Systems and methods for determining and disambiguating the location of the shooter of supersonic projectiles based on shockwave-only signals are described. Using several spaced sensors, an initial portion of the shockwave-only signals is sensed to determine Time-Differences-Of-Arrival (TDOA) for the sensor pairs. The resulting TDOAs are used to determine the gradient of curvature of the shockwave wavefront on the sensors. The gradient of curvature is then used to determine the disambiguated projectile trajectory.