## 2 Magnet Anomaly Motion Target Feature Detection  
### Magnetic Dipole Motion Detection Model  
Due to the complex shape and inhomogeneous magnetization of magnetic targets, it is difficult to solve their magnetic fields using analytical methods directly. Currently, the common method models the magnetic target using the measurement data and then obtains the magnetic field distribution around the magnetic target [21]. The common magnetic target magnetic field models include the uniformly magnetized rotating ellipsoid model, the uniformly magnetized rotating ellipsoid array model, the magnetic dipole model, the magnetic dipole array model, and the rotating ellipsoid and magnetic dipole hybrid array model. Among them, the magnetic dipole model is simple and easy to use, so it has been widely used in magnetic signal detection, the recognition and localization of mines, nuclear waste, and military targets. The experimental data show that the magnetic target can be treated as a magnetic dipole in the spatial range larger than 2.5 times the length of the magnetic target, which meets the requirements of general engineering applications. Therefore, in this study, the magnetic field of the magnetic target was analyzed using the magnetic dipole model. Figure 1 illustrates the magnetic target motion detection model, where the heading of the accelerometer and the magnetic target motion platform concern the three-axis fluxgate magnetometer platform's CPA. \(dm\) represents the distance between the magnetic target and the CPA, \(Rm\) is the distance between the CPA and the three-axis fluxgate magnetometer platform, and \(r\) signifies the distance between the accelerometer and the magnetic target motion platform. To streamline the calculations, we use the center of the detection platform as the reference point and establish a three-dimensional Cartesian coordinate system with it as the coordinate origin. Assuming that the magnetic target moves along a straight path, we convert the target's motion velocity into relative motion velocity with respect to the reference point. Thus, a magnetic dipole motion detection model is successfully established. In magnetic anomaly detection, adhering to the principles of magnetic dipole theory, we derive the vector expression of the magnetic induction intensity \(\mathbf{B}\) at the detection platform's location, as presented in Equation (1):  
\[\mathbf{B}(\mathbf{M},\mathbf{r})=\frac{\mu_{0}}{4\pi}r^{-3}\left[\frac{3 \mathbf{r}^{-2}(\mathbf{M}\cdot\mathbf{r})\mathbf{r}}{\left|\mathbf{r}\right| ^{5}}-\frac{\mathbf{M}}{\left|\mathbf{r}\right|^{5}}\right] \tag{1}\]  
where \(\mu_{0}=4\pi\times 10^{-7}\ \mathrm{H/m}\) denotes the vacuum permeability, and \(\mathbf{r}=\left[x\quad y\quad z\right]^{T}\) represents the position vector of the dipole. The magnetic field generated by the magnetic target at the detection platform can be decomposed into three orthogonal axis directions of magnetic fields: \(B_{x}\), \(B_{y}\), and \(B_{z}\). This magnetic field is influenced by the three-dimensional magnetic moment \(\mathbf{M}(M_{x},M_{y},M_{z})\) of the target, which can be expressed as the three-dimensional magnetic moment of the magnetic target and the relative position between the magnetic target and the magnetic acquisition system. Then, the three-dimensional magnetic field generated by the magnetic target at the detection platform can be expressed  
Figure 1: Magnetic target motion detection model. by the three-dimensional magnetic moment and the relative position between the target and the detection platform, as illustrated in Equation (2):  
\[ \begin{bmatrix}B_{x}\\ B_{y}\\ B_{z}\end{bmatrix} = \begin{bmatrix}3x^{2}-r^{2}&3 xy&3 xz\\ 3 xy&3y^{2}-r^{2}&3 yz\\ 3 xz&3 yz&3z^{2}-r^{2}\end{bmatrix}\begin{bmatrix}M_{x}\\ M_{y}\\ M_{z}\end{bmatrix}  \tag{2}\]  
where \(r=\sqrt{x^{2}+y^{2}+z^{2}}\), and \( \begin{bmatrix}B_{x}&B_{y}&B_{z}\end{bmatrix} ^{T}\) denote the components of \(\mathbf{B}\) along the three orthogonal directions.