Multifrequency TR-MUSIC Processing to Locate Soft Faults in Cables Subject to Noise

Time-reversal multiple signal classification (TR-MUSIC) has recently been shown to be an effective technique to locate multiple soft faults in wire networks, thanks to its sub-millimeter location accuracy. TR-MUSIC processes transmission and reflection data measured at a single frequency into a function of space, the pseudo spectrum, expected to present singularities only at a fault position. At frequencies high enough, the spatial periodicity that comes with the propagation of harmonic signals leads to multiples of such singularities, of which only one represents the fault position, while the remaining are ghosts faults. TR-MUSIC was therefore introduced using a single continuous-wave excitation at frequencies low enough to avoid ghosts, an approach suitable only for noiseless configurations. This paper explores the effects of noise on TR-MUSIC fault location by first highlighting its high sensitivity to noise at low frequency. A potentially lower sensitivity is shown to exist at high frequencies, where ghosts positions are found. A multifrequency processing is introduced, allowing at the same time to solve the ambiguity in the fault position and to effectively control the impact of noise on its location accuracy. The proposed processing is shown to reinstate precise super-resolved estimates of fault locations even for signal-to-noise ratios as low as 5 dB, without requiring the use of wideband signals.