Processing of a scalar magnetometer signal contaminated by 1/fα noise

Magnetic anomaly detection (MAD) is a passive method for detection of a ferromagnetic target. A magnetic field generated by a ferromagnetic target is assumed as a dipole field, resulting in an anomaly in the ambient Earth magnetic field. Magnetic anomaly detection method using orthonormal basis functions (OBF) decomposition is a known approach. The method, which relies on matched filtering, should be optimal for detection of a known signal in the presence of Gaussian white noise. In this work, we expand the method to the more general case of magnetic noise with a power spectral density of 1/fα, where 0 < α < 2. We have designed a whitening filter, which improves magnetic anomaly detection using the basis functions decomposition approach. It turned out that the measured magnetic noise, comprising intrinsic sensor noise and geomagnetic noise, may be considered as an autoregressive (AR) process. Thus, by calculating the coefficients of the autoregressive model, we can build a whitening filter. Application of a whitening filter transforms the noise from 1/fα into a white noise, but also distorts the target signal. As a consequence, the original orthonormal basis functions should be modified in order to form a basis for the distorted target signal. The results in the present work demonstrate the advantage of the proposed method.