# Magnetic Moment Estimation Algorithm Based on Convolutional Neural Network
## 1 Introduction  
Magnetic anomaly detection (MAD) technology is used to detect and localize local magnetic targets by analyzing magnetic anomaly signals [1]. It can be categorized into aeromagnetic, ground-based, and satellite-based surveys, depending on the platform employed for detection. Among these, aeromagnetic surveys involve placing magnetic detectors on aircraft to detect magnetic anomalies. This method offers advantages such as a wide detection range, high operational efficiency, and precise detection accuracy [2]. Aeromagnetic surveys are extensively utilized in various fields, including mineral exploration [3], where they are used for geological mapping as well as anomaly detection, anti-submarine early warning [4, 5], and unexploded ordinance detection [6, 7], among others. In airborne MAD surveys, estimating the magnetic moment of magnetic targets from detection data is a critical step [8, 9], as it can significantly reduce the false alarm rate [10]. [PERSON] inverted the magnetic dipole moment information using the magnetic field vector and magnetic gradient signals measured by a magnetic gradiometer and sensor array, thereby estimating the magnetic moment of the target [11]. [PERSON] employed a multi-tensor gradiometer and fluxgate array for the triangulation of the magnetic target andproposed the STAR algorithm to estimate the magnetic moment [12]. However, the STAR algorithm is affected by issues such as significant measurement noise and inherent errors due to the tensor contraction assumption. To address these limitations, [PERSON] enhanced the direction vector selection mechanism relying on rotation invariance and optimized the distance estimation, thereby improving positioning accuracy [13]. [PERSON] introduced a nonlinear optimization approach using simulated annealing relying on the magnetic dipole model [14]. [PERSON] examined the geometric characteristics of magnetic targets by studying how magnetic materials influence the vertical component of the geomagnetic field [15]. [PERSON] et al. developed an algorithm grounded in a full magnetic gradient orthogonal basis function, which can accurately estimate the vector magnetic moment of the target under low SNR conditions [16]. [PERSON], [PERSON], and colleagues integrated the target speed, movement direction, the distance between the sensor and the magnetic target, and the magnetic dipole model to construct a magnetic dipole motion model, which they used to identify the magnetic target by comparing the waveforms of the model signal with those of the collected signal [17]. Currently, most magnetic moment estimation algorithms rely on magnetic field data collected by vector magnetic sensors and magnetic gradiometers. However, vector magnetic sensors are prone to issues such as large steering errors [18] and low sensitivity, making them less suitable for mobile platforms. In contrast, scalar magnetic sensors offer higher sensitivity and stability [19], making them ideal for use on high-speed airborne platforms. [PERSON] utilized a scalar magnetic sensor array combined with a particle swarm optimization algorithm to perform target detection [20]. [PERSON] proposed an estimation method relying on magnetic field data from multiple scalar magnetic sensors, employing orthogonal basis decomposition and average filtering techniques [21]. While these algorithms offer valuable insights, they require a larger number of sensors and more complex data processing, placing high demands on the platform. [PERSON] introduced a correlation detection method established on normalized magnetic moments. This approach performs well for estimating the magnetic moment modulus under low SNR conditions, but it struggles with accurately estimating the direction of the magnetic moment [22]. This paper proposes a magnetic moment estimation algorithm that integrates a scalar magnetic sensor with CNN. The input of algorithm includes the three components of 2D geomagnetic field and 2D scalar magnetic anomaly signal, while the output consists of magnetic moment vector.