], underground metal pipeline modeling [5] and other fields. Electromagnetic induction (EMI) detection technology is an underground metal detection method that uses secondary field information generated by a changing magnetic field acting on the metal target to detect the state of a target [6]. In the EMI model, the secondary field is related to nine parameters of a target, which are grouped into the target's position \(\mathbf{r}=\left[ \begin{smallmatrix}r_{x}&r_{y}&r_{z}\end{smallmatrix} \right]^{T}\), polarizability \(\mathbf{\beta}=\left[ \begin{smallmatrix}\beta_{x}&\beta_{y}&\beta_{z}\end{smallmatrix}  \right]^{T}\), and posture \(\left[ \begin{smallmatrix}\psi&\phi\end{smallmatrix} \right]^{T}\)[7]. \(\psi\), \(\theta\), \(\phi\) are the yaw angle, pitch angle and roll angle of the target, respectively. Compared with other underground metal detection technologies, such as infrared imaging and seismic wave technology, EMI detection technology has the advantages of having a strong penetration capability and being nondestructive [8], so it is widely used in the underground metal detection field. EMI technology includes time domain electromagnetic (TDEM) induction [9; 10] and frequency domain electromagnetic (FDEM) induction [11]. In the TDEM method, a pulse signal is transmitted. Then, the position and polarizability of the target are obtained by analyzing the attenuation characteristics of the secondary field signal. Unlike the TDEM method, the FDEM method transmits harmonic signals with multiple frequencies. Through analyzing the amplitude and phase information of the secondary field signal, the position, polarizability and posture of the target can be obtained. Both TDEM induction and FDEM induction are based on the same fundamental physical principles, but the types of information obtained from secondary fields are different. The FDEM method measures the phase and amplitude of the secondary fields, which is different from the primary fields, mainly due to the subsurface properties [12]. We focus on the FDEM method in this paper. Inversion algorithms are used to calculate the target's physical parameters from the observed data. It includes recursive inversion algorithms [8; 13] and nonrecursive inversion algorithms [1; 14]. For example, filter methods are classified as recursive inversion algorithms, and gradient methods are classified as nonrecursive inversion algorithms. The filter method uses the system's dynamic state space model (DSSM) to solve the target detection problems and offers good real-time performance. Filter algorithms mainly include particle filters (PFs) and Kalman filters (KFs). When PFs are in the face of high-dimensional problems such as dipole tracking, the number of required particles increases exponentially, which results in the \"curse of dimensionality\". When the noise satisfies the Gaussian distribution, the KFs have the best performance, and this assumption is also reasonable in practical applications. Consequently, we focus on KFs in this paper. Although nonrecursive inversion algorithms have higher accuracy than recursive algorithms, their computational efficiency is lower than that of filter algorithms. We focus on improving the accuracy of KF algorithm in underground target detection. Filter methods have long been used to solve underground metal detection problems. For example, [PERSON] et al. used a KF and an extended Kalman filter (EKF) to solve the problem of underground unexploded ordnance detection [8]. However, in the traditional EMI model, the secondary field of the target has a nonlinear relationship with six parameters that relate to the position and posture and has a linear relationship with the three parameters of polarizability. The high nonlinearity of the model results in poor performance of the filter algorithm. [PERSON] et al.