## 1 Introduction  
The electromagnetic fields generated by naval vessels and other underwater carriers have become important signals for tracking targets of interest in marine warfare [1, 2]. When ships and underwater carriers are in seawater, in addition to the influence of ferromagnetic materials (such as iron, cobalt, and nickel), the metal material in the carrier composition (such as the steel shell and copper propeller) electrochemically reacts to generate a corrosive current around the vessel [3]. In order to protect the hull from corrosion, the impressed current cathodic protection system and the sacrificial anode cathodic protection system are widely used to generate corrosion protection currents in modern ships. These currents create electro-static and magneto-static anomalies around the ships. At the same time, the corrosion current and the protection current flow from the hull to the propeller through the seawater. Then, the currents return to the hull from the propeller through various bearings and mechanical wires [4]. The loop electrical impedance periodically changes as the drive shaft rotates, causing the current flowing through the seawater to be modulated, thereby forming an extremely low-frequency electromagnetic field in the seawater and propagating outward. The signal has frequency characteristics that are consistent with the propeller rotation frequency and its harmonic frequency. To a large extent, the signals can be transmitted several kilometers away. Therefore, they are considered important signal sources for detecting underwater military targets [5]. As a significant passive detection method, aeromagnetic exploration is widely used in underwater target detection [6; 7; 8]. The development and updating of aeromagnetic testing technologies is often concentrated in the military field. Tracing back to World War II, the British Army started to use aircraft to carry fluxgate sensors to detect underwater submarines. With the development of high-precision magnetometers, such as optically pumped magnetometers (OPMs), aeromagnetic surveying has become one of the most important means of underwater target detection. Given that the aircraft platform affects the accuracy of OPM measurements, [PERSON] proposed a classical aeromagnetic compensation model in the 1940s [9; 10]. [PERSON] proposed sinusoidal maneuvers to improve compensation performance in 1961 [11]. In 1980, [PERSON] proposed a ridge regression algorithm to solve the aeromagnetic compensation parameters, and the experimental results showed that this method performed well in improving the compensation performance [12]. In 1995, [PERSON] designed an innovative three-axis aeromagnetic gradiometry flown on a fixed-wing platform [13]. Around 2005, [PERSON] carried out a series of experiments with an experimental flight system [14; 15]. In 2011 and 2013, [PERSON] proved the viability and reliability of using the standard deviation of the signal as an assessment criterion through a large number of aeromagnetic trials [16; 17]. The traditional aeromagnetic compensation model has a good effect on eliminating the interference field caused by aircraft attitude changes, which are generally less than 2 Hz. For time-varying interferences with an unknown signature, [PERSON] proposed an adaptive magnetic interference cancelation method by using a pair of magnetometers, which obtained good results for highly correlated interference magnetic fields [18]. However, for magnetic measurement systems with the magnetometers on a probe of a helicopter, the probe vibrates when the helicopter is flying. In this case, there is a vibration frequency and its harmonic interference field that can be captured by the magnetometers. The harmonic interference magnetic field that is caused by aircraft vibration seriously affects the detection of target signals to a large extent.