| d1, d2 | distances between the leak and sensors 1 and 2 |
| D | distance between two sensors |
| B | fluid bulk modulus |
| E | Young’s modulus of the pipe wall |
| a, h | pipe radius and wall thickness |
| β | wave attenuation factor |
| k, kf | fluid-borne wavenumber and free-field fluid wavenumber |
| T 0 | estimate of the time delay |
| η | loss factor of the pipe wall |
| c, cf | propagation and fluid wavespeeds |
| x1(t), x2(t) | leak signals measured |
| l(t) | leak source signal |
| n1(t), n2(t) | background noise |
| H(ω,d1), H(ω,d2) | FRFs between l(t) and x1(t), x2(t) |
| h1(t), h2(t) | IRFs between l(t) and x1(t), x2(t) |
| S12(ω) | CSD between x1(t) and x2(t) |
| Φ12(ω), Φ21(ω) | phase spectra of x1(t) and x2(t) |
| h21(n), h12(n), h(n) | IRFs for measured signals |
| H(ω), H12(ω), H21(ω) | FTs of h12(n), h21(n), h(n) |
| T ref | reference time delay |
| λ max | maximum order in the LMS algorithm |