Energy Detection Based on Undecimated Discrete Wavelet Transform and Its Application in Magnetic Anomaly Detection

Magnetic anomaly detection (MAD) is a passive approach for detection of a ferromagnetic target, and its performance is often limited by external noises. In consideration of one major noise source is the fractal noise (or called 1/f noise) with a power spectral density of 1/f(a) (0<a<2), which is non-stationary, self-similarity and long-range correlation. Meanwhile the orthonormal wavelet decomposition can play the role of a Karhunen-Loève-type expansion to the 1/f-type signal by its decorrelation abilities, an effective energy detection method based on undecimated discrete wavelet transform (UDWT) is proposed in this paper. Firstly, the foundations of magnetic anomaly detection and UDWT are introduced in brief, while a possible detection system based on giant magneto-impedance (GMI) magnetic sensor is also given out. Then our proposed energy detection based on UDWT is described in detail, and the probabilities of false alarm and detection for given the detection threshold in theory are presented. It is noticeable that no a priori assumptions regarding the ferromagnetic target or the magnetic noise probability are necessary for our method, and different from the discrete wavelet transform (DWT), the UDWT is shift invariant. Finally, some simulations are performed and the results show that the detection performance of our proposed detector is better than that of the conventional energy detector even utilized in the Gaussian white noise, especially when the spectral parameter α is less than 1.0. In addition, a real-world experiment was done to demonstrate the advantages of the proposed method.