Optimization of Magnetic Anomaly Detection Under 1/<i>f</i>α Noise Based on Karhunen–Loève Expansion and Frequency Characteristic Function

The primary challenge facing the field of magnetic anomaly detection (MAD) currently lies in how to effectively improve detection performance in low signal-to-noise ratio (SNR) and real 1/<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i>α noise scenarios. To overcome these difficulties, this article proposes an optimized MAD method based on random forest (RF) classifier. This method utilizes an orthonormal basis function (OBF) detector based on Karhunen-Loève expansion (KLE) to extract energy from the raw data as time domain features. Meanwhile, the spectral information derived from lowpass filtering (LPF) and fast Fourier transform (FFT) serves as frequency domain features of the raw data. The cutoff frequency of the LPF is determined based on a frequency characteristic function that defines the high-frequency boundary of the target signal. Combining these time and frequency domain features, a simulated dataset is constructed for the training and testing of the detection model. Subsequently, the trained model undergoes further validation and evaluation on semi-real and real datasets built upon measured data from a tunnelling magnetoresistance (TMR) magnetic sensor. Through a series of simulations, we demonstrate that our designed method exhibits superior detection capability and stronger generalization ability compared to other similar OBF-based methods. Furthermore, the superiority of this method is also confirmed by experimental results based on actually measured data.