###### Abstract  
Traditional methods of orthogonal basis function decomposition have been extensively used to detect magnetic anomaly signals. However, the determination of the relative velocity between the detection platform and the magnetic target remains elusive in practical detection. And, the non-ideal uniform motion of the magnetic target further complicates the process and adversely impacts the detector's performance. To address this challenge, this paper introduces an adaptive scale factor method based on orthogonal basis function decomposition. This new method can be used to adjust the relative velocity between the detection platform and the magnetic target and to refine the characteristic time in the basis functions. In this paper, a mathematical relationship between the scale factor and the relative velocity is established, which is subsequently fitted into a Gauss function curve. The optimal scale factor, denoted as \(\beta\), is adaptively chosen from the fitting curve when the magnetic target moves at a non-ideal uniform velocity with an unknown motion state. The results of simulations indicate that the scale factor improves the signal-to-noise ratio of the magnetic anomaly signals in a non-ideal state. And, this method can improve the energy value of OBF decomposition by 17.7%. Simultaneously, this method ensures that the moment the magnetic target passes the CPA coincides with the energy peak of the orthogonal basis detection, which improves the accuracy by 54.1% compared with the traditional method. The effectiveness and precision of the proposed method are verified using simulations and practical experiments. m pacs: 1
Footnote 1: School of Electrical and Control Engineering, Shaarxi University of Science and Technology, Xi’an 710021, China  
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Footnote 1: School of Electrical and Control Engineering, Shaarxi University of Science and Technology, Xi’an 710021, China  
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Footnote 2: School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China  
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Historical research has shed light on magnetic anomaly signal detection methods grounded in the magnetic dipole model, like the orthogonal basis function (OBF). The OBF method, relying on scalar magnetometer analyses, seeks to discern distinct target signal patterns under given premises, such as linear movement with a predetermined velocity [7; 8]. Nonetheless, deviating from these foundational assumptions can complicate deriving an analytical representation using the OBF technique. Recent studies have unveiled a palpable link between magnetic anomaly characteristics and factors like target presence, orientation, distance, velocity, and classification [9; 10]. Some experts embarked on experimental ventures with variably paced magnetic targets, capturing magnetic anomaly readings using ultra-sensitive sensors. Notably, when privy to the relative velocity data, they corroborated the assertion that sensor coverage angles remain unaffected by velocity fluctuations and the closest point of approach (CPA) [11; 12]. Simultaneously, some scholars have harnessed deep learning and neural networks to craft magnetic anomaly models, optimizing network efficiency by fine tuning the learning rate to improve the signal-to-noise ratio of target features. Constructed on the basis of ideal uniform motion, these models, when meshed with enhanced networks and OBF detectors [13; 14; 15; 16], manifest a marked reduction in noise interference, fostering adept magnetic anomaly detection. In essence, magnetic anomaly detection strategies must duly factor in the attributes of the target, including the motion state, velocity, and other characteristics. In summary, magnetic anomaly detection methods are usually based on the assumed conditions of the ideal case, i.e., the magnetic target is assumed to move at a uniform speed, and the relative velocity is known [17]. However, the intensity of the magnetic anomaly signal may change under different motion states, and the motion state of the magnetic target may also affect the magnetic field.