In order to diminish the deviation of far-field time-difference-of-arrival (TDOA) measurements from the ideal line-of-sight (LOS) model due to some microphones shadowed by the system shell of an embedded planar microphone array

which is not considered and cannot be resolved by existing TDOA correction studies

a novel convex optimization method was proposed for correcting the measured TDOA matrix. A closed-form solution was obtained by integrating the rank-2 algebraic constraint with a set of linear geometric constraints corresponding to the equilong parallel lines (EPLs) that are easily achieved in practical acoustic detection systems using approximately symmetric convex polygons as preferable array shapes.As long as the array shape contains at least one pair of linearly independent EPLs

the proposed method gains the capability of effectively suppressing the diffraction induced deviations in measured TDOAs relevant to non-line-of-sight (NLOS) array elements. Meanwhile

the adverse effects of measurement noise and TDOA outliers can be also mitigated. Considering both the above capabilities and the low computational complexity

the proposed method is more suitable for ever-growing applications of small-scale

real-time acoustic detection systems. Numerical simulations verified its effectiveness.